A Treatise on Simple Counterpoint in Forty Lessons Part 3

To cantus firmus _b_ write one above and one below, in the second species.

CANTI FIRMI

[Ill.u.s.tration: Fig. 40.]

LESSON IV

THIRD SPECIES

[Ill.u.s.tration: Fig. 41.]

In this species, four notes are written in the counterpoint to each note of the cantus firmus. The counterpoint may begin on the first, second, or fourth quarter. The second quarter is, however, the most usual. [Fig. 42.]

[Ill.u.s.tration: Fig. 42.]

The exercises should begin and end with tonic harmony.

When the counterpoint begins on the first quarter it must form a perfect consonance with the cantus firmus. When on the second or fourth quarter, any consonance may be used.

All previous rules are to be regarded, unless exceptions are made.

At least one of the first three quarter-notes of a measure should be left degreewise. [Fig. 43.]

[Ill.u.s.tration: Fig. 43.]

The last quarter of a measure is usually left degreewise. If approached by a skip or by a degreewise progression of at least two quarter-notes, it may be left by a skip in the opposite direction from which it was approached. A skip of a third in the same direction is also good when this skip is preceded by a skip of a third (_d_). [Fig. 44.]

[Ill.u.s.tration: Fig. 44.]

Parts may cross occasionally.

The use of non-harmonic tones, as in Fig. 45, is good in either part. At _a_ the pa.s.sing-tone, instead of progressing directly to the adjacent chord-tone, skips a third to the other side of it and then returns. The embellishment is treated in the same way, but is most effective when the princ.i.p.al tone is the leading-tone, as at _b_. In both cases the counterpoint should continue degreewise through the chord-tone. [Fig. 45.]

[Ill.u.s.tration: Fig. 45.]

The fifth, when in the lower part, may be used on any but the first quarter, provided it is treated as a pa.s.sing-tone, e.g., approached and left by stepwise progression in one direction.

[Ill.u.s.tration: Fig. 46.]

Consecutive fifths and octaves are forbidden when appearing on the accented beats of successive measures; between prominent notes of successive measures not more than four quarters apart; and between a prominent note of one measure and the first quarter of the next. [Fig. 47.]

[Ill.u.s.tration: Fig. 47.]

Oblique motion to the unison is bad. It is permitted if it continues in the same direction through the unison. [Fig. 48.]

[Ill.u.s.tration: Fig. 48.]

The unison may be used on any but the first quarter of a measure.

Frequent repet.i.tion of a figure as in Fig. 49 is not good.

[Ill.u.s.tration: Fig. 49.]

The embellishment may be used either above or below, whether a semitone or a whole tone; but when it is a whole tone below, it is most satisfactory as the ninth of the implied chord. [Fig. 50.]

[Ill.u.s.tration: Fig. 50.]

In minor the sixth and seventh degrees of the scale are raised both ascending and descending, when used in harmonies containing the leading-tone as a chord-tone. They are unaltered both ascending and descending in harmonies containing the sixth degree of the scale as a chord-tone. In other harmonies they are raised in ascending only.

The sixth or seventh degrees may be chromatically altered with only one note intervening. [Fig. 51.]

[Ill.u.s.tration: Fig. 51.]

Six notes may be written to one of the cantus firmus, as in Fig. 52.

[Ill.u.s.tration: Fig. 52.]

The cadences in Fig. 53 are good.

[Ill.u.s.tration: Fig. 53.]

EXERCISES

To cantus firmus _a_ write three counterpoints above and three below, in the third species.

Write two eight-measure phrases, using second species continuously in both parts. [Fig. 34.]

CANTUS FIRMUS

[Ill.u.s.tration: Fig. 54.]

LESSON V

THIRD SPECIES IN BOTH PARTS

[Ill.u.s.tration: Fig. 55.]

The suggestions given for writing second species in both parts apply here, except that when both parts move degreewise, any interval may come on the second and fourth quarters, preferably a consonance. The third quarter is treated the same as the second half when writing the second species in both parts.