fux workbook 0.1
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Species Counterpoint Exercises from Fux’s Gradus ad Parnassum
1 Introduction
This workbook supplements Alfred Mann’s The Study of Counterpoint from Johann Joseph Fux’s Gradus ad Parnassum . Itincludes a comprehensive set of blank staves associated with each of the six cantus firmi that Aloysius, the master teacher, offersyoung Josephus. Each set of exercises is prefaced with a list of newly introduced rules. All quotes are from Mann’s translation.
Melodic rules common to all species
1. “The counterpoint must be in the same mode as the cantus firmus.” In other words, avoid accidentals, and stronglyestablish the mode in the opening bar. Practically speaking, when the cantus firmus is in the upper part, the counterpointin the first bar must be an octave or unison (not a perfect fifth). When the counterpoint is above the cantus firmus, theopening interval may be a unison, octave, or perfect fifth.
2. Forbidden skips: augmented fourths (aka tritones), sevenths, any interval greater than an octave, descending sixthswhether major or minor, and ascending major sixths.
3. “Exposed tritones” are forbidden. That is, no run of notes in a single direction should be an augmented 4th from end toend.
4. Leaps of an ascending minor sixth or octave, or a descending octave must be “recovered.” That is, such a leap must befollowed immediately by a step back into the range covered by the leap. (Fux often “recovers” using a skip of a third backinto the leap.)
5. Avoid repeated notes. (Though Fux makes many exceptions in Species One, repeated notes are rare in the other species.)
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6. Avoid multiple skips in the same direction. (This is a guideline—Fux contradicts this advice all the time. See, e.g., page46, in the 2nd species phrygian example, he skips 4th, 5th, and 4th in the same direction: c-f-c’-f’.)
2 Two Voices
2.1 First Species
First species counterpoint consists of a whole note set against each note of the cantus firmus; dissonances are forbidden.
1. Never enter a perfect consonance (an octave, unison, or fifth) by means of direct motion.
2. “Contrary and oblique motion should be employed as often as possible.”
3. “More imperfect than perfect consonances should be employed” (lest the result be lacking in harmony).
4. Closing formulas. “In the next to the last bar there must be a major sixth if the cantus firmus is in the lower part; and aminor third, if it is in the upper part.”
Dorian
8
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Phrygian
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Lydian
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Mixolydian
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Aeolian
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Ionian
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2.2 Second SpeciesSecond species counterpoint consists of two half-notes set against each whole note in the cantus firmus.
1. The first half-note in each bar must be consonant with the cantus firmus.
2. The second half-note in a bar may be dissonant, but only if it is approached and left by a step.
3. Fifths or octaves on the downbeat of successive measures are only permitted if the intervening note leaps by an intervallarger than a third.
4. Closing formula: above the cantus firmus is 5, 6, 8. Below is 5, 3m, 1.
Dorian
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Phrygian
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Lydian
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Mixolydian
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Aeolian
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Ionian
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2.3 Third Species
Third species counterpoint consists of four quarter-notes set against each whole note in the cantus firmus.
1. The first note of each bar must be consonant with the cantus firmus.
2. The second, third, or fourth notes may be dissonant only if they are step-wise passing notes between two consonant notes.
3. The counterpoint may also use the cambiata formula: above the cantus firmus, this is 8, 7, 5, 6. Below, 3, 4, 6, 5.
4. Closing formulas. A counterpoint above the cantus firmus may close two ways: either with a cambiata formula, 8, 7, 5, 6,8; or with a scale run, 3, 4, 5, 6, 8. A counterpoint below the cantus firmus must close as 3m, 5, 4, 3m, 1.
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Dorian
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Phrygian
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Lydian
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8
Mixolydian
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Aeolian
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Ionian
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2.4 Fourth Species
Fourth species counterpoint, also called ligature , consists of two half-notes set against each whole note in the cantus firmus.The second half-note in each bar is tied to the first half-note in the following bar.
1. The second half-note in each bar must be consonant.
2. The half-note on the downbeat, carried over from the previous bar, may be dissonant. It must be resolved by stepwisemovement downward.
3. Dissonant ligatures resolving to an octave or a unison in successive bars are forbidden. However successive resolutions toa perfect fifth are permitted.
4. In some situations, no ligature is possible. In these cases, the half-notes may be separated, as in the second species.Return to ligature as soon as possible.
5. Closing formulas. A counterpoint above the cantus firmus must close 7 (tied to the previous bar), 6, 8. A counterpoint
below the cantus firmus must close 2 (tied to the previous bar), 3m, 1.
Dorian
8
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Phrygian
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Lydian
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Mixolydian
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Aeolian
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Ionian
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2.5 Fifth SpeciesFifth species counterpoint, also called florid , consists of the combination of the first four species.
1. In florid counterpoint, there are three substitutions that can be made on the second beat of a suspended (or dissonant)ligature. 1) The second beat may be replaced by two eighth notes, a second and a third below the dissonance, resolving toa single step below the original dissonance. 2) The second beat may be replaced by a consonant quarter note a fifth lowerthan the dissonance, followed by the resolution on the third beat, a step below the original dissonance. 3) The secondbeat may be replaced by a quarter note a step below the dissonance, which resolution is then repeated on the third beatof the bar.
2. “Two eighths may occasionally be used... on the second and fourth beats of the measure—but never on the first andthird.”
3. “Not as a rule but by way of advice: since the melodic line seems to lag if two quarters occur at the beginning of themeasure without a ligature following immediately, it will be better—if one wants to write two quarters at the beginningof the measure—to connect them by a ligature with the notes following, or else to make it easier for these two quarters togo on by using some additional quarters.”
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4. The required closing formulas for species five are the same as species four. A counterpoint above the cantus firmus mustclose 7 (tied to the previous bar), 6, 8. A counterpoint below the cantus firmus must close 2 (tied to the previous bar),3m, 1.
Dorian
8
Phrygian
8
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Lydian
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Mixolydian
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Aeolian
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Ionian
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3 Three Voices
3.1 First Species
Dorian
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Phrygian
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Lydian
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Mixolydian
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3.2 Second Species
Dorian
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Phrygian
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Lydian
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Mixolydian
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Aeolian
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Ionian
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3.3 Third Species
Dorian
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Phrygian
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Lydian
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Mixolydian
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Aeolian
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Ionian
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3.4 Fourth Species
Dorian
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Phrygian
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Lydian
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Mixolydian
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Aeolian
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Ionian
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3.5 Fifth Species
Dorian
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Phrygian
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Lydian
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Aeolian
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Ionian
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4 Four Voices
4.1 First Species
Dorian
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Lydian
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Mixolydian
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Aeolian
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Ionian
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4.2 Second Species
Dorian
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Phrygian
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Lydian
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Aeolian
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Ionian
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4.3 Third Species
Dorian
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Phrygian
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Lydian
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Mi l di
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Mixolydian
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Aeolia
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Aeolian
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Ionian
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Ionian
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4 4 Fourth Species
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4.4 Fourth Species
Dorian
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Phrygian
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Phrygian
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Lydian
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y
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Mixolydian
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y
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Aeolian
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4.5 Fifth Species
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Dorian
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Lydian
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Mixolydian
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Aeolian
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Ionian
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