Open Music Theory

Open Music Theory

an open-source, interactive, online “text”book for college-level music theory courses

Bryn Hughes, Brian Moseley, Kris Shaffer, Mark Gotham, Kyle Gullings, Chelsey Hamm, Brian Jarvis, Megan Lavengood, and John Peterson

Contents

1

The new version of this book is still in production—think of this as the “alpha” test for the new version. You will find many typos, incomplete pages, broken links, and so on!

A complete draft of the book should be complete by Summer 2020.

2

Acknowledgments

3

Statement on Spotify Usage

To keep this resource accessible and low-cost, we have opted to use Spotify links for audio examples for tracks which otherwise would cause OMT to incur considerable copyright costs. This book is best accessed if the user has a Spotify Premium account. Student accounts are half the cost of normal premium accounts, so we are hopeful that this does not dissuade many users. Sign up for Spotify Premium for Students here.

We also state that Spotify is well-known to be bad for artists because of its pay scheme. We encourage readers to support artists directly by purchasing music when they can.

I

Fundamentals

1

Other Aspects of Notation

Intro text Here

Dynamics

dd

Tempo

dd

Other Symbols

Style periods???

Dynamics, tempi, etc.

Fermata

Repeat signs

D.C. and endings, etc.

2

The Basics of Sight Singing and Dictation

Contour; strategies for singing and dictation

Rhythm dots

Contour lines

Conducting here or in own chapter?

II

Counterpoint

Punctum contra punctum … point against point … note against note.

This section explores the wonderful world of counterpoint. Basically counterpoint is about the combination of notes in general, though the terms is sometimes used as a categorical complement to ‘harmony’, with counterpoint concerning the ‘horizontal’ or ‘melodic’ aspect, and harmony addressing the ‘vertical’. In practice, there two are not so easily separated as that division implies, but there is perhaps something to the increased attention to linear elements that distinguishes the study of counterpoint.

Apart from the subject matter, this section is also characterized by the prominent emphasis on try it yourself exercises spanning Species Counterpoint, and pastiche composition in sixteenth and eighteenth century styles.

Species Counterpoint

Kris Shaffer, Bryn Hughes, and Brian Moseley

The study of the theory of Western music involves three main components: voice-leading, harmony, and form. Voice-leading deals with the relationship of two or more musical lines (or melodies) combined into a single musical idea. Harmony addresses the rules or norms for combining chords into successions. Form addresses the rules or norms for the combination of phrases and other small musical units into larger units—including whole movements and works. We will address all three of these facets of musical theory. However, of the three, voice-leading is the most fundamental. Thus, we begin our study of music theory, then, with strict voice-leading, or counterpoint. Twentieth-century musician and theorist, Heinrich Schenker, wrote:

The purpose of counterpoint, rather than to teach a specific style of composition, is to lead the ear of the serious student of music for the first time into the infinite world of fundamental musical problems (Kontrapunkt, p. 10).

Following this line of thinking, our early voice-leading exercises will not be in a specific style (classical, baroque, romantic, pop/rock, etc.). Instead, these exercises will eliminate important musical elements like harmony, orchestration, melodic motives, formal structure, and even many elements of rhythm, in order to focus very specifically on a small set of musical problems. These other elements of music will be introduced one-by-one as we progress through the course (and into future courses).The “fundamental musical problems” we will address in the study of counterpoint center around the way in which some basic principles of auditory perception and cognition (how the brain perceives and conceptualizes sound) play out in Western musical structure. For example, our brains tend to assume that sounds similar in pitch or timbre come from the same source. Our brains also listen for patterns, and when a new sound continues or completes a previously heard pattern, it assumes that the new sound belongs together with those others. On the other hand, the breaking of these regularities in the sonic environment can signal danger, or at the very least the need for heightened attention to be applied to the sonic “culprit.” Identifying irregularities in the sonic environment and boosting attention and adrenaline when one is found have been absolutely essential to the survival of the human species. These abilities are also what allows music to have the emotional effect that it does on so many people. Whether or not a composer or songwriter is aware of the science and psychology of hearing, a masterful composer mediates and plays with these basic concepts.

“Mediates” and “plays” are important ideas here. Music that simply makes it easy for the brain to parse and process sound is boring—it calls for no heightened attention, it doesn’t increase our heart rate, make the hair on the back of our neck stand up, or give us a little jolt of dopamine. On the other hand, music that constantly activates our innate sense of danger is hardly pleasant for most listeners. Thus, fundamental to most of the music we will study is the dance between tension and relaxation, motion and rest.

The study of counterpoint will help us to engage several important musical “problems” in a limited context, so that we can master them compositionally and understand them analytically. Those problems arise as we seek to bring the following traits together:

These traits are based in human perception and cognition, but they are often in conflict in specific musical moments, and need to be balanced over the course of larger passages and complete works. Counterpoint will help us begin to practice mediating these conflicts.

Also, note Schenker’s expression “lead the ear.” Counterpoint is not a pencil-and-paper (or lecture-and-homework) study. Rather, the exercises are mini- (micro-? nano-?) compositions that must be performed—with voice and/or keyboard, often with a partner—so that the ear, the fingers, the throat, and ultimately the mind can internalize the sound, sight, and feel of good (and bad) musical lines, and good (and bad) combinations of musical lines.

The specific method we will use is called species counterpoint—so called because the study progresses through stages, or species, where one or two new musical “problems” are introduced. This approach has existed in some form since the early seventeenth century. The specific method we will use is very close to that articulated by Johann Joseph Fux, in his Gradus ad Parnassum (Steps to Parnassus, 1725). Master composers from the eighteenth to the twenty-first centuries have used this method, or some variation on it. While Fux proposed five species, moving from two-voice combinations up to six- and eight-voice combinations, we will focus here on species one through four, in two voices only. The next chapter [link not currently working] provides all of the exercises from Gradus ad Parnassum in an editable format so you can try this yourself.

Composing a cantus firmus

Exercises in strict voice-leading, or species counterpoint, begin with a single, well formed musical line called the cantus firmus (fixed voice, or fixed melody; pl. cantus firmi. Cantus firmus composition gives us the opportunity to engage the following fundamental musical traits:

Our first exercises in strict voice-leading will be to compose good, well formed cantus firmi. The first step is to perform and analyze model cantus firmi, such as the following cantus firmus in C major, composed by Heinrich Schenker.

From these cantus, notice how the general musical characteristics of smoothness, melodic integrity, variety, and motion towards a goal are worked out in specific characteristics. The following characteristics are typical of all well formed cantus firmi:

Melodic tendencies

The characteristics listed above are fairly detailed, and some of them are specific to strict species counterpoint. However, taken together, they express in detail some general tendencies of melodies in a variety of styles.

David Huron identifies five general properties of melodies in Western music that connect to the basic principles of perception and cognition listed above, but play out in slightly different specific ways in musical styles. They are:

First-species counterpoint

Counterpoint is the mediation of two or more musical lines into a meaningful and pleasing whole. In first-species counterpoint, we not only write a smooth melody that has its own integrity of shape, variety, and goal-directed motion, but we also write a second melody that contains these traits. Further, and most importantly, we combine these melodies to create a whole texture that is smooth, exhibits variety and goal-oriented motion, and in which these melodies both maintain their independence and fuse together into consonant simultaneities (the general term for two or more notes sounding at the same time). In first species counterpoint, we begin with a cantus firmus (new or existing) and compose a single new line—called the counterpoint—above or below the cantus firmus. That new line contains one note for every note in the cantus: both the cantus firmus and the counterpoint will be all whole notes. Thus, first species is sometimes called one-against-one or 1:1 counterpoint.

The counterpoint line

In general, the counterpoint should follow the principles of writing a good cantus firmus. There are some minor differences, to be discussed below, but generally a first-species counterpoint should consist of two cantus-firmus-quality lines.

Beginning a first-species counterpoint

To exemplify goal-oriented motion, the first-species exercise should begin and end with the most stable of sonorities: perfect consonances. Thus, when writing a counterpoint above a cantus firmus, the first note of the counterpoint should be do or sol (a P1, P5, or P8 above the cantus).

When writing a counterpoint below a cantus firmus, the first note of the counterpoint must always be do (P1 or P8 below the cantus). (Beginning on sol would create a dissonant fourth; beginning on fa would create a P5 but confuse listeners about the tonal context, since fa–do at the beginning of a piece is easily misheard as do–sol.)

Ending a first-species counterpoint

The final note of the counterpoint must always be do (P1 or P8 above/below the cantus).

To approach this ending smoothly, with variety, and with strong goal orientation, always approach the final interval by contrary stepwise motion. If the cantus ends redo, the counterpoint’s final two pitches should be tido. If the cantus ends tido, the counterpoint’s final two pitches should be redo. Thus the penultimate bar will either be a minor third or a major sixth between the two lines. This is the case for both major and minor keys.

Independence of the lines

Like the cantus firmus, the counterpoint should have a single climax. To maintain the independence of the lines and the smoothness of the entire passage (so no one moment is hyper-emphasized by a double climax), these climaxes should not coincide.

A single repeat/tie in the counterpoint is allowed, but try to avoid repeating at all. This promotes variety in the exercise, since there are so few notes to begin with.

Avoid voice crossing, where the upper voice is temporarily lower than the lower voice, and vice versa. Voice crossings diminish the independence of the lines and make them more difficult to distinguish by ear.

Avoid voice overlap, where one voice leaps past the previous note of the other voice. For example, if the upper part sings an E4, the lower part cannot sing an F4 in the following bar. This also helps maintain the independence of the lines.

Intervals and motion

The interval between the cantus and counterpoint at any moment should not exceed a perfect twelfth (octave plus fifth). In general, try to keep the two lines within an octave where possible, and only exceed a tenth in “emergencies,” and only briefly (one or two notes). When the voices are too far apart, tonal fusion is diminished. Further, it can diminish performability, which though not an essential principle of human cognition is an important consideration for composers, and it has a direct effect on the smoothness, melodic integrity, and tonal fusion of what listeners hear during a performance.

In general, all harmonic consonances are allowed. However, unisons should only be used for first and last intervals. Unisons are very stable, and serve best as goals rather than mid points. They also diminish the independence of the lines.

Imperfect consonances are preferable to perfect consonances for all intervals other than the first and last dyads, in order to heighten the sense of arrival at the end, and to promote a sense of motion towards that arrival. In all cases, aim for a variety of harmonic intervals over the course of the exercise.

Never use two perfect consonances of the same size in a row: P5–P5 or P8–P8. This includes both simple and compound intervals. For example, P5–P12 is considered the same as P5–P5. (Two different perfect consonances in a row, such as P8–P5, is allowed, however, but try to follow every perfect consonance with an imperfect consonance if possible.) These “parallel fifths and octaves” significantly promote tonal fusion over melodic independence at the same time that the consecutive stable sonorities arrest both the variety and the motion of the exercise. Thus, they are far from ideal, and to be avoided in species counterpoint.

Vary the types of motion between successive intervals (parallel, similar, contrary, oblique). Try to use all types of motion (except, perhaps, oblique motion), but prefer contrary motion where possible. It is best for preserving the independence of the lines, in addition to variety.

Because similar and parallel motion diminish variety and melodic independence, their use should be mediated by other factors:

Second-species counterpoint

In second-species counterpoint, the counterpoint line moves in half notes against a cantus firmus in whole notes. This 2:1 rhythmic ratio leads to two new “fundamental musical problems”—one metric and one harmonic: the differentiation between strong beats and weak beats, and the introduction of the passing tone dissonance.  The introduction of harmonic dissonance into second species adds to the variety of the musical texture. However, it brings a tension that must be balanced with consonance to promote tonal fusion, and it requires careful attention in order to maintain smoothness in and out of the dissonance.

The counterpoint line

As in first species, the counterpoint line should be singable, have a good shape, with a single climax and primarily stepwise motion (with some small leaps and an occasional large leap for variety). However, because a first-species counterpoint had so few notes, in order to maintain smoothness in other aspects of the exercise, the melody frequently employed small leaps. In second species, the increase in notes and the added freedom involving the use of dissonance makes it easier to move by step without causing other musical problems. Thus, a second-species counterpoint is even more dominated by stepwise motion than in first species.If the counterpoint must leap, take advantage of the metrical arrangement to diminish the attention drawn to the leap: leap from strong beat to weak beat (within the bar) rather than from weak beat to strong beat (across the barline) when possible.Also, because there are more notes in a second species line, there should usually be one or two secondary climaxes—notes lower than the overall climax that serve as “local” climaxes for portions of the line. This will help the integrity of the line, by ensuring it has a coherent shape and does not simply wander around.

Beginning a second-species counterpoint

As in first species, begin a second-species counterpoint above the cantus firmus with do or sol. Begin a second-species counterpoint below the cantus firmus with do. Unisons are permitted for the first and last dyads of the exercise.

A second-species line can begin with two half notes in the first bar, or a half rest followed by a half note. Beginning with a half rest establishes the rhythmic profile more readily, making it easier for the listener to parse, so it is often preferable. It is also easier to compose. Regardless of rhythm, the first pitch in the counterpoint should follow the intervallic rules above.

Ending a second-species counterpoint

The final pitch of the counterpoint should be do, as in first species.

The penultimate note of the counterpoint should be ti if the cantus is re, and re if the cantus is ti, as in first species.

The penultimate bar of the counterpoint can either be a whole note (making the last two bars identical to first species), or two half notes. Which option you use will depend on how you are approaching the final bar. (This is simply a historical convention, not a musical necessity. But the added degree of freedom makes it easier to move into the final arrival smoothly without adding too many complicating factors.)

Strong beats

Because the inclusion of dissonance in a musical texture creates new musical problems that need to be addressed, second species introduces dissonance in a very limited way. This is not a musical necessity, and it’s not the only way to address dissonance, but it helps by introducing a small number of new musical difficulties in each species.

Strong beats (downbeats) in second species are always consonant. As in first species, prefer imperfect consonances (thirds and sixths) to perfect consonances (fifths and octaves), and avoid unisons.

Because motion across bar lines (from weak beat to strong beat) involves the same kind of voice motion as first species (two voices moving simultaneously), follow the same principles as first species counterpoint. For instance, if a weak beat is a perfect fifth, the following downbeat must not also be a perfect fifth.

Likewise progressions from downbeat to downbeat must follow principles of first-species counterpoint. The following are some examples, but not an exhaustive list:

Hidden or direct fifths/octaves between successive downbeats are fine, as the effect is weak, and the intervening note in the counterpoint diminishes that effect.

Weak beats

Since harmonic dissonances can appear on weak beats, a mixture of consonant and dissonant intervals on weak beats is the best way to promote variety.

Unisons were problematic in first species because they diminished the independence of the lines. However, when they occur on the weak beats of second species and are the result of otherwise smooth voice-leading, the rhythmic difference in line is sufficient to maintain that independence. Thus, unisons are permitted on weak beats when necessary to make good counterpoint between the lines.

Any weak-beat dissonance must follow the pattern of the dissonant passing tone, explained below. Also explained below are a number of standard patterns for consonant weak beats. Chances are high that if your weak beats do not fit into one of the following patterns, there is a problem with the counterpoint, so use them as a guide both for composing the counterpoint, and for evaluating it.

Weak beat patterns

The following patterns (whose terms are either standard or taken from Salzer & Schachter’s Counterpoint in Composition) should guide your use of weak-beat notes in a second-species counterpoint line. A good general practice is to start with a downbeat note, then choose the following downbeat note, and finally choose a pattern below that will allow you to fill in the space between downbeats well.

Most of these are used as examples in the demonstration video at the bottom of the page.

Dissonant weak beats

All dissonant weak beats in second species are dissonant passing tones, so called because the counterpoint line passes from one consonant downbeat to another consonant downbeat by stepwise motion. The melodic interval from downbeat to downbeat in the counterpoint will always be a third, and the passing tone will come in the middle in order to fill that third with passing motion.

Since all dissonances in second species are passing tones, you will never leap into or out of a dissonant tone, nor will you change directions on a dissonant tone, nor will any dissonances occur on a downbeat.

Consonant weak beats

A consonant passing tone outlines a third from downbeat to downbeat, and has the same pattern as the dissonant passing tone, except that all three tones (downbeat, passing tone, downbeat) are consonant with the cantus. A consonant passing tone will always be a sixth or perfect fifth above/below the cantus.

A substitution also outlines a third from downbeat to downbeat. However, instead of filling it in with stepwise motion, the counterpoint leaps a fourth and then steps in the opposite direction. It is called a substitution because it can substitute for a passing tone in a line that needs an extra leap or change of direction to provide variety. Like the consonant passing tone, all three notes in the counterpoint must be consonant with the cantus.

A skipped passing tone outlines a fourth from downbeat to downbeat. The weak-beat note divides that fourth into a third and a step. Again, all three intervals (downbeat, skipped passing tone, downbeat) are consonant with the cantus.

An interval subdivision outlines a fifth or sixth between successive downbeats. The large, consonant melodic interval between downbeats is divided into two smaller consonant leaps. A melodic fifth between downbeats would be divided into two thirds. A melodic sixth between downbeats would be divided into a third and a fourth, or a fourth and a third. Not only must all three melodic intervals be consonant (both note-to-note intervals and the downbeat-to-downbeat interval), but each note in the counterpoint must be consonant with the cantus.

A change of register occurs when a large, consonant leap (P5, sixth, or octave) from strong beat to weak beat is followed by a step in the opposite direction. It is used to achieve melodic variety after a long stretch of stepwise motion, to avoid parallels or other problems, or to get out of the way of the cantus to maintain independence. It should be used infrequently. And as always, each note must be consonant with the cantus.

A delay of melodic progression outlines a step from downbeat to downbeat. It involves a leap of a third from strong beat to weak beat, followed by a step in the opposite direction into the following downbeat. It is called a “delay” because it is used to embellish what otherwise is a slower first-species progression (motion by step from downbeat to downbeat).

A consonant neighbor tone occurs when the counterpoint moves by step from downbeat to weak beat, and then returns to the original pitch on the following downbeat. If the first downbeat makes a fifth with the cantus, the consonant neighbor will make a sixth, and vice versa.

Third-species Counterpoint

In third-species counterpoint, the counterpoint line moves in quarter notes against a cantus firmus in whole notes. This 4:1 rhythmic ratio creates a still greater differentiation between beats than in second species: strong beats (downbeats), moderately strong beats (the third quarter note of each bar), and weak beats (the second and fourth quarter notes of each bar). Third species also introduces the neighbor tone dissonance, and two related figures in which dissonances can participate in leaps.

The counterpoint line

As in first and second species, the counterpoint line should be singable, have a good shape, with a single climax that does not coincide with the climax of the cantus firmus, and primarily stepwise motion (with some small leaps and an occasional large leap for variety). Like second species, a third-species counterpoint should be even more dominated by stepwise motion than in first species, because there are less sticky situations that would require a leap. If the counterpoint must leap, prefer to do so within the bar rather than across the barline. Also like second species, there should usually be one or two secondary climaxes—notes lower than the overall climax that serve as “local” climaxes for portions of the line.

Beginning a third-species counterpoint

Begin a third-species counterpoint above the cantus firmus with do or sol. Begin a third-species counterpoint below the cantus firmus with do. Unisons are permitted for the first and last dyads of the exercise.

A third-species line can begin with four quarter notes in the first bar, or a quarter rest followed by three quarter notes. Regardless of rhythm, the first pitch in the counterpoint should follow the intervallic rules above.

Ending a third-species counterpoint

The final pitch of the counterpoint must always be do, and must be a whole note.

The penultimate note of the counterpoint (the last quarter note of the penultimate bar) should be ti if the cantus is re, and re if the cantus is ti.

Strong beats

Principles for strong beats (downbeats) are generally the same as in second species.

Strong beats are always consonant, and not unisons. Prefer imperfect consonances (thirds and sixths) to perfect consonances (fifths and octaves).

Motion across bar lines (from beat 4 to downbeat) follows the same rules as first species counterpoint.

Progressions from downbeat to downbeat follow principles of second-species counterpoint, with one exception (see below). The following are some examples, but not an exhaustive list:

If a downbeat contains a perfect fifth, neither the third or the fourth beat of the previous bar can be a fifth. If a downbeat contains an octave, neither the second, third, or fourth beat of the previous bar can be an octave. Like in second species, the negative effects of parallel fifths and octaves are not mitigated by the addition of a note or two.

Hidden or direct fifths/octaves between successive downbeats are allowed.

Other beats

Beats 2–4 should exhibit a mixture of consonant and dissonant intervals to promote variety. Among consonances, unisons are permitted on weak beats when necessary to make good counterpoint between the lines. Any dissonance must follow the pattern of the dissonant passing tone or the dissonant neighbor tone, explained below. Also explained below are a number of standard patterns for consonant weak beats.

Harmonic dissonances

Generally, dissonances in third species can occur on beat 2, 3, or 4, and should be preceded and followed by stepwise motion (with the exception of the double neighbor and the nota cambiata, explained below). This promotes smoothness, both by keeping the dissonances off of the strongest beat of the bar, and by coupling them with the smoothest melodic motion. If all dissonant notes in the counterpoint follow one of the following models, they should have a pleasing effect. If not, they may sound harsh or unresolved, or will be difficult to sing.

The dissonant passing tone fills in the space of a melodic third via stepwise motion. The notes before and after the passing tone must be consonant with the cantus.

Note that it is possible to have two dissonant passing tones in a row (P4–d5 or d5–P4). As long as these dissonances do not fall on downbeats and the counterpoint moves in stepwise motion in a single direction, there is no negative effect.

The dissonant neighbor tone ornaments a consonant tone by stepping away and stepping back to the original consonance (6–7–6 over the cantus, for example). It is melodically identical to the consonant neighbor tone of second species, with the difference being the harmonic dissonance. Employing it on a weak beat (2 or 4) ensures the greatest smoothness.

The double neighbor occurs when beats 1 and 4 in the counterpoint are the same tone, and beats 2 and 3 include the notes a step higher and a step lower than the original tone. For example, C–D–B–C or C–B–D–C. Both beats 2 and 3 are dissonant, but since both are embellishing the original tone by step, the leap between them does not significantly diminish the smoothness of the line. When using a double neighbor, the direction between beats 3 and 4 should be the same as between beat 4 and the following downbeat. That motion across the barline should also be stepwise. This further maintains smoothness to temper the effect of the dissonances.

The nota cambiata (changing tone) is a five-note figure that outlines a step progression from downbeat to downbeat. It follows one of two patterns:

The first pattern will result in a step down from downbeat to downbeat, and the second pattern will result in a step up from downbeat to downbeat. For a nota cambiata to be effective, the first, third, and fifth notes must be consonant with the cantus. The second note will be dissonant and will leap to the third tone. However, like the double neighbor, the overall pattern minimizes the negative effect of the leap away from the dissonance. It is surrounded by stepwise motion, the overall progression is a single step, and the dissonant tone and the following downbeat are the same pitch.

Consonances

The counterpoint can move in and out of consonant tones freely by step, as well as by leap from another consonance, with the following considerations:

Fourth-species counterpoint

In fourth-species counterpoint, the counterpoint line and cantus firmus both move once per bar, but they are rhythmically offset from each other by a half note. (Think syncopation on the bar level.) The counterpoint line will be notated in half notes, with each weak-beat half note tied across the bar line to the following strong beat. This arrangement means that in pure fourth-species counterpoint, the two lines always move in oblique motion. It also introduces a new kind of dissonance: the suspension

The suspension

The suspension is an accented dissonance, meaning it always occurs on strong beats. Because of the increased emphasis, even greater care must be taken to promote smoothness and overall coherence. Thus, like the passing tone and neighbor tone dissonances, the suspension is always preceded and followed by harmonic consonances.A suspension figure has three parts:- the preparation: a weak-beat note in the counterpoint that is consonant with the cantus. This note will be tied into:

It will always be a step lower than the suspended tone.Use dissonant suspensions as much as possible in fourth species. Not only are they the characteristic sound of fourth species, but they sound nice, and proper use of them in fourth species will prepare you for the use of both suspensions and dissonant chord tones in later composition and arranging work.

Types of suspensions

Suspensions are categorized according to the intervals of the suspension and resolution tones above/below the cantus firmus. A 7–6 suspension, for example, includes a strong-beat suspension that forms a seventh with the cantus, which resolves down by step to a weak-beat tone that forms a sixth with the cantus.

Possible dissonant suspensions above the cantus firmus are 7–6, 4–3, and 9–8. (These are the only options that start on a dissonance and resolve down by step to an allowable consonance.) Possible dissonant suspensions below the cantus firmus are 2–3, 5–6, and 4–5. (7–8 is theoretically possible, but it tends to sound less pleasing than the others. It is best avoided.)

Using suspensions

Treat suspensions in fourth species the same way you would treat their intervals of resolution in first species. For example, do not use two 9–8 or 4–5 suspensions in a row (since you cannot use two octaves or two fifths in a row in first species). Use 7–6 and 4–3 (above) or 2–3 and 5–6 (below) liberally, but no more than three times in a row (like thirds and sixths in first species).

Following the same principle, do not use the “consonant suspension” 6–5 twice in a row, since its interval of “resolution” is a fifth. In fact, because the pattern set forward by a fourth-species line invites listeners to interpret the weak beats as the main consonances, avoid any configuration that would create two fifths or two octaves on consecutive weak beats in fourth species (called “after-beat” fifths or octaves).

The fourth-species counterpoint line

Use dissonant suspensions whenever possible. This will create a line consisting mostly of downward, stepwise motion. That is fine. It will also make it hard to direct motion towards a climax. That is also fine. Do not worry about the shape of the line if it is smooth, singable, and the suspensions are properly prepared and resolved. (It is simply too difficult to create a fourth-species counterpoint with the same shape as a cantus firmus, and the pedagogical import in fourth species is the treatment of the suspensions. So we temporarily ignore melodic shape to hone our suspension skills in fourth species.)

If a dissonant suspension is not possible, try to use a tie from weak beat to strong beat. This can be a “consonant suspension,” or you can leap up from downbeat consonance to weak-beat consonance. At least one or two upward leaps will be necessary to counteract the downward resolutions in order to keep the line in a singable range.

If neither a dissonant suspension or consonant tied figure is possible, it is permissible to break species (see video demo below). When you break species, follow the principles of second-species counterpoint and resume fourth-species ties as soon as possible. Try not to break species more than once per exercise, and for just a bar or two.

Beginning a fourth-species counterpoint

Begin a fourth-species counterpoint above the cantus firmus with do or sol. Begin a second-species counterpoint below the cantus firmus with do. Unisons are permitted for the first and last dyads of the exercise.

Always begin with a half rest.

Ending a fourth-species counterpoint

There is only one option for ending fourth species.

The cantus firmus must end with redo. Do not use a cantus that ends with tido.

The counterpoint will end with a dissonant suspension. The penultimate bar will contain doti, and the final bar will contain a whole note do. The doti will form a 7–6 suspension above the re in the cantus, or a 2–3 suspension below the re in the cantus. As a dissonant suspension, that do will always be tied over from the previous bar.

3

"Gradus ad Parnassum" Exercises

Mark Gotham

The previous chapter introduced Species Counterpoint, and the iconic pedagogical treatise on cantus firmus composition, Johann Joseph Fux’s Gradus ad Parnassum (1725). This page provides the full cantus firmus exercises of that treatise so you try your hand are Species Counterpoint a la Fux.

Gradus ad Parnassum is in three sections:

  1. Two Voices (46 exercises)
  2. Three Voices (44 exercises)
  3. Four Voices (32 exercises)

For each of these sections, we provide four files:

  1. ‘Exercises’: all of the cantus firmus exercises with only the cantus firmus present and the other part(s) left blank for you to complete.
  2. ‘Solutions’: all of Fux’s solutions to those exercises – i.e. both the cantus firmus and the additional part(s) that Fux wrote as answers.
  3. ‘Annotations’: Those solutions annotated with the interval that every note in each additional part forms with the cantus firmus part.
  4. ‘Distinct’: Every distinct cantus firmus in all parts. All of the exercises are based on this format, so these simple files distill all possibilities: you can use this file to do any species exercise, on any cantus firmus, in any part arrangement.

Everything is provided in an editable format so teachers can adjust and combine exercises freely for their own class’ needs.

Downloads

These files are provide in both .mxl and .mscz format. Click on the blue links to download any particular type. Please note that the files are hosted externally on http://fourscoreandmore.org/species/ so you will be redirected and may prefer to open in a new tab.

In .mxl format (open these in any music notation package like MuseScore, Sibelius, Finale … ):

Part Exercises Solutions Annotated Distinct
I I-Exercises.mxl I-Solutions.mxl I-Annotated.mxl I-Distinct.mxl
II II-Exercises.mxl II-Solutions.mxl II-Annotated.mxl II-Distinct.mxl
III III-Exercises.mxl III-Solutions.mxl III-Annotated.mxl III-Distinct.mxl

In .mscz format (for MuseScore specifically, preserving all original formatting):

Part Exercises Solutions Annotated Distinct
I I-Exercises.mscz I-Solutions.mscz I-Annotated.mscz I-Distinct.mscz
II II-Exercises.mscz II-Solutions.mscz II-Annotated.mscz II-Distinct.mscz
III III-Exercises.mscz III-Solutions.mscz III-Annotated.mscz III-Distinct.mscz

For Reference

Each exercise includes the following information:

For ease of reference, the following sub-section / tables set out that information in full.

Finally, a note on clefs. Those given also follow the Norton/Mann edition (1965) for parts I and II. Part III keeps the same clefs throughout to be consistent both internally and with the modern choral score layout (treble, treble, treble 8vb, bass). Teachers may wish to choose their own clefs as part of adapting these files for class.

Part I

Figure Species Mode (final) Cantus Firmus Part
5 1 d Lower
6 1 d Upper
11 1 e Lower
12 1 e Upper
13 1 f Lower
14 1 f Upper
15 1 g Lower
21 1 g Upper
22 1 a Lower
23 1 a Upper
33 2 d Lower
35 2 d Upper
36 2 e Lower
37 2 e Upper
38 2 f Lower
39 2 f Upper
40 2 g Lower
41 2 g Upper
42 2 a Lower
43 2 a Upper
44 2 c Lower
45 2 c Upper
55 3 d Lower
56 3 d Upper
57 3 e Lower
58 3 e Upper
59 3 f Lower
59 3 f Upper
73 4 d Lower
74 4 d Upper
75 4 e Lower
76 4 e Upper
77 4 f Lower
78 4 f Upper
82 5 d Lower
83 5 d Upper
84a 5 e Lower
84b 5 e Upper
85a 5 f Lower
85b 5 f Upper
86a 5 g Lower
86b 5 g Upper
87a 5 a Lower
87a 5 a Upper
88a 5 c Lower
88b 5 c Upper

Fux basically uses one cantus firmus for each modal final throughout. The note sequences are as follows, along with their usage counts (46 total) and the minor exceptions:

Modal final Pitches Counts and exceptions
D D4, F4, E4, D4, G4, F4, A4, G4, F4, E4, D4 10 counts
E E4, C4, D4, C4, A3, A4, G4, E4, F4, E4 10 counts
F F3, G3, A3, F3, D3, E3, F3, C4, A3, F3, G3, F3 10 counts including one at the octave above, (fig.13: starting F4)
G G3, C4, B3, G3, C4, E4, D4, G4, E4, C4, D4, B3, A3, G3 6 counts
A A3, C4, B3, D4, C4, E4, F4, E4, D4, C4, B3, A3 6 counts including one lacking the first D (fig.42: A3, C4, B3, C4, E4 …)
C C4, E4, F4, G4, E4, A4, G4, E4, F4, E4, D4, C4 2 counts. The most anomalous case.
C C4, D4, F4, E4, G4, E4, F4, E4, D4, C4 2 counts. More divergent than for the other modes

Part II

Figure Species Mode (final) Cantus Firmus Part
101 1 d 1
104 1 d 2
105 1 d 3
106 1 e 1
108 1 e 2
109 1 e 3
110 1 f 1
111 1 f 2
112 1 f 3
113 1 g 1
114 1 g 2
115 1 a 1
116 1 a 2
117 1 a 3
118 1 c 1
119 1 c 2
121 2 d 1
122 2 d 2
123 2 d 2
124 2 e 2
125 2 e 3
126 2 e 1
127 2 f 1
128 2 f 2
129 2 f 2
130 3 d 2
131 3 d 3
132 3 d 2
134 2,3 d 3
141 4 d 2
143 4 d 3
144 4 d 1
146 4 e 2
147 4 e 1
148 4 e 2
149 4 f 2
150 4 f 3
151 4 f 1
154 5 d 2
155 5 d 1
156 5 d 2
157 5 e 2
158 5 e 1
159 5 e 2

… and the cantus firmus collection …

Modal final Pitches Counts and exceptions
D D4, F4, E4, D4, G4, F4, A4, G4, F4, E4, D4 16 counts at two octaves (D3 and D4)
E E4, C4, D4, C4, A3, A4, G4, E4, F4, E4 12 counts at two octaves (E3 and E4)
F F3, G3, A3, F3, D3, E3, F3, C4, A3, F3, G3, F3 9 counts at two octaves (F3 and F4)
G G3, C4, B3, G3, C4, E4, D4, G4, E4, C4, D4, B3, A3, G3 2 counts
A A3, C4, B3, D4, C4, E4, F4, E4, D4, C4, B3, A3 3 counts at three octaves (A2, A3 and A4)
C C4, E4, F4, G4, E4, A4, G4, E4, F4, E4, D4, C4 2 counts. Corresponds to the first case for Part I.

