Chapter 2

In skipping from the fifth to the root, or the reverse, in the lower part, do so in an upward direction. The fifth, when treated as an harmonic passing-tone, may, however, be approached either ascending or descending.

The retardation should be used only when prepared by the leading-tone. It rises a semitone in resolving. [Fig. 66.]

The following dissonant intervals may be used on the first half of the measure:--When the counterpoint is above, the fourth and seventh in suspension, and second and fifth in retardation; and when below, the second in suspension, and the fourth and seventh in retardation. [Fig. 67.]

Consecutive fifths on consecutive strong beats of the measure are good when one of the tones of the second fifth is prepared, as in Fig. 68.

The following cadences are good:

EXERCISES

Write one eight-measure phrase with two notes to the measure in one part and six in the other; one with three notes in one and six in the other; and one with two notes in one part and four in the other. (Fig. 59.) In combining the species in this and succeeding lessons the student may place any species in any part.

To the cantus firmus write two counterpoints above and two below, in the fourth species.

CANTUS FIRMUS

LESSON VII

FOURTH SPECIES (Continued)

The first and fourth species may be mixed as in Fig. 71. Rules for writing other than the first species in both parts are to be regarded.

EXERCISES

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

To cantus firmus _b_ write two above and two below, three half-notes to the measure, with syncopations.

Write two eight-measure phrases, mixing the first and fourth species.

CANTI FIRMI

LESSON VIII

COMBINING THE FOURTH SPECIES WITH THE OTHERS

All previous rules for combining species still apply.

In combining the fourth species with other than the first, the following intervals may be used on the first half of the measure, in addition to those mentioned in Lesson VI: When the counterpoint is below, the fourth, fifth and seventh in suspension, and the ninth in retardation; and when above, the fifth in suspension, and the seventh in retardation; but in every such case the part having other than the fourth species must skip to some other chord-tone before resolving the suspension. [Fig. 73.]

The leading-tone may be doubled as in Fig. 74. Here the leading-tone that is prepared skips to some other chord-tone, while the new leading-tone remains stationary.

The minor or diminished seventh, major or minor ninth, may be used as preparation of a suspension in either part, provided it is approached by a skip in an upward direction, and is consonant with the other part, or is one of the permitted dissonances. [Fig. 75.]

The fourth species may be combined with the second or third species, and two or three notes syncopated may be written in one part with six in the other. [Fig. 76.]

EXERCISES

To the cantus firmus write one counterpoint above and one below, in the fourth species.

Write one eight-measure phrase each, of the following combinations: The fourth species with the second; the fourth with the third; two notes syncopated against six notes; and three notes syncopated against six notes. Write some in major and some in minor. [Fig. 76.]

CANTUS FIRMUS

LESSON IX

FIFTH SPECIES: FLORID COUNTERPOINT

Florid counterpoint is a mixture of the second, third and fourth species.

In addition to these species eighth-notes may be used in groups of two on the second and fourth quarters of the measure. Both notes should be approached and left stepwise, with the exception that the first may be taken by a skip. [Fig. 79.]

Not more than one and one-half measures of any one species should be used continuously in one part. [Fig. 80.]

In the use of quarter-notes it is necessary to exercise care. They may be used on the first half when preceded by quarter-notes, when the entire measure is filled, or when they precede a half-note which is the preparation of a suspension. On the second half they are always good. [Fig. 81.]

For the present the suspension should not be less than a half-note or its rhythmic equivalent in the ornamental resolution.

In this species the suspension may resolve ornamentally, that is, it may have some note or notes interpolated between the suspension and its resolution. The relative position of the suspension and its resolution must remain the same as in the regular resolution. [Fig. 82.]

When the suspension is left by a leap, the note skipped to should be consonant with the other part (_b_). When eighth-notes are used, as at _a_, they must be approached and left stepwise.

The suspension, instead of being sustained as a half-note, may be repeated on the second quarter, as at _c_. In this case it is best to continue stepwise through the tone of resolution.

