The cantus firmus: construction, Fux's six melodies and treatment above and below

Definition

The cantus firmus (fixed song) is a given melody, in long, equal values, against which the counterpoint is written. In the Middle Ages and the Renaissance it was often a Gregorian chant or a secular melody; in Fux's method it is a short, simple melody built specifically for the exercise, always in whole notes (one note per bar).

Fux's six melodies

Fux uses one cantus firmus for each of the six modes and reuses it in all the species, in two, three and four voices:

Each melody begins and ends on the finalis, closes with a descending step (2–1) and has a single climax.

How to build a cantus firmus

1. Length: 8 to 16 notes.
2. Begin and end on the finalis; the penultimate note is the supertonic (2–1). If the melody will be in the bass, the 2–1 closure is still the most comfortable.
3. Motion: mostly stepwise, a few leaps of a third, fourth or fifth, no augmented or diminished intervals, no sevenths.
4. A single climax, preferably in the second half.
5. Range within a tenth, better within an octave.
6. No repeated notes and no obvious sequences.
7. The melody must suggest the mode: touch the reciting tone and the characteristic leaps (D–A in Dorian, E–C in Phrygian).

Treatment: cantus below and cantus above

Every exercise is written twice.

• Cantus in the bass, counterpoint above: the first note of the counterpoint may be a unison, an octave or a fifth above the finalis. The penultimate note forms a major sixth with the cantus (C#5 over E4 in Dorian) that opens out to the octave.
• Cantus above, counterpoint in the bass: the first note must be a unison or an octave; the fifth below is forbidden because it would suggest another mode (G below D suggests G). The penultimate note forms a minor third (C#4 below E4) that closes on the unison, or a tenth that closes on the octave.
• The cantus can be transposed by an octave to fit the range of the voices (soprano, alto, tenor, bass), but its relative pitch is not changed.

Example in D Dorian, cantus above

Cantus D4 F4 E4 D4 G4 F4 A4 G4 F4 E4 D4; counterpoint D3 A3 G3 B3 E3 A3 F3 G3 D4 C#4 D4. Intervals: 8, 6, 6, 3, 10, 6, 10, 8, 3, 3, unison. It opens on an octave, closes with a minor third → unison, and contains only one internal octave, reached by contrary motion.

The cantus firmus in history

• Masses on a cantus firmus: a chant (Gregorian or secular, such as L'homme armé) placed in the tenor in long values.
• Lutheran chorales: the chorale in long values in the soprano or bass, with florid counterpoint in the other voices (Bach's chorale preludes, cantatas).
• Teaching exercises: from Fux to modern textbooks, with new melodies or ones taken from Gregorian chant.

Typical errors

• Writing a cantus that is too interesting, full of leaps: it makes good counterpoint impossible.
• Starting the bass counterpoint on the fifth of the finalis.
• Forgetting that, with the cantus above, the cadential sixth becomes a third (or tenth).
• Transposing the cantus into the wrong mode by adding accidentals: Dorian on D is transposed to G with one flat (G A Bb C D E F G), not without it.

Modern application

• Pop: a simple, repeated bass line is a cantus firmus; writing a second voice over it in first species gives solid vocal harmonies.
• Soundtracks: a slow theme given to horns or cellos, with florid counterpoints in the woodwinds, is the orchestral version of the chorale on a cantus firmus.
• Choirs: teaching the singers a melody in long notes and then adding voices in different species is a quick way to build a multi-voice piece with short rehearsals.
• DAW: enter the one-note-per-bar cantus on one track and the counterpoint on another, and assign two different timbres (e.g., organ and flute) to hear the intervals clearly.

Related topics

Church modes, melody in strict counterpoint, modal first species, Bach chorale, mass and motet.