Part III

Figure Species Mode (final) Cantus Firmus Part
160 1 d 2
163 1 d 1
164 1 d 3
165 1 d 4
166 1 e 1
167 1 e 2
168 1 e 3
169 1 f 2
170 1 f 1
171 1 f 3
172 1 f 4
173 2 d 1
174 2 d 2
175 2 d 3
176 2 d 4
177 3 d 2
180 3 d 4
181 3 d 2
182 3 d 2
183 3 e 2
184 3 e 1
185 3 e 2
186 3 e 3
193 4 d 2
195 4 d 4
196 4 d 1
197 4 d 2
200 5 d 2
201 5 d 1
202 5 d 4
203 5 d 2
204 2,3,4 d 4

… and the cantus firmus collection …

Modal final Pitches Counts and exceptions
D D4, F4, E4, D4, G4, F4, A4, G4, F4, E4, D4 21 counts at two octaves (D3 and D4)
E E4, C4, D4, C4, A3, A4, G4, E4, F4, E4 7 counts, one at E5 (fig.184)
F F3, G3, A3, F3, D3, E3, F3, C4, A3, F3, G3, F3 4 counts at two octaves (F3 and F4)

4

Sixteenth Century Contrapuntal Style

Mark Gotham

The sixteenth century contrapuntal style has historically enjoyed a prominent position in the teaching of music theory. ‘Pastiche’ or ‘counterfactual’ composition of sixteenth century imitative choral polyphony (especially in the style of Palestrina) has frequently appeared in curricula and sometimes conflated with the later, 18th Century notion of ‘species counterpoint’ which we met in the previous chapters.

This chapter sets out some rules of thumb to bear in mind when completing style-composition exercises based on this repertoire where you are given a partial score to complete. For a more complex and data-driven survey of this, see Gotham and Cuthbert’s ‘Species or Specious’ (2020, in press).

Imitation

Melody

Rhythm and Meter

Text Setting

Texture

‘Harmony’

5

High Baroque Fugal Exposition

Mark Gotham

We now move on from imitative practices common in the sixteenth century to the fugue which may be thought of as the eighteenth century equivalent and successor to this tradition. This chapter deals with the basics of writing a fugal exposition from a given subject according to the ‘high Baroque’ technique of Bach, Handel and their contemporaries. First let’s define some of the terms we’ll need:

Basic Definitions

Structure / Voice Entries

Basically, the fugal exposition works as follows:

Voice 1 Subject Countersubject Free part
Voice 2 Answer Countersubject
Voice 3 Subject

One voice begins with the subject; then the next voices enters with the answer while the fist continues with a countersubject and so on.

Note that we’re numbering the voices here simply on the basis of their successive entries. While it is perfectly common for the voices to enter in order from highest to lowest or lowest to highest, this is not strictly necessary. What you will commonly find in the repertoire is an avoidance of inner parts entering last; specifically: at the moment of a new part entering, it should be the highest or lowest voice at that stage. That leaves us plenty of options. For instance the order of voice entries in a four voice fugue could be:

Any further subjects / answers entering (beyond the total number of voices) are described as ‘redundant’ entries.

Subject

When considering how to handle a subject, look at its structure and character.

The structure of a subject can often be thought of in three parts. As in many tonal contexts this charts a course from a distinctive opening to a generic cadence:

Types of character include the:

Answer

We distinguish between two types of answer: ‘Real’ for an exact transposition, and ‘tonal’ for one that has been altered further.

We need a tonal answer if the subject:

In all cases, we seek to make minimal adjustment such that the subject and answer are still as alike as possible, and both make melodic sense.

Countersubject

Try working up a skeletal version of your countersubject first before. It’s frustrating to dash off a lovely tune and then realise that it doesn’t fit. Additionally, sketch the version that will go with the answer at the same time as the version that goes with the subject. It’s just as frustrating to write a countersubject that works beautifully with the subject, but which the answer makes harmonically nonsensical.

Hold on, harmony? Yes indeed! Countersubjects are melodies but they only work if they make sense harmonically as well. To that effect, remember that your countersubject will first appear in a two-voice passage so consider how best to outline clear, larger harmonies (triads and sevenths) with only two voices.

You may wish to set yourself the additional constraint of a countersubject which is invertible at the octave – basically, one which can appear above or below the subject and still work. In this case, again work on both versions as you go, and specifically make sure to:

To create your skeletal countersubject, first look for skeletal patterns in the subject. Find the simple, un-embellished form of the subject and treat is as a kind of tonal cactus firms against which to write your counterpoint (skeletal countersubject) which you can then embellish into a more interesting musical line.

When it comes to embellishing, try to:

‘Free part’

Frankly, the idea of a ‘Free part’ is a bit of a misnomer, especially if you’re writing an invertible countersubject because the subject and countersubject will leave your options highly constrained. This part is ‘free’ in the sense that it doesn’t necessarily recur later on, so you might like to think of it as a ‘freer’ part, relative to the even less free subject and countersubject! Alternatively, you can embrace the extreme order, and replace the ‘free part’ with a second regular countersubject which dos recur later.

Links

Your fugal exposition may include short interpolations between the subject/answer entries. We call these ‘links’. Links frequently make use of a melodic idea from the subject, for instance with sequential repetition of a short fragment. They may appear between any or all voice entries, and be of varying lengths.

There are many musical motivations for including one of more link. Links provide an opportunity to:

General Matters

Apart from the specific considerations of the fugue, naturally much of the general practice of writing (tonal) music applies here. Remember in particular to:

6

Ground Bass

Ground Bass

Mark Gotham

‘Ground bass’ compositions are based on a bass line that repeats throughout the piece, usually exactly, or nearly so. Many musicians have found this a compelling compositional constraints for keeping them … well … grounded!

How many musicians are we talking about? Well, this practice was highly popular in the Baroque. Purcell was a particularly keen and expert protagonist; it is even more common in popular songs of recent years (see Harmonic Schemas in Pop Music); and there are more than a few example from in between. In short, it is an extremely and enduringly popular form.

It it’s easy to confuse the ‘Ground bass’ with some other terms; the key terms to distinguish are:

This chapter provides some files and instructions to help you explore some of the ways to create effective ground bass compositions. We focus on the Baroque model, and on creating variety through re-harmonising the same bass in different ways and varying the texture. The Anthology’s Form section lists some important ground bass works from the Baroque [ref. chapter].

Files

  1. A cheat sheet for the many ways of re-harmonising any bass interval;
  2. Template scores based on Baroque ground bass compositions, but with only the ground bass provided so you can compose a completion of the rest;
  3. Those Baroque compositions again, but with the upper parts now included along with annotated files with Roman Numerals and more.

In all of these templates and annotated scores, there is exactly one iteration of the ground per system so you can compare equivalent moments directly (vertically).

Here are links to the files for 2. and 3.:

Template Score Full, Annotation
Bach Crucifixus Template Score Annotation
Purcell Sonata in G Minor Z 807 Template Score Annotation
Purcell Chacony in G Minor Z730 Template [To follow]
Purcell Here the Deities Approve Template [To follow]

Multiple Harmonisations of a Given Bass

This ‘cheat sheet‘ shows how you can harmonise any bass interval in several different ways. It is organised by bass interval: both ascending and descending forms of each interval from minor seconds to tritones. This is supposed to help you work out your options – you definitely don’t need to use all of these! We’ll see below how Purcell uses just a few of these to create harmonic variety in a very long work that’s almost entirely in g minor. We’ll be especially interested in moments where Purcell avoids the main, perfect cadence at the start/end of each iteration of the ground, joining two grounds together with a subtler seam, and varying not just the harmony, but also the phrase rhythm of the piece.

Composition Exercises

These template scores allow you to try your hand at composing music based on some of the repertoire’s great ground basses.

Take a template and try to compose:

  1. A simple, predominantly diatonic harmonisation of the ground, with simple blocks chords, making sure to follow good voice-leading practice. Use this as a prototype.
  2. A set of alternative harmonizations including tonicizations of other keys and re-harmonizations of the first note in particular to vary the apparent phrase length (as discussed above in reference to the ‘cheat sheet’);
  3. Melodic parts that fit with the bass and create more interesting textures. Seek out ways of writing upper parts that can recur in another voice in imitation. We’ll see how Purcell approaches this below.
  4. Finally, combine the best of your ideas into an overall piece that balances textural and harmonic interest and charts an overall trajectory. Why not try a piece with 6 iterations of the ground, of which the first and last are simple and alike.

Analysis: Purcell’s Sonata in G Minor (Z 807)

To explore some of the options here, let’s take a look at Purcell’s Sonata in G Minor (Z 807). We’ll look at how Purcell uses (extensive) imitation and (occasional) tonicisation. All of these matters are summarized in the tables at the end of this page, and are also included on the downloadable score as text annotations at the relevant moment.

Harmony. Harmonically, the piece is resolutely in g minor almost throughout, though Purcell tonicizes several keys along the way as summarized in the second table below. Notice especially how Purcell finesses that boundary between the start/end of a ground iteration by avoid yet another perfect cadence in g. For instance, see m.16 and 106 for uses of G major as part of V7d-ib in d minor, broadly reversing tonic and dominant function, and likewise m.26 and 86 for g diminished as viio6-I in F major.

As a wider matter, notice how extensively Purcell uses 5-6 steps in the melodic parts and how this creates ambiguity in the harmony. Is the 5 or the 6 harmonic, or perhaps both? Is this consistent or does it change? This all makes it harder to pin down exactly what the harmony is and where it changes, adding ever further layers of interest to the score. It also helps set up the sequences of 7-6 suspensions such as from m.71.

Imitation. Imitation is prevalent throughout. The melodic imitations are labelled ‘D’ and ‘C’ on the score, and in the table below. This is short for ‘Dux’ and ‘Comes’ – ‘leader’ and ‘follower’. For instance, the violin 1 parts starts a melodic line in measure 1 (beat 1) which is imitated by the violin 2 entering in measure 3 (beat 1). Notice from the table how often these imitations start in the same part of the bar. This is consistent with what we discussed in the context of 16th century and 18th century imitative traditions. Visit those chapters to learn more. Entering on equivalent beats lead to temporal gaps between entries of 3 or 6 beats (beat gaps on the table). Note the many exceptions where Purcell uses closer imitation.

As the score and first table show, there is a great deal of imitation in this piece; almost every iteration of the ground is accompanied by a new imitative relationship in the upper parts (the exceptions are given in the second table, below). Perhaps the two most special and interesting cases are the:

  1. double imitation starting in m.196 and imitated with parts swapped in m.201;
  2. imitation of the ground itself in the violin 2 part at m.99/102.

The second table summaries the iterations without imitation.

Rhythm and Meter. Finally, note how Purcell continually varies the rhythmic values (metrical levels) involved, using a wide range of options. This includes introducing continuous eighth-notes (m.36), sixteenth-notes (m.81 and 146), syncopation (m.126), dotted rhythms (136), and for one passage near the end, changing the notated meter to compound time (m.166–185). This is a common device in Baroque ground bass (and other variations-style works of the time); again these changes usually (but not always) coincide with the start of a new iteration of the ground.

D. Part D. Measure D. Beat D. Pitch C. Part C. Measure C. Beat C. Pitch Beat gap Pitch interval
1 1 1.0 D5 2 3 1.0 G4 6.0 P5
1 6 1.0 G5 2 7 1.0 D5 3.0 P4
2 10 3.0 D5 1 11 3.0 D5 3.0 P1
1 20 2.0 D5 2 21 2.0 G4 3.0 P5
2 27 2.0 C5 1 29 2.0 D5 6.0 M2
2 30 2.0 D5 1 31 2.0 D5 3.0 P1
2 33 1.0 D5 1 34 1.0 C5 3.0 M2
2 36 1.0 G4 1 36 2.0 G4 1.0 P1
2 41 2.0 E-5 1 41 3.0 B-5 1.0 P5
2 46 1.0 D5 1 47 1.0 E-5 3.0 m2
2 51 1.5 G5 1 52 1.5 D5 3.0 P4
2 56 1.0 E-4 1 56 2.0 C5 1.0 M6
1 61 2.0 G4 2 62 2.0 D5 3.0 P5
1 63 1.0 G5 2 63 2.0 C5 1.0 P5
2 66 1.5 G5 1 67 1.5 D5 3.0 P4
2 71 2.0 D5 1 71 3.0 G5 1.0 P4
1 81 1.25 G5 2 82 1.25 D5 3.0 P4
1 91 1.0 B-4 2 94 1.0 D4 9.0 m6
1 95 2.0 A4 2 97 2.0 D5 6.0 P4
1 99 1.0 D5 2 102 1.0 D5 9.0 P1
1 106 1.0 E5 2 108 1.0 B-4 6.0 A4
2 111 2.0 D5 1 112 2.0 A4 3.0 P4
2 117 2.0 D5 1 118 2.0 A5 3.0 P5
2 121 1.0 G4 1 121 3.0 D5 2.0 P5
1 129 2.0 D5 2 130 2.0 A4 3.0 P4
1 133 1.5 D5 2 133 2.5 G4 1.0 P5
2 136 1.0 G4 1 137 1.0 D5 3.0 P5
2 141 1.0 G4 1 142 1.0 D5 3.0 P5
2 146 1.0 G4 1 147 1.0 D4 3.0 P4
1 151 1.0 G4 2 153 1.0 G4 6.0 P1
1 156 2.0 E-5 2 157 2.0 A-4 3.0 P5
1 161 2.0 E-5 2 162 2.0 A-4 3.0 P5
1 166 1.0 G4 2 167 1.0 D4 3.0 P4
1 171 1.0 G4 2 171 2.0 G4 1.0 P1
2 176 1.0 G5 1 177 1.0 D5 3.0 P4
2 178 1.0 E-5 1 178 2.0 E-5 1.0 P1
1 181 1.0 G5 2 181 2.0 G5 1.0 P1
1 182 1.0 D5 2 182 2.0 D5 1.0 P1
1 186 2.0 D5 2 187 2.0 A4 3.0 P4
2 196 1.0 G4 1 201 1.0 B-4 15.0 m3
1 196 1.5 G5 2 201 1.5 D5 15.0 P5
1 206 1.0 B-4 2 208 1.0 B-4 6.0 P1

 

Notes Measure Beat
Tonicization: Bb 12 3
No imitation; more homophonic 16 1
Tonicization: d 17 1
Tonicization: F 27 1
Tonicization: Bb (but deceptive cadence) 28 1
Imitation freer intervalically 31 1
Tonicization: c 33 1
Imitation freer intervalically 46 1
Cycle of 5th? But missing every other root … 71 3
Tonicization: Eb 78 1
Tonicization: F 87 1
Tonicization: Eb 88 1
Tonicization: c 93 1
Tonicization: d 107 1
Tonicization: F 117 1
Homophonic 126 1
Tonicization: c 131 2
Tonicization: c 133 1
Two notes 156 1
Tonicization: Eb 158 1
Repeat 161 1
Tonicization: Eb 163 1
Meter change 166 1
Chromatic ascents 186 1
Meter changes back 186 1
Chromatic descents 191 1
Sequences and double imitation 196 1

III

Strict Four-Voice Composition, Partimenti, and Schemata

7

Introduction to thoroughbass

Brian Moseley, Kris Shaffer, and Bryn Hughes

J.S. Bach, Flute Sonata in C Major, ii., BWV 1033. The upper part is played by the flute, the lower part is the basso continuo line, played by a keyboardist who uses the numbers below the staff (figures) to guide the chords played above this bass line.The historical origin of the thoroughbass part was in church settings where a piece for 6–8 singers was to be performed by one or two voices with a keyboard instrument. The keyboardist, rather than play the 4–7 remaining parts, would transcribe the lowest note and shorthand figures to indicate the (simple) intervals present above that lowest voice. This would allow the keyboardist to play one or two of the more important lines, and fill the rest of the texture with blocked or arpeggiated chords. (Think seventeenth-century lead sheet.) A good keyboardist, who knew their harmony and voice-leading, could simply follow the bass line without figures (an unfigured bass) and listen to the melody, improvising the rest. Less experienced keyboardists, however, could manage otherwise complicated pieces by reading a bass line and memorizing a small number of figures and basic voice-leading rules. (You can read a more detailed explanation of its history here.)

Coming after species counterpoint in our studies, basso continuo exercises provide a new, more complicated environment in which to practice mediating the demands of smoothness, independence of lines, tonal fusion (now considering triads and seventh chords), variety, and motion. New considerations of performability are introduced, and the presence of dissonances within the core harmonies themselves will call for new approaches to harmonic dissonance in this style.

We will use thoroughbass lines for a number of purposes in this book:

  • harmonic “reductions” of pieces and passages with dense textures or complicated voice-leading
  • shorthand representations of stock harmonic patterns
  • the harmonic basis for model composition exercises (akin to the cantus firmus of species counterpoint)

Thoroughbass is a simple, and foundational, concept. Master it early, and subsequent activities will be much easier.

Note on figure placement: Thoroughbass figures can appear above or below the bass line. Both are common, but in this book, we generally place them above the bass line. This connects them to our habits of interval analysis during species counterpoint, keeps figures separate from other harmonic symbols we will place below the bass line, and make typesetting in notation software easier when both figures and other symbols are in play simultaneously.

Figures

In general, a thoroughbass figure indicates the simple intervals above the bass for all pitch classes present in the chord.

The largest number typically found in thoroughbass figures is 7. In general, compound intervals (an octave or larger) are reduced to their simple interval equivalent. A tenth becomes a third, a thirteenth becomes a sixth, etc.

The most common chords in tonal music are triads and seventh chords. The following figures apply to these chords:

  • 5/3: use a fifth and a third above the bass (one note of the chord will be doubled)
  • 6/3: use a sixth and a third above the bass (one note of the chord will be doubled)
  • 6/4: use a sixth and a fourth above the bass (one note of the chord will be doubled)
  • 7/5/3: use a seventh, a fifth, and a third above the bass
  • 6/5/3: use a sixth, a fifth, and a third above the bass
  • 6/4/3: use a sixth, a fourth, and a third above the bass
  • 6/4/2: a use a sixth, a fourth, and a second above the bass

These figures are so common, that most of them have shortcuts:

  • no figure = 5/3
  • 6 = 6/3
  • 6/4 is never abbreviated
  • 7 = 7/5/3
  • 6/5 = 6/5/3
  • 4/3 = 6/4/3
  • 4/2 (or just 2) = 6/4/2

Other shortcuts generally follow two simple rules:

  • Assume a fifth is present above the bass unless there is a “6” in the figure.
  • Assume a third is present above the bass unless there is a “4” or a “2” in the figure.

Unfamiliar figures and chords

Only seven figures are given above. If you see a figure you do not recognize, simply follow the intervals (using the two shortcut rules). Likewise, if analyzing a chord that is not a triad or seventh chord, simply label the simple intervals you see/hear above the bass, from top to bottom in descending order: 7/6/3 or 5/4, for example. In time, you will become familiar with a number of other harmonic possibilities, and their corresponding figures.

Chords of the fifth and chords of the sixth

All chords can be categorized as either a chord of the fifth or a chord of the sixth. This distinction will be important for our study of voice-leading.

A chord of the fifth contains a fifth above the bass, but no sixth above the bass.

A chord of the sixth contains a sixth above the bass.

Chromatic alteration

If a note is chromatically altered (different than the key signature), the figure must be altered as well. Since bass notes are already present in the bass, a chromatic alteration in the bass will not make it into the figure. However, any other alteration in the upper voices (such as a raised leading tone in minor) must be reflected in the figure. To do so, simply put a sharp, flat, or natural to the left of the appropriate number.

Of course, there are some shortcuts. For example, draw a line (a “slash”) through a number to denote that it is raised by half-step (can substitute both for sharp or for natural). Also, when altering the third above the bass, simply use the sharp, flat, or natural and leave out the “3.”

In general, if there is a shortcut available, use it. The shortcuts are more standard than the corresponding full notation.

Keep in mind that some chords have abbreviated figures. For example, it is common for the leading tone to be the third above the bass in a 5/3 chord. In such a situation, a bass note that otherwise would have no figure needs a sharp or a natural for its thoroughbass figure.

8

A brief history of basso continuo keyboard-style voice-leading

Brian Moseley, Kris Shaffer, and Bryn Hughes

The thorough bass emerged as that shortcut. The “thorough” or “continuous” bass is a musical line that includes the lowest note at any given time. Usually, works would not include a single part that could function as this line, so the organist would alternate between voices, as they exchanged registers or took rests. The resulting line, unline the regular “bass” part, was “continuous” (or “thorough”)—hence the name thoroughbass or basso continuo.A good musician could perform this bass line, and with an eye (or ear) on the vocal parts and with knowledge of how to improvise good voice-leading, that musician could accompany the thoroughbass line with chords that made musical sense. (This is the original meaning of the term accompany—to accompany a bass line with chords. The fact that keyboardists did this in the context of supporting a soloist or small ensemble led to that term later being applied to any situation where a keyboardist accompanied spotlight performers.)

As this technique grew, publishers began publishing thoroughbass reductions of large-ensemble pieces to support smaller groups of musicians. In these publications, figures (numbers above or below the bass line) were included—sometimes only for difficult or non-standard chords, and eventually for most chords, enabling more amateur musicians, as well as students, to make use of the technique. These bass lines with figures became known as “figured bass” lines.

J.S. Bach, Flute Sonata in C Major, ii., BWV 1033. The upper part is played by the flute, the lower part is the basso continuo line, played by a keyboardist who uses the numbers below the staff (figures) to guide the chords played above this bass line.

To this day, harpsichordists performing in Baroque ensembles will often put their left hand to the same “bass” line that the cellos play, and will improvise right-hand chords (with contrapuntally sound embellishment) according to the figures provided with the bass line.

Though most music students are not Baroque keyboard specialists in training, thoroughbass, or basso continuo, can be a valuable tool in the study of harmony and voice-leading. In the study of harmony, a thoroughbass line can play a valuable role as a harmonic reduction of a complex texture, in order to example and understand better the harmonic skeleton underlying a passage. In aural dictation, transcription, and analysis, the bass line and the melody are often the most prominent (and most important) lines in a passage, and knowing how the inner voices tend to relate to the bass line and melody can aid in a number of listening and aural-analysis tasks. In voice-leading, the basso continuo texture affords a straightforward environment in which to make a gradual, staged progression through the intricacies of writing musical lines in a harmonic texture—and to do so without paying significant attention to harmony.

9

Composing in basso-continuo style

Brian Moseley, Kris Shaffer, and Bryn Hughes

Basso continuo (It. for “continuous bass” or “thoroughbass”) is essentially a chordal version of first-species counterpoint. However, instead of composing a single line above a cantus firmus, one composes a succession of chords (performed in the right hand) above a bass line (performed in the left hand). Basso continuo writing, also referred to as realizing a figured bass, gives no consideration to melody, only to the use of proper chords and the smoothest voice-leading possible. Thus, basso continuo style is a simple place to begin engaging the “fundamental musical problems” that arise when more than two lines are combined.

Chord voicing

In strict keyboard-style writing, there are four voices: the bass line (which is usually a given in basso continuo style), and three upper voices: the melody or soprano, the alto, and the tenor (from highest to lowest). Since all three upper voices must be played by a single hand, they should never span more than an octave.

The melody always has an upward-pointing stem. Alto and tenor share a downward-pointing stem. If the alto and tenor share a note, that note receives a single downward-pointing stem. (See m. 1 of the example below.) If melody and alto share a note, that notehead is double-stemmed. (See m. 4 of the example below.)

When choosing the notes to place in the upper voices above a figured bass, use the bass and figures to determine the pitch classes present in the chord. (When realizing an unfigured bass, you must determine appropriate figures before realizing.) If the chord is a four-note chord, use each chord member once, including the bass (exceptions will be noted later). If a chord has three pitch-classes (a triad, for instance), use each pitch-class once, and “double” one of them according to the following principles:

  • If the figure is 6/4, 5/3, or other chord of the fifth, double the bass pitch class.
  • If the figure is 6/3 and the bass is a fixed scale degree (do, re, fa, or sol), double the bass pitch class.
  • If the figure is 6/3 and the bass is a variable scale degree (mi/me, la/le, or ti/te) or a chromatically altered pitch, double one of the upper voices at the octave or unison.
  • Generally, do not double a variable scale degree or a chromatically altered pitch.

In basso continuo style, if the chord is properly voiced (correct pitch classes and correct doublings), two key principles of voice-leading will ensure good counterpoint between the voices most of the time:

  • The law of the shortest way (a term coined by composer Arnold Schoenberg): move each voice as little as possible. Prefer repetition to steps, steps to leaps, and one leap at a time to several voices leaping at the same time.
  • Move the right hand in contrary or oblique motion to the bass. When the bass leaps by fourth or fifth, though, this rule can be ignored.

In some cases, these rules cannot be followed absolutely (such as when a functional dissonance must be resolved, or when a melody makes it impossible—two cases to be considered later). In all cases, observe the following:

  • No parallel fifths or octaves between any pair of voices.
  • No contrary fifths or octaves between outer voices.
  • Do not approach an octave between the outer voices by similar motion unless the melody moves by step. (All other direct/hidden fifths and octaves are permissible.)

10

Style and tendency

Brian Moseley, Kris Shaffer, and Bryn Hughes

In explaining musical styles, Leonard Meyer divides musical characteristics into three categories: laws, rules, and strategies. Laws are characteristics of music that are based on human biology and psychology, and as a result laws are more-or-less universal. Rules are culturally conditioned. They are hallmarks of a particular style that are more-or-less universal within the style, but differ from style to style and culture to culture. Finally, strategies are specific ways in which composers work within a style — the things that make one composer’s work sound different from another’s, even if they compose in the same style.For the most part, principles of voice-leading or harmonic progression are “rules” according to Meyer’s definitions. They are specific to a style. Or, in some cases, they are shared among a few styles of Western music, but are far from universal. Thus, it can be helpful to think of them as collective traits of some music(s) we seek to understand and emulate, rather than hard-and-fast it-must-be-done-this-way strictures for all musical practice.However, these rules are also related to laws, in as much as they represent one set of practices that mediate the various demands on music from basic principles of human auditory perception and cognition. For instance, the prohibition against parallel fifths is a specific way in which Western tonal composers have mediated the conflict between tonal fusion, goal-directed motion, and independence of line. There are many other similar cases.Note, however, that while “avoid parallel fifths” takes on the form of what we consider “rules” in day-to-day speech, Meyer’s rules of musical style are different. Meyer’s rules are descriptive: these things tend to happen universally, frequently, rarely, never, in specific situations. “Avoid parallel fifths” is a prescriptive instruction based on that descriptive observation: because parallel fifths occur rarely in this style, and only in specific cases, avoid them in your own strict-style compositions until we have a chance to engage those specific cases — all the while remembering that other styles may have different tendencies.

That word tendencies is an important one. There are rarely absolutes in the musical parameters we engage most as performers, analysts, composers, listeners, etc. The absolutes of common styles fell into our unconscious background long ago. Instead, what makes each piece, composer, or style special and unique — what we care about — are the little ways in which they bend the “rules,” the ways in which they express, thwart, and play with the tendencies of the style they engage — the ways they play with our expectations as listeners.

Over time, as we familiarize ourselves with a musical style, the tendencies of the style become expectations in our mind, and composers can, in turn, compose with those listener expectations in mind. Though those tendencies are subjective, and to a large extent statistical, the shared stylistic knowledge and the shared psychological expectancy create a kind of quasi-objective language. That musical “language,” like spoken/written languages, is both reliable and bendable/breakable. The meaningfulness of a piece of music is dependent on that reliability. But its specialness is dependent on the ability for the “rules” of that language to be bent, even broken.

With this in mind, as we progress in our study of voice-leading, we will encounter more exceptions to the prescriptive rules, even in strict-style composition, and our hard-and-fast strictures will transition more and more into the language of tendency.

11

Tendency tones and functional harmonic dissonances

Brian Moseley, Kris Shaffer, and Bryn Hughes

In strict keyboard style, there are two main types of pitch tendency to keep in mind: tendency tones and functional dissonances.

Tendency tones

A tendency tone is a pitch (class)—usually represented as a scale degree—that tends to progress to some pitch classes more than others. Sometimes this tendency is absolute within a style, but more often it is context-dependent.

The most prominent tendency tones in Western tonal styles are ti (not te) and le (not la).

Generally speaking, when ti appears it tends to be followed by do in the same voice. In a harmonic context, this tendency is strongest when ti occurs in a dominant-functioning chord, and the “resolution” of that tendency comes upon change of function (to tonic or subdominant).

Likewise, when le appears, it tends to be followed by sol in the same voice. This tendency is less dependent on function.

Exceptions to these tendencies include:

  • When ti is in the middle of a stepwise descent (redotilasol, for example), it can progress down by step. (Note that step inertia here diminishes the effect of an “unresolved” tendency tone. Because there are two conflicting tendencies in play, in this case, either can be “resolved” unproblematically.)
  • When ti is in an inner voice, it can progress down to sol if necessary to accomplish good voice-leading in the other voices and ensure complete chords. This is called a frustrated leading-tone.
  • When ti is a functional dissonance of a tonic-functioning chord (see below) it should progress down by step.

Functional dissonances

Some tendencies, such as the tendency for le to progress down, are relatively context-independent. Others are heavily contextualized. The primary contextual tendency for how melodic notes progress is the concept of functional dissonance.

Keep in mind from the Harmonic functions resource that chords tend to cluster in one of three functional groups (T, S, or D) When pitches fuse into a chord expressing one of these three functions, the pitches that comprise that have certain tendencies of progression that they may or may not have in other contexts.

Following are the scale degrees which act as dissonances for their respective functions:

function dissonances
T or Tx 7, 5 when 6 is also present
S 3, 1 when 2 is also present
D 4, 6

In purely diatonic music (triads and seventh chords, no chromatics), these will include the seventh of every seventh chord, the fifth of viiº or VII (fa), and the fifth of III or iii (ti/te).

Keep in mind that only sometimes do these functional dissonances express themselves in chords or intervals that are acoustically dissonant. However, they do introduce a degree of tension that, like an acoustically disonant interval in species counterpoint, requires a smooth introduction and a specific resolution.

When one of these scale degrees is present in a chord with the corresponding function, the dissonant scale degree has a strong tendency to resolve down by step over the next change in function. In strict composition, we will always follow these tendencies.

In strict keyboard style, these functional dissonances should be “prepared” (approached) by common tone or by step. Thus, though they are proper members of the chord, melodically they will look like one of the three dissonance types of species counterpoint: a passing tone or neighbor tone dissonance that is approached by step, or a suspension dissonance that is approached by a common tone. The suspension type is preferred.

Once a functional dissonance is introduced, it must be resolved down by step in the same voice when the function changes. The dissonance can also be transferred to another voice before resolution—for instance, if there are multiple chords in a row exhibiting the same function, a dissonance that appears in the alto can be transferred to the tenor in the following chord, and then resolve in the tenor when the function changes. (It is more typical, and smoother sounding, to transfer dissonances between inner voices or from an inner voice to an outer voice than from an outer voice to an inner voice. Once a dissonance appears in the melody or bass, where it is more noticeable, it tends to resolve in that voice.)

Functional dissonance resolutions often cause conflicts with other principles of voice leading. Except in special cases such as schemata (standard patterns that are common enough to sound appropriate, even if they follow different rules), the functional dissonance resolution takes precedence over other principles such as the law of the shortest way, contrary motion with the bass, and preferring common tones and steps to melodic leaps. A dissonance resolution is never an excuse for illegal parallels, and only rarely will lead to non-standard doublings.

12

Melodic keyboard-style voice-leading

Brian Moseley, Kris Shaffer, and Bryn Hughes

The outer voices (melody and bass) draw the most attention, and therefore they should make good counterpoint with each other. The melody should largely follow the principles of composing a cantus firmus or a first-species counterpoint line. In a strict keyboard-style melody that means:
  • The melody should begin on a member of the tonic triad.
  • The melody should end on do.
  • The melody should have a single climax and good, smooth shape.
  • The melody should be “singable” (even though it will be played on the keyboard).

These melodic constraints may make following the law of the shortest way and contrary/oblique motion with the bass difficult, and at times impossible. When that happens, keep the voice motion as smooth (and playable) as possible, and be very careful not to compose voice-leading errors such as forbidden parallels.

In general, if you follow the figures, double the correct chord tone, move the upper voices as little as possible and in contrary or oblique motion to the bass, and take special care when the melody makes the latter impossible, your voice leading will sound smooth and will be fairly easy to perform. Those are the goals of strict keyboard-style voice-leading.

A number of specific situations come up frequently enough that they are worth tucking away as “stock patterns” to be pulled out when appropriate. See the Keyboard-style voice-leading schemata resource.

13

Keyboard-style voice-leading schemata

Brian Moseley, Kris Shaffer, and Bryn Hughes

Voice exchange

A voice exchange occurs when the melody and bass lines exchange pitches over the course of a simple contrapuntal prolongation. For example, in the progression T1 D2 T3, the bass begins on do and ends on mi. In a voice exchange, the melody would reverse this, starting on mi and ending on do. This common pattern can use a V6/4, V4/3, or a VII6/3 chord for D2:

Using this voice exchange pattern will ensure smooth voice-leading throughout the prolongation.

Note that the fa in the D2 passing chord (a functional dissonance) of the second example does not resolve down to mi. This is permissible because mi is required of the bass line but cannot be doubled, and because the smooth outer-voice counterpoint and stepwise inner-voice motion counteract any harshness perceived by the unresolved dissonance.

The voice exchange can also be used with a D4 substitution chord. Note that the upper voices will be exactly the same as using a V6/4 for D2.

These patterns can be used in major or minor, transposed to any key, and the D2 voice exchanges can be used in reverse, as well—T3 D2 T1. They can also be used to prolong S and D: S4 T5 S6 or D5 S6 D7, for example.

Parallel tenths

Do–re–mi in the bass is also frequently accompanied by mi–fa–sol in the melody, making parallel tenths.

Note here that, like the fa in the D2 voice exchange, the fa in the melody is an unresolved functional dissonance. In this case, the voice leading once again is so smooth that it overrides the need for the functional dissonance to resolve.

This pattern can also be used in major or minor, transposed to any key, and in reverse. It almost always uses a V4/3 for D2.

Champagne progression

While T(1 D2p 3) is a perfectly acceptable way to accompany mi–fa–sol in the melody, a more interesting (and also more involved) way to harmonize that melody is what theorist Gene Biringer called the champagne progression: T1 S6 T3. (He called it this because it is “the progression you use when you want to impress a date.”)