At _d_ the resolution, instead of coming on the second half, appears on the quarters on either side. This is good.

The ornamental resolution may be used in either part.

Use the suspension freely.

The solutions should be musical, and are to be written over and over again until such are secured.

All cadences of the second, third and fourth species, or any combination of these, may be used.

EXERCISES

To canti firmi _a_ and _b_ write two counterpoints above and two below, in the fifth species

CANTI FIRMI

LESSON X

FLORID COUNTERPOINT (Continued)

When florid counterpoint is combined with other than first species, the dotted half followed by a quarter-note (_a_), or two eighth-notes (_b_), is good. Also, a rhythmic figure, as at _c_, where a half-note occupies the second and third quarters, may be used. [Fig. 84.]

EXERCISES

Write one eight-measure phrase, each, of the following combinations: The fifth species with the second; the fifth with the third; and the fifth with the fourth. Write also two eight-measure phrases with fifth species in both parts. [Fig. 85.]

SIMPLE COUNTERPOINT IN THREE PARTS

LESSON XI

FIRST SPECIES

Regard all rules for two-part counterpoint, unless otherwise mentioned.

If possible, each measure should contain a complete chord. When in the first species it becomes necessary to double an interval, let it be preferably the root. The third should be doubled only when a decidedly smoother melodic progression is thereby obtained; and when both thirds are in outer parts, each should be approached and left stepwise in one direction (Fig. 87). The doubling of the fifth is, of course, impossible, since it necessitates the omission of the third.

All triads may be used in their first inversion.

Diminished and augmented triads, however, are best used in their first inversion.

The six-four chord may be used at the close as the cadencing tonic six-four chord. Do not approach the root and fifth in similar motion, as at _b_. [Fig. 88.]

The dominant seventh may be used in any but its second inversion, the fifth being omitted.[2] The seventh requires no preparation. Other chords of the seventh are better not used until second species and later.

If possible, let the chord in the first measure appear complete. The last chord but one should be complete, unless some form of V or V_7 is used. [Fig. 89.]

[2] In severely strict counterpoint all parts above the lowest must be consonant with it. Dissonances, when entering simultaneously with it, must be treated as suspensions, and when used in the progression of a part from one chord to another, should be treated as passing-tones or embellishments. This excludes the use of the unprepared seventh and ninth; all diminished and augmented triads except in their first inversion; and all six-four chords, except when the lowest part is treated as a passing-tone.

Consecutive major thirds may be used when three or more parts are employed. [Fig. 90.]

A note may now be repeated in the lowest part when it becomes the seventh of a dominant seventh-chord. [Fig. 91.]

In writing, use soprano, alto and tenor, or alto, tenor and bass; and do not separate upper parts more than an octave. For a chord or two they may (for the sake of better voice-leading) separate a tenth.

All hidden fifths and octaves are bad, except between I and V and V and I. [Fig. 92_a, b_.]

The perfect fifth following the diminished fifth is good when taken in an upward direction stepwise in the higher parts. [Fig. 92_c_.]

All cadences used in harmony are good.

Unless otherwise mentioned, put the cantus firmus in any part, but avoid its continued use in the same part.

EXERCISES

To canti firmi _a_ and _b_ write the first species in all parts. Write each three times, setting the cantus firmus in a different part in each solution. This necessitates transposing the cantus firmus, when setting it in the other parts.

CANTI FIRMI

LESSON XII

THE SECOND SPECIES

The second species is written in one part and the first in the other two.

All suggestions made for the second species in two-part counterpoint are to be observed, unless otherwise mentioned. Those regarding consecutive perfect intervals are especially to be observed.

The fifth, when in the lowest voice, should be used as in two-part counterpoint, except when used in V4/3 or the cadencing tonic six-four chord.

The V4/3 chord may be used on the weak beat, necessitating the omission of the third. [Fig. 95_a_.]

