The big change in Second Species (aside from the quicker movement) is that you can now introduce dissonances formed with the bass, and they can be any kind of dissonance, including 2nds, 7ths, etc. But these can come only on the second note of each pair within a measure, and must be approached and left by step and otherwise follow the below style rules.
Melodic movement:
(As in first species) No voice should make a leap larger than a fifth, except for the octave and the ascending minor sixth.
(As in first species) Avoid making successive same-direction leaps in the same voice unless they outline a triad. If they can't be avoided they should at least total less than an octave.
(As in first species) Leaps greater than a fifth should be compensated by stepwise movement in the opposite direction.
(As in first species) No voice should move by a chromatic interval (any augmented or diminished interval).
(As in first species) Avoid repeating a pitch in the lowest voice. In upper parts you can repeat a pitch as many as three times successively if necessary.
(As in first species) Keep each voice confined to a singable range for the part, preferably not exceeding a 10th from its highest to its lowest pitch.
(New) Avoid writing the same melodic interval twice on the same pitches. For example:
Rhythm:
(New) In binary meter one voice has two notes to each note of the cantus firmus; in ternary meter the faster part moves 3 to 1. If there are additional voices, they move with the cantus firmus as in first species.
(New) In both binary and ternary meter you may occasionally substitute a rest for the first note of each group (that is, the one that coincides with the cantus firmus).
(New) The faster voice should begin after the cantus firmus, following a rest. The parts will still end together and can use the same note value for the final sonority. In three or more parts only one voice will be moving faster than the others; the others can still enter together.
Independence of voices:
(As in first species) Avoid writing parallel fifths or octaves (moving two voices in the same direction from one fifth or octave to another).
(As in first species) Avoid writing direct fifths or octaves (moving two voices in the same direction to a fifth or an octave). There are exceptions: these may be acceptable at a cadence, or if one voice is inner and the exposed voice moves stepwise. Direct 5ths in the outer voices will be accepted if the upper voice moves by step.
(New) Avoid writing parallel octaves or fifths between two adjacent downbeat notes (beginnings of measures) unless the intervening accompaniment note leaps by more than a third. In the second of these parallels between downbeats the leap of a fourth is thought to mask the effect of the parallel.
(As in first species) Do not let two voices leap to a perfect interval unless one of them is an inner part.
(As in first species) One perfect interval can follow another in the same voice only if one of the voices moves stepwise.
(As in first species) Avoid parallel fourths unless the lower tone of the fourth is not the bass and the pitch class a third below that note is present (that is, parallel 1st-inversion triads are OK). Fourths can also be allowed if one of the tones is nonessential.
(As in first species) Upper voices can sometimes cross if necessary, but avoid "overlapping" (in an overlap voices do not cross, but one moves to a position that is at or beyond the previous pitch of another voice).
(As in first species) Avoid the unison except at the beginning or end. Authorities disagree: Fux forbids unisons except at terminals (though he occasionally shows on in his examples). Jeppeson is much more free with unisons. But since these exercises are mostly based on the Fux method we'll keep his objection to unisons.
(As in first species) In all species of counterpoint, use contrary motion frequently to emphasize the independence of voices.
Dissonance handling:
(New) The second (unaccented) note of each pair in the fast voice can be either consonant or dissonant. The accented notes must be consonant. In triple meter either the second or third note of each group can be dissonant, but not both.
(New) Any dissonant note must be approached and left by step.
Harmony:
(As in first species) If in two parts the music must begin with perfect consonances (octaves, fifths, or unisons) and end with octaves or unisons. In three or more parts you can begin and end with full triads, but the ending must be either a major triad or a perfect consonance. Fux advises that if the mode does not contain a major third over the tonic, then it is best to leave the third out of the final chord rather than to raise it to a major third.
(As in first species) Avoid doubling a seventh.
(As in first species) The cantus firmus will always begin and end with the tonic. If the cantus firmus is in an upper voice, be sure not to harmonize it with a fifth below at the beginning. That would give the impression of a different mode.
(As in first species) Avoid placing the chromatically altered form of a note immediately adjacent to its unaltered form in a different voice (i.e. cross relation).
(As in first species) In two-part writing, avoid adjacent use in different voices of two pitches that form the tritone (tritone cross relation).
(As in first species) In general keep to the pitch classes of the mode expressed by the cantus firmus. Unless you transpose a cantus firmus this will in practice mean the "white key" notes in Counterpointer's species exercises. Nonmodal tones may be introduced, however, if they accord with conventional principles for altered tones.
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