[Illustration:  Fig. 15.]

A close as in Fig. 15_b_ may be used occasionally.  In this case the leading-tone is better in the higher part.

EXERCISES

To each of the following canti firmi write two counterpoints above, and two below.

CANTI FIRMI

[Illustration:  Fig. 16.]

LESSON II

SECOND SPECIES

[Illustration:  Fig. 17.]

All rules for the first species must be observed.

Two notes are written in the counterpoint to one of the cantus firmus, except in the last measure. [Fig. 18_a_.] In the last measure but one the first species may sometimes be used. [Fig. 18_b_.]

[Illustration:  Fig. 18.]

Repetition of a note in any but the first species is forbidden. [Fig. 19.]

[Illustration:  Fig. 19.]

The counterpoint may begin on the first or the second half of the measure, preference being given to the second half.  When it begins on the first half it must be a unison, fifth, or octave; when on the second half, it may be any consonance. [Fig. 20.]

[Illustration:  Fig. 20.]

After the first measure the interval on the first beat should be an imperfect consonance, as in the first species, but the fifth, or octave, may be used occasionally.

In this and succeeding lessons, all notes in the measure not belonging to the harmony implied on the first beat, must be treated as dissonances, e.g., those belonging to the implied harmony may be left by a skip (a) or stepwise progression (b) unless dissonant with the cantus firmus; then avoid their use; if foreign to it, whether consonant (c) with the C.F. or not (d), they must be treated as embellishments or passing-tones. [Fig. 21.]

[Illustration:  Fig. 21.]

The embellishment may be used as follows:  when above the principal tone, it may be a semitone (a) or a whole tone (b) distant from it; and when below, a semitone (c). [Fig. 22.]

[Illustration:  Fig. 22.]

When the counterpoint is below the cantus firmus, the fifth of the chord needs special treatment.  It is permitted on the weak beat when the lower is treated as an harmonic passing-tone.

An harmonic passing-tone is the second of three tones belonging to the same chord. [Fig. 23_a_.] While the third tone should be a member of the chord containing the fifth as an harmonic passing-tone, the chord above it may change as in Fig. 23_b_.

The fifth is permitted on the strong beat when it is only an implied fifth (six-four chord); that is, the third and fifth appear on the strong beat, and the root does not come in until the second half of the measure. [Fig. 23_c_.]

[Illustration:  Fig. 23.]