The champagne progression is very nice, but must be treated carefully. Only use it with mi–fa–sol (or me–fa–sol) in the melody, and always use the following voice-leading (note the non-standard doubling of the bass—la/le—in the S6 chord).

The standard champagne progression (above) uses a I6 chord for T3. Following is a variant using III for T3, which Biringer dubbed “pink champagne,” because it is especially nice. It should also be especially rare, or it loses its punch.

The champagne progression should only be used to prolong tonic function.

Deceptive resolution

A deceptive resolution occurs When a D5 (V or V7) chord does not progress, as expected, to I to form an authentic cadence, but instead progresses to VI. In the deceptive resolution, it is important for ti to resolve to do—as it would in an authentic cadence—not la/le. This fulfills its role as a tendency tone, helps the “deception” to work, and avoids the dissonant augmented second tile in minor. This results in a non-standard doubling of VI (do, rather than the bass).

Leaving out the fifth

When tido appears in the melody of an authentic cadence involving V7, it is impossible to fully voice both chords and resolve the functional dissonance.

It is imperative to resolve this functional dissonance, as that resolution is an important contributor to the goal-oriented motion and the releasing of harmonic tension into the cadential arrival. In order to do so, either leave out the fifth of the I chord (and triple the bass):

or leave out the fifth of the V7 chord, and double the bass:

The incomplete V7 is preferable to the incomplete I, but voice-leading into the V7 will usually dictate which option you choose.

Leaving out the third

When an S4 progresses into a D5, and both are seventh chords, it can be impossible to prepare and resolve the functional dissonances of both chords while fully voicing them.

Instead, leave la/le out of the S4 chord and double the bass. This will retain the trigger and bass note fa, as well as the two pitches making the dissonance (do and re or mi/me and fa), and will allow a second fa in an upper voice that can prepare the seventh of the D5 chord.

14

Generating Roman numerals from a figured bass line

Brian Moseley, Kris Shaffer, and Bryn Hughes

Both bass lines and root progressions are important for the study and mastery of tonal harmony. Most of our work will focus on the bass lines, and what follows will help you analyze the root progressions present in any figured bass line. In other words, this will help you perform a Roman numeral analysis of a figured bass line.Note that on the charts below, generic capital Roman numerals are provided.

Chords of the fifth

In any chord of the fifth (“root position”: 5/3 or 7/5/3 chord), the bass note and the root of the chord are the same. The Roman numeral to be assigned to any chord of the fifth, then, is the scale degree of its bass note. If do is in the bass, the bass is scale-degree 1, and the Roman numeral is I. If re is in the bass, the Roman numeral is II. And so on.

“First-inversion” chords of the sixth

Chords of the sixth that take the figures 6/3 or 6/5/3 are first-inversion chords. They are so named because the third of the chord (the next chord member above the root) is in the lowest voice. However, thinking about inversions while performing an analysis can be cumbersome. It is often simpler to remember that if the figure is 6/3 or 6/5/3 (or an abbreviation such as 6 or 6/5), the root of the chord is the sixth above the bass. If mi is in the bass, and the figure is “6”, the root is do, and the Roman numeral is I. If fa is in the bass and the figure is “6/5”, the root is re, and the Roman numeral is II. And so on.

“Second-inversion” chords of the sixth

Chords of the sixth that take the figures 6/4 or 6/4/3 (or an abbreviation such as 4/3) are second-inversion chords. They are so named because the fifth of the chord (the second member of the chord above the root) is in the lowest voice. Again, it is often simpler to remember that for 6/4, 6/4/3, and 4/3 chords, the root is the fourth above the bass. If re is in the bass, and the figure is 4/3, the root is sol, and the Roman numeral is V.

“Third-inversion” chords of the sixth

Chords of the sixth that take the figure 6/4/2 (or its abbreviation 4/2 or simply 2) are third-inversion chords. Their root is a second, or a step, above the bass. The most common 4/2 chord has fa in the bass, and sol is its root, making its Roman numeral V.

15

Embellishing tones

Brian Moseley, Kris Shaffer, and Bryn Hughes

A passing tone is a melodic embellishment (typically a non-chord tone) that occurs between two stable tones (typically chord tones), creating stepwise motion. The typical figure is chord tone – passing tone – chord tone, filling in a third (see example), but two adjacent passing tones can also be used to fill in the space between two chord tones a fourth apart. A passing tone can be either accented (occurring on a strong beat or strong part of the beat) or unaccented (weak beat or weak part of the beat).

Complete Neighbor Tone (NT)

Like the passing tone, a complete neighbor tone is a melodic embellishment that occurs between two stable tones (typically chord tones); however, a complete neighbor tone will occur between two instances of the same stable tone. Also like the passing tone, movement from the stable tone to the neighbor tone and back will always be by step. A complete neighbor can be either accented or unaccented, but unaccented is more common.

Double Neighbor Figure (DN)

Like the complete neighbor figure, the double neighbor figure begins and ends on the same stable tone (typically a chord tone). Between those two instances of the stable tone are two embellishing tones — one a step above and the other a step below the stable tone being embellished. Though individually we may consider each of the two embellishing tones to be incomplete neighbors (below), working together in the double-neighbor figure they balance each other out and create a contiguous whole, with the overall stability of a complete neighbor. A double neighbor figure is typically unaccented.

Incomplete Neighbor Tone (INT)

The incomplete neighbor tone is an unaccented embellishing tone that is approached by leap and proceeds by step to an accented stable tone (typically a chord tone). Broadly speaking an incomplete neighbor tone is any embellishing tone a step away from a stable tone that proceeds or follows it (and is connected on the other side by leap), but other kinds of incomplete neighbor tones have special names and roles that follow below.

Appoggiatura (APP)

An appoggiatura is a kind of incomplete neighbor tone that is accented, approached by leap (usually up), and followed by step (usually down, but always in the opposite direction of the preceding leap) to a more stable tone (typically a chord tone).

Escape Tone (ESC)

An escape tone, or echappée, is a kind of incomplete neighbor tone that is unaccented, preceded by step (usually up) from a chord tone, and followed by leap (usually down, but always in the opposite direction of the preceding step).

Anticipation (ANT)

An anticipation is essentially an otherwise stable tone that comes too early. An anticipation is typically a non-chord tone that will occur immediately before a change of harmony, and it will be followed on that change of harmony by the same note, now a chord tone of the new harmony. It is typically found at the ends of phrases and larger formal units.

Syncopation (SYN)

Syncopation occurs when a rhythmic pattern that typically occurs on strong beats or strong parts of the beat occurs instead on weak beats or weak parts of the beat. Like the anticipation, the syncopated note is an early arrival — it tends to belong to the chord on the following beat. Unlike the anticipation, the syncopation is tied into a note in that chord; it is not rearticulated. Rather than anticipating a note in the chord that follows, a syncopation is simply an early arrival.

Suspension (SUS)

A suspension is formed of three critical parts: the preparation (accented or unaccented), the suspension itself (accented), and the resolution (unaccented). The preparation is a chord tone (consonance). The suspension is the same note as the preparation and occurs simultaneous with a change of harmony. The suspension then proceeds down by step to the resolution, which occurs over the same harmony as the suspension. The suspension is in many respects the opposite of the syncopation: if the anticipation is an early arrival of a tone belonging to the following chord, a suspension is a lingering of a chord tone belonging to the previous chord that forces the late arrival of the new chord’s chord tone. However, in composition and improvisation, the suspension must be treated with a great deal more care than the syncopation. The most common suspensions (and their resolutions) in upper voices form the following intervallic patterns against the bass: 9–8, 7–6, 4–3. (With the exception of 9–8, the pitch class of the resolution tone should never sound in another voice simultaneous with the suspended tone.) Instead of SUS, it is more typical to notate the intervallic pattern in the thoroughbass figures.

Retardation (RET)

A retardation is essentially an upward-resolving suspension. It is almost always reserved for the final chord of a large formal division (or a movement), and it frequently appears simultaneously with a suspension (as seen in the example). Instead of RET, it is preferable to notate the intervallic pattern in the thoroughbass figures.

16

Galant schemas – The Rule of the Octave and Harmonising the Scale with Sequences

The Rule of the Octave

Mark Gotham

This section provides some downloadable resources for studying partimenti, especially the ‘rule of the octave.’ Files are downloadable in either .mscz or .mxl format.

In this chapter specifically:

  1. The Rule of the Octave
    • Building the Rule, approaching the ‘Rule’ by incrementally nuancing a succession of parallel 63s: .mscz, .mxl
    • Part by Part, taking a closer look at the component parts of the ‘Rule’: .mscz, .mxl
  2. Harmonising the scale with sequences

The Rule of the Octave

The ‘Rule of the Octave’ is an important part of the schema/partimento tradition.
You might like to think of it as a kind of ‘cheat sheet’ for harmonising bass lines: there’s one chord for each scale degree and you can go a long way by just matching up those bass notes with their corresponding chord.

There are many, subtly different versions of The Rule of the Octave harmonization. The version used here is closely based on that of Fedele Fenaroli (Naples 1775), with just a couple of modifications to preserve a consistent number of voices throughout (four voices, including the bass) and to avoid any suggestion of parallels.

Approaching the ‘Rule’ from parallel 63s

File downloads: .mscz, .mxl

This section builds up our version of the Rule of the Octave by proceeding in incremental steps from parallel 63s to the rule proper.
You could also think of this as a matter of moving from a flat to a rich harmonic hierarchy, or else as a ‘Regolo recipe’: how to make or understand the rule in four easy steps.

  1. We begin with a simple harmonisation of the bass scale using parallel 63 chords only. There’s nothing grammatically incorrect about this, but neither does it have much of a sense of hierarchy or variety. In short, it’s not very interesting.
  2. Next we put in strategic 53s on the first and last chords to give a sense of closure on the tonic.
  3. Then we also add a 53s on the dominant chords of both ascending and descending forms to further nuance the hierarchy (these are important chords too).
  4. Finally, we precede each of the tonic and dominant chords (including those in inversion) with 7th chords. In one case, this also involves a chromatic alteration for a stronger sense of tonicising the dominant. Why do you think we might only make that change this one time, and not anywhere else in the progression?

Examining the Rule Part by Part

File downloads: .mscz, .mxl

Having arrived at the Rule, this second file deconstructs it again so you can practice and engage with it in parts, with any number of voices, and in any ‘position’ (inversion of the right hand harmonisation). Keep practicing each component part separately and in a range of keys to build fluency with and abstraction of the Rule. (NB: you can transpose scores in MuseScore with the ‘Notes’ menu: Notes/Transpose.)

We begin by combining the bass scale with each of the three upper-voice parts in turn, centred respectively on the:

We then combine those upper parts into three-note, right-hand chords to generate ‘the rule’.
Here the three versions (‘positions’ in Fenaroli’s language) are given by the inversion of the chord. Again the top voice is centred successively on the:

Harmonising the Scale with Sequences

File Downloads:

NB: The open and short score versions of this material are otherwise identical so these introductory comments apply equally to both.

As we’ve seen above, the Rule of the Octave can be thought of as in terms of a sequential harmonisation of bass scales (parallel 6/3 chords).
This section looks at some other sequential harmonisation of the bass scale here.
Basically, this involves patterns of one or more harmonies which repeat sequentially in the direction of the scale.
Some of these work in the same way for both ascending and descending forms; others require some modification.

We begin just as we did before, with a simple harmonisation of the scale using parallel 63 chords only.
The following systems, proceed to patterns of:

5-6 patterns

7-6 patterns: Chains of Suspensions

Cycles of Fifths

The cycles of fifths is a based on a progression of root motion descending by fifths.
Hiding in this pattern is another (usually descending) scalic progression between alternate bass notes.
This arises because instead of literally going down two fifths, we usually go down a fifth and up a fourth, which is the equivalent progression, just keeping is in the same register / octave.
At the end of one such down a fifth, up a fouth, we end up a step lower than where we started, and so we also have a step-wise progression that can be scalic (if diatonic – i.e. not modulating).
We set this out in some of the main forms:

2-3: More Chains of Suspensions

So far, we’ve used 7-6 and 4-3 suspensions, so that leaves us one more important type: the 2-3 suspension (which is the inversion of 7-6).

17

Galant Schemas – opens and closes

Brian Moseley, Kris Shaffer, and Bryn Hughes

Schemas are “stock musical phrases” (Gjerdingen 2007, p. 6) that act as melodic, harmonic, and rhythmic/metric skeletons for passages of music in the Galant style. We can apply the term schema in three specific ways. First, a schema is a prototype—an idealized version of a common pattern. Second, a schema can be an exemplar—a single pattern that resembles the prototype. Third, a schema can be a theory—an explanation of a commonly occurring musical event. All of these ideas go into how we understand schemas. We understand an individual pattern (exemplar) as a version of an ideal general pattern (prototype), and that relationship helps us understand how that pattern is functioning within a particular passage of music (theory). schemas are often give names, sometimes based on descriptions from earlier theorists (“Monte, Fonte, Ponte,” were described by Joseph Riepel) or at other times, named after theorists themselves (“Meyer” is named after Leonard Meyer). Schemas have both internal defining characteristics and normative placements within a series of musical events. Internal characteristics describe a schema’s (1) melodic features—shown with scale degrees; (2) harmonic features—shown with figured bass, and (3) metric features—indicating whether a “stage” in the schema occurs in a weak or strong metric position. A schema’s normative placement describes it temporal location. For example, an “opening gambit” such as the “Meyer” is associated with the beginning of theme, perhaps constituting the whole of the presentation phrase or of a basic idea. A closing “riposte” like the “Prinner” is used as closing gesture.

Opening Gambits

“The Meyer”

 

A Meyer is archetypal”opening” schema in the galant style that prolongs the tonic contrapuntally. It begins and closes on a tonic chord, with non-tonic sonorities occuring in the middle two stages. Because the Meyer closes with mi/me in the top voice, it is not so strong as to imply the finality we associate with a cadence. So it works well at the beginning of a theme. This melodic skeleton is the most important feature of the Meyer, and occurs invariably even when the bass is somewhat altered.

When each sonority receives one “measure” of music, it is commonly found in the presentation or antecedent part of an opening theme. If those stages occur at the rate of two per measure, the Meyer may form a basic idea that would be followed by a closing gesture, such as the “Prinner” described below.

A fairly exhaustive list of opening schemas can be found on the Galant schemas – summary page. Many of them follow the same general pattern as the Meyer. For example, “The Pastorella,” “The Jupiter,” and “The Aprile,” all prolong tonic by moving away for the two middle stages before a tonic return. Like the Meyer, they are ideal prototypes for the first phrase of an opening theme. As with the Meyer, the bass and harmonic structure are less fixed than is the melody. The two central stages may articulate dominant harmony in all three schemas, and the second stage is also commonly accompanied by predominant harmony.

Closing gestures

“The Prinner”

The Prinner is a typical response to an opening schema. It often occurs in a sentence (or a hybrid theme type) as the continuation phrase. Or if the harmonic rhythm is quicker, it may be used as the basis for a constrasting idea in an antecedent or consequent phrase.

The Prinner has four stages corresponding to four bass notes: fa –mi/me – re – do. The skeleton of the Prinner’s melody typically accompanies the bass in parallel tenths: la/le – sol – fa – mi/me. Harmonically, the fa and do bass notes tend to take 5/3 chords while the two middle bass notes, mi/me and re, take 6/3 chords.

Some Prinner exemplars insert a sol bass note before the last chord, resulting in an authentic cadence. Prinners that operate as continuation phrases often contain this move in order to end the sentence or hybrid theme satisfactorily.

To complete a modulation to the dominant, the Prinner schema can be transposed up a fifth. When this occurs, the first stage of the Prinner (the 5/3 chord on fa) is the tonic of the home key and the subdominant of the dominant key, making a particularly smooth transition. Modulating Prinners are used in sentence or hybrid themes either to modulate to the dominant key or to effect a strong half cadence. They also commonly appear at the beginning of the Transition (TR) zone in a sonata movement, effecting the same move to the dominant.

For more continuation/cadential schemas, see the Galant schemas – summary page.

References

Gjerdingen, Robert O. Music in the Galant Style. Oxford University Press, 2007.

18

Galant Schemas – continuation patterns

Brian Moseley, Kris Shaffer, and Bryn Hughes

Fonte

A Fonte (It. for “fountain” or “well”—think going down) is a common pattern to begin the contrasting middle of a small ternary form. In other words, it follows the double-bar in a minuet, minuet trio, or rounded-binary theme. A Fonte is a model/sequence schema: a two-bar pattern is immediately repeated one step lower than the original.

Harmonically, the first two-bar unit (the model) contains two chords, one per bar: an applied dominant chord, and the tonicized chord to which the applied dominant points. The most common chord pattern for the Fonte’s model is D7/II T1/II of the home key, with the D7 being a chord of the sixth and the T1 being a chord of the fifth. (Other “inversions” are possible, such as D4/II T3/II.) When the model composes out D7/II II, the sequence will transpose it down to tonic: D7 T1 of the home key.

As an example, the functional-bass analysis of a typical Fonte in a small ternary whose home key is G major looks like:

Note the non-cadential progressions, D7–T1. Normally such progressions would need to be interpreted as prolonging a tonal function (i.e., tonic function), which would be difficult to interpret here. schemas often contain such progressions. Simply analyze the chords individually and label the schema, rather than trying to interpret these progressions as prolongational. (Indeed, they are not.)

A common model for a minuet containing a Fonte is as follows:

: EXPOSITION ending with V:PAC : : Fonte – phrase ending with I:HC – RECAPITULATION :

The Fonte is a quick and easy way for a composer to transition from the key of the dominant (where a major-key minuet’s exposition cadences immediately before the double-bar) to the key of the tonic. It will usually be followed by a phrase that stands on or moves to the dominant of the home key. The half cadence or dominant arrival at the end of that phrase will prepare for the return to the opening material in the home key, the recapitulation of the minuet or small ternary.

Monte

A Monte (It. for “mountain”—think going up) functions similarly to a Fonte. It typically occurs as part of the contrasting middle section of a minuet or other small ternary, it is a model/sequence schema, and it involves an applied chord resolving to a tonicized chord—typically a D7 T1 pattern. The difference is that where a Fonte goes down (D7/II T1/II D7 T1), a Monte goes up (D7/IV T1/IV D7/V T1/V). And where a Fonte is almost exclusively four bars long (one model followed by one transposed repetition), a Monte sometimes extends to six or more bars (one model followed by one or more transposed repetitions).

Ponte

A Ponte (It. for “bridge”) was another common schema for the contrasting middle of a minuet. Unlike the Fonte and the Monte, the Ponte need not be a model/sequence schema. It effects delay rather than motion. A Ponte typically functions like what Caplin calls standing on the dominant. The exposition of the major-key minuet will end with a PAC in the dominant of the home key. When a Ponte follows that cadence, it holds onto that T1/V, heightens tension melodically, and often adds a seventh to the chord (making it D5 of the home key). A passage built on a Ponte does not have a cadence, since there is no harmonic progression, but instead ends with a punctuated dominant chord in the home key, which Caplin calls a dominant arrival rather than a half cadence. This dominant arrival prepares the return of the home key and the opening basic idea that come at the minuet’s recapitulation.

References

Caplin, William. Classical Form. Oxford University Press, 2000.

Gjerdingen, Robert O. Music in the Galant Style. Oxford University Press, 2007.

19

Galant Schemas – Template Scores

Schema Templates

Mark Gotham

These templates each provide a combination of schemas which can be thought of as prototype pieces, both to illustrate how they work, and as a template for scaffolding exercises in pastiche composition.

N.B. To be abundantly clear, these prototype pieces are not intended as ‘real music’! It takes a lot of fleshing out to get from these to anything worthwhile: that’s the exercise. Use these templates but bury them beneath layers of musical character and embellishment. Here are some tips for getting started:

20

Galant schemas – Summary

Mark Gotham

These files provide a set of schemas, with the constituent parts set out as prototypically as is possible in musical notation: that is, with melody and figured bass lines, along with (in the first file’s case) chords in a middle part realizing those figures. Really, schemas are prototypes that exist apart from any specific realization, so the non-musical notations on this page are truer representations of the ideas at play.

Overall, Short Summary

This table summarizes those canonical schemas.

Name When Melodic line Bass line Meter Harmony (figures)
Romanesca Opening 1, 5, 1, 1 1, 7, 6, 3 S W S W 5, 6, 5, 6
Do-Re-Mi Opening 1, 2, 3 1, 7, 1 S W S 5, 6, 5
Sol-Fa-Mi Opening 5, 4, 4, 3 1, 2, 7, 1 W S W S 5, 5, 6/5, 5
Meyer Opening 1, 7, 4, 3 1, 2, 7, 1 W S W S 5, 6/4/3, 6/5, 5
Aprile Opening 1, 7, 2, 1 1, 2, 7, 1 S W S W 5, 6/4/3, 6/5, 5
Jupiter Opening 1, 2, 4, 3 1, 7, 5, 1 S W S W 5, 6, 5, 5
Pastorella Opening 3, 2, 4, 3 1, 5, 5, 1 S W S W 5, 5, 7, 5
Prinner Answer/Process/Transition 6, 5, 4, 3 4, 3, 2, 1 S W S W 5, 6, 7-6, 5
Modulating Prinner Answer/Process/Transition 3, 2, 1, 7 8, 7, 6, 5 S W S W 5, 6, 7-#6, 5
Fonte Answer/Process/Transition 5, 4, 4, 3 #1, 2, 7, 1 W S W S 6/5, 5, 6/5, 5
Monte Answer/Process/Transition 1, b7, 6, 2, 1, 7 3, 4, #4, 5 W S W S 6, 5, 6, 5
Ponte Answer/Process/Transition 5, 7, 2 5 S W S 5, 7, 7
Fenaroli Pre-Cadential 4, 3, 7, 1 7, 1, 2, 3 S W S W 6, 5, 6, 6
Indugio Pre-Cadential 2, 4, 6, 1, 7 4, 4, 4, 4#, 5 S W S W S 6/5, 6/5, 6/5, 6/5, 5
Deceptive Cadence Pre-Cadential 1, 2, 2, 1 3, 4, 5, 6 W S W S 6, 6/5, 5, 5
Evaded Cadence Pre-Cadential 1, 2, 2, 1 3, 4, 5, 5, 1 W S W S 6, 6/5, 5, 6
Passo Indietro Pre-Cadential 7, 1 4, 3 S W S W S 6/4/2, 6
Comma Pre-Cadential 4, 3 7, 1 W S 6/5, 5
Converging Cadence Pre-Cadential 3, 2, 1, 7 3, 4, #4, 5 W S 6, 6/5, 6/5, 5
Cadenza Semplice Cadence 1, 2, 2, 1 3, 4, 5, 1 W S W S 6, 6/5, 5, 5
Cadenza Composta Cadence 1, 2, 3, 2, 1 3, 4, 5, 5, 1 W S () S W S 6, 6/5, 6/4, 7, 5
Cadenza Doppia Cadence 4, 3, 2, 1 5, 1 S W S W S 5, 6/4, 4, 3, 5
Quiescenza Post-Cadential b7, 6, 7, 1 1 W S W S b7, 6/4, 7/4/2, 5

Itemized List

Opening Gambits

Romanesca

Stage: 1 2 3 4
Meter S W S W
Melody Treble: 1 5 1 1
Bass: 1 7 6 3
Harmony Figures: 5 6 5 6
Roman numerals: I V vi I

Do-Re-Mi

Stage: 1 2 3
Meter S W S
Melody Treble: 1 2 3
Bass: 1 7 1
Harmony Figures: 5 6 5
Roman numerals: I V I

Many of the schemas involve two steps which can be considered schemas on their own.
These often take the form of question-answer pairs.
Here, we have the Do-Re opening part as the opening question:

Stage: 1 2
Meter S W
Melody Treble: 1 2
Bass: 1 7
Harmony Figures: 5 6
Roman numerals: I V

That Do-Re is answered by the Re-Mi:

Stage: 1 2
Meter W S
Melody Treble: 2 3
Bass: 7 1
Harmony Figures: 6 5
Roman numerals: V I

The Do–Re–Mi may also appear in a four-stage version by putting those constituent parts back together.
This basically involves doubling up the central stage of the three-stage version.

Sol-Fa-Mi

Stage: 1 2 3 4
Meter W S W S
Melody Treble: 5 4 4 3
Bass: 1 2 7 1
Harmony Figures: 5 5 6/5 5
Roman numerals: I ii V I

Again this comprises two parts.

Opening part (Sol-Fa):

Stage: 1 2
Meter W S
Melody Treble: 5 4
Bass: 1 2
Harmony Figures: 5 5
Roman numerals: I ii

Answering part (Fa-Mi):

Stage: 1 2
Meter W S
Melody Treble: 4 3
Bass: 7 1
Harmony Figures: 6 5
Roman numerals: V I

This schema may also appear with the harmony slightly altered, as follows:

Stage: 1 2 3 4
Meter W S W S
Melody Treble: 5 4 4 3
Bass: 1 2 7 1
Harmony Figures: 5 6 6/5 5
Roman numerals: I vii V I

Meyer

Stage: 1 2 3 4
Meter W S W S
Melody Treble: 1 7 4 3
Bass: 1 2 7 1
Harmony Figures: 5 6/4/3 6/5 5
Roman numerals: I V V I

Opening Part:

Stage: 1 2
Meter W S
Melody Treble: 1 7
Bass: 1 2
Harmony Figures: 5 6,4,3
Roman numerals: I V

Closing Part:

Stage: 1 2
Meter W S
Melody Treble: 4 3
Bass: 7 1
Harmony Figures: 6,5 5
Roman numerals: V I

Aprile

Stage: 1 2 3 4
Meter S W S W
Melody Treble: 1 7 2 1
Bass: 1 2 7 1
Harmony Figures: 5 6,4,3 6,5 5
Roman numerals: I V V I

Jupiter

Stage: 1 2 3 4
Meter S W S W
Melody Treble: 1 2 4 3
Bass: 1 7 5 1
Harmony Figures: 5 6 5 5
Roman numerals: I V V I

Pastorella

Stage: 1 2 3 4
Meter S W S W
Melody Treble: 3 2 4 3
Bass: 1 5 5 1
Harmony Figures: 5 5 7 5
Roman numerals: I V V I

Answer/Process/Transition

Prinner and Modulating Prinner

Stage: 1 2 3 4
Meter S W S W
Melody Treble: 6 5 4 3
Bass: 4 3 2 1
Harmony Figures: 5 6 7-6 I
Roman numerals: IV I vii I

A slight variant on this inserts a root position dominant before the final stage:

Stage: 1 2 3 4 5
Meter S W S W S
Melody Treble: 6 5 4 4 3
Bass: 4 3 2 5 1
Harmony Figures: 5 6 7–6 7 5
Roman numerals: IV I vii V I

The Prinner can also be used to modulate from the tonic to the dominant.
This variant is called the ‘Modulating Prinner’:

Stage: 1 2 3 4
Meter S W S W
Melody Treble: 3 2 1 7
Bass: 8 7 6 5
Harmony Figures: 5 6 7-#6 5
Roman numerals: I V vii/V V

Again, this can come with an additional root position dominant:

Stage: 1 2 3 4 5
Meter S W S W S
Melody Treble: 3 2 1 1 7
Bass: 1 7 6 2 5
Harmony Figures: 5 6 7–#6 7/# 5
Roman numerals: I V vii/V V/V V

Fonte

Stage: 1 2 3 4
Meter W S W S
Melody Treble: 5 4 4 3
Bass: #1 2 7 1
Harmony Figures: 6/5 5 6/5 5
Roman numerals: V/ii ii V I

The Fonte has a strong relation to the Meyer and indeed to the cycle of 5ths.
This effectively tonicises the a minor key (e.g. the supertonic minor) and then a major key a tone below (the overall tonic).
The modular part is just one of those tonicisations:

Stage: 1 2
Meter W S
Melody Treble: 4 3
Bass: 7 1
Harmony Figures: 6/5 5/3
Roman numerals: V I

Monte

Stage: 1 2 3 4
Meter W S W S
Melody Treble: 1-b7 6 2-1 7
Bass: 3 4 #4 5
Harmony Figures: 6/5 5 6/5 5
Roman numerals: V/IV V V/V V

Like the Fonte, the Monte also goes through two tonicisations with a sequential treatment of a modular half:

Stage: 1 2
Meter W S
Melody Treble: 5-4 3
Bass: 7 1
Harmony Figures: 6/5 5
Roman numerals: V I

Ponte

Stage: 1 2 3
Meter S W S
Melody Treble: 5 7 2
Bass: 5 5 5
Harmony Figures: 5 7 7
Roman numerals: V V V

Pre-Cadential / Incomplete Cadences

Fenaroli

Stage: 1 2 3 4
Meter S W S W
Melody Treble: 4 3 7 1
Bass: 7 1 2 3
Harmony Figures: 6/5 5 6/5 6
Roman numerals: V I V I

Indugio

Stage: 1 2 3 4 5
Meter S W S W S
Melody Treble: 2 4 6 1 7
Bass: 4 4 4 4# 5
Harmony Figures: 6/5 6/5 6/5 6/5 5
Roman numerals: IV IV IV V/V V

Deceptive Cadence

Stage: 1 2 3 4
Meter W S W S
Melody Treble: 1 2 2 1
Bass: 3 4 5 6
Harmony Figures: 6 6/5 5 5
Roman numerals: I ii V vi

Evaded Cadence

Stage: 1 2 3 4
Meter W S W S
Melody Treble: 1 2 2 1
Bass: 3 4 5 3
Harmony Figures: 6 6/5 5 6
Roman numerals: I ii V I

Passo Indietro

Stage: 1 2
Meter S W
Melody Treble: 7 1
Bass: 4 3
Harmony Figures: 6/4/2 6
Roman numerals: V I

The ‘Passo Indietro’ is essentially the first two stages of a Prinner.
Literally a ‘stepping back’, the ‘Passo Indietro’ often precedes a significant cadence.

Comma

Stage: 1 2
Meter W S
Melody Treble: 4 3
Bass: 7 1
Harmony Figures: 6/5 5
Roman numerals: V I

Converging Cadence

Stage: 1 2 3 4
Meter W S W S
Melody Treble: 3 2 1 7
Bass: 3 4 #4 5
Harmony Figures: 6 6/5 6/5 5
Roman numerals: I ii V/V V

This cadence is also known as the ‘fa–fi–sol’ half cadence after the definitive bass line: 4–#4–5.
Note the correspondence between this schema and the Indugio.

Cadences and Post Cadential

Cadenza Semplice

Stage: 1 2 3 4
Meter W S W S
Melody Treble: 1 2 2 1
Bass: 3 4 5 1
Harmony Figures: 6 6/5 5 5
Roman numerals: I ii V I

Cadenza Composta

Stage: 1 2 3 4 5
Meter W S S W S
Melody Treble: 1 2 3 2 1
Bass: 3 4 5 5 1
Harmony Figures: 6 6/5 6/4 7 5
Roman numerals: I ii Cad. V I

Cadenza Doppia

Stage: 1 2 3 4 5
Meter S W S W S
Melody Treble: 4 3 2 2 1
Bass: 5 5 5 5 1
Harmony Figures: 5 6/4 4 3 5
Roman numerals: V V V V I

Quiescenza

Stage: 1 2 3 4
Meter W S W S
Melody Treble: b7 6 7 1
Bass: 1 1 1 1
Harmony Figures: b7 6/4 7/4/2 5
Roman numerals: V/IV V V I

The Quiescenza is a post-cadential schema.

IV

Harmony

Neo-Riemannian Triadic Progressions

Bryn Hughes

In the late nineteenth century, composers often used triadic progressions that confound conventional Roman numeral analysis. Consider the following excerpt from Brahms’s concerto for violin and cello:

Brahms, Concerto for Violin and Cello, mm. 268-79
Example 1: Brahms, Concerto for Violin and Cello, I, mm. 268-79 (10:22)

A reduction of the chord progression in the excerpt above can be found in Example 2. The passage connects two A-flat major triads, however the chords in between those triads do not belong to A-flat major in any useful way, nor do they follow any of the conventions of functional harmony.

Example 2: Brahms, Concerto for Violin and Cello, I, mm. 270-76, reduction.

One might dismiss the passage all together as “non-functional harmony,” but when you listen to it, it follows a certain kind of logic. As Richard Cohn (1996) writes, “if  this  music [music that is triadic but functionally indeterminate] is not fully  coherent according to the principles of diatonic tonality, by what other principles might it cohere?”

Neo-Riemannian theory, named after music theorist Hugo Riemann, provides a means of rationalizing these kinds of triadic progressions.

Neo-Riemannian Operations

Each of the three Neo-Riemannian operations describe a way of connecting major and minor triads without a tonal context. While Riemann’s original intent was to convey relationships between primary and secondary triads within a key, Neo-Riemannian theory adopts his approach as a way of accounting for relationships between triads solely through voice leading.

Example 3 shows the three basic Neo-Riemannian operations. Each operation preserves two common tones in a triad and changes its mode. The Relative transformation (R) preserves the major third in the triad, and moves the remaining note by whole tone. The Parallel transformation (P) preserves the perfect fifth in the triad, and moves the remaining note by semitone. The Leading-Tone Exchange (L) preserves the minor third in the triad, and moves the remaining note by semitone.

The three Neo-Riemannian operations: Parallel, Relative, and Leading-Tone Exchange
Example 3: The three Neo-Riemannian operations: Relative, Parallel, and Leading-Tone Exchange

Each of these voice-leading “moves” is an involution, meaning that each operation undoes itself. For example, if you do the L transformation on a C major triad, you get an E minor triad. If you do the L transformation on an E minor triad, you get a C major triad. Successive iterations of the same transformation would simply alternate between two chords, as is shown in Example 4.

Successive L operations on C major and E minor triads
Example 4: Successive L transformations on C major and E minor triads

While most nineteenth-century composers didn’t write progressions using the same transformation over and over again, you will find this technique used in twentieth-century works like “O Superman” by Laurie Anderson, which uses successive L transformations throughout.