The third may be omitted (_b_), or doubled (_c_), on the weak beat in this and succeeding species. [Fig. 95.]

The minor or diminished seventh may be approached by a skip in an upward direction on the weak beat in any part. This usually necessitates the omission of some other chord-member on the weak beat.

The major or minor ninth may also be used in the same way, except in the lowest part, provided it is at least a ninth above the root. [Fig. 96.]

The progression from vii_6° to V in root-position or any inversion in the same measure, is good. [Fig. 97.] Use _b_ and _c_ only when using other than first species in two or more parts.

Each measure should usually contain a complete chord. If not complete on the first beat, bring the missing interval in on the second. [Fig. 98.]

The cadences in Fig. 99 are good, and will suggest others. The use of the fourth species is permitted as at _a_. A note may be repeated in the final cadence in all species as at _b_.

EXERCISES

To cantus firmus _a_ write the first species in all parts, as previously directed.

To cantus firmus _b_ write second species in one part. Write three times, changing cantus firmus and counterpoint about so that they will appear in each part in turn.

CANTI FIRMI

LESSON XIII

SECOND SPECIES IN TWO PARTS

The suggestions for second species in both parts, in two-part counterpoint, apply for the two parts having the second species in three-part counterpoint.

Accidental harmonies sometimes appear on the weak beat. All tones in this accidental harmony foreign to the chord on the strong beat must be treated as dissonances. This must be regarded whenever two or more parts have other than the first species. [Fig. 102.]

At Fig. 102_a_, the accidental harmony _f-a-c_ is on the weak beat. The _f_ and _a_, being foreign to the chord _c-e-g_ on the strong beat, are correctly treated as dissonances. At _b_, the _f_ and _a_ are left by skip, which is not permitted.

The second species may be written continuously in all parts; the tones appearing on the weak beat must be harmonically related to one another, and those foreign to the chord on the strong beat must be treated as dissonances. [Fig. 103.]

The first and second species may be mixed, as in Fig. 104.

The cadences in Fig. 105 are good, and will suggest others. Those with first species in all parts may also be used.

EXERCISES

To cantus firmus _a_ write a counterpoint in the second species in one part. Write three settings, as directed in the previous lesson.

Write two eight-measure phrases mixing the first and second species in all parts.

To cantus firmus _b_ write counterpoints in the second species in the other two parts. Write two settings, with the cantus firmus in different parts.

CANTI FIRMI

LESSON XIV

THIRD SPECIES

The suggestions for third species in two-part counterpoint, as well as those for writing the second species in three-part counterpoint, apply when writing third species in three-part counterpoint.

The cadences at Fig. 108 are good, and will suggest others.

EXERCISES

To cantus firmus _a_ write third species in one part. Write three settings as previously directed.

To cantus firmus _b_ write second species in two parts, as previously directed.

Write one eight-measure phrase, using second species in all parts.

CANTI FIRMI

LESSON XV

THIRD SPECIES IN TWO OR MORE PARTS

Previous suggestions when two or more parts have other than first species, apply here.

In using the ninth of a chord it is well to keep it at least a seventh distant from the third, as well as a ninth above the root, except in the case of the dominant ninth in minor keys, where it may be separated by only an augmented second ([b]). [Fig. 111.]

In writing the third species in all parts, notes appearing simultaneously should be harmonically related. Treat all tones foreign to the chord on the first quarter as dissonances.

The cadences in Fig. 112 are good.

EXERCISES

To cantus firmus _a_ write third species in one part, as previously directed.

To cantus firmus _b_ write third species in two parts, as in Fig. 110_b_. Write twice, changing the cantus firmus about.

Write one eight-measure phrase, mixing first and third species as in Fig. 110_a_.

CANTI FIRMI

LESSON XVI

THIRD SPECIES (Continued)

EXERCISES

To the cantus firmus write third species in one part, as previously directed.

