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Title: A Treatise on Simple Counterpoint in Forty Lessons

Author: Friedrich J. Lehmann

Release Date: July 21, 2005 [EBook #16342]

Language: English

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_SEVENTH EDITION_




A Treatise on
Simple Counterpoint
in
Forty Lessons

By

Friedrich J. Lehmann

_Instructor of Theory in the Oberlin Conservatory of Music Author of
"Lessons in Harmony"_

G. SCHIRMER, INC.

NEW YORK




PREFACE


The purpose of this work is to supply the need in the Oberlin Conservatory
of Music of a text-book on Simple Counterpoint containing a definite
assignment of lessons, and affording more practice than usual in combining
species.

It is a treatise on strict counterpoint, but strict in a limited sense
only. In two-part counterpoint with other than the first species in both
parts, dissonances are permitted under certain conditions, and in three-
and four-part writing the unprepared seventh and ninth, and the six-four
chord, are allowed in certain ways.

While the illustrations have been written in close score, it is
nevertheless urged that all exercises be written out in open score, as the
movement of the different parts is thus more clearly seen.

The use of the C-clefs is left optional with the teacher.

A knowledge of harmony is presupposed, hence nothing is said pertaining to
it.

The author wishes to express his indebtedness to Professor A.E. Heacox for
his help and advice.

                                            F.J. LEHMANN.

OBERLIN, OHIO, _Jan. 6, 1907._




TABLE OF CONTENTS


    SIMPLE COUNTERPOINT

    LESSON I. Definitions and Illustrations.


    SIMPLE COUNTERPOINT IN TWO PARTS

    First Species: Note against Note. Examples and Exercises.

    LESSON II. Second Species: Two Notes against One. Examples and
    Exercises.

    LESSON III. Second Species in Both Parts. Examples. Second
    Species Mixed in Both Parts. Examples and Exercises.

    LESSON IV. Third Species: Four Notes against One. First Species
    against Six Notes. Second Species Continuously in Both Parts.
    Examples and Exercises.

    LESSON V. Third Species in Both Parts; Mixed. Third Species
    Continuously in Both Parts. Two Notes against Four; Two against
    Six; Three against Six. Examples and Exercises.

    LESSON VI. Fourth Species: Two Notes Syncopated against One.
    Three Notes Syncopated against One. Two Notes against Four; Two
    against Six; Three against Six. Examples and Exercises.

    LESSON VII. Fourth Species (continued). Mixed, in Both Parts.
    Three Notes Syncopated against One. Examples and Exercises.

    LESSON VIII. Fourth Species (continued). Two Notes Syncopated
    against Two; Two against Four; Two against Six; Three against
    Six. Examples and Exercises.

    LESSON IX. Fifth Species: Florid Counterpoint. Examples and
    Exercises.

    LESSON X. Florid Counterpoint (continued). Combining Fifth
    Species with Second; with Third; with Fourth; with Fifth.
    Examples and Exercises.


    SIMPLE COUNTERPOINT IN THREE PARTS

    LESSON XI. First Species in All Parts. Examples and Exercises.

    LESSON XII. Second Species in One Part. Examples and Exercises.

    LESSON XIII. Second Species in Two or More Parts. First and
    Second Species Mixed in All Parts. Second Species in All Parts.
    Examples and Exercises.

    LESSON XIV. Third Species in One Part. Second Species in All
    Parts. Examples and Exercises.

    LESSON XV. Third Species in Two or More Parts. First and Third
    Species Mixed in All Parts. Examples and Exercises.

    LESSON XVI. Third Species (continued). Mixing First, Second, and
    Third Species in All Parts. Third Species in All Parts. Examples
    and Exercises.

    LESSON XVII. Fourth Species in One Part. Three Notes Syncopated
    in One Part. Combining First, Second, and Third Species.
    Examples, and Exercises.

    LESSON XVIII. Fourth Species (continued). Mixed in All Parts.
    Combining First, Second, and Fourth Species, and First, Third,
    and Fourth. Examples and Exercises.

    LESSON XIX. Fifth Species in One Part. Examples and Exercises.

    LESSON XX. Fifth Species (continued). Combining First, Second,
    and Fifth; First, Third, and Fifth; First, Fourth, and Fifth;
    Fifth in Two Parts. Example and Exercises.

