This workbook supplements Alfred Mann's translation of The Study of Counterpoint from Johann Joseph Fux's Gradus ad Parnassum, providing blank staves for each of the six cantus firmi that Aloysius (the master teacher) sets before the young pupil Josephus. Each exercise set is prefaced by a list of the rules newly introduced at that stage. All quotations derive from Mann's translation. The cantus firmi are given in six modes — Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Ionian — and the exercises proceed through the five species in order, each species realized as a complete set of modal examples.
Key Points
The workbook supplies blank staves for six cantus firmi in six modes: Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Ionian.
Every species section is organized identically: a walk through the eight church modes in a fixed order (Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Ionian), each with its own worked example.
Each species section forms a complete set of modal realizations: Second Species (items 61–72), Third Species (73–84), Fourth Species (85–96), Fifth Species (97–108) — twelve items each, two examples per mode.
Part 1 of the source covers the First Species set in the same modal order; the material then resumes at Second Species.
Species progression: First Species (one whole note per cantus note), Second (two half-notes), Third (four quarter-notes), Fourth, and Fifth Species.
All species share a core of melodic rules governing mode, forbidden skips, exposed tritones, recovery of leaps, repeated notes, and multiple skips in one direction.
Concepts
The six modes / cantus firmi: modal melodies against which the student writes counterpoint; the counterpoint must be in the same mode as the cantus firmus.
The five species: progressively more elaborate rhythmic settings of the cantus firmus, from whole notes to florid mixed values.
Opening and closing formulas: mode-establishing opening bars and prescribed cadential figures that differ according to whether the counterpoint lies above or below the cantus firmus.
Dissonance treatment: dissonances are permitted only as step-wise passing notes (or in the cambiata formula), with downbeats held consonant.
Perfect vs. imperfect consonances: direct motion into octaves, unisons, and fifths is prohibited; imperfect consonances are to outnumber perfect ones.
Details
Melodic rules common to all species
The counterpoint must be in the same mode as the cantus firmus: avoid accidentals and strongly establish the mode in the opening bar. When the cantus firmus is in the upper part, the counterpoint's first bar must be an octave or unison (not a perfect fifth); when the counterpoint is above the cantus firmus, the opening interval may be a unison, octave, or perfect fifth.
Forbidden skips include augmented fourths (tritones), sevenths, any interval greater than an octave, descending sixths whether major or minor, and ascending major sixths. "Exposed tritones" are likewise forbidden — no run of notes in a single direction should span an augmented fourth from end to end.
Leaps of an ascending minor sixth or octave, or a descending octave, must be "recovered": followed immediately by a step back into the range covered by the leap. Fux often recovers using a skip of a third back into the leap.
Repeated notes should be avoided; Fux makes many exceptions in First Species, but they are rare in the other species. Multiple skips in the same direction should be avoided, but this is a guideline only — Fux contradicts it often. On page 46, for example, in the second-species Phrygian example he skips a 4th, 5th, and 4th in the same direction: c–f–c'–f'.
Two-voice species rules
First Species — one whole note against each cantus firmus note; dissonances are forbidden.
Never enter a perfect consonance (octave, unison, or fifth) by direct motion.
"Contrary and oblique motion should be employed as often as possible."
"More imperfect than perfect consonances should be employed," lest the result lack harmony.
Closing formula: in the next-to-last bar there must be a major sixth if the cantus firmus is in the lower part, and a minor third if it is in the upper part.
Second Species — two half-notes against each whole note.
The first half-note in each bar must be consonant with the cantus firmus.
The second half-note may be dissonant, but only if approached and left by a step.
Fifths or octaves on the downbeat of successive measures are permitted only if the intervening note leaps by an interval larger than a third.
Third Species — four quarter-notes against each whole note.
The first note of each bar must be consonant with the cantus firmus.
The second, third, or fourth notes may be dissonant only as step-wise passing notes between two consonant notes.
The cambiata formula may also be used: above the cantus firmus it is 8, 7, 5, 6; below it is 3, 4, 6, 5.
Closing formulas: a counterpoint above the cantus firmus may close either with a cambiata, 8, 7, 5, 6, 8, or with a scale run, 3, 4, 5, 6, 8. A counterpoint below must close as 3m, 5, 4, 3m, 1.
Fourth and Fifth Species — the workbook continues this progression, each species given its full set of modal examples (see structure below). Fourth Species (the syncopated species) and Fifth Species (florid counterpoint) follow the same modal plan as the earlier sections.
Rendering diagram…
Structure of the exercise sets
The source's second part opens with section 4.2 Second Species, preceded by the Dorian example, and continues through 4.3 Third Species, 4.4 Fourth Species, and 4.5 Fifth Species. Every species section is organized the same way: a walk through the eight church modes in the fixed order Dorian, Phrygian, Lydian, Mixolydian, Aeolian, Ionian, each presented with its own worked example — likely two-example pairs, given the alternating blocks within each mode.
The mode labels are printed as headers within each species section (e.g., "Dorian…", "Phrygian", "Lydian", "Mixolydian", "Aeolian:", "Ionian:"). The Ionian entries in each species are marked with a colon-style heading ("Ionian:") and the Aeolian entries likewise appear as bare mode headers.
Each species section repeats the identical sequence of mode examples: Second Species (items 61–72), Third Species (items 73–84), Fourth Species (85–96), and Fifth Species (97–108) — indicating that each section is a complete set of modal realizations in that species. This structure implies that the first part of the source covered the First Species set in the same modal order, with the later part resuming at Second Species.
Note on legibility: in the second part of the source the musical notation itself renders as garbled glyphs, so what can be captured faithfully from that portion is its structural and labeling content (section numbers and mode names) rather than the notes themselves; no further prose explanation, definitions, or numerical data beyond the section numbers and mode names is legible there.