the opposite direction from the first_. [Fig. 28.]

[Illustration: Fig. 28.]

In minor the sixth degree may occasionally be raised on the strong beat, if
it is desired to proceed upward to the raised seventh degree. [Fig. 29.]

[Illustration: Fig. 29.]

In the last measure but one, both the supertonic and leading tone should
appear. [Fig. 30.]

[Illustration: Fig. 30.]

_Three_ notes may be written to one of the cantus firmus, as in Fig. 31.
For this no new rules are required.

[Illustration: Fig. 31.]

The cadences in Fig. 32 are good. It will be seen that the cadences of the
first species may also be used.

[Illustration: Fig. 32.]

EXERCISES

To cantus firmus _a_ write two counterpoints above and two below in the
first species.

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

CANTI FIRMI

[Illustration: Fig. 33.]

LESSON III

SECOND SPECIES IN BOTH PARTS[1]

[Illustration: Fig. 34.]

[1] In this and similar cases the term "species" will be
understood as referring simply to the number of notes, or to the
note-combinations, of the contrapuntal part or parts in question.
"Second species in both parts" means, therefore, that both parts
progress in half-notes.

When writing second species in both parts no cantus firmus is used, both
parts being original. One part begins on the first beat, the other may
begin on either the first or second beat. [Fig. 35.]

[Illustration: Fig. 35.]

The interval formed by the two notes appearing on the second beat should be
a consonance, or one of the following dissonances: The augmented fourth,
the diminished fifth, the minor or diminished seventh when properly
resolved, and the perfect fourth when approached in contrary motion.

All tones not belonging to the harmony implied on the first beat, must be
treated as dissonances. [Fig. 36.]

[Illustration: Fig. 36.]

The seventh or ninth of the implied harmony of a measure, when approached
in an upward direction, may be used in either part, provided it is
consonant with the other part, or comes within the requirements of the
exceptions. [Fig. 37.]

The passing major seventh and its root may appear on the weak beat, even
when approached in similar motion as in Fig. 37_a_. The seventh must then be
treated as a passing-tone.

[Illustration: Fig. 37.]

The cadences in Fig. 38 are good when writing second species in both parts.
Those having the second s