    LESSON XXI. Combining the Various Species: Second, Third, and
    Fourth; Second, Third, and Fifth; Second, Fourth, and Fifth;
    Third, Fifth, and Fifth; Fourth, Fifth, and Fifth. Examples and
    Exercises.

    LESSON XXII. Fifth Species in All Parts. Examples and Exercises.


    SIMPLE COUNTERPOINT IN FOUR PARTS

    LESSON XXIII. First Species in All Parts. Examples and Exercises.

    LESSON XXIV. Second Species in One Part. Examples and Exercises.

    LESSON XXV. Third Species in One Part. Second Species Mixed in
    Three Parts. Examples and Exercises.

    LESSON XXVI. Third Species (continued). Mixed in Three Parts.
    Second Species Continuously in Two Parts. Examples and Exercises.

    LESSON XXVII. Fourth Species in One Part. A Cantus Firmus with
    First, Second, and Third Species in the Other Three Parts.
    Examples and Exercises.

    LESSON XXVIII. Fourth Species (continued). A given Cantus Firmus,
    with First, Second, and Fourth Species; with First, Third, and
    Fourth; with Fourth Species Mixed. Examples and Exercises.

    LESSON XXIX. Fifth Species in One Part. Examples and Exercises.

    LESSON XXX. Fifth Species in Two Parts. Mixing Second, Third, and
    Fourth Species in All Parts. Combining First, Second, Third, and
    Fourth Species. Examples and Exercises.

    LESSON XXXI. Fifth Species in Three or Four Parts. Examples and
    Exercises.

    LESSON XXXII. Fifth Species in All Parts, with Imitation.
    Examples and Exercises.


    FLORID MELODIES AS CANTI FIRMI

    LESSON XXXIII. Two-part Florid Counterpoint. Free Harmonization.
    Examples and Exercises.

    LESSONS XXXIV and XXXV. Three-part Florid Counterpoint. Free
    Harmonization. Examples and Exercises.

    LESSON XXXVI. Three-part Florid Counterpoint (continued).
    Exercise in Original Writing.

    LESSONS XXXVII to XL. Four-part Florid Counterpoint, Example and
    Exercises.




SIMPLE COUNTERPOINT

LESSON I


Counterpoint is the art of combining two or more melodies of equal melodic
individuality.

In simple counterpoint all parts must remain in the same relative position
to one another.

The Cantus Firmus is a given melodic phrase that is to receive contrapuntal
treatment, that is, one or more parts are to be added above or below it.

The Counterpoint is any part other than the Cantus Firmus.

Intervals are harmonic or melodic.

An Harmonic interval is the difference in pitch between two tones sounding
at the same time.

A Melodic interval is the difference in pitch between two tones sounded in
succession by the same voice. [Fig. 1.]

[Illustration: Fig. 1.]

Harmonic intervals are divided into Consonances and Dissonances.

Consonances are classed as perfect or imperfect.

The Perfect consonances are the Unison, Fifth, and Octave. [Fig. 2_a_.]

The Imperfect consonances are the Major and Minor Thirds and Sixths. [Fig.
2_b_.]

All other intervals are dissonances.

[Illustration: Fig. 2.]

A Diatonic progression is one in which both name and pitch are changed.
[Fig. 3_a_.]

A Chromatic progression is one in which the pitch is changed a semitone,
while the name remains the same. [Fig. 3_b_.]

[Illustration: Fig. 3.]

Progression from one chord to another is called Harmonic progression; from
one tone to another, Melodic progression.

In melodic progression all major, minor, perfect and diminished intervals
are allowed except the major and minor seventh. The minor seventh may,
however, be used when harmony does not change (_a_). [Fig. 4.]

[Illustration: Fig. 4.]

In counterpoint there are Five Species, or orders. When the counterpoint
has one note for each note of the cantus firmus, it is of the First Species
(_a_); if it has two notes for each note of the cantus firmus, it is the
Second Species (_b_); if four notes, the Third Species (_c_); if two notes
syncopated, the Fourth Species (_d_); and a mixture of these species is the
Fifth Species, or Florid Counterpoint (_e_). [Fig. 5.]

