Discussion 5b - Cantus Firmus and 1:1 Counterpoint

Cantus Firmus stuff

Constructing a melodic line and melodic intervals:

  • Length: 10-12 bars is average for 1:1 counterpoint, but the full range is 8-14.
  • Starting and ending pitches: the tonic of whatever key we’re in.
  • Approaching the final note: contrary stepwise motion. Ex: re in one voice and ti in another, both will move to do.
  • Repeated pitches, yay or nay? : NAY. You cannot repeat pitches in your line.
  • Melodic intervals: stepwise, skips, and leaps are all ok!
    • How to approach and resolve leaps?: Approached and followed by stepwise motion in the opposite direction of the leap. Ex: step up, leap down, step up. Think of a sine wave!
  • Range: about an octave or less. It should be easily singable.
  • Climax: happens on the highest (or lowest) note, depending on how your counterpoint curves. There should only be one highest/lowest note.

Accpetable harmonic intervals:

  • Starting and ending harmonic intervals?: P8.
  • Approaching perfect intervals: contrary motion.
  • Number of times an interval size can be used consecutively?: never more than 3 times in a row. No consecutive perfect intervals.

Accpetable motion between lines:

  • Acceptable types of motion: parallel, similar, and contrary.

“Will there ever be oblique motion resulting from a cantus firmus with static motion?”

  • Not in what we’ll be looking at in class, though some exception probably exists somewhere.

Further reading

From Open Music Theory

Cantus firmi

A number of others are provided [here][CFs]. 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 redo, sometimes tido)
  • 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.

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).

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, ever, ever 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:

  • Do not use more than three of the same imperfect consonance type in a row (e.g., three thirds in a row).
  • Never move into a perfect consonance by similar motion (this is called direct or hidden octaves). This draws too much attention to an interval which already stands out of the texture.
  • Avoid combining similar motion with leaps, especially large ones.

Demonstration

In the following video, I illustrate the process of composing a first-species counterpoint. This video provides new information about the compositional process, as well as concrete examples of the above rules and principles.