We begin with a specific method called species counterpoint. The term “species” is probably most familiar as a way of categorizing animals, but it is also used in a wider sense to refer to any system of grouping similar elements. Here, the species are types of exercises that are done in a particular order, introducing one or two new musical “problems” at each stage. (So no, we won’t have any elephants or monkeys singing polyphony, sorry!)

While there are many variants on this approach, the chapters here are closely based on Johann Joseph Fux’s Gradus ad Parnassum (Steps to Parnassus, 1725). Many composers from the 18^th to the 21^st centuries have used this method, or some variation on it. In the first part of Gradus ad Parnassum, Fux works through five species for combining two voices, which will be the focus of our next five chapters. The “Gradus ad Parnassum” Exercises chapter provides all of the exercises from Gradus ad Parnassum in an editable format so you can try this yourself.

Before getting into the five species, we begin in this chapter by introducing principles that apply to writing lines in any species. These principles build on concepts from the Fundamentals section, such as intervals and scale degrees.

Consonance and dissonance

Consonance and dissonance was introduced in a previous chapter, but in counterpoint, we further distinguish between:

• Perfect consonances (perfect unisons, fifths, and octaves)
• Imperfect consonances (major and minor thirds and sixths)
• Dissonances (all seconds, sevenths, and diminished and augmented intervals)

These categories are summarized in Example 1 below.

The elusive perfect fourth

As in many theories of tonal music, the perfect fourth has a special status in species counterpoint that depends on where it appears in the texture. Basically, the interval of a perfect fourth is dissonant when it involves the lowest voice in the texture, but it is consonant when it occurs between two upper voices.

As this survey of species counterpoint will only cover two-voice textures, all fourths will involve the lowest part and therefore be classed as dissonant. Later chapters in this section will address the resolution of this dissonance, and the Strengthening Endings with Cadential [latex]^6_4[/latex] and [latex]^6_4[/latex] Chords as Forms of Prolongation chapters in the Diatonic Harmony section discuss this topic further.

Types of motion

Species counterpoint also concerns the motion between melodic lines (demonstrated in Example 2):

• Contrary: the two parts move in opposite directions (one up, the other down)
• Similar: the two parts move in the same direction (both up or both down)
• Parallel: the two parts move in the same direction (both up or both down) by the same distance, such that the starting and ending intervals are of the same type (e.g., parallel thirds)
• Oblique: one part moves, the other stays on the same pitch

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”; plural “cantus firmi”). Cantus firmus composition gives us the opportunity to engage the following fundamental musical traits:

• smoothness
• independence and integrity of melodic lines
• variety
• motion (toward a goal)

Example 3 contains all the cantus firmi that Fux uses throughout Gradus at Parnassum: one for each mode, presented here in the upper and lower of two parts. Apart from using this to review the type of cantus firmi Fux composed, you can use this to practice any of the species, on any of the modes, and in both the upper and lower parts.

Example 3. Cantus firmi from Gradus ad Parnassum.

Notice how in each case, the general musical characteristics of smoothness, melodic integrity, variety, and motion toward a goal are worked out in specific characteristics. The following characteristics are typical of all well-formed cantus firmi:

• length of about 8–16 notes
• arhythmic (all whole notes; no long or short notes)
• begin and end on do [latex](\hat1)[/latex]
• approach final tonic by step: usually re–do [latex](\hat2-\hat1)[/latex], sometimes ti–do [latex](\hat7-\hat1)[/latex]
• all note-to-note progressions are melodic consonances
• range (interval between lowest and highest notes) of no more than a tenth, usually less than an octave
• a single climax (high point) that usually appears only once in the melody
• clear logical connection and smooth shape from beginning to climax to ending
• mostly stepwise motion, but with some leaps (mostly small leaps)
• no repetition of “motives” or “licks”
• any large leaps (fourth or larger) are followed by step in opposite direction
• no more than two leaps in a row and no consecutive leaps in the same direction (except in the F-mode cantus firmus, where the back-to-back descending leaps outline a consonant triad)
• the leading tone progresses to the tonic
• leading notes in all cases, including in “minor”-type modes for which that seventh degree needs to be raised

Melodic tendencies

Some of the characteristics listed above are specific to strict species counterpoint; however, taken together, they express some general tendencies of melodies found in a variety of styles.

