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:

• smoothness
• independence and integrity or melodic lines
• variety
• motion (towards a goal)

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.

A number of others are provided here. Performing these is a helpful practice to develop an internal sense of the sound and feel of a well formed cantus, and many of the characteristics of well formed cantus firmi carry over into other musical styles. (These model cantus firmi can also be used as the starting points for our two-voice exercises.)

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:

• length of about 8–16 notes
• arhythmic (all whole notes; no long or short notes)
• begin and end on do
• approach final tonic by step (usually re–do, sometimes ti–do)
• 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 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; no consecutive leaps in the same direction (Fux’s F-major cantus is an exception, where the back-to-back descending leaps outline a consonant triad.)
• the leading tone progresses to the tonic
• in minor, the leading tone only appears in the penultimate bar; the raised submediant is only used when progressing to that leading tone

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:

• 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 towards a state of rest).
• step inertia – the tendency for melodies to change direction less frequently than they continue in the same direction. (I.e., 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 towards the middle. An expression of motion towards 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 less 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.

Practice exercise

Before composing a cantus firmus from scratch, try building a well formed cantus around the following skeleton. Length, starting pitch, penultimate pitch, ending pitch, and climax have been provided. Create a smooth, consonant melodic line that exemplifies the characteristics listed above—both the specific characteristics of strict species cantus firmi and the general characteristics of tonal melodies. Click the staff to hear the melody. Be sure to listen each time you make a change.