A summary of Fux's rules for 2v species counterpoint
Two voices
First species (semibreve against semibreve)
1. Move to a perfect consonance in oblique or contrary motion -- never in direct motion (direct motion means both similar and parallel motion).
2. In general, contrary motion is preferred. Gauldin 27
3. Use more 6ths and 3rds than octaves and fifths.
4. Begin and end the exercise with a perfect consonance.
5. In the first measure, be sure that the tonic pitch is in the lower voice.
6. If the cantus is below, the interval in the penultimate measure is a M6; the cantus is below, the penultimate measure will be a m3 (p. 28 bottom). This of course assumes that scale degree ^2 is in the cantus.
7. Voice crossing is okay.
8. Avoid "beaten" (batutta) octave, fifth, and unison -- approach to any of these perfect consonances by contrary motion with a leap in the upper voice. Of these, the beaten octave and unison are the worst.
Second species (two minims against a semibreve)
1. If the cantus is below, the penultimate measure should have the intervals 5-6; if the cantus is above, the intervals should be 5-3. This of course assumes that scale degree ^2 is in the cantus. [EXAMPLE TO BE ADDED]
2. The succession 5-3 5-3 is bad, because the fifths are heard as though parallel. 8-6-8-6 is also bad, but 8-5 8-5 is okay because a leap larger than a third in the second species voice mitigates the feeling of parallels.
3. The counterpoint (second voice) may have a rest of a minim length in the first measure.
4. In his examples, Fux has one descending m6, a string of 5 or 6 seconds in the melody, and a number of triad arpeggiations in the counterpoint.
5. The skip of the m6 ascending or the octave is useful to separate voices that have come too close together.
Third species (four semiminims against a semibreve)
1. If one has five quarter notes moving by step in the same direction:
the first is consonant, the 2d cons or diss, the 3d cons, the 4d diss, the 5d cons.
or: the first is cons, the 2d cons, the 3d diss, the 4d and 5d cons.
(The first beat of the measure must always have a consonant interval.)
2. The nota cambiata is an acceptable figure.
3. Cadence formulas: . [EXAMPLE TO BE ADDED]
Fourth species (minims against semibreve, with suspensions):
1. Whenever the ties characteristic of this species are used, the accented beat of the measure may be either consonant or dissonant. If not tie, is used, one reverts to second species, and the first beat must be consonant. One should try to use as many ties as possible.
2. The only kind of dissonance allowed when the tie is used is the suspension, which must be prepared with a consonance and resolved stepwise downward. Fux's examples at this point in the text show 7-6 and 4-3 suspensions.
3. 2-1-2-1 or 9-8-9-8 suspensions in sequence are bad, because they reduce to parallel unisons or octaves. One 2-1 or 9-8 suspension, however, is okay. This shows that one must judge progressions with suspensions according to the sonority formed byt the two whole notes and resolution note in each measure (p. 56 ff).
4. 2-3, 4-5, 9-10 bass suspensions are usable, but not 7-8.
5. No upward resolutions or dissonance are possible.
6. One should write second species minims when a tie cannot be written, but should try to make a suspension as soon thereafter as possible.
Fifth species (semibreve, minim, semiminims in combination against semibreve)
1. Fifth species is a combination of the other four.
2. Suspensions may be ornamented (by a pair of eighth notes acting as neighbor notes or by a leap forming an interval consonant with the cantus or by anticipation of the resolution notes. See pp. 62-63.
3. One may use a pair of eighth notes on the second or fourth quarter (never on the first or second).
4. Use oblique motion or suspensions in approach to the downbeat as much as possible "since it brings about the greatest beauty in the counterpoint."
5. semiminim-semiminim-minim is not good, except when the half note is tied to a note in the next measure.