The Tonnetz

The Tonnetz
Example 5: The Tonnetz

Example 5 shows a Tonnetz. A Tonnetz is a visual representation of pitches arranged such that perfect fifths are read from left to right, major thirds are read diagonally from the top left to the bottom right, and minor thirds are read diagonally from the bottom left to the top right. Any three pitches in a triangle form a major or minor triad. Neo-Riemannian transformations can be visualized by flipping a triangle along one of its three edges.

Example 6 shows each of the transformations on the tonnetz. If you perform a P transformation on the C major triad, highlighted with red edges, it will flip along the C-G side to become C minor. Similarly, L will flip the triad along the G-E edge to become E minor, and R will flip the triad along the C-E edge to become A minor. Note that if you start on a minor triad, such as the G minor triad highlighted with green edges, all of the flips will be in the opposite directions.

Tonnetz showing the three Neo-Riemannian operations (P,L, and R) performed on a C major and a G minor triad
Example 6: Tonnetz showing the three Neo-Riemannian operations (P,L, and R) performed on a C major and a G minor triad

Returning to the example from Brahms’s concerto for violin and cello, we now have a means of understanding how this chord progression works. Example 7 shows that the two A-flat major triads are connected by a series of P and L transformations.

Reduction of Brahms's concerto for violin and cello, mm. 270-76, showing the alternating P and L transformations between chords.
Example 7: Reduction of Brahms’s concerto for violin and cello, mm. 270-76, showing the alternating P and L transformations between chords.

The excerpt from the Brahms concerto navigates a column of triangles moving upward from the bottom right of the tonnetz, shown in Example 8. Note that you need to enharmonically re-interpret the G-sharp major triad as an A-flat major triad at the starting point.

Analysis of the chord progression from Brahms's concerto for violin and cello, mm. 270-76. The analysis is written on the tonnetz, connecting two A-flat major triads using a series of P and L operations.
Example 8: Brahms’s concerto for violin and cello, mm. 270-76 on the tonnetz.

The tonnetz is useful for visualizing the proximity of major and minor triads; notice that all of the triads in a given key are close together, while tonally disparate keys are also far apart on the tonnetz.  Conversely, the tonnetz is helpful for imagining interesting chord progressions that you might not think of if you’re limiting yourself to typical common-practice syntax.

Cycles of Triads

While you can use Neo-Riemannian theory to create or analyze just about any chord progression, composers often focused on patterns of operations that create closed cycles of triads. Cycles begin and end on the same chord, and follow a specific pattern of transformations (much like a sequence). The progression from the Brahms example above is a PL cycle because it alternates P and L transformations and begins and ends on the same chord.

There are three possible cycles that use two transformations: The PL cycle, the RP cycle, and the RL cycle. As you can see in Example 9, the PL and RP cycles “close the loop” after relatively few transformations: 6 for the PL cycle, and 8 for the RP cycle.

Two staves in treble clef. The first stave shows a C major triad going through alternating P and L transformations. The second stave shows a C major triad going through alternating R and P transformations.
Example 9: PL and RP cycles.

Conversely, the RL cycle (Example 10) is is quite long: it passes through all 24 major and minor triads. Since this cycle takes so long to “close the loop,” it is often ignored or presented in truncated form.

A single staff with treble clef. A C major triad goes through alternating R and L transformations until an F minor chord is reached. The score is then annotated with "etc." indicating that the pattern could continue.
Example 10: The RL cycle

There is one three-transformation cycle that is noteworthy: the PLR cycle. As Example 11 shows, it takes two cycles of the PLR transformations to return to the starting chord.

Single treble clef staff showing a series of P, L, and R transformations, starting and ending on a C major triad.
Example 11: The PLR Cycle

Of the cycles mentioned above, both the PL and RP cycles generate a parent scale made up of all of the notes used by its constituent triads. The PL cycle, generates the hexatonic scale; a symmetrical scale made up of alternating semitones and minor thirds. The RP cycle generates an octatonic scale, another symmetrical scale, this time made up of alternating semitones and major seconds. You might consider these scales to represent the “overall sound” of the cycle. Similarly, each PLR cycle is centered around a single pitch, which is contained in each of the triads within the cycle. Each of these cycles is illustrated in Example 12.

Three polygons showing PL, RP, and PLR cycle beginning on C major triads, with each triad represented by a vertex on the polygon.
Example 12: PL, RP, and PLR cycles and their parent scales/common tones.

Other Transformations

There are three other types of Neo-Riemannian transformations that occur frequently enough in the repertoire that they are worth mentioning here. The S transformation (short for “slide,” coined by David Lewin) is effectively the opposite of the P transformation: it moves the two pitches that form the perfect fifth in a triad by semitone, and changes the mode of the triad. N stands for Neberverwandt, meaning “neighbor-related.” It was introduced by Richard Cohn and characterizes the motion of moving both members of the minor third in a triad by semitone, and again changing the mode. Both S and N move pairs of notes in parallel motion against a single common tone. The last transformation that we’ll discuss here is that which connects a triad to its modal opposite by moving each voice by a single semitone. Robert Cook is attributed with referring to this as the H transformation, because the chords it connects are “hexatonic poles” in the hexatonic cycle discussed above. These three transformations are shown in Example 13.

Single treble staff showing three Neo-Riemannian transformations of a C-major triad: S, connecting C to C#m; N, connecting C to Fm; and H, connecting C to Abm
Example 13: S, N, and H transformations.

Of course, all of the above transformations can be considered combinations of the staple P, L, and R transformations. For example, you could describe H as “PLP.” Indeed, you can describe the connection between any two major and/or minor triads as combinations of transformations: you can get from one triad to any other in five steps or less. The most interesting are those that use parsimonious voice leading: voice leading in which no single voice moves more than a step.  There are numerous other combinations you could come up with–try some on your own!

Going Beyond Major and Minor Triads: The Augmented Triad

Although it is not part of the staple Neo-Riemannian transformations, which only deal with major and minor triads, the augmented triad provides a useful link between major and minor triads, specifically those that are connected by R transformations. Upon scrutinizing the above examples, you may have noticed that the R transformation isn’t quite the same as the P and L transformations, because it moves its non-preserved note by two semitones, while the others move their non-preserved note by one semitone. In a sense, the R transformation is twice as much “work” as the P and L transformations. If we fill in the gap between two R-related triads, an augmented triad emerges, as is shown in Example 14.

A single staff with a treble clef, showing a C major triad, followed by a C augmented triad, followed by an A minor triad
Example 14: The R transformation with an intervening augmented triad

Things get interesting when you consider the augmented triad’s ambiguity. Because it is a symmetrical chord (like the diminished seventh chord), you can enharmonically respell the augmented triad such that any of its chord members can act as the root. For example, the C augmented triad in Example 14 could also be spelled as an E augmented triad (E-G#-B#), or an A-flat augmented triad (Ab-C-E). As a result, you can resolve the augmented triad to three different minor triads by moving a single voice by semitone, depending on how its root is interpreted. Example 15 shows the three possible resolutions of the C+ triad.

A single staff with a treble clef, showing three spellings of the C+ triad and their resolutions to Am, C#m, and Fm
Example 15: Three different spellings of the augmented triad resolving to three different minor triads .

Likewise, the same augmented triad can connect to three different major triads by moving a single voice by semitone, as is shown in Example 16.

A single staff with a treble clef showing three major triads (C, E, and Ab) leading to different spellings of the C+ triad.
Example 16: Three different major triads connect to the same augmented triad.

Example 17 illustrates the four augmented triads (yes, there are only four, due to the symmetry of the chord) and the major and minor triads that they can resolve to by moving only one voice by semitone. Each augmented triad and its six associated triads are referred to as Weitzmann regions, named after the theorist Carl Friedrich Weitzmann, who wrote at length about the augmented triad and its versatility in several nineteenth century treatises.

 

The four Weitzmann regions, showing the four augmented triads and the major and minor triads that connect to them by moving only one note by semitone.
Example 17: The four Weitzmann regions.

Each line in a Weitzmann region represents moving one note in a triad by a single semitone. When you trace a path from a triad on the left to a triad on the right, you’ll find several of the transformations discussed previously. R, S, and N each require a total move of two semitones, and each of these can be traced through any given Weitzmann region.

The Cube Dance

Recall that the LP, RP, and PLR cycles are “closed loops.” These recurring patterns are interesting, but could grow stale after a while. What if there were a way to “modulate” between cycles? Enter, the augmented triad.

Take another look at the major triads connected to the C+ Weitzmann region: C, E, and A♭. Notice that these three major triads are the same as those found in the PL cycle that started on C, found in Example 12. The minor triads in that PL cycle can be found in a different Weitzmann region: the E♭+ region. If we add augmented triads into our PL cycles, we grow the group of possible chords within a cycle from 6 to 8. Instead of representing these cycles on a hexagon, let’s illustrate them using a cube, as shown in Example 18.

Four cubes, illustrating the four PL cycles, with attached augmented triads
Example 18: PL cycles with added augmented triads.

The PL cycle that starts on C can be found in the top right of Example 18. Each side of the cube represents the motion of one note in the triad moving by semitone. When the triads move from major to minor, these are either P or L transformations. The augmented triads that connect to the major and minor triads are on opposite corners of the cube, and, of course, these connect to each adjoining triad by a one-semitone move, as well.

Now, how might we “modulate” from one PL cycle to another? Notice that the same augmented triad can be found in two different cubes. If we wrote a chord progression within one PL cycle, we could “jump” to an adjacent PL cycle by navigating to one of the two augmented triads and continue in the new cycle. In a sense, each cube is connected to two other cubes via an augmented triad. We can use these connections to create a single illustration that provides us a map of all major and minor triads connected by a single semitone. This was first explained by Jack Douthett and Peter Steinbach (1998), who referred to this diagram as a “cube dance.” The cube dance has been reproduced in Example 19 below.

A reproduction of the "cube dance" diagram, originally conceived of by Jack Douthett and Peter Steinbech in their 1998 article, which is listed under "further reading."
Example 19: The Cube Dance (originally conceived by Douthett and Steinbach).

Using the cube dance model, you could create a chord progression that starts in the PL cycle that includes C, and modulate to a new PL cycle via either the C+ or Eb+ triads. If you wanted to get from C to, say, D, you would have to modulate twice: either through C+ and Db+, or Eb+ and D+. Though the other cycles are not depicted clearly on the cube dance model, you can also use augmented triads to modulate between RP cycles, or PLR cycles, or indeed any group of Neo-Riemannian transformations that include R transformations.

Perhaps even better than the tonnetz, the cube dance illustrates the proximity of major and minor triads. If we equate proximity with the total number of semitones needed to move from one triad to another, the cube dance diagram puts chords together that we would intuitively consider to be “close” to one another, while those that we might consider “distant” are relatively far apart. Moreover, the cube dance (and even the tonnetz) does this without reference to a tonal center, making it useful for rationalizing chord progressions from music of the nineteenth and twentieth (and even twenty-first) centuries that is triadic, but shies away from functional tonality. This can be incredibly helpful when analyzing this kind of music, or even when writing your own.

Further Reading

Cohn, Richard. “Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective.” Journal of Mathematics & Music. Mathematical and Computational Approaches to Music Theory, Analysis, Composition and Performance 42, no. 2 (October 1, 1998): 167–80.

———. “Maximally Smooth Cycles, Hexatonic Systems, and the Analysis of Late-Romantic Triadic Progressions.” Music Analysis 15, no. 1 (1996): 9–40.

———. “Neo-Riemannian Operations, Parsimonious Trichords, and Their ‘Tonnetz’ Representations.” Journal of Music Theory 41, no. 1 (1997): 1–66.

———. “Square Dances with Cubes.” Journal of Music Theory 42, no. 2 (1998): 283–96.

———. “Uncanny Resemblances: Tonal Signification in the Freudian Age.” Journal of the American Musicological Society 57, no. 2 (2004): 285–323.

Douthett, Jack, and Peter Steinbach. “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.” Journal of Music Theory 42, no. 2 (1998): 241–63.
Engebretsen, Nora, and Per F. Broman. “Transformational Theory in the Undergraduate Curriculum – A Case for Teaching the Neo-Riemannian Approach.” Journal of Music Theory Pedagogy 21 (2007): 39–69.
Mason, Laura Felicity. “Essential Neo-Riemannian Theory for Today’s Musician.” University of Tennessee, Knoxville, 2013. https://trace.tennessee.edu/utk_gradthes/1646.

Media Attributions

  • brahms concerto for vln vc 268-79
  • brahms_vc_vln_concerto_reduction
  • NROs_-_basic_voice_leading_examples PLR
  • multiple L transforms
  • The Tonnetz
  • tonnetz with NROs in color
  • brahms reduction with analysis
  • Brahms analysis on the tonnetz
  • PL and RP cycles
  • RL cycle
  • PLR cycle
  • PL, RP, and PLR cycles
  • SNH transformations
  • R transformation with intervening augmented triad
  • augmented_triads2
  • augmented_triads3
  • weintzmann regions
  • individual cubes
  • cube dance

VI

Jazz

21

Swing rhythms

Megan Lavengood

Key Takeaways

  • Swing eighths are notated as regular straight eighths, but are performed unevenly, in a quasi-triplet rhythm where the first note is twice as long as the second.
  • Backbeat, a syncopation created through accent on beats 2 and 4 of a quadruple meter, is common in jazz.
  • Syncopation is extremely important to jazz styles. Syncopation occurs when the hierarchy of the meter is obscured.

 

The basic swing groove

Swing eighths

notation
Example 1. Swing eighths are performed so that the first eighth is roughly twice as long as the second.

One of the most recognizable features of swing rhythms is swung eighth notes. Swing eighths are performed as uneven eighth notes in a quasi-triplet rhythm, shifting the proportion from 1:1 to, roughly, 2:1—that is, the first eighth note is about twice as long as the second eighth note. This is illustrated with notation in Example 1.

While in some sense it may be more accurate to notate the eighth notes of a jazz tune as a triplet rhythm as notated in Figure 1, imagine how cluttered that would be! Instead, swing eighth notes in jazz are always written as straight eighth notes, and performers are expected to know to swing them.

Thumbnail for the embedded element "Overture"

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notation
Example 2. The entire ensemble plays the notated rhythm at 0:36 of the overture to Anything Goes.

The overture from the musical Anything Goes contains passages with overt straight and swung eighths.The first few minutes are swung; this is easiest to hear at 0:36 when all the instruments in the ensemble play swung eighths together (Example 2).While listening, tap along to the swung eighths—and note that the tempo is very brisk, so you’ll be tapping quite quickly.

Contrast this with the straight eighths in the middle section of the overture, which begins at 0:52 (Example 3). The feel changes dramatically during this straight section. As you listen, tap along to the straight eighths, which are at a considerably slower tempo than the first part’s swung eighths.

After a quick transition in the trumpets, swing eighths return for the third part of the song, which begins at 1:39. The swing eighths are audible in the hi-hat cymbal of the drumset.

notation
Example 3. This rhythm, with straight eighths, occurs in a drum part throughout the second part of the Anything Goes overture.

As you listened to these examples, you may have noticed that the swing eighths are not exactly like the triplet rhythm notated in Example 1. In reality, the exact ratio of the swung eighths varies from piece to piece and from performer to performer. Generally speaking, though, the faster the tempo goes, the eighth notes tend to be more straight; at slower tempos, more dramatic swung eighths can be employed.

Backbeat

The next most significant rhythm in jazz is the backbeat. The backbeat is an accent that is heard on beats 2 and 4 of a quadruple meter. This is opposite of the typical accent structure of classical music, where beats 1 and 3 are usually the most accented.

The backbeat and the swing eighth together make up is an important part of a standard swing drum beat (Example 4). The backbeat is accented with the closed hi-hat cymbal, while the swung eighths are given on the ride cymbal. Drum beats vary widely and are typically improvised, but these are two components you will find in most jazz drum patterns.

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Example 4. Swing drum beats usually use the closed hi-hat on beats 2 and 4 (the backbeat) while playing swing eighths on the ride cymbal.

When tapping along with jazz tunes, try tapping along to the backbeat, rather than the downbeat.

Syncopation

Before understanding syncopation, it is important to understand meter more generally. Meter is when a series of equally-distant beats are imbued with a sense of hierarchy. For example, 4/4 time, which most jazz is in, is a series of 4 quarter notes (equally-distant beats) in which beat 1 is most important, beat 3 less important, and beats 2 and 4 least important of all. “Importance” here means that important things happen on beat 1: things like chord changes, key changes, and so on. These important things might also happen on beat 3, but it is less common; it’s relatively unusual to see chord changes on beat 2 or 4.

Syncopation occurs when this sense of hierarchy is transgressed in some way. There are many ways to achieve this transgression, and the backbeat is actually one such example. By sounding on beats 2 and 4, but not on beats 1 and 3, the backbeat creates syncopation by effectively accenting the less important beats of the 4/4 meter.

Syncopation is extremely important in jazz music. Other common manifestations of syncopation in jazz include accenting the second offbeat eighth of an eighth-note pair, and avoiding downbeats when beginning melodic lines. Syncopation is often created through ties, rests, and accents that obscure the beat.

Further reading
Assignments

Media Attributions

22

Lead sheet symbols

Megan Lavengood

Key Takeaways

  • Lead sheet symbols tell you the root of the triad, the quality of the triad, any extensions to the triad, and any non-root bass note.
  • Lead sheet symbols don’t reference a specific key. Instead, symbols are always assumed to be a certain quality unless otherwise indicated:
    • Triads are assumed to be major.
    • 7ths are assumed to be minor.
    • All other extensions and added tones are assumed to be major/perfect.
  • Alterations are shown through sharp and flat symbols, or through plus and minus symbols. Both systems are prevalent in the real world; when writing your own charts, pick one system and stick with it consistently. This textbook will use the sharp/flat system of showing alterations.
annotations on a lead sheet symbol Cm(add#11)/Eb
Example 1. There are four components to a lead sheet symbol:
• the root of the triad
• the quality of the triad
• the presence of extensions to the triad
• the bass note of the chord

There are two systems of shorthand for discussing harmony used in this textbook: lead sheet symbols and Roman numerals. The term “lead sheet symbols” comes from the fact that you will find these on lead sheets, which are jazz scores that typically notate only a melody and these chord symbols; Roman numerals are broadly applied to many different types of music.

Lead sheet symbols can pack a lot of information into a few letters. A complex symbol is given in Example 1, with annotations to show the various possible components of a lead sheet symbol.

Lead sheet symbols basics

Triads

Lead sheet symbols are based on the major triad as the norm. If you see nothing but a note name as a lead sheet symbol, this means to play a major triad. Other symbols are added to indicate other triad qualities. This is summarized in the table below.

triad quality symbol (for a chord with a root of C)
major C
minor Cm, C-
diminished Cº, Cdim, Cm(♭5), Cm(-5)
augmented C+, Caug

Example 3. Lead sheet symbols for triads.

Notice that there are several ways to represent each non-major triad quality. This is because lead sheet symbols were created along the way, and were never completely standardized. The examples in these tables are not comprehensive, but you can likely decode other variations based on the ones here. It’s good to be aware of all the possible ways of representing these different triad qualities, but stick to one method for yourself. The symbols used in this textbook are given first.

Seventh chords

The most common addition to a triad is its seventh. Sevenths are indicated with the Arabic number 7, written after the root, superscript (higher than the other letters).

As with the triad, there is a default understanding of 7, and alterations to the 7 indicate other possibilities. The default quality for 7 is minor. This results in the seventh chord symbols summarized below.

seventh chord quality symbol (for a chord with a root of C)
dominant 7th C7
major 7th Cmaj7, C∆7, Cma7
minor 7th Cm7, C-7, Cmi7
half diminished 7th Cø7, Cm7♭5, C-7♭5♭
diminished 7th 7

Example 5. Lead sheet symbols for seventh chords.

This table only shows the five traditional seventh chord qualities, but others are possible, such as a m(maj7), aug7, and more. Again, these tables are not comprehensive, but they will prepare you to extrapolate from this information when you encounter an unfamiliar symbol.

Bass notes

In much of jazz and pop, the bass note is the root of the chord. (Bassists may improvise around other notes, rather than strictly staying on the root of the chord, but this wouldn’t affect how the harmony is written down.) For this reason, lead sheet symbols are assumed to indicate root position chords, unless otherwise indicated.

If the bass note should be something other than the root, this is shown with a slash followed by the letter name of the bass note. For example, C/E means to play a C major triad with an E in the bass. Significantly, the bass note does not need to be a member of the chord! C/F♯ would indicate to play C major over an F♯.

Extensions

notation
Example 4. Adding more thirds beyond the 7th produces 9ths, 11ths, and 13ths.

Jazz harmony often involves playing not only the notes explicitly indicated by the lead sheet symbol, but also adding upper extensions. The term extension comes from the idea of extending the stack of thirds that creates harmonies. The 7th is the most common triadic extension, but jazz often makes use of higher extensions—stacking more and more thirds onto the basic triad results in the 9th, 11th, and 13th (Example 6).

Interval size

You may notice that 9ths, 11ths, and 13ths are just compound versions of 2nds, 4ths, and 6ths, respectively, so why use the more difficult-to-conceptualize compound intervals, instead of just calling these intervals 2nds/4ths/6ths? There are two reasons:

  1. The presence of an extension in a chord symbol implies the presence of all other extensions below it as well. So an 11th chord is not just a triad plus the 11th—it’s a triad plus an 11th, 9th, and 7th.
  2. Extensions are usually voiced (played) above the other chord members. In other words, in actual performed music, the extension really sounds a 13th above the root, not a 6th (for example).

Interval quality

Like the 7th, extensions have an assumed interval quality. Unlike the 7th, extensions are assumed to be major or perfect unless otherwise indicated. The chord in Example 6, then, is simply a C13 chord: all the extensions are major/perfect intervals above C, except the seventh (B♭), which is minor.

Other interval qualities are shown with sharp and flat symbols. So a C(♯11) chord would include an F♯ above the root—an augmented 11th—instead of the typical F♮. These altered extensions are often placed in parentheses to clarify that the accidental is to be applied to the extension, not to the root of the chord.

Alterations

add

To indicate that a note is added to a chord without implying additional extensions, the word “add” is written into the symbol. For example, Cadd2 indicates to play a C major triad with an additional D note, C D E G. (Because the added interval is 2, not 9, the D may be voiced within the triad. Cadd9 would imply that the D is voiced above the triad, C E G D.)

sus

Another alteration is the suspended chord, abbreviated “sus,” which indicates that the third of the chord should be replaced with the fourth above the root. Csus, then, would yield the notes C F G—the E of the C triad is replaced with F.

Occasionally, you may see a sus2 chord, which replaces the third with the second above the root (Csus2 = C D G). The term comes from a common type of suspension, in which the fourth above the bass resolves to the third above the bass. Indeed, a sus chord will often be followed by a non-sus chord with the same root.

Exercise

Check and see if you understand lead sheet notation by taking out a sheet of scrap paper and notating the harmonies indicated by the chord symbols below. As you complete each chord, you can pull the slider to the right to reveal the correct answer.

An interactive or media element has been excluded from this version of the text. You can view it online here:
https://viva.pressbooks.pub/openmusictheory/?p=2624

You can also view and listen to the answer on Musescore.com.

Lead sheet symbols vs. Roman numerals

It’s important to understand that lead sheet symbols are absolute labels, while Roman numerals are relative labels. Roman numerals are more theoretical and abstract, because they tell you the location of a chord relative to the key of the song. Lead sheet symbols, on the other hand, tell you exactly (absolutely) which notes are being played in this given chord, without reference to any outside system. It’s important to leave the relative thinking behind temporarily when you interpret lead sheet symbols. Lead sheet symbols do not reference keys.

notation
Example 5. In many contexts, the simpler symbol C/A♭ may be preferred to something more analytically descriptive, like A♭7(#5).

Lead sheet symbols are not analytical—they’re a shorthand way of writing a score. In other words, the purpose of lead sheet symbols is to get performers’ fingers to the right notes at the right time. Lead sheet symbols may represent things in a less functional sense if it means the symbol is easier to interpret. Example 5 is one example: although the second chord really functions as an A♭7(#5) chord, neighboring to the regular A♭ triad, the symbol C/A♭ is probably easier to process, and thus preferred. (However, neither symbol is inherently right or wrong—both will result in the right notes being played.)

Keeping this issues in mind helps to understand the logic present in the system of lead sheet notation. Even though there is a lot of variation in lead sheet symbols, learning a few rules will help you decipher any symbol.

Assignments

Media Attributions

23

Jazz voicings

Megan Lavengood

Key Takeaways

  • Space chords to mimic the spacing of the harmonic series: use large, wide intervals in lower registers, and smaller, closer intervals in upper registers.
  • Voice extensions in the higher voices.
  • If you double a note, usually double the bass or root of the chord.
  • Omitting the fifth of the chord is almost always a safe bet.
  • Use smooth or “lazy” voice leading: move each voice as little as possible between chords to achieve a smooth, easy-to-perform sound. A common smooth voice leading schema in jazz is to lead from the third of one chord to the seventh of the next.
  • Guidelines can be ignored, but this should be a conscious and deliberate decision to achieve an effect.

So far in this unit, you have written chords in an unvoiced format. While unvoiced chords are useful for conceptualizing harmony, you would not want to perform these tall stacks of thirds. This chapter will discuss how to voice these harmonies in a manner that is idiomatic to jazz.

Spacing

The common spacings of chord members in musical textures has much to do with acoustics. We discuss pitches as specific frequencies—for example, A 440, the note to which most orchestras tune, refers to pitch A that has a frequency of 440 Hertz (Hz). But in fact, when an acoustic instrument plays A 440, 440 Hz is only one of the frequencies that is activated at that moment in time. The instrument will also activate the harmonics above that pitch, because the vibrating body causes other, shorter vibrations to occur simultaneously. These harmonics are part of what create an instrument’s unique timbre.

The harmonic series is approximated in Example 1.The notes of the harmonic series do not conform to 12 tone equal temperament, but they have been notated at the nearest pitch, for the sake of convenience.

Notation
Example 1: The harmonic series, as approximated in notation.

Note that the pitches are spaced widely apart in the lower harmonics, but become closer and closer together in the upper harmonics: the distance between partials 1 and 2 is an octave, but beginning at partial 13, the distance between subsequent partials is only a half step.

In general, spacing in music approximates the harmonic series: notes are further apart in lower registers, and closer together in higher registers. Putting notes close together in a low register tends to sound muddy and dissonant, even when the chords are consonant. Spacing notes wide apart in the upper registers will result in that upper note being quite prominent and isolated in the texture (which can sometimes be a good thing).

Remember that the bass line is probably played by the upright bass—and this instrument sounds an octave lower than written, so its lowest note is an E1, three Es below middle C. It’s normal for the bass to be in a register very much apart from the rest of the ensemble.

Chord extensions should be left in the upper registers of the texture. Recall that this is reflected in their names—a 13th is not the same as a 6th in jazz harmony. Voice the 13th somewhere above the seventh of the chord, otherwise it will sound like the 6th.

Doubling

Most chords have at least three notes in them—but most textures have more than three notes going at a time. This necessitates doubling some of the notes of the chord—putting the same note in more than one voice.

In general, a safe note to double is the bass note. Most often, the bass note is a relatively stable member of the chord. As the foundation of the texture, it sounds good to double the bass.

Another good option is to double the root of the chord, even if it is not in the bass. The root note, like the bass, is typically a stable tone, and will strengthen the chord when doubled.

Omitting notes

Jazz harmonies often contain many notes, thanks to the common practice of extending the harmonies. Oftentimes, it is not desirable that all these notes be given equal weight in your voicing. It’s common to omit some notes when voicing these extended harmonies.

The most common note to omit is the fifth of the chord. Because the 5th is an early pitch in the harmonic series (partial 3), it tends to strengthen the root of the chord without adding much character on its own. Listen and compare the various chords in Example 2, and notice that removing the fifth does very little to alter the overall sound of the chord, whereas omitting the seventh or root alters the sound substantially!

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Example 2. Omitting the 5th is common, as it does not substantially alter the sound. The 7th or root are hardly ever omitted.

Omitting the root runs the risk of destabilizing the entire chord. However, you may deliberately omit the root in most voices if a bass player is present in the performing ensemble. The bassist will typically provide the root of the harmony and ensure that the chord sounds stable. The last chord in Example 2, then, would sound just fine if a bassist were playing a G below that voicing.

When dealing with extended chords, it becomes possible or desirable to omit other members of the chord besides the 5th, but it is difficult to generalize here. Usually omitting tones is done to avoid excessive dissonance with other important chord members.

Voice leading

We have been discussing harmonies as vertical entities so far: as a stack of notes that go bottom-to-top on the page. Vertical thinking is used a lot in music theory, and by pianists and guitarists, but for almost everyone else, music is experienced horizontally: as a sequence of notes in time. It’s important for musicians to be able to think of music both vertically and horizontally through voice leading.

Voice leading in jazz and many other styles should, generally, be smooth—that is, voices should ideally move as little as possible when going to a new chord (except the bass, which often leaps). Smooth voice leading helps different chords sound more logically connected (Example 3). When writing your own chord progressions, it may be helpful to imagine your voices as lazy. They want to move as little as possible! The smallest possible move is the common tone: not moving at all, but instead remaining on a single tone that is common to both chords. The next most preferable movement is movement by whole or half step. Skips are also easy to perform and easy to sing, and there are many situations that will force you to skip when voice leading.

Leaps are primarily used to provide contrast and excitement in voice leading. They are to be used sparingly, and with good reason. Leaps sound most natural when they are within a single chord: because the chord underpinning the horizontal movement is staying the same, it’s easy for the voice to leap within that chord. When the chord is changing, though, adding leaps tends to make the chords sound disconnected, and can make the piece difficult to perform. Leaping over a chord change is certainly possible, but may take extra practice, and remember: your voices are lazy!

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Example 3. Smooth voice leading helps chords sound connected to one another.

In jazz, a common voice leading trick is to connect the thirds and sevenths of adjacent chords, as the saxophone and trumpet do in Example 3: the instrument that has the third of the chord in the first chord moves to the seventh in the second chord, and vice-versa (Example 4). This voice leading pattern works with any two chords whose roots are related by fifth (e.g., G–C, A–E, etc.) This is a good foundation for all your voice leading. Build onto this foundation by playing with adding extensions and keeping the principle of smooth or lazy voice leading in mind. For example, adding an alternation between 9ths and 13ths to this voice leading schema adds a third smooth line to this progression between fifth-related chords.

Notation
Example 4. For chords whose roots are related by fifth, like F and C, the third of one chord can be connected smoothly to the seventh of the next, and vice-versa.
notation
Example 5. In chords related by fifth, alternating between 9ths and 13ths will create another smooth line.

Adding extensions

For major 7ths: C6, Cmaj9, C6/9, Cmaj11, Cmaj7♯11, Cmaj13, Cmaj13♯11. For dominant: C7♯5 aka Caug7, C9, C7♭9, C7♭9, C11, C7♯11, C13, C7♭13, C7alt. "Alt" implies that every extension is altered, and 9 can be sharp or flat. For minor: Cm7, Cm(maj7), Cm6, Cm9, Cm9(maj7), Cm6/9, Cm11, Cm13. For half-dim: Cm9♭5, Cm11♭5, Cdim7, Cdim(maj7). For sus: Csus, C7sus, C9sus, C13sus.
Example 6. Common chord symbols and possible extensions, organized from simplest to most complex.

Extensions can often be added to create additional smooth voice leading lines, as discussed in Example 5 above. But how do you know which extensions to use? There are no hard-and-fast rules about choosing extensions, and because extensions are typically improvised and not notated, it can be difficult for a beginner to know what’s common. Example 6, which you may also download as a handout, demonstrates the most common extensions for chords of certain qualities, organized from simple to complex. Experimenting with these extensions will help a beginner to develop a sense of what sounds most stylistic.

Guidelines versus rules

Most of the above are not really rules that you must follow, but rather guidelines for writing stylistically. The guidelines here represent what is most common in jazz music.

Guidelines are not always followed, but knowing what the guidelines are empowers you to choose not to follow them with the full understanding of the resulting sound. In other words, feel free to break the rules, but make sure you know why you’re doing it!

Further reading
Resources
Assignments

Media Attributions

24

ii–V–I

Megan Lavengood

Key Takeaways

  • ii7–V7–Imaj7 in major, or iiø7–V7–iin minor, is a fundamentally important progression in traditional jazz.
  • The ii–V–I progression can be identified through a combination of root motion by fifths plus its distinctive sequence of chord qualities (m7–7–maj7 in major, or ø7–7–m7 in minor).
  • Because this progression is so important to jazz, the concept of applied chords can expand to include applied subdominant chords—i.e., the ii chord.
  • Incomplete ii–V–Is, i.e., ii–Vs, can also be identified because the combination of root motion and quality is so distinctive.

 

Example 1 shows final cadences from four jazz tunes. Look at the harmonies—a pattern should be apparent (you can listen to the tunes through the chapter Spotify playlist).

Notation and lead sheet symbols. Afternoon in Paris: Dm7, G7, Cmaj7. All the Things You Are: B♭m7, E♭7, A♭maj7. My Funny Valentine: Fm7, B♭7, E♭6. Joy Spring: Gm7, C7, F.
Example 1. Afternoon in Paris,” “All the Things You Are,” “My Funny Valentine,” and “Joy Spring” all share similar harmonic progressions at their final cadences: ii–V–I.

All the examples end in perfect authentic cadences (PACs). But the similarities don’t end there: each PAC is preceded by the ii chord. So we have three chords, each related to the next by fifth.

This ii–V–I progression is one of the most important progressions in jazz music. You can find it reliably at cadences, but also as a building block that occurs throughout a tune. When the progression occurs in a major key, as in the snippets in Example 1, the chord qualities of these chords are m7–7–maj7. When the tune is in minor, the shift in mode changes the quality of the harmonies to ø7–7–min7 (the V chord is major whether you are in a major or a minor key). Both of these progressions and a typical voice leading pattern are summarized in Example 2.

