I. Fundamentals

Chelsey Hamm

Key Takeaways

• A is a three-note chord whose notes can be arranged in thirds. A triad can always be “stacked” so that its notes are either on all lines or all spaces.
• When stacked in its most compact form in thirds, the lowest note of a triad is called the , the middle note is called the , and the highest note is called the .
• There are four qualities of triad. A third is major and its fifth is perfect, while a third is minor and its fifth is perfect. A third is minor and its fifth is diminished, while an third is major and its fifth is augmented.
• In  notation, major triads are represented with capital letters that correspond to the triad’s root. Minor triads have a lowercase “m” after the letter, diminished triads have a lower-case “dim” or a degree sign (“°”), and augmented triads have a lower-case “aug” or a plus sign “+.”
• Within major and minor keys, triads have particular qualities that correspond to scale-degree. These are the same in every major and minor key, which makes memorizing them useful.
• There are five steps to drawing a triad: drawing a root, adding a third and fifth, visualizing the root’s major key signature, adding accidentals from the key signature (if applicable) for a major triad, and adding additional accidentals for a minor, diminished, or augmented triad.
• Musicians often prioritize the note that is in the , often simply called the “bass” by musicians, which is the lowest part (or voice) of a composition, regardless of what instrument or voice type is singing or playing that lowest note. It is important to note that the bass voice of the chord is NOT the same thing as the chord’s root.
• When a triad is stacked in thirds we say the triad is in root position. The bass note in root position is the root. Chords that do not have the root in the bass are said to be . When the third appears in the bass we say the triad is in first inversion, and when the fifth appears in the bass we say the triad is in second inversion.
• symbols are used to indicate inversion. Figured bass uses Arabic numerals and some symbols which indicate intervals above a bass note. These are turned into chords by musicians. A triad in first inversion received a superscript “6,” while a triad in second inversion received the figures . In figured bass larger numerals are always stacked above smaller ones.
• Triads are identified by their , , and . You can identify a triad by identifying and writing its root, its quality, and its inversion.
A is any combination of three or more pitch classes that sound simultaneously. This chapter focuses on , three-note chords whose notes can be stacked into thirds.

The three notes of a triad can always be arranged in thirds. Example 1 shows two triads, each written both and :

The first triad is shown on three adjacent spaces, while the second triad is shown on three adjacent lines. A triad can always be “stacked” so that its notes are either on all lines or all spaces.

When a triad is stacked in its most compact form (measures 2 and 4 of Example 1), it looks like a snowperson. Example 2 shows several snowpeople:

A snowperson consists of a bottom, middle, and head. Likewise, a triad consists of a lowest note, a middle note, and an upper note. When stacked in “snowperson form,” the lowest note of a triad is called the , the middle note is called the , and the highest note is called the . Example 3 shows this:

As you can see in Example 3, the third is so named because it is a generic third above the root, and the fifth is so named because it is a generic fifth above the root. The root is analogous to a snowperson’s bottom, the 3rd to its middle, and the 5th to its head.

# Triadic Qualities and Listening to Triads

There are four qualities of triad: major, minor, diminished, and augmented. Example 4a shows these four qualities of triad, each with a root of F and their quality of fifth labeled, while Example 4b shows these qualities with their quality of third labeled:

As seen in Examples 4a and 4b, a fifth is perfect and its third is major, while a fifth is perfect and its third is minor. A fifth is diminished and its third is minor, while an fifth is augmented and third is major. Major, minor, and diminished triads are more common in many genres of music, such as Classical and popular, which is why these triads are listed first in Examples 4a and 4b. Augmented triads are less common is most Classical and popular music.
Listen carefully to the different qualities of triad in Example 5.

It is common to pair expressive qualities with triads when learning what they sound like. You might think of major triads as sounding “happy,” minor triads as “sad,” diminished triads as “scary,” and augmented triads as having a “fantasy” or “mystical” sound.

Triad’s frequently appear in , which are jazz scores that notate a melody and chord symbols. Lead-sheet symbols for triad often include the letter name of the triad’s root, the triad’s quality, and sometimes the pitch class that occurs in the , which is the lowest part (or voice) of a composition, regardless of what instrument or voice type is singing or playing that lowest note.

A lead-sheet symbol begins with a capital letter (and, if necessary, an accidental) denoting the root of the chord. That letter is followed by information about a chord’s quality:

• major triad: no quality symbol is added
• minor triad: lower-case “m”
• diminished triad: lower-case “dim” or a degree sign “°”
• augmented triad: lower-case “aug” or a plus sign “+”

Finally, if a pitch class other than the chord root is the lowest note in the chord, a slash is added, followed by a capital letter denoting the pitch class in the bass (lowest) voice. Example 6 shows four triads with lead-sheet symbols:

As seen in Example 6, a triad that has a root of C and a major quality is shown as “C” in lead-sheet notation. A C minor triad, which consists of the notes C, E♭, and G, is written as “Cm” in lead-sheet notation if C were the lowest note. If E♭ were the lowest note of a C minor triad (see the third chord in Example 6), the lead-sheet symbol would be “Cm/E♭.” If G were the lowest note of a C minor triad (see the fourth chord in Example 6), the lead-sheet symbol would be “Cm/G.” This topic will be explored more below in the section titled “Triadic Inversion and Figures.”