Write one eight-measure phrase, mixing first and third species; also one mixing first, second and third. [Fig. 114.]

Write one eight-measure phrase, using third species in all parts. [Fig. 110_c_.]

CANTUS FIRMUS

LESSON XVII

FOURTH SPECIES

When the syncopation is a suspension or retardation, it is treated the same as in harmony.

The retardation should always be prepared by the leading-tone.

When the syncopated note belongs to the harmony of the measure, it may be left by a skip or stepwise progression. [Fig. 117.]

The third may be omitted on the strong beat in this species, provided the part having fourth species skips to the missing third, as at Fig. 117_a_.

Consecutive fifths, but not octaves, are saved by the suspension. Whenever they occur, do not use the note of resolution as preparation of a suspension, or tie it into the next measure (_a_), since it is really the passing seventh, and that does not lend itself well to either of the above, except in sequence as at _b_. [Fig. 118.]

The seventh or ninth of a chord, except the major seventh, may be used as preparation of a suspension when approached by a skip in an upward direction, as in Fig. 119.

This species may also be written in triple rhythm. [Fig. 120.]

The cadences in Fig. 121 are good, as well as those of the second species.

EXERCISES

To cantus firmus _a_ write fourth species in one part. Write three settings, as usual.

To cantus firmus _b_ write fourth species in one part in triple rhythm. Write three settings, as above.

To cantus firmus _b_ write second species in one part and third in the other. [Fig. 122.]

CANTI FIRMI

LESSON XVIII

FOURTH SPECIES (Continued)

EXERCISES

Write two eight-measure phrases, using the fourth species mixed in all parts. [Fig. 124_a_.]

To cantus firmus _a_ write second species in one part and fourth in the other. [Fig. 124_b_.]

To cantus firmus _b_ write third species in one part and fourth in the other. [Fig. 124_c_.]

CANTI FIRMI

LESSON XIX

FIFTH SPECIES

No suggestions other than have already been given for two- and three-part counterpoint are necessary for this species.

EXERCISES

To canti firmi _a_ and _b_ write fifth species in one part. Write each three times, as usual.

CANTI FIRMI

LESSON XX

FIFTH SPECIES (Continued)

EXERCISES

To cantus firmus _a_ write second species in one part and fifth in the other. [Fig. 128_a_.]

To cantus firmus _b_ write third species in one part and fifth in the other. [_b_.]

To cantus firmus _c_ write fourth species in one part and fifth in the other. [_c_.]

To cantus firmus _d_ write fifth species in two parts. [_d_.]

CANTI FIRMI

LESSON XXI

COMBINING THE VARIOUS SPECIES

EXERCISES

Write one eight-measure phrase each, of the following combinations: (1) 2nd, 3rd and 4th species (Fig. 130a); (2) 2nd, 3rd and fifth species (_b_) (3) 3rd, 5th and 5th species (_c_); (4) 2nd, 4th and 5th species (_d_); (5) 4th, 5th and 5th species (_e_).

LESSON XXII

FIFTH SPECIES IN ALL PARTS

EXERCISES

Write five eight-measure phrases with fifth species in all parts, making use of imitation at the beginning as in Fig. 131. The imitation need only be relative and continue for three or four notes. It is also well, when a part uses a striking melodic figure, to have some other part imitate it immediately after.

SIMPLE COUNTERPOINT IN FOUR PARTS

LESSON XXIII

No new suggestions are needed, except as follows: All covered fifths and octaves permitted in harmony are allowed here. When the cantus firmus is in the lowest part and the choice of the last chord but one is V4/3 or vii_6°, use the latter, as in Fig. 133.

EXERCISES

To canti firmi _a_ and _b_ write the first species in the other parts. Write each four times, setting the cantus firmus in each part in turn.

CANTI FIRMI

LESSON XXIV

EXERCISES

To cantus firmus _a_ write the first species in all parts, as in the previous lesson.