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Example 2. Prototypical harmonies and voice leadings in ii–V–I progressions, in both major and minor modes.

ii–V–I as schema

Schema is a useful concept in music theory, used in many ways within this book (pop harmony, for one). Put simply, schemas are common patterns our brains can recognize, even when variations are altering a specific presentation of that schema.

The ii–V–I progression is an example of a schema. It happens so frequently that informed listeners can recognize the schema in many formats. Some examples of alterations are given in Example 3. In “Misty,” the maj7 chord is replaced with a 6 chord (this occurred in “My Funny Valentine” in Example 2 also). In “Prelude to a Kiss,” the typically dominant-quality V chord is replaced with an augmented chord (the minor 7th is preserved). The V chord is altered in “A Night in Tunisia,” but this time, the fifth is lowered instead of raised.

notation
Example 3. The ii–V–I is still recognizable, even if alterations occur.

Applied ii–Vs

An important marker of dominant-function chords is the chord’s quality. This is most obvious in the case of the dominant seventh quality, which shares a namesake with dominant function: the dominant chord. Fully-diminished chords also have dominant function.

The compositional technique of applied chords capitalizes on the relationship between quality and function by taking dominant chords out of their key, and dropping them into a new key. The applied dominant chords retain their function as dominant chords even when applied to a chord other than I (this concept is fully explained in the Applied Chords chapter).

The omnipresence of ii–V–I as a schema in jazz means that, in this style, we can have not only applied dominants, but applied ii chords as well. In other words, the entire ii–V–I progression can be used in keys other than the tonic key to tonicize another chord. The association between these chord qualities and root motions is so strong that a ii–V progression need not even resolve to its I chord to create the effect of a ii–V.

Take the rest of the A section of “Afternoon in Paris” as an example (Example 4). Not only does it end with a ii–V–I progression, but it begins with two other ii–V–Is: one tonicizing B♭ major, which is ♭VII in the key of C, immediately followed by another in A♭ major, which is ♭VI in the key of C.

Chord symbols over measures. Cm7 F7 B♭maj7 is bracketed as tonicizing B♭. B♭m7 E♭7 A♭maj7 is bracketed as tonicizing A♭.
Example 4. Afternoon in Paris” by John Lewis uses ii–V–I progressions in different keys in sequence.

ii–V space

By relating all possible ii–V–I motions together, we can come up with a space in which these progressions operate, and visualize how the ii–V–Is in “Afternoon in Paris” are related. This idea comes from McClimon (2017), and his “ii–V space” is reproduced in Example 5. The space is arranged as the circle of fifths (note the letter names at the end of each progression), with each chord in the circle preceded by a ii–V.

visual diagram described in-text
Example 5. McClimon’s ii–V space relates ii–V progressions of keys related by fifth.

Each arrow indicates a type of transformation from the first chord to the chord at the other end of the arrow. There are four different variations of arrows in Example 5, and each signifies a different transformation. The two solid arrows have to do with root motion: the black arrows connect chords within a ii–V–I schema, while the gray arrows show the circle-of-5ths relationships. The dashed arrows show changes to chord quality. The larger dashes indicate that the chord is the same, except the seventh has been lowered. So each larger-dashed arrow connects a maj7 chord to a (dom)7 chord with the same root. The smaller dashes show that the chord is the same, but the third has been lowered: each smaller-dashed arrow connects a 7 chord to a m7 chord with the same root.

diagram
Example 6. “Afternoon in Paris” transforms Imaj7 chords into minor seventh chords, thus changing their function: they become ii7 chords.

Example 6 traces the progressions in “Afternoon in Paris” that were annotated in Example 4. Notice how the space helps illustrate the logic of the progression: by transforming the preceding Imaj7 chords into ii7 chords, it forces a modulation down by whole step.

Understanding a piece through the ii–V schema

The logic of a chromatic progression like the one in Lee Morgan’s “Ceora” becomes more intelligible when viewed through this lens. An analysis originally by McClimon is explained in the video below.

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Example 7.Ceora” by Lee Morgan is entirely composed of ii–V–Is.

Turnarounds

A particularly common version of applied ii–Vs comes in what is called the turnaround. In the broadest sense, a turnaround is a progression that serves to loop back to the original tonic chord, and the typical progression that achieves this is I–vi–ii–V–I. Using the concept of applied chords, we can substitute a V7/ii for the vi chord, since they share the same root. But we can also precede that V7 with its ii chord—effectively, a ii/ii (two of two). Thus, the ii chord of the turnaround is tonicized with its own ii–V–(I) progression. This tonicized version of the turnaround is a very common variant (Example 8).

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Example 8. The turnaround schema has diatonic and chromatic variants.

Further reading
Assignments
  • ii–V–I worksheet (.pdf, .docx). Spotify playlist here. Note that these lead sheets are not public domain and thus cannot be posted here; however, the lead sheets are not difficult to find if you search the internet or ask around.
  • Composing with ii–V–I worksheet (.pdf, .mscx, .musicxml). This functions as a preparatory assignment for the Tin Pan Alley AABA Composition.

Media Attributions

25

Embellishing chords

Megan Lavengood

Key Takeaways

This chapter presents two ways of adding new harmonies to an existing chord progression.

  • An applied ii chord, as in the ii–V–I schema, can be used to embellish a dominant-quality chord. In other words, preceding a dominant-quality chord with the m7 or ø7 chord a fifth above it creates the effect of a ii–V.
  • Common tone diminished seventh chords (ctº7) create neighboring motion in all voices that embellish a chord. The root of the chord of resolution is always shared as a member of the ctº7—thus, the term “common tone.”

Jazz performers often aim to add their own twist to existing jazz standards. One way of doing this is to add new chords that embellish existing chords in the progression. This chapter explores two ways that performers improvise by embellishing harmonies in jazz.

This chapter will use the opening few bars of “Mood Indigo” by Duke Ellington as a backdrop, and add embellishing chords to that. Therefore, familiarity with the tune will make the following discussions more intelligible. Listen to Louie Armstrong’s interpretation of this song, embedded below, while following the chords of the first few bars, given here.

(piano intro: 2 bars)

B♭  | C7 | Cm7 F7 | B♭ |
B♭ | C7 | Gb7 | F7 |

 

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Embellishing applied chords

Applied V7

Any chord in a progression can be embellished by preceding it with an applied dominant chord. Example 1 takes the surprising G♭ chord of measure 7, divides it in half, and replaces the first half note of the chord with its applied V7 chord. In principle, this can be done with any chord in the progression.The G♭ chord is, itself, a tritone substitution for C7, which would be the applied Vof F7. Tritone substitutions are discussed in another chapter.

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Example 1. Inserting a D♭7 chord before the G♭7 chord creates an applied V of G♭, which is not present in the original chord progression of “Mood Indigo.”

Applied ii

The chapter on ii–V–I discusses the use of applied ii–V–Is, i.e., ii–V–I progressions that occur in keys other than the tonic key. Many jazz tunes have these applied ii–Vs built in, but a performer could add their own, as well. Many dominant chords can be embellished by adding its ii chord before it, transforming it into a ii–V schema.

“Mood Indigo” by Duke Ellington begins with the progression B♭–C7–Cm7–F7–B♭. That first C7 could be embellished by adding a Gm7 before it, creating a temporary ii–V that then proceeds to another ii–V. Rhythmically, this means cutting the duration of the C7 into two halves, and replacing the first half with the applied ii chord. The result is the progression in Example 2 below.

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Example 2. Inserting a Gm7 chord before the C7 chord creates a ii–V in F, which is not present in the original chord progression of “Mood Indigo.”

Common tone diminished 7th chords

Notation. C, Cº7, C. F/C, Bº7, F/C.
Example 3. Common tone diminished sevenths share a common tone with the root of the chord being embellished, shown here with ties.

The common tone diminished 7th chord (hereafter ctº7) is a voice-leading chord, which means that the chord is not based on a particular scale degree like most other harmonies, but rather the result of more basic embellishing patterns. In this case, the embellishing motion is the neighbor motion. To create a ctº7, the root of the chord being embellished is kept as a common tone (hence the name), and all other voices move by step to the notes of the diminished 7th chord that includes that common tone. This is best explained in notation, as in Example 3.

The ctº7 can be used to prolong any chord. Rhythmically, the chord would be inserted somewhere in the middle of the total duration of the harmony, leaving the prolonged harmony on either side of it (as in Example 3). Another option is to skip the initial statement of the prolonged harmony, and instead jump straight into the ctº7. Example 4 adds both types of ctº7 to “Mood Indigo,” the melody of which is particularly suggestive of ctº7 embellishments. In this example, the ctº7 chords are not given their own Roman numeral, to show that they do not significantly affect the harmonic progression of the phrase—instead, they embellish the chords around them with chromatic neighbor tones. Similarly, the ctº7 chords are not shown with lead sheet symbols, because these chords are often not written into lead sheets, but improvised by the performers.

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Example 4. A ctº7 embellishes the opening B♭ chord, inserted on beat 3 of the whole-note harmony. A ctº7 also embellishes the C7 chord, displacing the C7 by a half note.

Further reading
  • Levine, Mark. 1995. The Jazz Theory Book. Petaluma, CA: Sher Music.
Assignments

Media Attributions

  • ctº7 by Megan Lavengood

26

Substitutions

Megan Lavengood

Key Takeaways

This chapter discusses methods for altering chord progressions through chord substitution.

  • A progression that moves by fifth can substitute the first chord with the dominant chord that shares the same root. This makes the first chord an applied chord to the second chord.
  • Mode mixture is when a piece in a major key use chords borrowed from the parallel minor key (or vice-versa, though this is less common).
    • In jazz, the most common mixture chords are substituting iiø7 for ii7 and adding♭9 to a V7 chord.
    • The most common mixture chords, including iiø7 and V7♭9, substitute scale-degree ♭6 for the regular scale-degree 6.
  • Tritone substitutions replace dominant chords with another dominant chord a tritone away. The name refers to the fact that the substituted chord is a tritone away from the original chord, and also that the two chords share a tritone.

Creating new interpretations of old favorite tunes is one of the cornerstones of jazz, and because of this, the concept of chord substitutions is extremely important. Substitutions provide a way for performers and arrangers to put a new spin on more well-trod harmonic progressions. This chapter uses the turnaround as a basic progression to be altered, but these substitutions can be applied anywhere in a harmonic progression.

Applied chords as substitutions

As discussed in the Applied Chords chapter, applied chords can be productively related to the diatonic chord with which it shares a root note.

Because root motion by 5th is extremely common in jazz, there are many opportunities for performers to simply substitute the first chord in a fifth-wise chord progression with the dominant 7th built on the same root. One especially common place where this is implemented is in the turnaround, where, because each chord is related to the next by fifth, a chain of applied V7s is a common variant.

 

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Example 1. When a progression has root motion by fifth, the quality of the first chord can be changed to dominant 7th in order to transform it into an applied V7.

Mode mixture

“All of You” by Cole Porter is a composition that has mode mixture built into it. Listen to this recording by Ella Fitzgerald (transcribed in Example 2), conveniently in C major, and observe how the alternation between A-natural (scale-degree 6) and A♭ (scale-degree ♭6) creates catches the ear and imbues a sense of sentimentality in the song. A♭ here can be understood as being borrowed from the parallel minor (C minor), a practice known as mode mixture.

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Example 2. “All of You” by Cole Porter uses a minor iv chord (Fm) and a half-diminished ii chord (Dø7) even though the tonic is major.

Many songs, like “All of You,” have mixture built into their chord structure. But mixture chords can also work as improvised substitutions: a chord within a diatonic chord progression can be substituted with its minor-mode variant to produce a color change that won’t change the overall function of the chord. A mixture substitution works best when the scale degree being inflected is scale-degree 6, and is therefore being transformed into ♭6. As an example, consider the turnaround in Example 3: instead of a diatonic version, one may choose to incorporate scale-degree ♭6 to generate some more colorful harmonies. These particular substitutions—changing a ii7 to a iiø7, and a G7 to a G7♭9—are particularly common uses of mode mixture in jazz.

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Example 3. Mixture chords are most effective when they involve ♭6. Mixture and diatonic versions of the same chord have the same function.

Tritone substitutions

visualization of 12-tone scale mapped on clock face, tracing tritone transposition of a V7 chord
Example 4. Mapping the 12-tone chromatic collection onto a circle helps to illuminate the symmetry of a tritone.

While the above methods of substitution are common in pop and classical styles as well, the tritone substitution is unique to jazz. Tritone subs take the place of V7 chords, either applied or diatonic. The “tritone” part of the name comes from two ways in which tritones are important in these substitutions:

  1. The substituted chord is a tritone away from the chord it is replacing, and
  2. The chords are related because they share the same tritone.

Why this is true is best explained graphically, as in Example 4: because the tritone evenly divides the 12-tone collection, transposing by tritone maps the tritone onto itself. Speaking practically, the bottom line is that any dominant seventh chord can be replaced by the dominant seventh chord a tritone away, and the progression still functions the same way.

Example 5 shows how tritone substitutions are commonly used in the turnaround.

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Example 5. Because tritone substitutions can replace any applied dominant chord, in progressions moving by fifth like the turnaround, chords may be first (conceptually) substituted with their applied variants, and then tritone substitutions can be used to create a chromatic bass line.

Diagram
Example 6. The tritone substitution space parallels the diatonic space.

The ii–V–I chapter visualized the ii–V–I schema within a voice leading space constructed by  Michael McClimon (2017). McClimon further visualizes the tritone substitution as a kind of shadowing space behind the typical ii–V space (Example 6). Click here to view his animation of the progression of “Blues for Alice” and its movement through the ii–V space with tritone substitutions. Notice that the tritone-substituted V7 chord is preceded by its ii7 chord, and that both chords are in the green space that McClimon places behind the foreground ii–V space.

Further reading
Assignments

Media Attributions

27

Blues harmony

Bryn Hughes and Megan Lavengood

Key Takeaways

  • Blues harmony differs from tonal and jazz harmony in a number of important ways, especially in the treatment of the dominant seventh chord quality.
  • The most common form of the blues is the 12-bar blues, but 16-bar blues are also not uncommon.
  • The jazz blues blends jazz and blues harmonic languages together.
  • The blues is a schema that can have many alterations without ceasing to qualify as “a blues.”

The blues is an extraordinarily important genre in U.S. popular music. Not only is the tradition itself very old, with roots reaching back to the music of enslaved African-Americans, but it continues to exert influence on 21st-century popular music.

The documentation on the history of the blues is quite limited due to its age, but the earliest blues songs existed in the late 1800s, and it seems to have grown out from earlier African-American musical styles, such as field hollers and work songs, as well as microtonal and rhythmic characteristics of West African music. In this sense, although jazz musicians very frequently play the blues, the blues as a tradition has distinct origins from jazz. Jazz developed first in New Orleans through a mix of African, Caribbean, and European influences. The result of this distinction is that many of the truisms of jazz or tonal music do not hold true in the blues. Among the biggest harmonic differences are that

This chapter introduces some of the most common forms of the blues encountered in the 20th and 21st centuries.

12-bar blues

Like ii–V–I, the blues is a schema: a frame of reference for understanding lots of different chord progressions. Blues progressions can all be understood as outgrowths from a basic prototype.

The 12-bar blues progression is composed of three (typically) four-bar phrases. At its most basic, the harmony progresses as shown in Example 1:

  1. The first phrase is entirely tonic harmony (I).
  2. The second phrase contains two bars of subdominant (IV) and two bars of tonic (I).
  3. The final phrase begins with one bar of dominant (V) followed by one bar of subdominant (IV) and two bars of tonic (I).
Notation
Example 1. A basic twelve-bar blues has four measures of I for its first phrase, two measures of IV and two measures of I for its second phrase, and the final phrase has a bar of V, a bar of IV, and then two bars of I.

This is the simplest version of the 12-bar blues, but innumerable variations exist upon these changes. One of the most common additions is that the second bar may move to IV, then return to I in the third bar. Another especially common trick is to employ some type of turnaround in the final bar or two of the progression, from something as simple as a V7 chord to a full III–VI–II–V progression. It can be difficult to find a blues tune that doesn’t make some alteration from the basic form shown in Example 1. “You Can’t Do That” by The Beatles (1964) is nearly the same, but it does add a V chord in the final bar as a turnaround. 

notationClosely related is the 16-bar blues progression, which is composed of four (typically) four-bar phrases, usually two iterations of tonic, followed by subdominant and dominant (Example 2). “Hoochie Coochie Man” by Muddy Waters (1954) is one example of a 16-bar blues. Notice that the final phrase may or may not end with a turnaround. The 16-bar blues is not as common as the 12-bar blues, but has somewhat heightened frequency in blues-based rock music.

Jazz blues

As mentioned in the introduction to this chapter, the blues treats harmony differently from jazz, and one of the large differences is the reliance upon plagal rather than authentic cadences. The jazz blues is a variant of the 12-bar blues that mitigates this somewhat by adding several ii–V progressions to the blues.

Like the 12-bar blues, the jazz blues is composed of three four-bar phrases. A basic version of the jazz blues is presented in Example 3.

Notice that the jazz blues mixes typical blues harmony (i.e., the use of non-V dominant seventh chords and plagal resolutions) with jazz harmonic schemas (ii–Vs and turnarounds).

notation
Example 3. The jazz blues adds ii–V progressions, replacing structural plagal cadences.

One recording that performs the blues this way is the Lincoln Center Jazz Orchestra performing Duke Ellington’s “C Jam Blues.” This is easiest to hear during the solo sections, however not every repetition of this blues contains every chord shown in Example 3.

Examples of variations

The blues can be varied extensively, yet still qualify as the blues, the chapter’s Spotify playlist goes through several tracks that have some slight variations on the schemas outlined above.

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Musicians who have developed a familiarity with the blues will have no trouble recognizing the blues in a tune even with these, and more, variations.

Assignments

Worksheet on 12-bar blues (.pdf, .mscx, .musicxml). Asks students to write basic and jazz 12-bar blues progressions, voiced and unvoiced, and to analyze altered blues progressions. Spotify playlist available.

Media Attributions

28

Blues melodies and the blues scale

Megan Lavengood

Key Takeaways

  • Blues songs are often texted, and the lyrics consist of a lyric line which gets repeated, then followed by a contrasting line (aab). Melodies often follow this structure.
  • Blues melodies often leave large gaps to allow for call and response between the melodic instrument and other instruments.\
  • The blues scale is like a minor pentatonic scale with an additional chromatic passing tone: 1–♭3–4–♯4–5–♭7.
  • The blues scale can be rotated to begin on its second note,  create a major blues scale: 1–2–♯2–3–5–6.

This chapter discusses some of the trends in blues melodies that shaped the blues as we know it today. As an example, this text will focus on one of the earliest recorded blues songs, “Gulf Coast Blues” by Clarence Williams, as recorded by the enormously commercially successful blues singer Bessie Smith in 1923.

 

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Example 1. “Gulf Coast Blues,” recording by Bessie Smith and Clarence Williams.

Phrase and lyric structure

Much blues music is sung, and so lyrics play an important role in this genre. The four-bar phrases that make up the 12-bar blues are commonly matched with lyrics that have an aab structure: the first line is stated and then repeated (sometimes with some alteration), and the third line contrasts. “Gulf Coast Blues” by Clarence Williams (1923) is one example of this (Example 2). This does not happen in “Gulf Coast Blues,” but often, the repeated lyric will be set to a repeated melody, mimicking the aab structure in the music as well.

structure lyric
a The man I love, he has done left this town
a The man I love, he has done left this town
b And if it keeps on raining, I will be Gulf Coast bound.

Example 2. Lyrics of “Gulf Coast Blues” by Clarence Williams.

Another essential part of blues phrase structure is the notion of call-and-response, a feature likely inherited from the work songs of enslaved Africans and African Americans. The vocal, lyricized melody takes on the role of the “call” while an instrumental filler takes on the role of the “response.” Notice that in “Gulf Coast Blues,” each lyric labelled with an a is sung entirely and exclusively in the first two measures. Example 3 annotates a transcription of “Gulf Coast Blues” to show this call-and-response relationship.

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Example 3. Call-and-response in the melody of “Gulf Coast Blues.”

The blues scale

Much as the harmonies of the blues don’t tend to stick to one diatonic key, flouting the norms of tonal music, the melodies are similarly chromatic to match. The blues scale, notated in the upper staff of Example 4, attempts to generalize blues melodic practice into a scale on which beginning improvisers can base their melodies. The blues scale is essentially a minor pentatonic scale with an added chromatic passing tone leading up to scale-degree 5.

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Example 4. The C blues scale creates stylistic clashes with the I and V chords of C major.

Despite the clashes with the underlying harmony, this blues scale is used in blues tunes that are major or minor. When combined with the chords of the major blues—I, V, and IV, or C major, F major, and G major in the key of C—this creates characteristic clashes, especially between the lowered and natural scale-degree 3 and scale-degree 7.

These clashes often produce blue notes—notes that are not really flat or natural, but somewhere in between. Blue notes seem to split the difference between the natural scale-degrees 3 and 7 present in harmonies of the major blues with the flat scale degrees present in the blues scale.

The “major” blues scale

Some improvisers find it helpful to think of a major blues scale. The difference between a major and minor pentatonic scale is identical the difference between the major and minor blues scale: the major blues scale is a rotation of the blues scale of its relative minor. Begin the blues scale on scale-degree ♭3, and you will get a blues scale for the relative major. The relationships are summarized in Example 5.

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Example 5. Rotating the blues scale to begin on its second note yields the major blues scale.

The major blues scale is less dissonant with major chords. When improvising, it can be helpful to think of improvising with the major blues scale over major chords of the blues progression. But remember that using the blues scale (with flatted 3rds and 7ths) over major chords is also a perfectly normal practice.

Assignments

29

Rhythm and Meter

Bryn Hughes, Kris Shaffer, and Megan Lavengood

Straight Syncopation

In contemporary pop/rock music, syncopation typically involves taking a series of notes of equal durations, cutting the duration of the first note in half, and shifting the rest early by that half duration.

For example, a series of four quarter notes, all sounding on the beat, can be transformed in this way by making the first note into an eighth note, and sounding each successive quarter note on eighth note early—all on the offbeats.

This process can occur on any metrical level. If the duration of the series of “straight” notes is two beats, they will be syncopated by changing the first note to a single beat and shifting each other note early by a beat. If the duration of the straight notes is a beat, they will be syncopated by a division (one half beat in simple meter). If the straight notes are each divisions, they will be syncopated by shifting each note by a subdivision. The unit of syncopation (the duration of the first note, and the amount of shift applied to the following notes) is always half of the duration of the straight notes. All of these syncopations are relatively common in contemporary pop/rock music.

As a convention, when we take a series of notes that each have a duration of one beat and shift them early by half of a beat, we will call that beat-level syncopation (Example 1). When we take a series of notes that each have a duration of one division and shift them early by a subdivision, we will call that division-level syncopation.

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Example 1. Straight syncopation moves the attacks forward by half the value of the metric level.

Transcribing straight syncopations

Straight syncopated rhythms are easily identified by the frequently occuring off-beat rhythms. For example, if you conduct or tap the counting pulse while listening to a song, several notes in a row that are articulated between your taps or conducted beats, with no notes articulated simultaneously with the counting pulse, indicate syncopation.

Once you identify a syncopated passage—which may only involve two or three notes—figure out on what metrical level the syncopation occurs. For example, in simple meter, if no notes are articulated directly on the counting pulse beats and one note is articulated in between each beat, the syncopation is occuring at the beat level. If no notes are articulated directly on the counting pulse beats and two notes are articulated in between each beat, listen to the passage again while tapping the division. If no notes are articulated directly on the division taps and one note is articulated in between each tap, the syncopation is occuring at the division level.

Once you have determined the metrical level on which the syncopation occurs, determine the durational value of the shift. If the syncopation occurs on the beat level (one note sounding between each counting pulse beat), the value of syncopation is a division: each beat-length note has been shifted one division early. If the syncopation occurs on the division level, the value of syncopation is a subdivision: each division-length note has been shifted one subdivision early.

Lastly, determine how the syncopated pattern begins. Does the offbeat pattern simply begin offbeat? Or does the pattern begin with two quick notes back-to-back as above—one short note on the beat followed by the first of the longer syncopated notes?

Once you have determinted the level of syncopation, the duration of the shift, and whether or not the pattern begins with a truncated onbeat note, the rhythmic pattern should be easy to notate. If, however, you are still having difficulty, try using the lyric syllables and the stress patterns of the lyrics to help you keep track of the individual notes and which ones are on/offbeat. Writing lyrics down before notating the rhythm can be a big help.

Tresillo

Drawing on its roots in African and Cuban musical traditions, another common rhythmic pattern in pop/rock is to divide a beat (or two beats) into three almost-equal groups. For example, dividing a half note into two dotted-eighth notes and an eighth note (3+3+2). Since this pattern approximates a triplet while still maintaining the simple division of beats by 2, 4, 8, etc., creating an experience of something like a “fake triplet.” The term for this rhythmic pattern is tresillo.

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Example 2. Tresillo rhythms.

The tresillo pattern is actually more common than “real” triplets in most pop/rock genres, but both do occur, so take care to distinguish between the two. “Cathedrals” by Jump, Little Children contains examples of both (as well as some straight syncopation), and is an excellent example for practicing performing and identifying tresillo patterns and real triplets.

While tresillo patterns occur most often in 3+3+2 groupings, 3+2+3 and 2+3+3 are also possible.

The tresillo pattern can be expanded: here the 3+3+2 pattern is doubled, resulting in 3+3+3+3+2+2. Nicole Biamonte (2014) refers to this pattern as the double tresillo.

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Example 3. The double tresillo.

In the opening of “Electric Co.” by U2 (1980), the guitar plays subdivisions (sixteenths) grouped 3+3+3+3+2+2, while the kick drum plays straight beats (quarters) under the hi-hat playing straight subdivisions.

Assignments

30

Melody and phrasing

Bryn Hughes and Megan Lavengood

Key Takeaways

Sections in pop/rock music typically consist of two, three, or four phrases. These phrases are usually organized as follows:

  • Two-part: aa’
  • Three-part: aa’b (often a twelve-bar blues)
  • Four-part: srdc

Phrase. A phrase is a musical unit that typically lasts for four bars and includes one line of poetry for its lyrical content. Phrases are designated by lower-case letters.

Section structures

What follows below is a discussion of the structure of song sections, that is, Verse, Chorus, Bridge, etc. Each section consists of at least two phrases.

Two-part

A section is two-part when the phrases that make up the module can be grouped into a first half and a second half. In two-part modules, the second half is usually based on the same music as the first half, and thus it is labeled aa’. Often these two halves begin the same but have different endings, participating in an antecedent–consequent (weak → strong) relationship.

The chorus to “Livin’ on a Prayer” (1’33”) has an aa’ structure (Example 1). The first four-bar phrase (“Oh, we’re half-way there…”) and the second four-bar phrase (“Take my hand…”) have identical melody and harmony (hence the a), but different lyrics (hence the prime). Note that in many songs, this relationship is not as clear cut. However, if the two phrases begin with similar musical material, give them the same letter. New lyrics, new musical endings, or musical variations simply warrant a “prime.”

Very rarely a module’s phrases can be grouped into two clear halves based on different music. Such a module is labeled ab.

Lyrics Phrase
Woah, we're half way there
Woah, livin' on a prayer
a
Take my hand, we'll make it I swear
Woah, livin' on a prayer.
a'

Example 1. Livin' on a Prayer

Three-part

A section containing three phrases is a three-part section. If the first two phrases are based on the same music, the section is labeled aa’b.

12-bar blues progressions are the most common example of a three-part aa’b module. “Hound Dog”  contains aa’b strophes (Example 2).

Lyrics Phrase
You ain't nothin' but a hound dog
Cryin' all the time
a
You ain't nothin' but a hound dog
Cryin' all the time
a'
Well, you ain't never caught a rabbit and you ain't no friend of mine. b

Example 2. "Hound Dog."

Four-part

A section composed of four phrases often contains a sentential structure (presentation → continuation → cadential/conclusion). In pop/rock music, this often appears as a basic musical idea in the first phrase, a repetition or “response” to it in the second, contrasting material in the third phrase (often employing fragmentation, acceleration of harmonic rhythm, and movement away from tonic harmony), and a conclusion in the fourth phrase ― either with a return to the basic idea and tonic harmony or with still newer material that forms a strong melodic, rhythmic, and harmonic conclusion. Walter Everett has called such a four-phrase sentential structure in pop/rock music srdc (statement, restatement/response, departure, conclusion).

In conventional lettering, an srdc module could employ an aaba structure (with statement material returning as a restatement and again as the conclusion), or aabc structure (where the conclusion material is new). Occasionally abcd or abca are possible, but only if b is a clear response to a, not simply new material.

srdc structures tend to divide neatly into halves: sr and dc.

Bobby Darin’s “Dream Lover” (Example 3) provides a classic example of a four-part srdc phrase structure.

Lyrics Phrase
Every night I hope and pray
A dream lover will come my way
s (statement)
A girl to hold in my arms
And know the magic of her charms
r (repetition)
'Cause I want (yeah-yeah, yeah)
A girl (yeah-yeah, yeah)
To call (yeah-yeah, yeah)
My own (yeah-yeah)
d (departure)
I want a dream lover
So I don't have to dream alone
c (conclusion)

Example 3. "Dream Lover."

Assignments

 

32

AABA form and strophic form

Bryn Hughes and Megan Lavengood

Key Takeaways

  • Strophic form consists only of repeated strophes. Its form would be abbreviated as AAA.
  • AABA form, also known as 32-bar song form, consists of a twice-repeated strophe (AA), followed by a contrasting bridge (B), followed by another repetition of the initial strophe (A).
  • AABA and strophic form were common especially in older pop music (1960s and earlier).
  • AABA and strophic form both have strophe sections as the main section, which features the primary lyrical and musical content of the song.

Chapter Spotify Playlist

Strophic form

Songs that repeat the same basic multi-phrase unit throughout are in strophic form (sometimes abbreviated AAA, because the same basic material A is repeated), and the basic unit that is repeated is called a strophe. Strophic form is more common in early rock-and-roll (1950s–1960s) than in the 1970s and beyond.

For an example of a strophic song, consider “Blue Suede Shoes” by Carl Perkins.

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This song contains multiple sections, all of which have the same basic underlying music. Though the instrumentation and the lyrics change, the section beginning at 0:19 contains the same – or, at least, very similar – melody, harmony, and phrase structure as the sections that begin at 0:58, 1:37, and 1:54. Listening a bit more closely, we can hear a similar, but abbreviated, version of the same patterns at the opening of the song. Even the instrumental sections at 0:41 and 1:21 have the same underlying pattern, just a different melody in the form of a guitar solo. The entire song is a repetition of this same basic pattern, or slight variations of it, modeled at 0:19–0:41.

Example 1 is a bird’s-eye-view sketch of the form of “Blue Suede Shoes” to follow as you listen:

timestamp section abbreviation
0:00 strophe 1 A
0:19 strophe 2 A
0:41 instrumental strophe A
0:58 strophe 3 A
1:21 instrumental strophe A
1:37 strophe 1 (slightly varied) A
1:54 strophe 4 A

Example 1. "Blue Suede Shoes" is in strophic form.

While “Blue Suede Shoes” is composed entirely of strophes, it is important to note that strophic songs can also contain so-called auxiliary sections such as intros, outros, and codas. An example of a strophic song with auxiliary sections is “I Wanna Be a Cowboy’s Sweetheart” by Patsy Montana & The Prairie Ramblers. Follow the form chart in Example 2 as you listen to this song, and notice that the intro/outro do not change the fundamental strophic form significantly.

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timestamp section lyrics
0:00 intro [instrumental] Yodel-ey…
0:20 strophe 1 I wanna be a cowboy's sweetheart…
1:02 instrumental strophe
1:32 strophe 2 I wanna ride Old Paint…
2:17 strophe 1 I wanna be a cowboy's sweetheart…
2:49 outro Yodel-ey…

Example 2. "I Want to Be A Cowboy's Sweetheart" is in strophic form with auxiliary modules.

However, if a song has more than one main musical idea other than strophes and auxiliary sections, it is not strophic, but AABA form, which is discussed below, or verse-chorus form, discussed in the next chapter.

32-bar song form (AABA)

Another formal structure that is more common in early rock-and-roll is AABA form, also called 32-bar song form because of some of the features of earlier “Golden Age” songs that make use of this structure. AABA form, like strophic form, relies on the strophe to communicate the main lyric and musical ideas of the song, but add in a contrasting bridge section in the middle.

As an example, listen to “I Want to Hold Your Hand” by The Beatles.

Thumbnail for the embedded element "I Want To Hold Your Hand - Remastered 2009"

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After a brief introduction, the song begins with two strophes. However, where “Blue Suede Shoes” followed with an instrumental strophe, The Beatles move to a bridge at 0:52. This new section builds tension by contrasting and withholding the main strophe theme before it returns at 1:11. Note that the song begins and ends with the strophe, and the strophe contains the title lyrics. It also, for many people, is the more memorable part of the song. Thus, the strophe is still the primary section. But now it has a secondary section to add interest and tension, the bridge. (And an auxiliary section, the intro, to help get the song off the ground.)

timestamp section abbreviation
0:00 intro I
0:08 strophe 1 A
0:29 strophe 2 A
0:51 bridge B
1:11 strophe 3 A
1:33 bridge B
1:53 strophe 3 A

Example 3. "I Want to Hold Your Hand" is in AABA form, with a typical repeat of BA.

“I Want to Hold Your Hand” is a typical AABA song in that it does not just have four sections, AABA. AABA songs almost always have a complete AABA cycle, followed by either another complete AABA cycle, or an incomplete cycle (typically BA). Once the first AABA cycle is complete, there tend not to be any new lyrics, only repetition of the whole or the end of the main cycle.

Sections of AABA and strophic forms

The pop form terminology used here and throughout OMT is based on the research of Jay Summach.Jason Summach, “Form in Top-20 Rock Music, 1955–89” (Ph.D. diss., Yale University, 2012).