# Triad Qualities in Major and Minor

Triads can be built on any note of the major scale, as shown in Example 7.

Example 7 is in the key of G major. As you can see in Example 7, triads built on Do, Fa, and Sol in major keys are major. This is shown in this example with letter name of the triad’s root capitalized. Triads built on Re, Mi, and La are minor. This is shown with a lowercase letter “m” after the capital letter name of the triad’s root. Triads built on Ti are diminished; this is shown with a superscript “o” which you might know as the degree symbol. These triadic qualities do not change in different keys; in other words, the quality of a triad built on Do is always major in major keys, no matter which major key a musical work is in.

Triads can be build on any note of the minor scale, as shown in Example 8.

To build a triad from a lead-sheet symbol, you need to be aware of a triad’s root and quality. We will look at its bass note in the next section titled “Triadic Inversion and Figures.” Let’s say that, for example, we wanted to spell a major triad. We would complete the following steps:

1. Draw the root on the staff
2. Draw notes a third and fifth above the root (i.e. draw a snowperson)
3. Think of (or write down) the key signature of the triad’s root
4. Write any accidentals from the key signature if notes in that key signature appear in the triad for a major triad
5. For a minor, diminished, or augmented, add additional accidentals to alter the chord’s third and/or fifth when appropriate

Example 9 shows this process for a D major triad:

First, the note D, the chord’s root, is drawn on the staff. Second, a snowperson is drawn—an F and A, the notes a third and a fifth above the D. Third, the key signature of D major has been recalled. D major has two sharps, F♯ and C♯. Fourth, a sharp (♯) has been added to the left of the F, because F♯ is in the key signature of D major. No C♯ was necessary because there is no C in the chord.

Let’s complete this process for an A♭ minor triad (A♭m), as seen in Example 10.

First, the note A♭ is written because it is the root of the triad. Second, a snowperson is drawn; in other words, the notes C and E are added because they are a generic third and fifth respectively above A♭. Third, the key signature of A♭ major is recalled. A♭ major has four flats, B♭, E♭, A♭, and D♭. Fourth, E♭ is added, because it is in the key signature of A♭ major. No B♭ or D♭ are needed, because those notes aren’t in an A♭ triad. Now we have successfully spelled an A♭-major triad (A♭, C, and E♭). Minor triads contain a minor third, which is one half-step smaller than a major third. Therefore, our final step is to lower the chord’s third (the C) by a half-step (to a C♭). Now we have an A♭ minor triad (A♭, C♭, and E♭).

Don’t forget that diminished triads have a minor third and a diminished fifth, meaning you have to lower both the third and the fifth by a half-step from a major triad. An augmented triad has a major third and an augmented fifth, so its fifth must be raised by a half-step from a major triad.

# Triadic Inversion and Figures

As mentioned previously, musicians often prioritize the note that is in the , often simply called the “bass” by musicians, which is the lowest part (or voice) of a composition, regardless of what instrument or voice type is singing or playing that lowest note. Example 11 shows an A major triad with three different notes in the bass:

An A major triad consists of three notes, the root (A), the third (C♯), and the fifth (E). When a triad is stacked in thirds (i.e. “snowperson form”), we say the triad is in root position. The bass note in root position is the root. Chords that do not have the root in the bass are said to be . When the third appears in the bass we say the triad is in first inversion, and when the fifth appears in the bass we say the triad is in second inversion. It is important to note that the bass voice of the chord is NOT the same thing as the chord’s root. The root of an A major triad is always A, regardless of whether the triad is in root position, first inversion, or second inversion. However, the bass voice changes between these inversions, from A to C♯ to E, as seen in Example 11.

You might think of first inversion triads as looking like a snowperson whose feet have been moved above their head; a second inversion triad looks like a snow person whose head has been moved to where their feet would normally appear. Example 12 demonstrates this similarity:

Sometimes musicians use lead-sheet notation to indicate inversions, as seen in Example 11. However, most of the time we do not use lead-sheet notation in the study of Western classical music. Instead, we use symbols to indicate inversion. Figured bass uses Arabic numerals and some symbols which indicate intervals above a bass (NOT a root) note. These are turned into chords by musicians.