[Illustration: Fig. 5.]




SIMPLE COUNTERPOINT IN TWO PARTS

FIRST SPECIES


Two-part counterpoint comprises a cantus firmus and a counterpoint. [Fig.
6.]

[Illustration: Fig. 6.]

Although in two-part counterpoint we have to deal with intervals, rather
than harmonies, still the harmonic progressions represented by these
intervals should be regarded.

The exercises should begin and close with tonic harmony. At the beginning
the unison, fifth or octave, and at the close the unison or octave, are
permitted. [Fig. 7.]

[Illustration: Fig. 7.]

After the first measure it is better to use imperfect consonances only. The
perfect consonances, however, may be used sparingly when a more melodious
counterpoint is thereby obtained.

The unison may be used in the first and last measures only. [Fig. 7.]

All progressions must be diatonic, and parts should not cross.

The repetition of a note in a lower part should be avoided wherever
possible. In a higher part, repetition to the extent of three notes in
succession is allowed.

Do not use more than three thirds or sixths in succession. [Fig. 8.]

[Illustration: Fig. 8.]

Successive similar skips, except the minor third (_a_), in one direction,
are to be avoided. Successive skips of a fourth are good when the tones are
the fifths of the triads on I, IV and vii deg.. The last tone should return one
degree (_b_). [Fig. 9.]

Do not move more than an octave in one direction in two skips. [Fig. 9_c_.]

[Illustration: Fig. 9.]

Covered fifths and octaves, except from I to V, or V to I, are forbidden.
[Fig. 10.]

[Illustration: Fig. 10.]

Both parts skipping in contrary motion to a fifth or octave should be
avoided in two-part writing. [Fig. 11.]

[Illustration: Fig. 11.]

Avoid consecutive perfect intervals. [Fig. 12.]

[Illustration: Fig. 12.]

The augmented fourth (Tritone) is not only considered bad as a melodic
interval by some authorities, but its appearance between different parts in
successive intervals is also prohibited. This prohibition, however, holds
good only when the chords in which it appears are in fundamental position,
as in Fig. 13_a_. This is shown by the fact, that if one part skips as at
_b_, there is no unpleasant effect.

[Illustration: Fig. 13.]

Avoid consecutive major thirds in major keys. In minor keys they are good.
[Fig. 14.]

[Illustration: Fig. 14.]

Use adjacent voices in writing, and do not exceed the vocal compass of a
voice.

Modulation may be resorted to within the exercises, but only to nearly
related keys; for example, in C, to G, F, a, e, or d.

At the close parts should proceed stepwise to the unison, or octave. [Fig.
15_a_.]

[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.]

The unison is permitted on the weak beat. [Fig. 24.]

[Illustration: Fig. 24.]

Avoid broken-chord effects, that is, do not use more than three tones
belonging to the same chord in succession. [Fig. 25.]

[Illustration: Fig. 25.]

Avoid frequent skipping of parts. [Fig. 26.]

[Illustration: Fig. 26.]

Parts may cross occasionally, but should return immediately [Fig. 27.]

[Illustration: Fig. 27.]

Consecutive fifths or octaves on consecutive strong beats are bad; but they
are good on the weak beats _if the second fifth or octave is approached in
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 species in one part only, may also be used.

[Illustration: Fig. 38.]

Writing the second species in both parts will, in this lesson, be confined
to a mixture of the first and second species, as in Fig. 39.

In this do not use the second species more than four measures continuously
in one part. It will be noticed that the second species may occasionally be
used in both parts. In later lessons opportunity will be given to write it
continuously in both parts.

[Illustration: Fig. 39.]


EXERCISES

Write two eight-measure phrases mixing the first and second species. [Fig.
39.]

To cantus firmus _a_ write one counterpoint above and one below, three
notes to the measure. [Fig. 31.]

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


CANTI FIRMI

[Illustration: Fig. 40.]




LESSON IV

THIRD SPECIES


[Illustration: 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.]

[Illustration: 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.]

[Illustration: 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.]

[Illustration: Fig. 44.]

Parts may cross occasionally.

The use of non-harmonic tones, as in Fig. 45, is good in either part. At
_a_ the passing-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
principal tone is the leading-tone, as at _b_. In both cases the
counterpoint should continue degreewise through the chord-tone. [Fig. 45.]