Strophe (A)

The primary function of a strophe section is to present the primary lyric and musical content and to provide a point at which the song might satisfyingly end.

In strophic form (AAA), strophes are the only core sections, and thus do not participate in a functional progression. Functional progression takes place on the phrase level within the strophe. The strophe sections themselves tend to set a stanza of text each with music that is self-contained and harmonically closed.

In 32-bar form (AABA), the strophe’s functions—holding primary music/text and providing harmonic stability— are elevated through contrast with the bridge section. In AABA songs, strophe function often involves the prolongation of tonic harmony. Strophes tend to be longer in strophic songs than in AABA songs.

In both forms, srdc is by far the most common internal pattern for strophes. For three-part strophes, the 12-bar blues progression is the most common pattern.

Bridge (B)

Bridges share many traits with the continuation function of classical form. Bridge sections tend to play a transitional role (neither the point from which to depart, nor the point of arrival) in the formal cycle. This generates heightened expectation for the return of A, by contrasting with A and temporarily withholding it. A bridge section “must be followed by [the primary section] in order for its function to be satisfied.”Jason Summach, “Form in Top-20 Rock Music, 1955–89” (Ph.D. diss., Yale University, 2012), 79. Bridge sections tend to emphasize non-tonic harmonies and commonly end on dominant harmony.

As the next chapter discusses, in verse-chorus songs, bridge sections are more free to contrast verse and chorus sections without a strong need to build expectation for the return of the chorus than in AABA form. In an AABA song, building expectation for the return of the strophe and arriving on dominant harmony in preparation of that return are essential to bridge function.

Introduction (I)

Introduction sections transition from the unmetered silence that precede the song to the musical activity of the first core section. They tend to be short and untexted/instrumental, and tend to present musical material from one or more core sections to come. This is often accomplished by the building up of musical material, perhaps through layering (e.g., one instrument at a time) or through a more generic building of energy.

Occasionally intros include non-core material. Such intros often correspond to an outro based on the same material, and together they create a “bookend” effect. It is also possible to have multiple intro sections in a row, with each based on different music.Dexy’s Midnight Runners’s “Come On Eileen” contains several different intro sections with different musical content.

Outros (O) and Codas (X)

Outros function as a transition from song back to silence, and thus decrease energy. Often this is accomplished in the recording studio by way of a fadeout. When an outro section is present, it is almost always based on material from the last core section that preceded it. Otherwise, outros tend to draw material from the intro, creating a “bookend” effect (as in “I Want to Be a Cowboy’s Sweetheart” above). Outros exhibit closing rhetoric.

A coda is a song-ending section that presents new material—in other words, an outro not based on music previously heard. Like outros, codas exhibit closing rhetoric.

Muse’s “Resistance” is useful for distinguishing between these two terms, since it has both a coda and an outro. The coda, which contains new musical and narrative material, begins at 4:05, following the final chorus. This new section, which brings something of a conclusion (if an open-ended one) to the narrative, gives way to a song-ending outro at 4:54. Aside from the clear change in content and texture at 4:54, the outro is recognizable as an outro (versus a coda) by the return of material from the introduction, creating the “bookend” effect.

Standout passages within sections

Refrain

A refrain is a lyric-invariant passage within a section that is otherwise lyric-variant. A refrain is too short to form its own section—typically a phrase or less.

A refrain is most often the last line or so of a section’s text (tail refrain), and occasionally the material at the beginning of a section’s text (head refrain). “Cathedrals” by Jump Little Children contains a head refrain. Each strophe begins with the same line: “In the shadows of tall buildings…”. “Blue Suede Shoes” and “I Want to Hold Your Hand,” each discussed at the beginning of this chapter, both contain tail refrains at the ends of their strophes, emphasizing the title lyrics.

Further Reading
  • Summach, Jason. 2012. “Form in Top-20 Rock Music, 1955–89.” Ph.D. diss., New Haven: Yale University.
Assignments
  • Worksheet on AABA and Strophic Form (.pdf, .docx). Asks students to identify formal sections and any variations to the form. Worksheet playlist

33

Verse-chorus form

Bryn Hughes and Megan Lavengood

Key Takeaways

  • Verse-chorus form is a versatile song form that rapidly took over rock-and-roll in the 1960s and has dominated the genre ever since.
  • In verse-chorus form, the title lyrics, the most memorable music, and the main narrative are split between two core sections: the verse and the chorus.

Verse-chorus form is so named because the two most important sections are the verse and the chorus. Other possible sections in verse-chorus form are prechorus, bridge, and postchorus.

As an example, look at the form of Bon Jovi’s song “Livin’ on a Prayer,” given in Example 1.

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timestamp section notes
0:00 intro
0:47 verse
1:18 prechorus
1:34 chorus
1:48 interlude
1:53 verse
2:23 prechorus
2:39 chorus
2:56 postchorus
2:59 bridge (guitar solo)
3:16 prechorus
3:24 chorus modulation, repeat and fade out to end

Example 1. "Livin' on a Prayer" is in verse-chorus form, and uses many types of core and auxiliary sections in a typical way.

“Livin’ on a Prayer” follows a typical verse-chorus form. It also illustrates common usage of five core sections in verse-chorus forms (and a bonus truck driver’s modulation!).

Cycles

Notice that the sections used in “Livin’ on a Prayer” recur, and always come back in the same order. Sections within a verse-chorus form have certain prototypical orderings and groupings. The verse, prechorus, chorus, and postchorus sections, for example, always progress in this order (though not all need be present). These groupings are referred to as cycles. In “Livin’ on a Prayer”:

A prototypical verse-chorus form song is illustrated in Example 2.

Illustration showing sections as follows: intro, verse, prechorus, chorus, verse, prechorus, chorus, bridge, chorus, chorus
Example 2: A prototypical verse-chorus form. Does not reference a specific song. Click to enlarge.

Sections within verse-chorus form

Terms, concepts, definitions, and notational guidelines are taken either from common convention and a combination of the resources listed below under Further Reading.

Verse

Prechorus

Chorus

Postchorus

Bridge

Bridge sections are a flexible section type in verse-chorus form.

Each of these points contrasts with the way bridges are used in AABA form.

Standout lyrics within sections

Refrain

While refrains are primarily associated with AABA form and strophic form, they can occasionally be used within sections of a verse-chorus form song. However, take note that refrains are distinct from choruses—refrains are a lyric within a section, whereas a chorus is an entire standalone section.

Climb

A climb is a phrase that has prechorus function, but is too short to function as its own independent section.Jason Summach, “Form in Top-20 Rock Music, 1955–89” (Ph.D. diss., Yale University, 2012), 321. The climb is always the last phrase of a verse section.

“Come On Eileen” by Dexys Midnight Runners contains a one-phrase climb at the end of its verses and bridge (“Tu-ra-lu-ra…”), as heard at 0:48.

Further Reading
  • Barna, Alyssa. 2018. “The Dance Chorus in Recent Top-40 Music.” Paper presented at the Music Theory Southeast, Columbia, South Carolina, March 2.
  • Covach, John. 2005. “Form in Rock Music: A Primer.” Engaging Music: Essays in Music Analysis, 65–76.
  • Everett, Walter. 1999. The Beatles as Musicians: Revolver through the Anthology. New York: Oxford University Press.
  • Spicer, Mark. 2011. “(Per)Form in(g) Rock: A Response.” Music Theory Online 17 (3). http://www.mtosmt.org/issues/mto.11.17.3/mto.11.17.3.spicer.html.
  • Stroud, Cara. 2014. “The Postchorus in Millennial Dance Pop.” Paper presented at the Graduate Association of Musicologists und Theorists Conference, Denton, TX.
  • Summach, Jay. 2011. “The Structure, Function, and Genesis of the Prechorus.” Music Theory Online 17 (3). http://www.mtosmt.org/issues/mto.11.17.3/mto.11.17.3.summach.html.
  • Summach, Jason. 2012. “Form in Top-20 Rock Music, 1955–89.” Ph.D. diss., New Haven: Yale University.
Assignments
  • Pop Music Form — The Shape of Music Around You (.pdf). Writing assignment which students to find songs on their own; identify them as strophic, AABA, or verse-chorus; name the sections of the song; and justify their analyses using form vocabulary.
  • Listening to Pop Forms (.pdf, .docx). This worksheet uses two unusual verse-chorus form songs to challenge students’ analytical abilities. Uses Audacity to have students mark the form of .mp3s. Purchase “Terrified” and purchase “Broken Clocks” as .mp3s.

Media Attributions

Introduction to Harmonic Schemas in Pop Music

Bryn Hughes and Megan Lavengood

There are a number of common stock chord progressions that recur in many pop/rock songs. In pop/rock songs, these stock progressions, or schemas, will often occur in cyclical patterns; that is, the same progression will repeat multiple times in a row. This is particularly common in choruses of verse-chorus songs, but also happens in verses, strophes, and bridges. Knowledge of pop schemas is helpful for identifying harmonies by ear, since in addition to listening for bass scale degrees and considering whether the harmonies are in root position or first inversion, you can listen for common patterns that you have heard in other songs. Example 1 succinctly summarizes the most common forms of each schema.

[insert table of schemas with typical chord progressions]

A crucial feature of schemas is that they can be altered while still remaining recognizable as a manifestation of that schema. Think of the term “bird.” If someone asks you to imagine a bird without any extra context, you may not imagine a specific species of bird, but you would probably imagine a bird that looks something like a sparrow or robin. Your imaginary bird is your mental prototype for the schema “bird.” You can recognize all kinds of birds as being birds even if they do not look exactly like your imaginary bird—ostriches, penguins, flamingos, and swans are all clearly birds, despite their significant differences in appearance, behavior, and habitat. In the same way, you can and should recognize harmonic schemas as manifestations of the schemas listed here, even when they undergo some form of variation. Common variations include chromatic inflection or chord inversion.

The following chapters group together certain schemas that share several qualities, and go into detail about each individual schema and its most common variations. 

34

Blues-based schemas

Bryn Hughes

Key Takeaways

Blues-based schemas all include some kind of plagal motion.

  • Many songs simply use the two-chord vamp I–IV (very common in R&B and Soul music)
  • The “plagal sigh” schema, IV–iv–I, includes the scale-degree voice-leading \hat{6}-\flat\hat{6}-\hat{5} and can often be found at phrase endings
  • “Applied” IV chords can be used to create a Double Plagal schema: ♭VII–IV–I
  • These applied IV chords can be used to create extended plagal progressions such as ♭VI–♭III–♭VII–IV–I

Chapter Playlist

Blues-based schemas, or “flat-side” schemas, are those that mostly employ harmonies found on the “flat-side” of the circle-of-fifths. We draw the connection to the Blues here because of its propensity for using the IV chord (the first chord found in the flat-wise direction on the circle-of-fifths), and for the general ubiquity of the flattened seventh scale degree in Blues music.

Plagal motion

The IV chord, while certainly an extremely frequent predominant/subdominant chord in common-practice repertoire, has an even more prominent place in pop/rock music. Perhaps borne out of the 5–6 neighboring motion found in shuffle-blues guitar accompaniment patterns (Example 1), an alternation between I and IV is a common occurrence in numerous genres (Example 2).

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Example 1. The 5–6 shuffle pattern.

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Example 2. The plagal IV–I pattern.

In “Soul Man” by Sam and Dave, the chord progression used in the verse (Example 3) consists of an alternation of I and IV—listen carefully to the bass.

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Example 3. Sam and Dave, “Soul Man” (1967).

A similar oscillation between I and IV can be found in the verse to “In the Midnight Hour” by Wilson Pickett (Example 4). Perhaps unsurprisingly, Steve Cropper and Donald “Duck” Dunn play the guitar and bass, respectively, on both of these tracks.

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Example 4. Wilson Pickett, “In the Midnight Hour” (1965). 

This kind of chord progression isn’t limited to Soul and R&B, of course. The beginning of “After The Gold Rush” by Neil Young (Example 5) features a similar progression (it deviates after the the words “…drummers drummin…” Also, note the discrepancy between the melody notes and the chords throughout).

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Example 5. Neil Young, “After The Gold Rush” (1970).

Minor iv

A very common plagal schema in rock and popular music is the use of the minor iv chord as a kind of cadential gesture. It is most commonly found as part of the three-chord schema IV–iv–I. The schema is typically accompanied by the descending melodic scale-degrees \hat{\text{6}}-\flat\hat{\text{6}}-\hat{\text{5}}, which is found in the guitar part in our example. The semitone descent between \flat\hat{\text{6}}-\hat{\text{5}} creates an especially strong pull to the tonic.

This descent has been referred to  by J. Kent Williams and Frank Lehman as a “plagal sigh” in Golden Era American popular song and Classic Hollywood film scores, respectively.[reference] Both authors consider this gesture to invoke a sense of nostalgia and sentimentality. Indeed, even in pop music, musicians typically use this progression in conjunction with lyrics that suggest sentimentality.

“Wake Me Up When September Ends” by Green Day (Example 6) exhibits both of the tendencies discussed above: motion from IV–iv–I and a sense of nostalgia and sentimentality in the lyrics.

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Example 6. Green Day, “Wake Me Up When September Ends” (2005). 

Double-plagal

The “double-plagal” progression (Walter Everett’s term) is an expansion of the plagal progression discussed above to include the “IV/IV” chord prior to the IV chord.[citation] This is perhaps more simply explained as ♭VII–IV–I (or simply VII-iv-I in minor). The most famous instance of the double-plagal progression is likely the coda from “Hey Jude” by The Beatles (Example 7).

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Example 7. The Beatles, “Hey Jude” (1968).

Extended plagal

The “applied IV” chord can be used in sequence, similar to the descending-fifths progression in common-practice music. In the version of “Hey Joe” by Jimi Hendrix, the verse consists of three iterations of the plagal motion in a descending-fourths pattern, which results in the progression: ♭VI–♭III–♭VII–IV–I, in the key of E major.

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Example 8. Jimi Hendrix, “Hey Joe”  (1966).

Recognizing blues-based schemas

In all of these examples, the sense of forward motion is created by the harmonic motion from IV to I. The other alterations, such as IV/IV (♭VII) or minor iv, are extra embellishments on this essential plagal motion.

Further reading
Assignments

35

4-chord schemas

Megan Lavengood and Bryn Hughes

Key Takeaways

I, IV, V, and vi are the most common harmonies in pop music, and can be arranged into several schemas, each with a distinct sound. Each schema can have variations, such as chord substitution or rotation, while still remaining recognizable as that schema.

  • The doo-wop schema is I–vi–IV–V, and was common in 1960s pop music. Common variations:
    • I–vi–ii–V (ii substitutes for IV)
    • IV–V–I–vi (rotation)
  • The singer/songwriter schema is vi–IV–I–V or I–V–VI–IV, and was common in 1990s singer/songwriter music. It can also be understood in its relative minor: i–VI–III–VII. Common variations:
    • IV–I–V–vi (rotation)
  • The hopscotch schema is IV–V–vi–I, and is common in recent pop music (since 2010). It can also be understood in its relative minor: VI–VII–i–III. Common variations:
    • VI–V–i–III (V substitutes for VII in minor)

Chapter Playlist

The following progressions all have something in common. They all use the same four chords, which are probably the most common chords in all of pop music: I, IV, V, and vi. They all sound somewhat similar because of this; the difference is in the order in which those chords appear.

Doo-wop

Example 1 shows music notation, lead sheet symbols, and Roman numerals for the doo-wop schema:  I–vi–IV–V, or C–Am–F–G in C major.

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Example 1. The doo-wop schema (left) and a common variation of it that replaces IV with ii (right).

The name for this cyclical chord progression comes from the fact that it was was very common in rock ballads from the 1950s and early 1960s, such as  “Duke of Earl” by Gene Chandler (1962). However, it has continued to be used frequently ever since: examples include the verse and chorus of “Friday” by Rebecca Black (2011) and the chorus of “Total Eclipse of the Heart” by Bonnie Tyler (1983) (starts at 0:49).

Substituting ii for IV

Because ii and IV share the same function in this chord progression, ii can be swapped out for IV, as in Otis Redding’s “Try a Little Tenderness” (1966).

Rotation

Because the doo-wop schema is typically employed in cycles, it can also be found starting on a different chord in the cycle and then proceeding through the same succession of chords (rotation). For example, “Viva la Vida” by Coldplay (2008) works through a cyclical repetition of the same succession of chords, but their phrases begin on IV rather than I (Example 2).

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Example 2. “Viva la Vida” uses the doo-wop progression, but rotates it to start on IV rather than I. The chords still progress in the same order.

Singer/Songwriter

The singer/songwriter schema may be the best-known of all the four-chord schemas. A common Roman numeral analysis for this schema is vi–IV–I–V, or Am–F–C–G in C major. But this is not the only Roman numeral sequence you might use to understand this schema, because it is exceedingly common in two rotations. On top of that, either rotation may be understood as having either the major tonic or the relative minor tonic. This is best understood through Example 3.

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Example 3. The singer-songwriter schema has two rotations that are equally common. The schema is tonally ambiguous, meaning it can be interpreted in either its relative major or relative minor.

Like the 50s doo-wop, this is a four-chord cyclical progression. It has been around for some time but became increasingly common beginning in the mid-1990s with singer/songwriters such as Sarah McLachlan, Jewel, and Joan Osborne, though the chord progression can be found in a variety of musical styles.

Tonal ambiguity

One important feature of this progression is that it does not, on its own, clearly communicate a definitive tonic chord. This property is known as tonal ambiguity. An example is “Despacito” by Luis Fonsi and Daddy Yankee (2017). The chord progression, Bm–G–D–A, can sound like VI–IV–I–V in D major or like I–VI–III–VII in B minor to different listeners. One reason the singer/songwriter schema is ambiguous is because there is no authentic cadence: the two potential cadential motions are either plagal (IV–I) or stepwise (VII–i). Without a strong harmonic cadence, listeners might only be able to determine the tonic chord—if at all—by the progressions before and after the singer/songwriter, which chords in the cycle begin and end it, and the important pitches of the melody (Example 4).

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Example 4. Both D major and B minor are plausible tonic chords for “Despacito,” because of its use of the tonally-ambiguous singer/songwriter schema.

In fact, some songwriters take advantage of this duality in songs that modulate back and forth between relative major and minor keys, as well as in songs with some parallel ambiguity in the text (hence its usefulness for those mid-1990s songwriters). An example is “What About Love” by Heart (1982), which has an obvious D-minor intro, a D-minor/F-major verse (begins at 0:23) using the singer/songwriter progression, and a chorus obviously in F major (begins at 1:10)—listen while following along with the chart below (Example 5).

Thumbnail for the embedded element "What About Love?"

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timestamp section progression (lead sheet) progression (Roman numerals) implied key
0:00 intro Dm–C–B♭–C over D pedal i–VII–VI-VII over tonic pedal D minor
0:23 verse Dm–B♭–F–C vi–IV–I–V
or
i–VI–III–VII
ambiguous between D minor and F major
1:10 chorus F/A–Bb–C I6–IV–V F major
1:33 interlude Dm–C–B♭–C over D pedal i–VII–VI-VII over tonic pedal D minor
1:44 verse Dm–B♭–F–C vi–IV–I–V
or
i–VI–III–VII
ambiguous between D minor and F major
2:08 chorus F/A–B♭–C I6–IV–V F major
2:29 bridge (guitar solo) B♭–C IV–V F major
2:53 chorus F/A–B♭–C I6–IV–V F major
3:11 coda B♭–C–D over D pedal ♭VI–♭VII–I over tonic pedal D major

Example 5. "What about Love" by Heart exploits the singer/songwriter schema's tonal ambiguity to link between a minor-mode intro and a major-mode chorus.

Rotations

As discussed above, starting the progression on I or vi are two equally common rotations of this schema. From time to time, the singer/songwriter progression might also begin on the IV chord, resulting in a “deceptive” variant of this progression that ends with V–VI—a deceptive cadence (IV–I–V–VI). The chorus (starts at 1:11) of “Alejandro” by Lady Gaga (2009) uses this rotation of the singer/songwriter schema.

Hopscotch

In recent years (since about 2010), another type of four-chord schema has become increasingly common: IV–V–vi–I, or VI–VII–i–III in minor.  Examples include “Dancing with a Stranger” by Sam Smith (2019) and “No Brainer” by DJ Khaled, Justin Bieber, and Quavo (2018). We will refer to this as the hopscotch schema because of its root motion: step, step, skip.

Like the singer/songwriter schema, the hopscotch schema can be tonally ambiguous. In other words, in the progression F–G–Am–C, either Am or C might sound like tonic (Example 6). There is often no definitive cadential motion, especially moving into the C chord.

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Example 6. The “hopscotch” schema is tonally ambiguous, and can be interpreted in either its relative major or minor keys. The “hopscotch” name refers to the root motion in the chord progression, which proceeds step-step-skip, as shown by the annotations.

Replacing VII in minor with V

An especially common harmonic substitution that encourages a minor-mode interpretation of the hopscotch schema is to replace the subtonic VII chord with the major V chord, so that VI–VII–i–III becomes VI–V–i–III. One song that does this is “Nightmare” by Halsey (2019). Although these chords have the same harmonic function, the two chords have quite distinct colors, since the major V chord in minor raises scale-degree 7 to become the leading tone, while the subtonic VII chord uses the natural scale-degree 7. Some songs, like “Mixed Personalities” by YNW Melly, invert this V chord, which allows the bass motion of the hopscotch schema to stay the same (step-step-skip), even though the root motion has changed (Example 7).

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Example 7. A common alteration to the hopscotch schema is to replace VII with V. This means the G of the VII is replaced with the G-sharp of the V chord. The root and bass motion also changes (left), although sometimes, artists will invert the V chord, creating a more stepwise bassline that is more akin to the regular hopscotch schema (right).

Recognizing by Ear

All of these four-chord schemas sound similar to one another, since they all use I, IV, V, and vi. All the schemas can be rotated, so it’s not simply a matter of seeing where the progression begins and ends! Instead, try listening to how the major tonic is approached (Example 8).

 

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Example 8. Each schema approaches the major tonic from a different chord.

Even if you think the real tonic is the minor tonic, listening to the approach of the major tonic will help distinguish among these four-chord schema options. Listening to the approach of the minor tonic may not be helpful, since both the singer/songwriter and the hopscotch schemas approach the minor tonic by step.

Further reading
Assignments

36

Classical schemas (in a pop context)

Bryn Hughes and Kris Shaffer

Key Takeaways

The schemas discussed in this chapter are all based on those often found in common-practice music.

  • The Lament schema is a four-chord schema that descends down the minor tetrachord from the tonic to the dominant: \hat{1}-\flat\hat{7}-\flat\hat{6}-\hat{5}. Most typically, this is harmonized by I–♭VII–♭VI–V, however, \flat\hat{7} can be harmonized in numerous ways.
  • The Circle-of-Fifths schema is at least four chords in length, and consists of chords whose roots descend by perfect fifth. This schema has many possible variations, and does not necessarily start on the tonic.

 

Lament

This progression need not be included in a cycle, but occasionally it does. It is named the “lament” progression because in early classical music, this chord progression (almost always in minor) was used as the ground bass for songs of lament. Examples include “Dido’s Lament” by Henry Purcell, from the opera Dido and Aeneas, and J.S. Bach’s “Crucifixus,” from his Mass in B Minor.

Dire Straits’ “Sultans of Swing” provides a classic example of the lament in a pop/rock setting (Example 1). The phrase descends through the minor tetrachord: \hat{1}-\flat\hat{7}-\flat\hat{6}-\hat{5}, and is harmonized with diatonic triads: I–♭VII–♭VI–V. The middle two chords are syncopated and given less duration in order to make room for the seventh to be added to the dominant chord at the end of the phrase, which provides a turnaround to repeat the chord progression.

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Example 1. Dire Straits, Sultans of Swing” (1978)

Example 2 shows the opening of the verse in Muse’s “Thoughts of a Dying Atheist”. Importantly, note that \flat\hat{7} is harmonized by a B♭ major chord in second inversion. One may interpret this as a III chord in second inversion, or, as is shown in the transcription, a VII chord embellished with two upper neighbor notes.

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Example 2. Muse, Thoughts of a Dying Atheist” (2004)

Circle-of-Fifths

In this schema, each chord’s root moves down by fifth to the next root. This progression often happens in minor beginning on i, moving to the relative major. Like the “singer/songwriter” progression, there is some key ambiguity in this progression, as the starting chord is easily considered tonic, but the motion from VII to III can easily be heard as V–I in the relative major key. And indeed, it can be used to move from the relative minor to the relative major.

The chorus of Aqua’s “Barbie Girl” provides a somewhat tonally ambiguous example of the Circle-of-Fifths schema (see Example 3).

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Example 3. Aqua, “Barbie Girl” (1997). 

The verse of Muse’s “Thoughts of a Dying Atheist” also includes a four-chord circle-of-fifths schema, immediately following the lament discussed above. This progression immediately repeats, returning to the initial minor key. However, the second time through, this lament–circle-of-fifths pattern leads to a chorus in the relative major (taking the III chord as the new tonic).

Longer examples of the Circle-of-Fifths schema can be found in pop/rock music, too.

Radiohead’s “You and Whose Army?” (Example 5) presents a slightly more complex instance of a Circle-of-Fifths schema. Here we get a chromatic sequence of the schema, in which each pair of fifth-related chords functions locally as an applied ii–V progression of the following chord, much like the applied ii–V progressions found in jazz. Like “Barbie Girl,” “You and Whose Army?” is tonally ambiguous. The Circle-of-Fifths schema propels the music forward, without ever strongly confirming the tonic. Both E major and C♯ minor are viable interpretations, and thus have both been provided in the analysis below.

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Example 5. Radiohead, “You and Whose Army?” (2004).

Assignments

37

Puff schemas

Megan Lavengood and Bryn Hughes

Key Takeaways

  • Puff schemas are based on a I–iii–IV progression.
  • Common variations:
    • I–III♯–IV
    • i–III–iv

While many of the schemas discussed in other chapters are commonly used as repeating chord loops, others are more often used as a building block within a goal-oriented phrase. Puff schemas, which use the mediant triad (iii), are one such schema. The name comes from its use at the outset of phrases in the song “Puff, the Magic Dragon” by Peter, Paul and Mary (1963).

Lead sheet A C♯ D A
Lyrics Puff, the magic dragon, lived by the sea.
Roman numerals I iii IV I

Example 1. The puff schema begins most of the phrases in “Puff, the Magic Dragon.”

The puff schema is typically found in the opening of phrases, as it is here (Example 1). Again, the puff schema is not typically looped, so the chords that come after the IV chord can vary. In “Puff,” the fourth chord is I. But in “Let’s Get It On” by Marvin Gaye, the IV chord progresses to V (Example 2). “House of the Rising Sun” by the Animals (1964) is an example of the puff schema in a minor-key song (Example 3); a major IV progresses to VI in this song. This shows an example of how the puff schema can involve varied chord quality.

Lead sheet E♭ Gm7 A♭ A♭/B♭
Lyrics ………I’ve been really tryin, baby
Roman numerals I iii7 IV V11

Example 2. “Let’s Get It On”’s phrases begin with a puff schema before finishing with a V–I motion.

Lead sheet Am          C D          F Am         C E
Lyrics There is  a house in New Orleans they call   the Rising Sun
Roman numerals i             III IV          VI i            III V                    

Example 3. “House of the Rising Sun” uses the puff schema in minor. The IV chord is also major instead of the typical minor.

I–III♯–IV

One particularly common chromatic variant of the puff schema is I–III♯–IV. This progression   is prominently featured in Radiohead’s debut single, “Creep” (1993). It combines the puff schema with a plagal schema with mode mixture (Example 4).

Lead sheet G B C Cm
Lyrics When you were here before couldn’t look you in the eye. You’re just like an angel; your skin makes me cry.
Roman numerals I III♯ IV iv

Example 4. ”Creep” by Radiohead alters the iii chord of the puff schema by raising the third to make it a major III♯ chord.

Raising the third of the iii chord by a half step changes iii to a major III♯ chord. This leads nicely into the IV chord because the chromatic tone, scale-degree ♯5, resolves upward by half-step to scale-degree 6 (Example 5).

[example here]

III♯–IV as deceptive motion

In many cases, a III♯ chord should be interpreted as an applied chord: a V/vi. The III♯ chord, acting as V/vi, does sound good when followed by vi. A progression like C–E–Am–F can be understood as a variation on the singer/songwriter schema, in which a V/vi replaces the V chord.

Especially in a song that uses a progression like C–E–Am–F, a progression that moves from E straight to F could be understood as deceptively resolving the III♯ chord:

The play between deceptive and authentic resolutions of III♯ as a V/vi chord is a remarkable feature of the progressions used in “Weekend Wars” by MGMT (2007). Setting up the puff schema with an authentic V/vi–vi progression prepares the listener to experience the puff progression as a deceptive resolution (Example 6).

authentic resolution puff schema:
deceptive resolution
Lead sheet A/C♯ Dm C/E     F A                    B♭
Lyrics … Instant battle plans written on the sidewalk
Roman numerals V6/vi   vi   V6      I V/vi                 vi/vi
(or III♯          IV)

Example 6. “Weekend Wars” by MGMT makes the puff schema sound like a deceptive resolution of a V/vi chord. 

Further Reading
  • Doll, Christopher. 2017. Hearing Harmony: Toward a Tonal Theory for the Rock Era. Ann Arbor: University of Michigan Press.
Assignments

38

Modal schemas

Megan Lavengood

Key Takeaways

  • Many pop songs use harmonic progressions that imply modes other than major/minor.
  • A modal schema may be used without a pop song being entirely strictly within that mode.
  • Modes may be compared to major and natural minor to understand what characterizes their sound (their color notes)
  • Mixolydian schemas:
  • Aeolian schemas:
    • Subtonic shuttle i–♭VII (same as mixolydian, but with a minor tonic)
    • Aeolian shuttle i–♭VII–♭VI–♭VII
    • Aeolian cadence ♭VI–♭VII–i (or I)
    • Lament i–♭VII–♭VI–v
  • Dorian schemas:
    • Dorian shuttle i–IV
  • Lydian schemas:
    • Lydian shuttle I–II♯
    • Lydian cadence II♯–IV–I

“Mode” is a really complicated term. The article on mode in Grove Music Online, which is the standard academic encyclopedia for musicology, is 238 pages long and has nine authors.Harold S. Powers et al., “Mode,” in Grove Music Online (Oxford University Press, 2001), https://doi.org/10.1093/gmo/9781561592630.article.43718. This means that, even if you think you already know about modes, you may want to set that knowledge aside before learning how modes are used in pop music.

This chapter discusses modes as they appear in certain schematic chord progressions in pop and rock music. Most of this information is based on the work of Nicole Biamonte and Philip Tagg.Nicole Biamonte, “Triadic Modal and Pentatonic Patterns in Rock Music,” Music Theory Spectrum 32, no. 2 (October 2010): 95–110, https://doi.org/10.1525/mts.2010.32.2.95; Philip Tagg, Everyday Tonality: Towards a Tonal Theory of What Most People Hear, 1.3 (New York: The Mass Media Music Scholars’ Press, 2011). After showing the function of modal harmonies as they compare to diatonic harmonies, common modal schemas will be introduced, grouped by the mode they borrow from.

Grouping modes together into modes with a major tonic vs. modes with a minor tonic helps with aural identification of modal passages. This grouping is represented in Example 1.

Illustration in notation.
Example 1. The top line shows modes whose [latex]\hat{3}[/latex] is a major 3rd above tonic: major, mixolydian, and lydian. The top line shows modes whose [latex]\hat{3}[/latex] is a minor 3rd above tonic: aeolian, dorian, and phrygian. Dotted slurs connect the distinctive color pitch of each mode with its major/minor counterpart.

Example 1 also illustrates what differentiates certain modes from major or minor. Each mode has exactly one pitch shown in a lighter color; this pitch is inflected when compared to major/minor. These special pitches are referred to as the color note of each mode. These relationships are shown with the dotted slurs.

Function of Modal Harmonies

You may already have learned about tonic, subdominant, and dominant function in diatonic harmony. Modal harmonies basically align in function with their diatonic counterparts, although the additional modal inflections create greater overlap between these functions. This is summarized in Example 2.

Two staves connecting diatonic and modal versions of each chord function.
Example 2. Modal harmony allows many more “flavors” of the same chord to be implemented without changing the function of the chord.

This illustration of harmonic function may help you to understand why certain modal progressions seem as goal-oriented as diatonic progressions.

Mixolydian: ♭VII

Mixolydian’s color note is \flat\hat{7} (Example 3). In major-mode pop songs, the ♭VII chord is borrowed from the mixolydian mode. ♭VII typically has dominant function, and you might think of it as a substitute for the traditional major-mode V chord in both the double plagal and mixolydian cadence schemas (Example 4).

 

Illustration in notation.
Example 3. [latex]\flat\hat{7}[/latex] is the color note of the mixolydian mode. Important mixolydian harmonies have that color note in them: v and ♭VII. (iiiº is not used.)
Illustrated in notation
Example 4. The double plagal schema and the mixolydian cadence schema are two especially common mixolydian chord progressions.

Double plagal

The double plagal schema♭VII–IV–I, which is discussed further in the blues-based schemas chapter, is also a mixolydian schema, due to the major tonic and the \flat\hat{7}.

Subtonic shuttle

Transcription in notation.
Example 5. “Tired of Waiting for You” by The Kinks uses the subtonic shuttle in its intro and verses. Transcription begins at 0:07.

The most distinctive chord progression in mixolydian is the subtonic shuttle, ♭VII–I, or B♭–C in C major (Example 4 above). The subtonic shuttle is used continuously throughout the intro and first verse of “Tired of Waiting for You” by the Kinks (1965), where the instrumental parts shuttle between I and ♭VII throughout, while the melody emphasizes \flat\hat{7} as an embellishment and melodic goal.

