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Fourth Species Counterpoint
Fourth Species deals with syncopation. In duple meter one voice has two notes to each one of the other parts, and the second of each pair is tied forward. The second of each pair is the offbeat note, so each measure begins with a note held from before. The accented note that begins each measure can be either dissonant or consonant, but if dissonant it must resolve by step to a consonance. The second note of each measure must always be consonant. At the final cadence, however, or on rare occasions within the composition, you can revert to Second Species (we'll allow one such pre-cadence reversion for every 8 notes of the c.f.):

In a triple meter, the active voice will have three notes to each one of the other parts, and the third note of each group will be tied forward. In triple meter the second note of each group can be a dissonant passing or neighbor tone, though again the third note of each group must be consonant.
How to write in Fourth Species
Melodic movement:
(As it was in Second Species) No voice should make a leap larger
than a fifth, except for the octave and minor sixth.
(As before) 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 before) Leaps greater than a fifth should be compensated by
stepwise movement in the opposite direction.
(As before) No voice should move by a chromatic interval (any augmented
or diminished interval).
(As before) 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 before) Keep each voice confined to a singable range for the part,
preferably not exceeding a 10th from its highest to its lowest pitch.
(As before) Avoid writing the same melodic interval twice on the same
pitches.
Rhythm:
(New)As in Second Species, one voice has two notes to each note
of the cantus firmus, or in triple time it has three. The difference is that
the last of each group is tied to the first of the next. If there are additional
voices, they move with the cantus firmus as in first species.
(New) You may occasionally revert to Second Species if the
situation demands it, simply by not tying the last note of the group over
to the downbeat. But if you do, the downbeat note must be consonant as it
is in Second Species.
(As before) 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 before) Avoid writing parallel fifths or octaves (moving two
voices in the same direction from one fifth or octave to another).
(As before) Avoid parallel fifths or octaves between the downbeat (accented) notes of two successive measures,
unless the faster voice leaps by more than a third from the first perfect interval, or if the intervening note
is consonant.
(As before) 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.
(As before) Do not let two voices leap to a
perfect interval unless one of them is an inner part.
(As before) 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 before) Avoid writing more than three of the same interval
in a row in any two parts (e.g. four consecutive thirds or four consecutive
sixths).
(As before) 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). Overlap is allowed between upper voices in three
or more parts.
(As before) One perfect interval can follow another in the same voices
only if one of the voices moves stepwise.
(As before) In all species of counterpoint, use contrary motion
frequently to emphasize the independence of voices.
(Modified) The unison is acceptable on the second of a pair of
accompaniment notes if it is preparing a properly resolved dissonance:

Dissonance Handling:
(New) The note tied forward must be consonant (the suspension
is prepared by a consonance). Fux (see Mann, p. 98) allows for an exception
to this, saying that if the untied note is repeating a pitch then the preparation
can be dissonant. Maybe this derives from Palestrina's use of the 4th
as its own preparation (see Kitson, 117) - that can only be accomplished
if the longer tone is continuing the same pitch. For the present exercises
we'll require a consonant preparation except for the fourth, which can
serve as its own preparation if its bass is continuing.
(New) The downbeat note tied from before can now be either
consonant or dissonant, but if dissonant it must be left by downward step.
There can be no upward resolution of dissonance in Fourth Species.
(New) Accented dissonances (the only kind in Fourth Species)
are best resolved to an inperfect consonance (a third or a sixth) but there are exceptions: the ninth can resolve
to an octave, the second to a unison, and the fourth to a fifth.
(New) At the moment of dissonance the pitch class of the
resolution should not be already present somewhere else in the sonority.
In the following example the note of resolution is C, already present in
the middle voice.

Harmony:
(As before) 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 before) The c.f. will always begin and end with the tonic. If the
c.f. 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 before) Avoid doubling a seventh.
(As before) Avoid placing the chromatically altered form of a note immediately adjacent to its unaltered
form in a different voice (i.e. cross relation).
(As before) In two-part writing, avoid adjacent use in different voices of two pitches that
form the tritone (tritone cross relation).
(As before) 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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