[Illustration: Fig. 45.]

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

[Illustration: 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.]

[Illustration: Fig. 47.]

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

[Illustration: Fig. 48.]

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

Frequent repetition of a figure as in Fig. 49 is not good.

[Illustration: 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.]

[Illustration: 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.]

[Illustration: Fig. 51.]

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

[Illustration: Fig. 52.]

The cadences in Fig. 53 are good.

[Illustration: 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

[Illustration: Fig. 54.]




LESSON V

THIRD SPECIES IN BOTH PARTS


[Illustration: 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.

The augmented fourth, and diminished fifth and seventh, may be approached
in similar motion. [Fig. 56.]

[Illustration: Fig. 56.]

The augmented fourth following the perfect fourth, as in Fig. 56_a_, is good.

The minor seventh, and the major and minor ninth of a chord, may be used
freely on any but the first quarter, but must be consonant with the other
part. [Fig. 57.]

[Illustration: Fig. 57.]

The first and third species may be mixed, as in Fig. 58.

[Illustration: Fig. 58.]

The second species may be used in one part and the third in the other, also
six notes in one part and two in the other, and six in one and three in the
other. All tones appearing simultaneously, must comply with the suggestions
for tones appearing on the weak beat given in previous lessons, where both
parts have other than the first species. [Fig. 59.]

[Illustration: Fig. 59.]

The cadences in Fig. 60 are good, and will suggest others.

[Illustration: Fig. 60.]


EXERCISES

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

To cantus firmus _b_ write counterpoints in six notes, one above and one
below. [Fig. 52.]

Write one eight-measure phrase, mixing the first and third species. [Fig.
58.]

Write two eight-measure phrases, using third species in both parts. [Fig.
55.]


CANTI FIRMI

[Illustration: Fig. 61.]




LESSON VI

FOURTH SPECIES


[Illustration: Fig. 62.]

This species is the same as the second, except that the last note of the
measure is tied to the first note of the next, forming a syncopation. As in
the second species, the first note of the counterpoint should form a
unison, octave or fifth, and when the counterpoint begins on the second
half it may also be an imperfect consonance.

When the counterpoint begins on the first half, the second half is treated
the same as the second half of succeeding measures, described in the next
paragraph.

After the first measure, the second half of the measure should contain a
consonance (Fig. 63_a_), the first half a consonance (_b_), or dissonance
(_c_), preferably the latter, in which case a suspension is formed. This is
the most desirable form of syncopation. When the first half contains a
dissonance, the counterpoint must descend--or ascend in retardation
(_d_)--one degree to an imperfect consonance (_c_). When the first half is
a consonance, it may be left by a skip to some other chord-tone (_e_), or
by degreewise progression (_f_). In the latter case the second note is
non-harmonic, and therefore should not be used to prepare a syncopation
except as in Fig. 63_d_ (Retardation of the root in I_6).

[Illustration: Fig. 63.]

When writing three notes to one in the fourth species, the suspension may
resolve on the second beat (_a_), or the third (_b_). In the latter case,
the suspension skips (_c_) to some other chord-tone, before resolving. The
resolution to the leading-tone (_d_) forms an important exception to this
rule. [Fig. 64.]

[Illustration: Fig. 64.]

The fifth may be used in the lower part if it becomes the preparation of a
suspension (Fig. 65_a_). It may also be used in the lower part, as in Fig.
65_b_, provided it resolves by skipping to the third of the chord.

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.

[Illustration: Fig. 65.]

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

[Illustration: 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.]

[Illustration: 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.

[Illustration: Fig. 68.]

The following cadences are good:

[Illustration: Fig. 69.]


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

[Illustration: Fig. 70.]




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.

[Illustration: Fig. 71.]


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

[Illustration: Fig. 72.]




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.]

[Illustration: 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.

[Illustration: Fig. 74.]

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.]

[Illustration: 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.]

[Illustration: 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

[Illustration: Fig. 77.]




LESSON IX

FIFTH SPECIES: FLORID COUNTERPOINT


[Illustration: Fig. 78.]

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.]

[Illustration: Fig. 79.]

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

[Illustration: 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.]

[Illustration: 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.

