Summary
The third species of counterpoint sets four semiminims against one semibreve of the cantus firmus — in whole-note mensuration, four quarter notes per cantus-firmus note (a 4:1 ratio). The quarter note is the basic unit, and the measure is filled by a single run of four notes. The downbeat of every measure must be consonant with the cantus firmus; the remaining quarters are filled largely by stepwise passing tones, so dissonance appears on the weak quarters, mainly the second and fourth. Because four notes now occupy the space of one, the species requires rules for which of those four may be dissonant: normally the outer notes of a stepwise group are consonant and dissonances fall on weak positions, but two licensed exceptions — the diminution of the leap of a third and the cambiata (changed note) — permit dissonance on a strong position. In Fux's dialogue, Joseph also explains the special construction of the penultimate measure and justifies the occasional use of flats and sharps.
A specific worked example from Johann Joseph Fux's Gradus ad Parnassum (Fig. 55) is an eleven-measure, two-voice exercise in the Dorian mode on d, with the cantus firmus in the lower voice and the florid voice written above it, preserved as a Humdrum **kern encoding. The cantus firmus is Fux's standard Dorian melody (D F E D G F A G F E D), spanning a fifth (D–A). The added voice stays above the cantus firmus throughout, ranges only A4–F5, and moves mostly by step; its leaps (third, fourth, octave) are small and immediately recovered by step. The mode is Dorian with a flattened sixth degree (B♭), giving the exercise a minor colour, and the close uses the raised seventh (C♯) as a leading tone to the final. The exercise ends on the octave D–D, doubling the modal final.
The provenance of the 11-bar Dorian exercise is disputed: one account describes its line as hand-written by the report's author before consulting Fux's own third-species solutions, while the other identifies an eleven-measure Dorian exercise (Fig. 55) as Fux's own and preserved as a Humdrum **kern encoding. Both positions are retained here; it is not established whether they describe the same notation. The comparative study also distinguishes Fux's Fig. 55 from an AI researcher's own third-species line written above the same cantus.