To cantus firmus _b_ write the second species in one part. Write four times, and change with each solution, so that both the cantus firmus and the second species will appear in each part. [Fig. 135.]

CANTI FIRMI

LESSON XXV

EXERCISES

To cantus firmus _a_ write second species in one part as previously directed.

To cantus firmus _b_ write the first and second species mixed in the other three parts. [Fig. 137_a_.]

To cantus firmus _c_ write third species in one part, as directed for the second species (_b_).

CANTI FIRMI

LESSON XXVI

EXERCISES

To cantus firmus _a_ write the second species in two parts and the first in the others. Write twice, changing the parts about. [Fig. 139_a_.]

To cantus firmus _b_ write third species in one part as previously directed.

To cantus firmus _c_ write third species mixed in the other three parts, as at Fig. 139_b_.

CANTI FIRMI

LESSON XXVII

EXERCISES

To cantus firmus _a_ write the first, second and third species in the other three parts. Write twice, changing the parts about [Fig. 141_a_.]

To cantus firmus _b_ write fourth species in one part, as directed in previous lessons. [Fig. 141_b_.]

To cantus firmus _c_ write third species mixed in the other three parts. [Fig. 139_b_.]

CANTI FIRMI

LESSON XXVIII

EXERCISES

To cantus firmus _a_ write the fourth species in one part, as usual.

To cantus firmus _b_ write first, second and fourth species in the other three parts. [Fig. 143_a_.]

To cantus firmus _c_ write the first, third and fourth species in the other three parts. [Fig. 143_b_.]

To cantus firmus _c_ write fourth species mixed in the other parts. [Fig. 143_c_.]

CANTI FIRMI

LESSON XXIX

EXERCISES

To canti firmi _a_ and _b_ write fifth species in one part, as before.

CANTI FIRMI

LESSON XXX

EXERCISES

To the cantus firmus write the fifth species in two parts. Write four times, changing the cantus firmus into every part. [Fig. 147_a_.]

Write one eight-measure phrase mixing the second, third and fourth species (_b_). Also write one exercise combining the first, second, third and fourth species (_c_).

CANTUS FIRMUS

LESSON XXXI

EXERCISES

To the cantus firmus write the fifth species in all of the other parts. [Fig. 149_a_.]

Write four eight-measure phrases with the fifth species in all parts. [Fig. 149_b_.]

CANTUS FIRMUS

LESSON XXXII

EXERCISES

Write six eight-measure phrases, using the fifth species in all the parts. Let the parts begin one after the other in imitation. [Fig. 151.]

LESSON XXXIII

FLORID MELODIES AS CANTI FIRMI FREE HARMONIZATION IN TWO-PART COUNTERPOINT

Thus far, all notes in the measure foreign to the harmony on the first beat were treated as dissonances. Now, the cantus firmus may be harmonized at pleasure, the only restriction being that any tone foreign to the chord with which it enters must be treated as a dissonance. [Fig. 152.]

It is not necessary that each part be strictly florid, but that the effect of the parts as a whole should be so. This applies from this point to the end of these lessons.

The suspension may now be a quarter-note, or its rhythmic equivalent. It then comes on the first (_a_) or third (_b_) quarter of the measure, and the resolution on the quarter following. The preparation should be as long as, or longer than, the suspension. [Fig. 153.]

The eighth-note as in Fig. 154_a_ is good. It should be used only on the second half of a weak beat, and be preceded by a dotted quarter-note. Sixteenth-notes may be used in place of the eighth-note, but should be approached and left step-wise. [Fig. 154_b_.]

The first species may be employed occasionally in the course of an exercise.

Make plentiful use of imitation.

When more than one line of a choral is used, it may be treated by having the other parts continue through the holds, as at _a_, or letting them rest, as at _b_. [Fig. 155.]

When, in place of the hold, the movement continues, it is necessary to interpolate a full measure in place of the hold. [Fig. 155 and Fig. 159.]