Example 13 shows the full figured bass symbols for triads underneath their lead-sheet symbols:

As you can see in Example 13, a root position triad has a third and a fifth above the bass. A first inversion triad has a third and a sixth above the bass, while a second inversion triad has a fourth and a sixth above the bass. In figured bass, the larger numerals (intervals) always appear above the smaller ones.

However, many centuries ago musicians abbreviated the figured bass symbols for triads in order to save time and supplies (paper and ink were very expensive before the industrial revolution). Example 14 shows the abbreviated figured bass symbols for triads that we usually use today underneath their lead-sheet symbols:

As you can see, no symbol appears for root position. First inversion triads are abbreviated with the number “6,” while a second inversion triad keeps its full figures to distinguish it from a first inversion triad.

When musicians turn figured bass symbols into chords—either on paper or in performance—this is called the symbols. Example 15 shows the process of realization for several root position triads:

As seen in Example 15, an E♭ appears with no figured bass symbol next to it. Therefore, we can assume that we are realizing an E♭ major triad in root position. This chord is realized (written out with notes) in the next measure. In measure 3 we see an E♭below the staff. We can understand that notation to mean that we are realizing an E♭ diminished triad in root position. This chord is realized in the next measure.

Example 16 shows the process of realization for a triad in first inversion:

As seen in Example 16, we first see a Gm6 triad. This means that we must realize a G minor triad in first inversion. The root of the chord, G, has been placed in the first measure of the example. In the second measure of Example 16, a G minor triad in root position has been realized. In the third measure of Example 16 the third of the chord (the B♭) is in the bass; now the triad is in first inversion. The last measure of Example 16 is the correct “answer” or realization of this chord symbol.

Example 17 shows the process of realization for a triad in second inversion:

As seen in Example 17, we see a B $\begin{smallmatrix}6\\4\end{smallmatrix}$ triad—a B major triad in second inversion. The root of the chord, B, has been placed in the first measure of the example. In the second measure of Example 17, a B major triad in root position has been realized. In the third measure of Example 17, the fifth of the chord (the F♯) appears in the bass; this chord is now in second inversion. The last measure of Example 17 is the correct “answer” or realization of this chord symbol.

# Identifying Triads, Doubling, and Spacing

Triads are identified according to their , , and . Example 18 shows a triad in root position for the process of identification:

You can identify triads in five steps:

1. Identify and write its root
2. Imagine the major key signature of its root
3. Identify and write its quality
4. Identify its inversion
5. Write the appropriate figured bass figures if applicable

To identify this triad, you first identify and write its root. Because the triad is in root position, its lowest note is its root—in this case C♯. Now you can identify and write its quality. To do this, you will need to imagine the major key signature of its root. The key of C♯ major has seven sharps (every note is sharp). Therefore, E and G would be sharp in a C♯ major key. Instead, both of these notes have been lowered by a half-step. Therefore, this triad is diminished. Next, you need to identify the triad’s inversion. The triad is stacked in thirds and is therefore in root position. No figured bass figures are needed. We would correctly identify this triad as a C♯o chord.

Example 19 shows a triad in inversion and the process of identification:

To identify this triad, you must either write it or imagine it in root position. This has been shown in the second measure of Example 19. Once it is in root position you can identify the root, which in this case is “D.” Now you can imagine the key signature of its root, D, which has two sharps (F♯ and C♯). F is not sharp; therefore this triad must be minor. Finally, you can identify the inversion of the triad from the original example (not your imagined or written root position version). The original example is in first inversion. Therefore we would correctly identify this triad as a Dm6 triad.

Because musicians accept octave equivalence, the  of notes does not affect a triad’s identification. Example 20 shows several different triads with octave doublings and their correct identification:

As you can see, the identification of these triads is the same, regardless of octave doublings, even when more than one clef is used.

Furthermore, the spacing of notes more than an octave does not affect a triad’s identification. Notes that are written in appear the closest they can be to one another. Example 21 shows Example 11 once more:

As seen in Example 21, chords can inverted and still in closed spacing.
Notes can be spaced out further apart, which is called . Example 22 shows two triads in open spacing:

As you can see in Example 22, each of the notes of the triad appears, but they are widely spaced across several different octaves within a grand staff.

Doublings and open spacing can be combined, as seen in Example 23.

Neither of these factors will affect how you identify these triads. In order to identify them you need to either imagine or write the notes into a triad in closed spacing without any doublings, as we did in Example 19.

Online Resources
Assignments from the Internet
1. Triad Root Position Identification (.pdf.pdf, .pdf.pdf.pdf.pdf.pdf.pdf)
2. Triad Inversions Identification (.pdf.pdf.pdf.pdf)
3. Triad Identification and Writing in Major and Minor Keys (.pdf)
4. Triad Root Position Construction (.pdf)
5. Triad Inversions Construction (.pdf)
Assignments

Assignments for this chapter are in progress.