Aeolian: ♭VII and ♭VI

You may think of aeolian as equivalent to the natural minor scale. As a key or collection, though, aeolian and minor are different, because aeolian (as used in pop music) will prominently feature unraised \hat{6} and \hat{7}. These color note scale-degrees give us the ♭VI and ♭VII chords, which are the signature chords of the aeolian mode. (Note the use of flat signs in label of ♭VI and ♭VII, even though they are diatonic in minor/aeolian—this is to prevent confusion with viiº.) Aeolian schemas use one or both of these harmonies (Example 6).  The ♭VI chord has subdominant function, and the ♭VII chord has dominant function.

notation of aeolian schemas
Example 6. The subtonic shuttle, aeolian shuttle, aeolian cadence, and lament schemas are four common aeolian chord progressions.

 

transcription in notation of intro and chorus
Example 7. “Somebody that I Used to Know” by Gotye features the subtonic shuttle in its intro/verses and the aeolian shuttle in its choruses. The Intro transcription begins at 0:04, and the Chorus transcription begins at 1:32.

Subtonic shuttle

The subtonic shuttle was introduced as a mixolydian progression, but the same progression can be used in aeolian. The difference is only in the quality of the tonic chord. If it’s major, then the subtonic shuttle implies mixolydian; if it’s minor, then the subtonic shuttle implies aeolian. In other words, ♭VII–i, or B♭–Cm in C minor, is the minor version of the subtonic shuttle. This subtonic shuttle is used in the intro and verses of “Somebody that I Used to Know” by Gotye (2011, Example 7).

Aeolian shuttle

Another common shuttle in aeolian is i–♭VII–♭VI–♭VII. This progression can be understood as a shuttle between i and ♭VI, with a passing ♭VII chord along the way. This progression is featured clearly in the chorus of “Somebody that I Used to Know” by Gotye (2011, Example 7).

transcription of the fellowship theme
Example 8. The Fellowship Theme from the Lord of the Rings soundtrack by Howard Shore concludes its phrases with an aeolian cadence. Transcription begins at 0:27.

Aeolian cadence

In the aeolian shuttle schema, the consistent shuttling back and forth between I and♭VI makes it difficult for a true cadence to be implied—a cadence means that a goal has been reached, but a circular progression like the aeolian shuttle doesn’t seem to have a goal. The aeolian cadence ♭VI–♭VII–i, or A♭–B♭–Cm, is similar to the aeolian shuttle, but is goal-oriented: it cadences on the tonic chord, and does not tend to be used as a loop. The aeolian cadence very frequently uses a picardy third, which means all the chords are major: ♭VI–♭VII–I, or A♭–B♭–C.

The aeolian cadence has a lot of cultural associations for many people, and is typically associated with success and heroism. The cadence concludes the phrases of the Fellowship Theme from Lord of the Rings (Example 8, begins at 0:27). The aeolian cadence has also been called the Mario cadence, since the well-known fanfare at the end of each level of Super Mario Bros. uses this progression; the progression is often heard as a fanfare in other video games, such as Final Fantasy. In all of these examples, the cadence concludes with a picardy third.

transcription of "I Don't Like You"
Example 9. “I Don’t Like You” by Eva Simons uses a lament schema with ♭VII and minor v.

Lament

The lament schema has many variations, as discussed in the chapter addressing that schema. One particular flavor, i–♭VII–♭VI–v, strongly implies the aeolian mode due to the absence of a leading tone, which would imply a minor tonality, in favor of the unraised \hat{7}, a color note of aeolian. This variation of the lament schema is heard in “I Don’t Like You” by Eva Simons (2012).

Dorian: IV with a minor tonic

Dorian is a mode that sounds like minor, but with a \sharp\hat{6} (Example 10), which, among other altered harmonies, yields a major IV chord (compare with the minor iv in minor). Using a major IV chord in songs with a minor tonic is the primary marker of a dorian song, which would otherwise sound like it was minor/aeolian. The IV chord in dorian usually has a subdominant function.

transcription
Example 11. “Get Lucky” is in B dorian, and features a characteristic IV–i motion every four bars (shown here by the arrows) to emphasize Bm as tonic.

The dorian mode is especially associated with funk, disco, and its derivative genres, where the dorian shuttle is especially pervasive. One example of many is “Dance, Dance, Dance” by CHIC (1979). Some people who haven’t listened to much music from these genres have trouble aurally recognizing the dorian shuttle, and hear it instead as ii–V. Listening to a lot of funk and disco should help you learn to hear that “ii chord” as a i chord, even in more ambiguously dorian songs like Daft Punk’s “Get Lucky” (2013, Example 11).

Dorian shuttle

The dorian shuttle alternates between a major IV chord and a minor i chord (Example 12). The overall effect of this progression is one of tonic prolongation. The upper notes of the IV harmony often form a neighboring motion that emphasizes \sharp\hat{6}. A common variation on the dorian shuttle is expanded to i–IV–i7–IV. This further expands the neighboring effect in the upper voices.

 

Notation of the dorian shuttle
Example 12. The dorian shuttle uses minor i and major IV. It can be expanded to arch up to i7.

Lydian: II♯

\sharp\hat{4} is the color note of the lydian mode, which results in a major II chord instead of the minor ii found in major (Example 13). This text refers to this chord as II♯ for clarity, with the sharp sign representing the raised third of the chord.

If II♯ goes to V, as it typically does in classical music, the chord should be understood as as a secondary dominant V/V instead. But in pop tunes, II♯ often leads elsewhere, necessitating the II♯ label.

Very few pop songs are truly in the lydian mode all the way through the song, but many major-mode pop songs use a major II chord in place of the typical minor ii, giving a brief lydian flavor while remaining overall in the major mode.

II♯ can have either subdominant or dominant function, and each is used in the following two schemas (Example 14).

notation of schemas
Example 14. The II♯ chord is the characteristic chord of lydian and is used in both of these schemas.

Lydian shuttle

The most basic lydian chord progression is a simple shuttle between II♯ and I. Identifying this chord progression correctly can be tricky: because few pop songs are truly in lydian throughout, this II♯ chord is often neutralized later in the chord progression with a IV chord or a ii chord, which means the song is overall in major, but with a brief II♯ chord. This progression can be heard with some alterations in the opening of “Sara” by Fleetwood Mac (1979). “Sara” expands the lydian shuttle to include a Imaj7 chord to harmonize an arching melody, and it also uses a tonic pedal underneath the II♯ chord. Later on in the song, the II♯ is neutralized by the use of a doo-wop schema. This is illustrated by Mark Spicer.

If it is never neutralized, it’s possible that the chord progression isn’t really I–II♯, but another shuttle that relates roots by step. For example, Taylor Swift’s “Starlight” (2012) has verses that alternate between A and B major chords (begins at 0:26), but they are IV–V in E major, not a lydian shuttle. This becomes clear in the chorus (0:56), which is harmonized with a rotation of the doo-wop schema. The subtonic shuttle discussed earlier in this chapter is another chord progression that relates two major chords by step. Remember that lydian is rare in pop music, and be careful when identifying this progression!

In this progression, II♯ functions as a dominant chord, leading back into the tonic with the half-step between \sharp\hat{4} and \hat{5}.

transcription in notation
Example 15. “Forget You” loops a lydian cadence throughout the song. The background vocals always have the characteristic chromatic line.

Lydian cadence

The most popular progression using II♯ is the lydian cadence II♯–IV–I, or D–F–C in C major. Notice that the lydian \sharp\hat{4} is immediately neutralized by the regular IV chord, replacing it with \natural\hat{4}. This schema also features smooth chromatic voice leading, which may partially explain the appeal of this progression. The clearest example of this schema may be Cee Lo Green’s “Forget You” (2010, Example 15)."Forget You" is the classroom-friendly version of the more explicit original.

Identifying modes by ear

If you are not used to playing in and listening to modes, it can be daunting to identify and distinguish modes by ear. Here is a step-by-step process for aurally distinguishing all the modes discussed here, illustrated as a flowchart in Example 16.

1. Identify the quality of tonic.

EXAMPLE 16. Flowchart illustrating the process of identifying modes by ear.

Listen for the tonic pitch. Then, listen for the whole tonic chord. Is the third of that chord major or minor? This distinguishes the major-ish modes (major, mixolydian, lydian) from the minor-ish modes (minor, aeolian, dorian).

2. Listen for \hat{7}.

Compare the \hat{7} to the leading tone a half-step below tonic that we typically hear in minor and major songs. If \hat{7} is a whole step below tonic, then it’s lowered, which means that the song is (at least temporarily) in a mode.

If you chose a major tonic, and \hat{7} is lowered, then you are in mixolydian. 

If you chose a minor tonic and \hat{7} is raised, then you are in minor. 

If your mode is not already identified, proceed to step 3.

3. Listen for other raised color notes—\hat{4} in major, and \hat{6} in minor.

\hat{7} did not identify the mode for you.

But if \hat{4} is raised in a major-tonic mode, you are in lydian. If it is not, you are in major. 

If \hat{6} is raised in a minor-tonic mode, you are in dorian. If not, you are in aeolian. 

Further reading
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39

Pentatonic harmony

Bryn Hughes

Rock music, and more generally, popular music, owes a great debt to the Blues tradition. One of the most pervasive scales in pop and rock music is the pentatonic scale, a five-note scale also firmly rooted in the blues. The pentatonic scale is related to the blues scale and the diatonic scale (it is a subset of both), but it contains no semitones. In popular music, the pentatonic scale is typically found in one of two rotations: the major pentatonic and the minor pentatonic scale (Example 1).

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Example 1. Pentatonic scales.

Though the two listed above are the most common, you can build five different versions of the pentatonic scale by simply rotating the notes in the scale.

In rock music,  a harmonic system based on the pentatonic scale is typically created by using the scale as chord roots of major triads or power chords. This leads collections of chords that don’t belong to any mode or scale (Example 2). Note that in both of the collections of chords in the example below, there is a scale degree “conflict.” The first collection includes both \flat\hat{7} and \hat{7}; the second collection includes both \flat\hat{6} and \hat{6}.

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Example 2. Pentatonic harmony derived from two different rotations of the pentatonic scale.

Though many of the chord progressions drawn from the pentatonic chord families listed above could be accounted for by other schemas, it is helpful to relate them back to the pentatonic scale in this way, due to the scale’s inextricable link to the guitar itself, and especially to guitar solos that are performed in combination with these chord progressions.

Example 3 shows an excerpt from the Stevie Wonder song “Higher Ground,” in which the pervasive harmonic loop can be understood as derived from the pentatonic scale.

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Example 3. Stevie Wonder, “Higher Ground” (1973).

40

Melodic-harmonic divorce

41

Fragile, Absent, and Emergent Tonics

Megan Lavengood

Key Takeaways

  • Most songs have a clear tonic.
  • Tonal ambiguity arises when there is not enough information to confidently assign a tonic chord.
  • Tonal ambiguity occurs in pop songs in one of three ways:
    • Fragile tonic: the tonic chord is used in the song, but is weakened through inversion or another similar technique
    • Emergent tonic: the tonic chord is withheld until a triumphant moment, such as the chorus
    • Absent tonic: the tonic chord is implied through melody and harmonic conventions, yet never explicitly stated.

 

Chapter Playlist

Although many pop songs are harmonically simple, using only a handful of chords in root position, this can sometimes lead to tonal ambiguity. One way that tonal ambiguity is created is through de-emphasizing the tonic chord. According to pop theorist Mark Spicer, whose work is the basis of this chapter, this occurs through one of three techniques: fragile, absent, and emergent tonics.citation later

Fragile tonic

The fragile tonic technique is one in which the tonic chord is used in the song, but is weakened through inversion or another similar technique. Fragile tonics can be found in music by artists that seem to have composed at the piano, as in Sufjan Steven’s “Oh God Where Are You Now” (2003). The tonic chord, G♭, is only found as an incomplete passing chord in the midst of a contrapuntal series of parallel 10ths in the C phrase (Example 1). Otherwise, first-inversion E♭ minor chords are found where tonic chords may otherwise be expected.

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Example 1. “Oh God Where Are You Now? (In Pickerel Lake? Pigeon? Marquette? Mackinaw?)” by Sufjan Stevens uses a fragile tonic.

Fragile tonics usually connect to a theme in the lyrics of loneliness, vulnerability, and sensitivity. The Sufjan Stevens song in Example 1 follows this principle: the narrator in the lyrics seems to be desperate for comfort from God, and thus in a vulnerable state. Another example of a song that uses a fragile tonic to emphasize vulnerability is Elton John, “Somebody Saved my Life Tonight” (1975).This example comes from Spicer 2017.

Emergent Tonics

Songs with emergent tonics withhold the tonic chord until a triumphant moment, such as the chorus. The song will begin by using other chords, especially the relative major/minor, some of which may sound like tonic at first; but later in the song, the true tonic is revealed to be another chord that either did not sound like tonic initially or was not present at all.

Emergent tonics often accompany lyrical themes of triumph and overcoming, and this is just what happens in “Let It Go” from the movie Frozen. Listen to the song while following the form chart below (Example 2), which explains how the tonic emerges. The emergent tonic here emphasizes the theme of Elsa overcoming her self-doubt and owning her identity.

 

Thumbnail for the embedded element "Let It Go - From "Frozen"/Soundtrack Version"

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timestamp section chord progression notes
0:00–0:14 intro Fm–D♭–E♭–B♭(m) at this point in the song, the tonality sounds like F aeolian (i–VI–VII–iv).

The B♭ chord alternates between minor and major in subsequent repetitions of this progression, and the third time this happens, it's used to lead into the next section.

0:15–0:42 verse
0:43–0:58 prechorus E♭–D♭ Now the tonality has shifted: E♭ sounds like tonic, which implies a key of E♭ mixolydian (I–♭VII). The B♭ chord that closed the previous verse, in retrospect, sounds like it was a V in E♭ mixolydian.

But this progression also gets turned around! The closing D♭ chord is prolonged at the end of the prechorus to lead into the next section.

0:59–1:26 chorus A♭–E♭–Fm–D♭ A♭ major is triumphantly revealed as the emergent tonic. This means, in retrospect, that the ending D♭ of the prechorus was really a IV chord, leading into the singer/songwriter progression of the chorus (I–V–vi–IV).

(The end of the chorus also features a little chromatic diversion—after the last repetition of the singer/songwriter schema, the next chord is A♭/C followed by C♭ major, before resolving back up to the D♭).

1:27–1:31 interlude A♭–E♭/G A brief instrumental connects to the verse with a I–V progression…
1:32–1:44 verse Fm–D♭–E♭–B♭m Although this verse has the same progression as the first verse, because we've now heard the emergent tonic, the chords now sound more like vi–IV–V–ii instead. Similarly, the prechorus now sounds like a V–IV progression, building up energy toward the cadence by withholding the tonic (a classic prechorus function). The major tonality from the chorus still governs the song, even when the A♭ chord is missing.
1:45–1:59 prechorus E♭–D♭
2:00–2:25 chorus A♭–E♭–Fm–D♭
2:26–3:01 bridge D♭———
E♭———
Fm–D♭–E♭–B♭m
D♭
The bridge lets D♭, E♭, and Fm sound like tonic for a brief moment, but they are ultimately subsumed within the A♭ major tonality in the following chorus repeats.

(Notice how "I'm never going back" accompanies the verse progression heard at the outset of the song—"going back" to the opening progression!)

3:02–end chorus A♭–E♭–Fm–D♭

Example 2. Form chart of “Let It Go.”

You could also understand this song as using a different key for each section—F aeolian for the verses, E♭ mixolydian for the prechoruses, and A♭ major for the choruses. Undeniably, this is certainly what seems to be going on when first listening to the intro and prechorus.

While that is a perfectly acceptable analysis, notice how analyzing this song as belonging entirely to A♭ major allows for a nice narrative parallel between the chord progression and the lyrics: In the first verse, Elsa (the singer) begins the song describing a bleak, cold night, accompanied in the harmony by chords that emphasize the vi chord instead of tonic. In the prechorus, as Elsa wrestles with a choice between pleasing society (“be the good girl”) or letting it go, which is accompanied by repeating IV and V chords increasingly demanding a resolution. Right when Elsa makes up her mind—she decides to “let it go”— A♭ major, the tonic, finally brings resolution to the oscillation between IV and V in the prechorus, underscoring Elsa’s inner transformation.

Another example of an emergent tonic is “Little Red Corvette” by Prince (1982), which seems to be in B♭ minor until D♭ emerges as the true tonic chord in the chorus.This example comes from Spicer 2017.

Absent Tonics

The most extreme manipulation of our sense of tonic occurs when a song has an absent tonic. An absent tonic never actually materializes as a heard harmony in the song, but instead is established only melodically and by using familiar harmonic progressions that do not involve the tonic.

“Last Friday Night” by Katy Perry (2012) is an example of a song with an absent tonic. The progression is very conventional—IV–ii–vi–V—but I never sounds. The melody, as can be seen in Example 3, strongly outlines F♯ major in the chorus, with repeated descending [hat]3[/hat]–[hat]2[/hat]–[hat]1[/hat] lines. This melody combined with the familiarity of the chord progression, allow F♯ to sound like tonic even when it never occurs in the accompaniment.

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Example 3. The chorus of “Last Friday Night” by Katy Perry.

As with fragile and emergent tonics, absent tonics can also be interpreted as representations of lyrical themes. In the case of “Last Friday Night,” the absent tonic may depict the disconnect between constant partying and a need to function in the real world.

Further reading

VIII

Post-Tonal Music

42

Intervals

Brian Moseley and Megan Lavengood

Key Takeaways

  • In atonal music, intervals are usually measured in semitones, rather than using tonal interval names.
  • There are four types of interval: Ordered pitch intervals, unordered pitch intervals, ordered pitch class intervals, and interval classes (unordered pitch class intervals).
  • Ordered pitch intervals are as specific as possible: they measure specific pitches (in specific octaves) and represent the directionality of the interval.
  • Interval classes are the most abstract type of interval: they represent the smallest possible distance between two pitch classes.

In tonal music, because intervals are dependent upon the pitches that create them, the consonance and dissonance of intervals is determined by tonality itself. Imagine the interval create by G and B♭, a minor third. In the context of G minor, this is a consonant interval. Respelled as G and A♯, perhaps in the context of B minor, it creates a dissonant augmented second. From a tonal perspective, the two intervals are different even though they are the same in isolation (Example 1).

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Example 1. Even though B♭ and A♯ are the same key on the keyboard, the intervals of a minor third and an augmented second are distinct in tonal theory.

Contrast this with atonal music. Because atonal music has no tonality, the distinction between B♭ and A♯ no longer matters. For us, the intervals G–B♭ and G–A♯ are the same. For this reason, we will not use tonal interval names like “minor third.” Instead, we will measure the intervals by the number of semitones between the pitches or pitch classes.

We can describe intervals according to two types of information: pitches vs. pitch classes, and ordered vs. unordered intervals. Combined, this makes four types of intervals, summarized in Example 2. Each of these interval types is explained below.

  pitch intervals (pi) pitch class intervals
ordered intervals ordered pitch intervals ordered pitch class intervals
unordered intervals unordered pitch intervals unordered pitch class intervals / interval classes (IC)

Example 2. Four interval types in atonal theory.

Pitch intervals (pi)

Notation
Example 3. The top row of examples shows ordered pitch intervals: the number of semitones between the pitches, with a plus or minus sign to indicate direction. The bottom row shows unordered intervals, which simply disregards the direction, and thus drops the plus or minus sign.

Pitch intervals are the distance between pitches as measured in half steps, which is to say that octave is taken into consideration. Thus, the interval C4–E4 is 4: four half steps are between these notes. But if that E is moved up an octave (C4–E5), the interval becomes 16: four half steps between C and E, plus an octave (twelve half steps) between the lower E and the higher E.

Within pitch intervals, there are ordered and unordered variants. To create an ordered pitch interval, simply add a plus or minus sign, to indicate whether the interval is ascending or descending. Unordered pitch intervals, by contrast, do not indicate which direction the pitches move in—they are thus more suitable for harmonic intervals. The differences between ordered and unordered pitch intervals are summarized in Example 3.

Unordered pitch-class intervals

Pitch-class intervals are the distance between pitch classes as measured in semitones. Returning to our C4–E5 interval, we are now interested just in the pitch classes C and E. To go from C to E in pitch-class terms, we just have to move up 4.

Ordered pitch-class intervals measure the distance between pitch classes, always ascending. This is visualized most easily by picturing the twelve tones around a clock face, and measuring the interval by going around the “clock” in clockwise fashion. Thus, from C to E = 4, but E to C = 8 (Example 4).

notation
Example 4. Ordered pitch class intervals always travel clockwise around the clock face.

Interval class

Unordered pitch-class intervals are usually called interval classes. Interval class is the smallest possible distance between two pitch classes. On the clock face, this means traveling either clockwise or counter-clockwise, whichever is shortest. Interval class is a useful concept because it relates intervals, their inversions, and any compound versions of those intervals. You should be able to connect this concept to the concept of pitch vs. pitch class: a pitch class is a pitch, its enharmonic respelling(s), and any octave displacements of those spellings.

This means that there are only six interval classes: 1, 2, 3, 4, 5, and 6. If you reach the pitch class interval of 7, it becomes shorter to move counter-clockwise, and 7 becomes 5. For the same reason, 8 becomes 4, 9 becomes 3, and so on. Both C–E and E–C are interval class 4 (Example 5).

notation
Example 5. Unordered pitch class intervals are also known as interval classes. Interval classes measure the smallest possible distance between pitch classes.

Summary

Using various combinations of pitch interval, pitch-class interval, ordered, and unordered, we arrive at four different conceptions of interval.To wrap your mind around each of these and begin to understand their various analytical uses, think of them on a sliding scale of most concrete — the ordered pitch interval — to most abstract — the unordered pitch-class interval. You can find this related to other concepts in the Set Theory Quick Reference Sheet.

As you analyze atonal music, you will find that different types of interval are useful for describing different types of phenomena. This is exactly like how, in tonal music, it’s useful to distinguish between a 13th and a 6th in some situations, but not others.

Further reading
  • Straus, Joseph Nathan. 2016. Introduction to Post-Tonal Theory. 4th ed. Upper Saddle River, NJ: Prentice Hall.
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43

Collections and Scales - Analytical Considerations

Mark Gotham

In Theory

So, you’re faced with a new piece of music of music and you get the sense that it might be worth considering a modal view. It sure isn’t ‘tonal’ in the common practice sense, but neither does it seem ‘atonal’, ‘serial’, or the like. How do you go about identifying the modes used, and making analytical observations on that basis? In 20thCentury music, apart from having a wider range of modes to contend with, we also don’t usually get a key signature of any other notational shortcut to identify ‘the mode’. As such, it’s especially important to be able to identify modes from musical cues.

Firstly, let’s review some of the different considerations that can go into the definition of a mode:

  1. A collection of pitches in a particular intervallic relationship (e.g. C,D,E,F,G,A,B);
  2. ‘A tonic’ or final which acts as a primary or referential point (e.g. C);
  3. Further hierarchical levels between the pitch in the mode, and the primary, tonic pitch (e.g. G, and F).
  4. Melodic shapes and range considerations;

No.1 reminds us that modes can be transposed. While we often present the ‘early’ modes in their ‘white-note’ transposition (with Dorian on D, for instance), in 20thCentury music, you can just as easily have them on other pitches such a have Dorian on E and Phrygian on D. This leads to the frankly confusing terminology ‘D mode on G’. Don’t forget that you can also have ‘chromatic’ notes in modal music. Not every pitch used needs to be in the scale. So the question is, how many exceptions are too many?

No.2 helps to separate all the possibilities that No.1 throws into mix. If you only have white notes, which of those white notes is the modal final? All and any musical parameters might contribute to the case for one of those pitches as tonic; for a useful starting point, try the widely-applicable ‘first, last, loudest, longest’ maxim (Cohn 2012:47, after Harrison 1994:75ff.). Pitches that dominant in those ways tend to be marked for consciousness. Do phrases tend to start and / or end on a certain pitch, or emphasize that pitch in other ways, perhaps with strong metrical positions, or by reserving it for the top of the melodic contour?

No.3 also speaks to this difficulty. For instance, in tonal music you might well get more dominant notes than tonics – they fit in both the tonic and dominant chords, after all! 20thcentury modes complicate this with a more diverse set of candidates for hierarchical importance, but this can also help us to unpick the different roles. ‘First’ and ‘last’ might be your tonic; while the ‘dominant’ may be ‘loudest’ and ‘longest’. We might also use a less loaded-term than ‘dominant’ here. For instance, the early modes (discussed in the previous chapter) had a ‘tenor’ or ‘reciting tone’ in an analogous role, as shown on the table below.

Name Final Tenor Range   Name Final Tenor Range
Dorian D A D-D Hypodorian D F G-A
Phyrygian E C! E-E Hypophrygian E A! B-B
Lydian F C F-F Hypolydian F A C-C
Mixolydian G D G-G Hypomixolydian G C! D-D
+
Aeolian A E A-A Hypoaeolian A C E-E
Locrian B G! B-B Hypolocrian B E! (F)-G
Ionian C G C-C Hypoionian C E G-G

There are many reasons for promoting specific pitches in this way. One reason relevant to 20thcentury music is the notion of ‘characteristic notes’ as Persichetti had it, like the Lydian 4th, or the Phrygian 2nd. Without these notes, the term is unlikely to be relevant. You also need the tonic to stay put. For listeners accustomed to common practice tonality, the Lydian fourth (e.g. F# in C major) can very easily become a leading note in the dominant (G major). Otherwise tonal works written ‘in the Lydian mode’ can be highly ambiguous in this respect. Consider what you make of Beethoven’s ‘Heiliger Dankgesang’ from the Op.132 quartet and Bruckner’s Os Justi (WAB30) to this effect.

The table of ‘early’ modes also flags up the role that range considerations can play. This was fundamental to the definition of early modes in terms of authentic vs plagal forms, and has been a key consideration in many other musics besides. Likewise, melodic shapes have been key considerations for the definition of modes in many and varied musical contexts.

In Practice

So far, so investigatory; what about the really analytical? Well, all of this difficulty (or otherwise) in coming up with a modal reading is part of the analytical process. It’ll all depend on the work in question, of course, but here are some starting points for pivoting from one to the other:

Consider the three moments below which come from Bartók’s From the Island of Bali. Is the same mode in operation throughout or does it change? What pitches are in / out of the mode(s)? Does a modal final present itself? Are there any moments where two modes are combined? Some suggestions follow the images, so decide on what you think before scrolling down to compare notes.

I think of first case as being wonderfully ambiguous in relation to both mode and final. If you put the hands together, the pitches constitute a neat octatonic mode, but if you keep them apart then it’s the 1:5 distance model mode often associated with Bartók, or might even be best described by the pitch class set [0167]. There’s good Bartókian symmetry in all of this, and very little sense of a single modal final emerging.

In the latter two cases, I hear a strong sense of tonic arrival on the first downbeat, suggesting Gb and Eb and the respective tonics for these sections. So far, so different, but notice how closely the pitches relate to the opening. First we have [B,C,F,Gb], which were the exact pitches of the RH at the start. (Do you spot the one ‘chromatic’ note in this reading? I hear the one Abb as a chromatic upper neighbour note that doesn’t really ‘fit’ the mode).

Later we have [A,Bb,D,Eb] which are a close variant on those of the LH. I see this change as indicating a move from that opening ambiguity to a passage quite neatly redolent of Eb major which is swifty undone as the piece goes back to the technical and emotional place where it started.

So we have a balance between unity and variety, as well as trajectory for the piece overall, and that’s without even getting into the ‘East meets West’ implication of the title …

Media Attributions

  • Bartok1
  • Bartok2
  • Bartok3

1

Bibliography

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Glossary

12-bar blues progression

Comprised of three (typically) four-bar phrases. The first phrase is entirely tonic harmony (I). The second phrase contains two bars of subdominant (IV) and two bars of tonic (I). The final phrase begins with one bar of dominant (V) followed by one bar of subdominant (IV) and two bars of tonic (I). The third phrase may or may not end with a turnaround.

16-bar blues progression

A variation on the 12-bar blues progression. Composed of four (typically) four-bar phrases, usually two iterations of tonic, followed by subdominant and dominant. The final phrase may or may not end with a turnaround.

AABA form

Also called 32-bar song form. AABA consists of at least four sections. It begins by repeating two strophes, moving to a contrasting bridge section, and then repeating the primary strophe again. AABA forms typically then include another repetition of BA, making the entire form AABABA.

absent tonic

The tonic is never actually sounded as a harmony during the song, but is still implied through the melody or through the use of conventional harmonic progressions.

accidental

One of many symbols (the sharp (♯), flat (♭), and natural (♮) among others) that alter a pitch

acoustics

The physical science of sound.

aeolian cadence

♭VI–♭VII–i, or A♭–B♭–Cm in C minor. This schema implies the aeolian mode. Very frequently, the i chord is altered to be major, yielding a sequence of three major chords related by steps in the same direction. This progression, especially with a major I chord, is often associated with heroic themes in video games and movies.

aeolian shuttle

i–♭VII–♭VI–♭VII. This progression can be understood as a shuttle between i and ♭VI, with the intermediate ♭VIIs acting as passing chords.

alternative path

A technique of internal phrase expansion. It occurs when new material causes a phrase to deviate from its expected trajectory toward the cadence. These deviations may be permanent ("reroutes") or temporary ("detours").

alto

Also known as a "C" clef, an alto clef designates the lowest line of a staff as the pitch F3

antecedent

A phrase comprised of a basic idea followed by a contrasting idea that ends with a weak cadence.

antiphony
applied chord

A chord from another key inserted into a new key, in order to tonicize another diatonic chord other than I.

archetype

Phrases that are "archetypal" or that follow an archetype are related to the sentence, the period, or one of the hybrid phrase-level forms.

ASPN

A method of specifying musical pitches by combining note names with octave designations

audiate

To imagine hearing a sound in one's mind

aural

Auditory; related to hearing

authentic cadence

A cadence with the harmonies V–I. The harmonies are typically in root position. Authentic cadences can be further distinguished by their melody note in the I chord: an authentic cadence ending on scale-degree 1 in the melody is a perfect authentic cadence, while one with 3 or 5 in the melody is an imperfect authentic cadence.

auxiliary section (song form)

Auxiliary modules help frame the core modules, introducing them, providing temporary relief from them, or winding down from them.

Auxiliary Sections (classical form)

Sections that introduce, follow, or come between a work's core sections (A, B, primary & secondary themes, refrains, episodes, and developments/digressions/contrasting middles). Auxiliary sections are either external or internal. External Auxiliary Sections either introduce a piece/section (prefix) or follow the piece's/section's generic conclusion (suffix). Prefixes and suffixes come in small and large varieties. Internal auxiliary sections (connective sections) function to connect two core sections. Transitions generally help lead away from the piece's main section toward a contrasting section (B, secondary theme, episodes, developments/digressions/contrasting middles), and retransitions generally help to lead back to the piece's main section (usually A or a sonata form’s primary theme).

backbeat

An accent on beats 2 and 4 of a quadruple meter. Backbeats are common in jazz and pop styles.

Balanced Binary Form

Balanced is a term used to describe an aspect of a binary form (either simple or rounded). It means that the tail end of the first reprise, returns at the tail end of the second reprise. That return will be in the piece's home key even if it was in another key in the first reprise. In order to be considered a return, there needs to a crux point, that is a particular moment where the restatement begins at the tail end of the second reprise. This restatement is the point at which there is a direct bar-for-bar mapping of measures between the tail end of both reprises. Importantly, this excludes rounded binary examples where the entire first reprise is repeated verbatim in the second reprise because there is no crux point at the tail end of the second reprise.

basic idea

Basic ideas are short units that are typically associated with beginnings. They don't usually end with cadences, and they often establish tonic. They are they first units we hear in a presentation, an antecedent, a consequent, and a compound basic idea.

bass

Also known as the "F" clef, a bass clef designates the lowest line of a staff as the pitch G2

beam

The horizontal lines that connect certain groups of notes together

Becoming ⇒ (the process of)

The process of becoming is an analytical phenomenon that captures an in-time, analytical reinterpretation regarding a formal/phrasal unit's function. In this situation, a formal/phrasal label at first seemed fitting, but as that unit continues in time, a different label seems fitting. Even upon re-listening, this process of conversion is likely to still be experienced. The rightwards-double arrow symbol (⇒) is often used to denote this process. Examples include, primary theme ⇒ transition, continuation ⇒ cadential, suffix ⇒ transition, and any number of other combinations.

beginning

One of three formal functions (with the other two being middle and ending). Beginnings are often signaled by: establishment of a new melody, or repetition of the beginning of a previously heard melody, emphasis on tonic harmony (especially root position), a melody that opens up musical space by ascending, statement of a motive that is developed through the remainder of the phrase.