David Huron (2006) 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 ways in specific musical styles. They are:

• Pitch proximity: The tendency for melodies to progress by steps more than leaps and by small leaps more than large leaps. An expression of smoothness and melodic integrity.
• Step declination: The tendency for melodies to move by descending step more than ascending. Possibly an expression of goal-oriented motion, as we tend to perceive a move down as a decrease in energy (movement toward a state of rest).
• Step inertia: The tendency for melodies to change direction less frequently than they continue in the same direction. (That is, the majority of melodic progressions are in the same direction as the previous one.) An expression of smoothness and, at times, goal-oriented motion.
• Melodic regression: The tendency for melodic notes in extreme registers to progress back toward the middle. An expression of motion toward a position of rest (with non-extreme notes representing “rest”). Also an expression simply of the statistical distribution of notes in a melody: the higher a note is, the more notes there are below it for a composer to choose from, and the fewer notes there are above it.
• Melodic arch: The tendency for melodies to ascend in the first half of a phrase, reach a climax, and descend in the second half. An expression of goal orientation and the rest–motion–rest pattern. Also a combination of the above rules in the context of a musical phrase.

Rules for melodic and harmonic writing

In species counterpoint, we both write and combine such melodic lines. The following set of rules invoked in all the species begins with the melodic matters discussed already, then presents some harmonic considerations that we will focus on in the following chapters.

Melodic writing (horizontal intervals)

• Approach the final octave/unison of each exercise by step (this creates the clausula vera).
• Limit the number of:
  • consecutive, repeated notes: the same pitch more than once in a row
  • non-consecutive repeated notes: the same pitch more than once across the whole exercise
  • consecutive leaps: multiple intervals of a third or greater in a row (separate them with stepwise motion)
  • non-consecutive leaps: the total number of leaps within a short span, even if they’re not successive
  • consecutive repeated generic intervals: the same interval size (e.g., second) even if not the same specific interval (minor second)
• Control the melodic climax (highest note):
• Aim for exactly one unique climax in each melodic part
• Avoid ending on that climax
• Preferably leap to that climax
• Avoid the two parts reaching their respective climax pitches at the same time
• Avoid melodic leaps of:
  • an augmented interval
  • a diminished interval
  • any seventh
  • any sixth, except perhaps the ascending minor sixth
  • any interval larger than an octave
• Also avoid outlining (Example 4):
  • an augmented interval
  • a diminished interval
  • any seventh

Harmonic writing (vertical intervals and the combination of parts)

• The first interval should be a perfect unison, fifth, or octave, and the last interval should be a perfect unison or octave (not fifth).
• Restrict the gap between parts to a twelfth (compound fifth) maximum, and to an octave for the most part.
• Avoid “overlapping” parts (where the nominally “upper” part goes below the “lower” one).
• Make sure to avoid:
  • parallel octaves: when two parts start an octave apart and both move in the same direction by the same interval to also end an octave apart
  • parallel fifths: when two parts start an perfect fifth apart and both move in the same direction by the same interval to also end a perfect fifth apart
• Also try to avoid:
  • direct fifths and octaves: when two parts begin any interval apart and move in the same direction to a perfect fifth or octave
  • unisons at any point in the exercise other than the first and last intervals

The Psychology of Counterpoint

The chapters on species counterpoint will not involve a specific style (classical, baroque, romantic, pop/rock, etc.). Instead, these exercises will set aside important musical elements like orchestration, melodic motives, formal structure, and even many elements of harmony and rhythm, in order to focus very specifically on a small set of fundamental musical problems. These fundamental problems are closely related to how some basic principles of auditory perception and cognition (i.e., 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, we typically assume that the new sound belongs together with those others. This is related to some of the most deep-seated, fundamental parts of our human experience, and even evolution. Hearing a regular pattern typically indicates a predictable (and safe) environment, while any change can signal danger and will tend to heighten our attention to the source. This system for directing attention (and adrenaline) where it is most likely to be needed has been essential to the survival of the human species. While listening to music in the 21st century does not (usually!) require us to listen out for animal predators, some part of that evolutionary experience is “hard-wired” into the psychology of human listening, and it has a role in what gives music its emotional effect—even in a safe environment.

For Western listeners, 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. That being the case, a balance between tension and relaxation, motion and rest, is fundamental to most of the music we will study.

The study of counterpoint helps us to engage several important musical “problems” in a strictly limited context, so that we can develop composition and analytical skills that can then be applied widely. Those problems arise as we seek to bring the following traits together:

• smooth, independent melodic lines
• tonal fusion (the preference for simultaneous notes to form a consonant unity)
• variety
• motion (towards a goal)

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 working with that balance.

Finally, despite abstractions, it’s still best to treat counterpoint exercises as miniature compositions and to perform them—vocally and instrumentally, and with a partner where possible—so that the ear, the fingers, the throat, and ultimately the mind can internalize the sound, sight, and feel of how musical lines work and combine.

• Huron, David. 2006. Sweet Anticipation: Music and the Psychology of Expectation. Cambridge, MA: MIT Press.

1. Cantus firmus A (.pdf, .mscx). Asks students to critique one cantus firmus and write their own.
2. Cantus firmus B (.pdf, .mscx). Asks students to critique one cantus firmus and write their own.
3. For the complete set of Fux exercises, see the Gradus ad Parnassum chapter.