Binary Form

In the context of musical form, the term binary means a formal type that has two main parts often called reprises because each main part is typically repeated. There are three types of binary form: rounded, balanced, and simple. Binary forms are common in the 17th, 18th, and 19th centuries and they were used heavily in dance music. Binary form is typically one of the shorter forms and because of that, they are often embedded within larger, compound, forms like compound ternary form.

blue notes

Notes whose exact pitch sounds somewhere between the flat and regular versions a scale degree, particularly scale-degree 3 and 7.

bridge

Bridges tend to play a transitional role (neither the point from which to depart, nor the point of arrival) in the formal cycle, generating high expectation for the return of the primary section by contrasting with it and temporarily withholding it. Bridge sections tend to emphasize non-tonic harmonies and commonly end on dominant harmony.

cadence

A melodic and harmonic goal. In classical tonal music, cadence types include Perfect Authentic (PAC), Imperfect Authentic (IAC), and Half (HC).

cadential

One of the three common ending types. Its distinguishing characteristic is its bass line: M-F-S-D, which may be elaborated with chromaticism.

call-and-response

A feature of musical phrasing that features a simulated dialogue between two instruments or groups of instruments.

chord loops

Repeated chord progressions, often four bars long, that are repeated throughout a portion or all of a song.

chord substitution

Replacing a standard chord (i.e., within a harmonic schema) with a different chord. The substituted chord is typically identical in harmonic function to the standard chord, and often shares at least two notes with the standard chord.

chorus

Chorus sections are lyric-invariant and contain the primary lyrical material of the song. Chorus function is also typified by heightened musical intensity relative to the verse, including features like “a more dense or active instrumental texture; prominent background vocals; and/or a higher register melody” (Summach 2012, p. 106). Choruses most frequently (but not exclusively) begin on-tonic.
Chorus sections are distinct from refrains primarily by virtue of their being sections in and of themselves, where refrains are contained within a section.

chorusification

A process where modules are stripped away from the formal cycle until only the chorus module (C) remains.

chromatic

Relating in some sense to the chromatic scale. The term may be used to refer to notes that are outside the given key.

clef

A symbol placed on the left side of a staff, which indicates which notes are assigned to different lines and spaces

Closed vs Open endings (a.k.a. sectional and continuous)

An important factor in influencing the stability of a section is how the section closes harmonically. If the section closes with an authentic cadence (either PAC or IAC) in the home key, the section is harmonically closed but any other close is considered harmonically open. Examples of open harmonic endings are half cadences and any type of cadence involving a modulation, that is, a PAC in the key of the dominant is still harmonically open because of the modulation.

closing rhetoric

Closing rhetoric involves common patterns and techniques that signal that the end of the song is likely coming soon.

coda

A coda is a song-ending section that presents new material. Like outros, codas exhibit closing rhetoric.

Coda (classical)

A type of suffix (external auxiliary section). Codas are usually of the large variety (a phrase or longer), and they occur at the end of a work (or end of a movement within a multi-movement work) after the PAC that ends the piece proper. The word coda is Italian for “tail” because they are found at the tail end of a work. Sometimes composers communicate the location of the coda by writing the word in the score but this is not necessary to identify a section as a coda. Like all suffixes, codas are considered an expansion technique and therefore the are not essentially to the structural content of the work and it is often said that the work would still make complete syntactic sense if it were removed entirely.

codetta

A type of suffix (external expansion). Codettas are usually medium length (for example, between 4-8 measures), they often occur at the end of a section within a piece, and they often feature repeated units. They may or may not contain a full phrase.

collection

A group of pitches being used as the basis for a composition. This term is more neutral than "key," which may imply a hierarchy.

color note

For modes in pop music, the color note is the pitch that distinguishes a mode from major (in the case of mixolydian/lydian) or from minor (in the case of dorian/phrygian).

common tone

A tone that is present in more than one chord.

compound basic idea

A compound basic idea (c.b.i.) is an antecedent without a cadence. It consists of a basic idea followed by a contrasting idea. The reason it's called "compound" is that it often forms the basic idea for a large sentence, one in which the presentation is 8 measures long and consists of two four-measure c.b.i. units as stand-ins for the archetypal two-measure b.i.s

compound form

Occurs when one form is comprised of other smaller forms. For example, a period may be comprised of two sentences, or one or more of a ternary form's sections may be comprised of a binary form.

compound interval

An interval that is larger than an octave; or, the process of adding an octave to an interval. For example, you might say "a 9th is a compound interval," because it is larger than an octave. You could also say "a 9th is a compound 2nd" to indicate that a 9th is equivalent to a 2nd plus an octave.

Compound Ternary Form

A type of ternary form, where each of the form's parts (A B A′) each contain their own complete form, typically a type of binary form. In some compound ternary forms, only A is compound and in others only the first A is compound and the second A is shortened in some way and is not a complete form itself. The clearest examples of compound ternary forms can be found in the minuet-and-trio movements of the mid to late 18th century.

consequent

A phrase comprised of a basic idea followed by a contrasting idea that ends with a strong cadence. It usually forms the second half of a phrase-level form.

continuation

A subphrase that features a mix of any of the following: fragmentation, increase in harmonic rhythm, increase in surface rhythm, or sequences. Continuations end with a cadence and are usually found in the second half of a theme.

contraction

Contraction refers to the process of making a phrase shorter than we expect. It always occurs within a phrase.

Contraction (of a motive)

making the durations of a motive shorter than the original

contrasting beginning

The contrasting beginning is like an antecedent without a cadence. It is a beginning part of a phrase-level form that's comprised of a basic idea followed by a contrasting idea, and it doesn't end with a cadence.

contrasting idea

A small unit that contrasts with the material that came immediately before it, usually in terms of contour. It's featured in the antecedent and the compound basic idea.

Core (classical)

A core section is formal category including both main sections (e.g., A, primary theme, refrain) and contrasting sections (e.g., B, C, D, secondary theme, episode, contrasting middle, development, digression). In contrast to auxiliary sections, core sections present the main musical material of a work and generally represent the bulk of a composition.

core bass pattern

A core bass pattern is the basic series of notes that defines a common progression. This series of notes may be embellished with other, less important notes, but the pattern is still recognizable because the basic series is still present.

core section

Core sections comprise the main musical and poetic content of a song. Core sections include strophe (AABA and strophic form only), bridge, verse, chorus, prechorus, and postchorus.

Crux

The moment that the tail end of the first reprise returns at the tail end of the second reprise of a binary or sonata form. This moment is the beginning of a series of corresponding measures between those two formal locations. If the first reprise contained a modulation, then the corresponding measures of the second reprise will now be transposed to the home key. The term crux was coined by James Hepokoski and Warren Darcy in their book Elements of Sonata Theory.

cycles

A cycle is a grouping of contains one or more sections, typically in the same order. Sometimes one or more sections are omitted in the repetition of a cycle, especially toward the end of a song.

detour

A type of alternative path. A detour creates a temporary deviation from a phrase's expected trajectory toward a cadence. Detours are initiated by a diversion onto the detour and they end with a resumption of rhetoric from earlier in the phrase.

diatonic

A scale, mode, or collection that follows the pattern of whole and half steps WWHWWWH, or any rotation of that pattern. This term may also be opposed to "chromatic," in which case "diatonic" indicates that a note belongs to that collection.

diatonic harmony

Harmony that is based in a diatonic scale, such as the white notes of the piano. Diatonic harmony uses only chords within the scale, and is usually labeled with Roman numerals.

Displacement (of a motive)

Changing the metric position of the motive relative to its original statement.

dominant function

A harmonic function that provides a sense of urgency to resolve toward the tonic chord. Dominant function is most typically associated with the V chord, otherwise known as the dominant chord, but the viiº chord[/strong, otherwise known as the leading tone chord, is also a common dominant-function harmony.

dominant seventh chord

A seventh chord in which the triad quality is major and the seventh quality is minor. For example: C–E–G–B♭.

doo-wop schema

 𝄆I – VI – IV – V 𝄇, or C – Am – F – G in C major. 

Common alterations: substituting ii for IV; rotation.

dorian shuttle

IV–i, or F–Cm in C minor. This shuttle implies the dorian mode. It can sound like ii–V to someone who is not used to the dorian mode.

double flat

Lowers a note by two half-steps

double plagal schema

♭VII–IV–I, or B♭–F–C in C major. The term comes from duplicating the plagal relationship (IV–I) by applying it to IV as well (IV/IV–IV, or ♭VII–IV).

double sharp

Raises a note by two half-steps

doubling

Duplicating some notes of a chord in multiple parts.

Elision (phrase/form)

An elision is the overlapping of two phrases that functions as the ending of one phrase and the simultaneous beginning of the next.

emergent tonics

"The tonic chord is initially absent yet deliberately saved for a triumphant arrival later in the song, usually at the onset of the chorus." (Mark Spicer, "Fragile, Absent, and Emergent Tonics in Pop and Rock Songs," 2017).

energy gain

A quality in a passage of music that heightens the "energy" of the passage. This can be through more active rhythmic activity, faster harmony changes, thicker texture, expanded range, crescendo, or drive toward a cadence or goal.

enharmonic equivalence

Notes, intervals, or chords that sound the same but are spelled differently

Enlargement (of a motive)

Making the durations of a motive last longer than the original.

Episode

A term used when describing the sections of a rondo form that are not the main theme (a.k.a. A or refrain). Episodes provide contrast with the main theme through changes in multiple domains, primarily key and melodic/rhythmic/harmonic material.

expansion

Expansion refers to the process of making a phrase longer than we expect. This lengthening might occur within the phrase ("internal expansion") or outside of the phrase ("external expansion").

extended cadential ending

An extended cadential ending is like a continuation , but it always harmonizes the core bass pattern M-F-S-D.

extension (harmony)

Adding additional thirds on top of the triad. Most commonly refers to 9ths, 11ths, or 13ths rather than 7ths, although 7ths are also extensions.

external expansion

Lengthening a phrase by adding extra material to it either before it's begun ("prefix") or after it's cadenced ("suffix")

flag

A curved line placed at the end of a stem

 

flat

Lowers a note by a half-step

Foot

A combination of two or three syllables: typically one stressed syllable, and one or two unstressed syllables.

form

Refers to the structure of a passage or piece. Form can be understood as a hierarchical grouping of units, and we often speak of form at one or of two levels: phrase-level form (referring to motives, ideas, subphrases, or phrases) or composition-level form (referring to sections, movements, or whole pieces).

fragile tonic

The tonic chord is present, but weakened. Usually, the weakening comes from using the tonic chord in inversion, or otherwise from placing the tonic chord in a metrically unstable mid-phrase position (versus a more typical usage where the tonic is a stable point of arrival or departure). This term comes from Mark Spicer, "Fragile, Absent, and Emergent Tonics in Pop and Rock Songs" (2017).

Fragmentation

Making unit sizes smaller than the previously established size. For example, if units had previously been 2 measures long, fragments might be 1 measure long.

function

The role that a musical element plays in the creation of a larger musical unit.

generic interval

The number of scale steps between notes of a collection or scale

grand staff

Two staves placed one above the other, connected by a brace. The top staff has a treble clef, while the bottom staff has a bass clef.

ground bass

A repeated bass pattern that formed be foundation for a set of variations, not unlike the cyclical progressions of pop/rock songs.

half cadence

A kind of inconclusive cadence that occurs when a phrase ends on V. Occasionally, particularly in Romantic music, the final chord of a half cadence will be V7.

half-diminished seventh chord

A seventh chord in which the triad quality is diminished and the seventh quality is minor. For example: B–D-F-A.

half-step

Generally considered to be smallest interval in Western musical notation

harmonic rhythm

The rate at which chords change, usually expressed in chords per measure. A common rate of chord change in 18th-century classical music is 1 chord per measure, for example.

harmonically closed

A phrase or module is harmonically closed when it ends with tonic harmony (I in root position).

harmonically open

A phrase or module is harmonically open when it ends on a harmony other than tonic.

harmonics

An overtone of a complex sound that occurs at a whole-number ratio to the fundamental.

harmony

A vertical sonority.

head refrain

A refrain that is the first line or so of the section's text.

Hertz

A measurement of the frequency of a sound. Frequency is another word for the number of cycles of peaks and valleys there are per second (frequency) in a waveform.

Home Key

A term used to describe a piece's overall tonic. If a movement is in the key of A major, then the home key is A major. The term is used to distinguish itself from local keys.

hopscotch schema

IV–V–vi–I. This four-chord schema has become increasingly common in pop music since 2010.

hybrid form

A hybrid form is one that combines aspects of the sentence and the period into one phrase-level form.

iamb

A poetic foot consisting of one stressed syllable followed by one unstressed syllable.

idea

The smallest unit of music identified by a segmentation analysis. Ideas need not end with cadences, and they may combine to form subphrases or phrases. Examples include: basic idea, contrasting idea, unit, cadential idea, and fragments.

ii–V–I

ii7–V7–I∆7 in major, or iiø7–V7–i7 in minor. A fundamentally important progression in traditional jazz. 

imperfect authentic cadence

A V-I cadence in which (1) V, I, or both harmonies are inverted, and/or (2) Do (scale-degree 1) is not in the soprano over the tonic triad.

Additionally, IACs are often used to evade a cadence. Please see the chapter on cadences for a more thorough discussion.

inflected

Chromatically altered from the typical version.

internal expansion

Making a phrase last longer than we expect by lengthening it after it's begun, but before it's cadenced.

interval

The distance between two notes

interval class

The smallest possible distance between two pitch classes. The largest interval class is 6, because if order is disregarded, the tritone is the largest possible interval. A P5 can be inverted to a smaller P4, m6 to M3, and so on.

intro
Introduction (classical form)

A section of music that occurs before the start of the musical form proper. In faster movements, introductions tend to have noticeably slower tempi. Introduction can range considerably in length, ranging from less than a single phrase (small prefix) to one or more phrases (large prefix). In the 18th century, introductions often contained independent musical material that doesn't appear in the rest of the work proper, but in the 19th century, composers tended to explore the integration of the introduction's material with the rest of the work.

introduction (song form)

Introduction sections transition from the unmetered silence that precede the song to the musical activity of the first core section. They tend to be short and untexted (i.e., instrumental) and tend to present musical material from one or more core sections to come.

Inversion (of a motive)

Changing the direction of the motive (e.g. instead of going up, it goes down)

kinesthetically

Relating to movement of parts of the body

lament schema

A harmonization of a descending upper tetrachord (1–7–6–5) in the bass.

lead sheet

A type of jazz score that notates only a melody (and perhaps some bare-bones countermelodies) and the chord symbols.

leading tone

Scale-degree 7 that is one half-step below scale-degree 1. The leading tone is diatonic in major keys, but requires an accidental in minor keys.

ledger lines

Small lines written above or below a staff to extend the staff's range of notes

Lied

A German solo song form that reached an artistic apex in the 19th century.

Loose Formal Organization (Caplin)

This is William Caplin's terms that he defines as, "A formal organization characterized by nonconventional thematic structures, harmonic-tonal instability (modulation, chromaticism), an asymmetrical grouping structure, phrase-structural extension and expansion, form-functional redundancy, and a diversity of melodic-motivic material (compare tight-knit)." (Quoted from Caplin's 2011 book, Analyzing Classical Form, p. 709)

lydian shuttle

I–II♯, or C–D in C major. This progression can easily be confused with IV-V in major or ♭VII–I in mixolydian, so one should be careful when referencing this progression. It implies the lydian mode.

lyric-invariant

A module or phrase is lyric-invariant if each time it appears it brings (mostly) the same lyrics. Lyric invariance tends to come at points of formal closure (tail refrains at the ends of strophes, choruses at the end of a verse-chorus song’s formal cycle).

lyric-variant

A module or phrase is lyric-variant if each time it appears it brings (mostly) different lyrics.

major pentatonic scale

A scale that proceeds M2–M2–m3–M2–m3. For example, starting on C, the C major pentatonic scale is C–D–E–G–A.

major seventh chord

A seventh chord in which the triad quality is major and the seventh quality is also major. For example: C–E–G–B.

Mélodie

A French solo song form that reached an artistic apex in the late 19th and early 20th centuries.

microtone

A microtone is a tone that exists outside of the 12-tone equal tempered scale (for example, quarter tones).

mid-song introduction

Mid-song intros function similarly to introductions, but in the middle of the song. They usually introduce the first section in the formal cycle. “Livin’ on a Prayer” has a brief mid-song introduction at 1:48, which sets up the arrival of the second cycle (beginning with Verse 2). A more extended mid-song introduction comes at 1:57 of “Pride (In the Name of Love)” by U2, which sets up the verse that begins the final cycle.

middle C

C4; the C near the middle of the piano keyboard, written on the first ledger line below the treble clef staff or the first ledger line above the bass clef staff

milieu

A physical and/or social setting

minor iv schema

Use of a minor iv chord in a major key. This creates a semitone descent between scale-degrees ♭6 and 5. It is common to precede iv with IV (major), creating a descent 6–♭6–5.

minor pentatonic scale

A pentatonic scale with the intervals m3–M2–M2–m3–M2. For example, starting on A, the minor pentatonic would be A-C-D-E-G.

minor seventh chord

A seventh chord in which the triad quality is minor and the seventh quality is also minor. For example: C–E♭–G–B♭.

mnemonic device 

A technique used to aid memorization

mode mixture

The intermixing of major and minor versions of scale-degrees 3, 6, and/or 7 within a composition.

modulation

A change of key.

Monotonality

A piece that has one governing tonic, that is, it starts and ends in the same key and contains a single tonic that gives the impression of being the primary key of the work. This term is used to distinguish between works that present progressive tonality.

motive

A regularly recurring unit of music that's smaller than an idea, and which is typically transformed across a work. The word "motive" usually refers to pitch material, but other kinds of motives such as rhythmic or contour also exist.

music-invariant 

A module or phrase is music-invariant if each time it appears it brings (mostly) the same music.

music-variant

A module or phrase is music-variant if each time it appears it brings (mostly) different music.

natural

Cancels a prior accidental, such as a sharp or flat

neighboring

A type of motion where a chord tone moves by step to another tone, then moves back to the original chord tone. For example, C-D-C above a C major chord would be an example of neighboring motion. D can be described as a neighbor tone.

note

Includes both a pitch and rhythmic component; may include a stem, beam, and/or flag

notehead

The elliptical part of the note that can be either filled in (black) or outlined (white)

octave

Two pitches with the same letter name (e.g. "C"), twelve half-steps apart

octave equivalence

The assumption that pitches separated by one or more octaves are musically equivalent (e.g. an octave above "A" is "A")

octave equivalent

Pitches that are spelled the same but are one more more octaves apart

octaves

A series of eight notes (such as C to C)

off-tonic

A phrase or module is off-tonic when it begins on a harmony other than tonic.

on-tonic

A phrase or module is on-tonic when it begins with tonic harmony (I in root position).

one-more-time

A technique of internal phrase expansion. Coined by Janet Schmalfeldt, the technique involves three steps: (1) the music tries to cadence, (2) the attempted cadence is evaded, and (3) the music retries the cadence.

one-more-time technique
ordered pitch interval

The distance between two pitches measured in semitones, with a plus or minus symbol to indicate ascending or descending, respectively. For example: C4 to E5 would be an ordered pitch interval of +16.

ordered pitch-class intervals

The distance between pitch classes from lowest to highest. In other words, pitch class intervals are measured on the clockface, always going clockwise.

outro

Outros function as a transition from song back to silence, and thus decrease energy. Often this is accomplished in the recording studio by way of a fadeout.

partial

A component frequency within a complex tone's set of overtones.

pedal point

A type of embellishing tone that holds a single pitch or pitch class in the bass while the chords change above it.

perfect authentic cadence (PAC)

A V-I cadence in which both harmonies are in root position and in which Do (scale-degree 1) is in the soprano over the tonic chord.

perfect authentic cadences

A cadence that concludes with root position V to root position I, with the tonic in the soprano.

period

A phrase-level form that consists of two phrases: an antecedent and a consequent.

Phrase

A relatively complete musical thought that exhibits trajectory toward a goal. In much music, that goal is a cadence; so we might also say that a phrase is a relatively complete musical thought that ends with a cadence.

Phrase Expansion

The lengthening of a phrase, whether internally or externally, beyond its expected duration resulting from a "play" with grouping units.“Expected duration” is defined contextually, and it may rely on such factors as: era, genre, pre-established models (i.e., projection) “Play” may occur either within a single group (stretching) or by stringing together additional groups (adding). Stretching and Adding can also occur at the same time.

phrase-level form

Refers to the various ways in which a phrase may be constructed of subphrases, ideas, and motives. Examples of phrase-level forms include sentences, periods, repeated phrases, hybrid forms, etc.

phrasing

the way a passage might be shaped in performance (where to push and pull time, where and how to change dynamic levels, etc.)

picardy third

Substituting a major I chord for a minor I chord (for example, using C major instead of C minor in a piece that is in C minor overall).

pitch

Refers to how "high" or "low" a sound is

pitch class

All pitches that are equivalent enharmonically and which exhibit octave equivalence

pitches

Discrete tones with individual frequencies

plagal cadence

A plagal cadence uses the harmonies IV–I.

post-cadential extension (p.c.e.)

A type of suffix (external expansion). Post-cadential extensions are usually short, they often occur at the ends of phrases within a section, and they typically prolong the final chord of the cadence or re-state the two chords that created the cadence.

postchorus

A short section that follows a chorus and serves only to close the cycle—does not to introduce or transition to the beginning of the next cycle (Mark Spicer 2011, par. 9).

prechorus

Prechorus function is most significantly typified in energy gain. Prechorus sections often use motivic fragmentation, acceleration of harmonic rhythm, movement away from tonic harmony, and harmonic openness.

prefix

An external expansion that occurs before the beginning of a phrase. Prefixes are usually introductions, and they may be small, as when the accompaniment for a lied begins before the singer, or they may be large, as when a symphony begins with a slow introduction.

presentation

A subphrase consisting of a basic idea and its repetition. Presentations don't usually end with cadences.

Prime symbol

Prime symbol:

This small symbol (look similar to an apostrophe) is used in the analysis of phrases and forms to indicate that some repeated material has changed, in some way, from its initial statement. For example, A would be the symbol for the first section but A′ would be used to represent the return of the A section with some element(s) of change.

Progressive Tonality

Progressive tonality - A piece that starts and ends with different tonics. This concept is used to distinguish itself from monotonality which is the default harmonic plan in most tonal works from the 17th, 18th, and 19th centuries.

quality

When applied to an interval, the term "quality" modifies the size descriptor in order to be more specific about the exact number of semitones in the interval. For example, both A–C and A–C♯ are thirds, but the former has a minor (i.e., smaller) quality while the latter has a major (i.e., bigger) quality.

When applied to triadic harmony, "quality" refers to the arrangement of different qualities of thirds that make up the harmony. For example, a major triad has a major third above the root, a minor triad has a minor third above the root, and so on.

quatrain

A group of lyrics that is four lines long.

range

The span of notes a voice or instrument can sing or play

Refrain (rondo form)

In a rondo form, a refrain refers to the work's primary theme. It is often referred to as a refrain because of its recurrent nature. In most rondos, the refrain is stated at the beginning, restated after each contrasting episode, and then one more time as the last form sectional, though a coda may follow.

Refrain (song form)

A lyric-invariant passage within a section that is otherwise lyric-variant. A refrain is too short to form its own section—typically a phrase or less.

refrains
repeated phrase

Two phrases where the second one is a repetition of the first. The repetition is always written out (repeat signs don't signify a repeated phrase), and usually the repetition is a variation on the initial statement.

repetition

A technique of internal phrase expansion. Sometimes a composer repeats material to create extra length in a phrase. Such repetitions may be exact or varied.

Reprise

A section of a work that bears repeat signs like either of the parts of a binary form. Each reprise is typically referred to by number (i.e., reprise 1, reprise 2, or 1st reprise, 2nd reprise).

reroute

A type of alternative path. A reroute involves a permanent change of a phrase's trajectory toward the cadence. Reroutes are initiated by a diversion.

Retransition

A retransition is very similar to a transition but its location and function are different. Retransitions come between two sections where the upcoming section is the initiation of a large-scale return. In most cases, retransitions help prepare the return of the piece’s main section. In a ternary form this would be the A section, in a sonata form this would be the restatement of the primary theme at the onset of the recapitulation, and in a rondo this would be the return of the refrain (a.k.a. the A section). A retransition often drives toward attaining the dominant chord of the home key and will often prolong the dominant once attained, usually in the form of a suffix. Retransitions may have a clear half-cadential ending (possibly followed by a suffix), or they may have an elided ending that coincides with the initiation of the following section.

rhythm

The duration of musical sounds

rhythm dot

A notational symbol indicating that the affected note should be held 1.5 times as long.

rhythm section

In jazz, the piano, guitar, bass, and percussion.

root motion

The distance between roots (NB: not basses!) of adjacent chords. For example, "root motion by step" refers to the distance between two chords that are only one step apart, such as I and ii, IV and V, etc.

rotation (pop schemas)

Beginning a harmonic schema on a different chord within the schema, but proceeding through the harmonies in the same order. In other words, if the schema is 1-2-3-4, a rotation of the schema would be 3-4-1-2. Something like 1-3-2-4 would not be a rotation, because the chords appear in a different order than in the schema.

Rounded Binary Form

A type of binary form where the material at the start of reprise 1 returns somewhere near the middle of reprise 2. Both appearances of that repeated music are expected to be in the home key.

schema

A schema is a mental representation of a stock pattern. In music theory, the term "schema" usually refers to a prototypical chord progression or formal structure. Significantly, schemas can appear with variations while still being recognized as an instantiation of that schema. We understand an individual pattern in the music (exemplar) as a version of an ideal general pattern (prototype), and that relationship helps us understand how that pattern is functioning within a particular passage of music. Schemas are often give names, like "Meyer" or "double plagal."
Schemas can have both internal defining characteristics and normative placements within a series of musical events.
• Internal characteristics may describe a schema’s melodic features, harmonic features, and metric features.
• A schema’s normative placement describes it temporal location. For example, we will normally find a closing schema like the “Prinner” at a close of a phrase.

secondary dominant

A chromatic chord that temporarily tonicizes another key besides the tonic key, by taking on a dominant function in that new key.

section

In musical form, this refers to the highest-level division of the overall form of the piece. Examples include the exposition in sonata form, the first part of a binary form, or the chorus of a pop song.

segmentation

The process of dividing a passage or piece of music into its component parts. Most commonly, we show the idea level on a score using square brackets above the staff. For a discussion of the hierarchy of these "component parts" see Phrase-Level Forms 1.

sentence

A special kind of phrase consisting of a presentation and a continuation.

Sequence

A pattern that is repeated and transposed by some consistent interval. Usually the term "sequence" refers to both the melody and harmony being transposed by the same interval, but we can also speak of "melodic sequences" or "harmonic sequences" where only one domain participates.

sharp

Raises a note by a half-step

Simple Binary Form

A type of binary form that does not contain the types of material returns found in rounded and balanced binary.

singer/songwriter schema

I–V–vi–IV in major, or III–VII–i–VI in minor (C–G–Am–F, for example). This chord progression often loops throughout a pop song. Frequently, this progression begins on the vi/i chord instead of the I/III chord.

skip

Voice leading movement by third.

Sonata Form

Sonata form gets is name by association with the form that most multi-movement works had in the Classic era. It is one of the more complex forms and can be understood as an elaborate version of rounded binary form that features a balanced component. Because of its prevalence in classical music in general, it has been given very specific names for each part of its larger and smaller organization. The larger level names are as follows: Exposition (≈A), Development (≈B), and Recapitulation (≈A′). In general terms, the exposition contains two main sections separated by a transition (internal auxiliary section) and the exposition usually ends with a suffix (typically the large variety). The specific names for each section of the exposition are as follows:

Primary Theme (main section 1)
Transition (internal auxiliary section)
Secondary Theme (main section 2)
Closing Section (suffix)

These sections are often referred to with capitalized initials: P, T, S, C.

 

 

spondee

A poetic foot consisting of two stressed syllables in a row.

Stability - Form

A relative sense of stability in a work is a common means of delineating form, and is an important dramatic concern for creating momentum and engaging a listener's expectation about what might happen in a work, given the listener's familiarity with how other pieces in a given genre behave. Much like story telling, music often expresses the sense of beginning, middle, and end and listeners have the ability to pay attention to that aspect of music which typically engages their interest because once they feel the sense of being in the middle, for example, they can project an expectation that the middle will lead to an end at some, undetermined point in the future. The sense of expectation is something that composers regularly manipulate by establishing models (or relying on models established by other works and composers) and then altering those models which can give the listener a sense of having an expectation, an implicit prediction, and then an emotional response depending on whether or not their expectation came true.

This balance between stability and instability can generally be associated with beginnings, middles, and ends. Beginnings can be expected to be relatively stable and middles can be expected to be relatively unstable. Endings typically involve instability but also the promise of an arrival at which point the instability will come to a close, creating a sense of relative stability that helps to bring a section or work to a satisfying close.

staff

Five horizontal lines that are evenly spaced on which notes are placed

Standard, Classical-Era Cadence Types

In the Classical-era of western, classical music—which spans the middle to the end of the 18th century—there were a specific set of standard cadence types that were used to close phrases. They were the perfect authentic cadence (PAC), the half cadence (HC), and the imperfect authentic cadence (IAC).

Standard, Classical-Era Modulation Schemes

In the Classical-era of western, classical music—which spans the middle to the end of the 18th century—there were a specific set of standard modulation schemes that were used within a section of music. These are summarized below:

Tonality Starting Harmony Ending Harmony
Major Key I V
Minor Key i III
Minor Key i v
stanza

In lyrics, a stanza is a group of lines of lyrics. In music notation, a stanza is a group of staves that are played simultaneously.

stem

The vertical line that originates at the notehead

straight eighth notes

Eighth notes that are equal, as opposed to swung eighths (which are unequal).

stretching

A technique of internal phrase expansion. It occurs when a composer lengthens a harmony or melody by increasing its duration so that it lasts longer than expected. When that happens, we say that the unit that contains the harmony or melody has been stretched.

string instruments

An instrument that produces sound via one or more vibrating strings

strophe

A basic multi-phrase unit. In pop music, a strophe is a focal module within strophic-form and AABA-form songs.

strophic form

A large-scale song structure, in which the same basic multi-phrase unit is repeated throughout (AAA). The basic unit that is repeated is called a strophe. Strophic form is more common in early rock-and-roll (1950s–1960s) than in the 1970s and beyond.

subdominant

A harmonic function that may either lead toward a dominant-function chord or back to a tonic-function chord. Subdominant function is most typically associated with the IV chord, otherwise known as the subdominant chord, and the II chord, otherwise known as the supertonic chord.

subphrase

The unit of music that need not end with a cadence and which is one level smaller than a phrase, but one level larger than an idea. Subphrases do not exist in all phrase-level forms. Periods, for example, do not contain subphrases. Sentences contain two subphrases: a presentation and a continuation.

subtonic shuttle

♭VII–I, or B♭–C in C major. This shuttle can imply mixolydian if the tonic chord is major, or aeolian if it is minor. In this shuttle, the ♭VII chord has dominant function.

subversion of a cadence

Occurs when a potential cadence point is declined by the material that follows it. A common strategy is for a composer to write music that proposes a cadence, but then to "back up" in the phrase and try the cadence again. See also "One-more-time" technique in the chapter on phrase expansion.

suffix

A type of external expansion that occurs after the end of a phrase. There are three terms we commonly use to describe suffixes, ranging in size from smaller to larger: post-cadential extension, codetta, and coda.

swing eighths

A performance practice in which two notated eighth notes are performed unequally, in about a 2:1 proportion.

syncopation

A rhythmic phenomenon in which the hierarchy of the underlying meter is contradicted through surface rhythms. Syncopation is usually created through accents and/or longer durations.

syntax

the norms or principles according to which musical elements are combined into meaningful and stylistically appropriate successions

tail refrain

A refrain that is the last line or so of a section's text.

tenor clef

Also known as a "C" clef, a tenor clef designates the lowest line of a staff as the pitch D3

Through Composed

An attribute of a musical form where no sections of music return. For example, a form with sections A B C. Similar motivic material may be present in different sections, but the sections would each be considered distinct. A piece that doesn't have any clear sections and seems like a continuous churning of musical ideas can also be described as through composed.

Tight-knit (Caplin)

This is William Caplin's terms that he defines as, "A formal organization characterized by conventional theme types, harmonic-tonal stability, a symmetrical grouping structure, form-functional efficiency, and unity of melodic-motivic material (compare loose)." (Quoted from Caplin's 2011 book, Analyzing Classical Form, p. 714)

tonal ambiguity

A property of certain chord progressions, where the progression does not inherently imply a single chord as the tonic chord.

tonic function

A harmonic function that provides a sense of home or center. Tonic function is most typically associated with the I chord, otherwise known as the tonic chord.

tonicization

The process by which a non-tonic triad is made to sound like a temporary tonic. It involves the use of secondary dominant or leading-tone chords.

Transition

Generally, a section of music that functions to connect two thematic sections. In particular, a transition comes between two sections where the upcoming section is not the initiation of a large-scale return (e.g., transitions are commonly found between an A and B sections, or between the Primary and Secondary themes in a sonata). Transitions usually help to lead away from the piece's main section toward a contrasting section. Often a modulation is introduced to help prepare a section in a new key, though a modulation is not required. Transitions are a type of auxiliary section and they come in small and large varieties. Large transitions contain at least one complete phrase and small transitions don't contain complete phrases.

treble

Also known as the "G" clef, a treble clef designates the lowest line of a staff as the pitch E4

trochee

A poetic foot consisting of one stressed followed by one unstressed syllable.

turnaround

Broadly speaking, a turnaround is the use of a non-tonic chord (usually dominant) at the end of a harmonically closed unit to transition into the beginning of the following on-tonic unit. In jazz, the term "turnaround" often refers to the progression vi–ii–V–I. The exact qualities of these chords is highly variable, and one or more of the chords may be substituted with a different, related chord.

unit

A segment of music that expresses whatever the prevailing higher-level grouping expresses. For example, if a unit is contained within a continuation, it expresses continuation function. We often apply the term "unit" to ideas that aren't easily categorized using terms such as basic idea, contrasting idea, or cadential idea.

Unordered pitch intervals

The distance between two pitches, measured in semitones. C4 to E5 would be an unordered pitch interval of 16.

unvoiced

Spelling chords stacked in thirds or in closed position, within a single staff, usually for abstract or theoretical purposes, rather than for performance.

upright bass

The double bass.

verse

Verse sections are lyric-variant and often contain lyrics thatadvance the narrative. Until the 1960s, verse sections tended to be harmonically closed. Beginning in the 1960s, verse sections became more and more likely to be harmonically open (Summach, p. 114). Verses (like strophes) tend to begin on-tonic.

verse-chorus form

The most common form of pop songs today. The song is built of lyric-variant verses and lyric- and music-invariant choruses that deliver the primary narrative material of the song.

voice leading

The way a specific voice within a larger texture moves when the harmonies change. For example, in a choir with four parts, soprano/alto/tenor/bass, one might discuss the voice leading in the tenor part as the entire choir moves from I to V.

voicing

Distribution of notes in a chord into idiomatic registers for performance.

Western

Concerning European and European-colonized countries

whole-step

Two half-steps