[Illustration: Fig. 82.]

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

[Illustration: Fig. 83.]




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.]

[Illustration: 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.]

[Illustration: Fig. 85.]




SIMPLE COUNTERPOINT IN THREE PARTS

LESSON XI

FIRST SPECIES


[Illustration: Fig. 86.]

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.

[Illustration: Fig. 87.]

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.]

[Illustration: 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.

[Illustration: Fig. 89.]

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

[Illustration: Fig. 90.]

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

[Illustration: 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_.]

[Illustration: Fig. 92.]

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

[Illustration: Fig. 93.]




LESSON XII

THE SECOND SPECIES


[Illustration: Fig. 94.]

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.]

[Illustration: 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.]

[Illustration: Fig. 96.]

The progression from vii_6 deg. 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.

[Illustration: Fig. 97.]

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.]

[Illustration: 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_.

[Illustration: Fig. 99.]


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

[Illustration: Fig. 100.]




LESSON XIII

SECOND SPECIES IN TWO PARTS


[Illustration: Fig. 101.]

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.]

[Illustration: 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.]

[Illustration: Fig. 103.]

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

[Illustration: Fig. 104.]

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

[Illustration: Fig. 105.]


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

[Illustration: Fig. 106.]




LESSON XIV

THIRD SPECIES


[Illustration: Fig. 107.]

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.

[Illustration: Fig. 108.]


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

[Illustration: Fig. 109.]




LESSON XV

THIRD SPECIES IN TWO OR MORE PARTS


[Illustration: Fig. 110.]

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.]

[Illustration: 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.

[Illustration: Fig. 112.]


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

[Illustration: Fig. 113.]




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_.]

[Illustration: Fig. 114.]


CANTUS FIRMUS

[Illustration: Fig. 115.]




LESSON XVII

FOURTH SPECIES


[Illustration: Fig. 116.]

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.]

[Illustration: 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.]

[Illustration: 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.

[Illustration: Fig. 119.]

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

[Illustration: Fig. 120.]

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

[Illustration: Fig. 121.]


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.]

[Illustration: Fig. 122.]


CANTI FIRMI

[Illustration: Fig. 123.]




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_.]

[Illustration: Fig. 124.]


CANTI FIRMI

[Illustration: Fig. 125.]




LESSON XIX

FIFTH SPECIES


[Illustration: Fig. 126.]

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

[Illustration: Fig. 127.]




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_.]

[Illustration: Fig. 128.]


CANTI FIRMI

[Illustration: Fig. 129.]




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_).

[Illustration: Fig. 130.]




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.

[Illustration: Fig. 131.]




SIMPLE COUNTERPOINT IN FOUR PARTS

LESSON XXIII


[Illustration: Fig. 132.]

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 deg.,
use the latter, as in Fig. 133.

[Illustration: 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

[Illustration: Fig. 134.]




LESSON XXIV


[Illustration: Fig. 135.]


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

[Illustration: Fig. 136.]




LESSON XXV


[Illustration: Fig. 137.]


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

[Illustration: Fig. 138.]




LESSON XXVI


[Illustration: Fig. 139.]


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

[Illustration: Fig. 140.]




LESSON XXVII


[Illustration: Fig. 141.]


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

[Illustration: Fig. 142.]




LESSON XXVIII


[Illustration: Fig. 143.]


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

[Illustration: Fig. 144.]




LESSON XXIX


[Illustration: Fig. 145.]


EXERCISES

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


CANTI FIRMI

[Illustration: Fig. 146.]




LESSON XXX


[Illustration: Fig. 147.]


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

[Illustration: Fig. 148.]




LESSON XXXI


[Illustration: Fig. 149.]


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

[Illustration: Fig. 150.]


LESSON XXXII

[Illustration: Fig. 151.]


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


[Illustration: Fig. 152.]

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.]

[Illustration: 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_.]

[Illustration: Fig. 154.]

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.]

[Illustration: Fig. 155.]

The note under the hold may be continued the extra measure, or the part may
rest and then reenter. All that is required is that it begin after the
lapse of one measure, i.e., when the line ends on the accent the next line
begins on the weak beat of the measure following, and if it ends on the
weak beat then on the accent of the next measure.

The interval at any hold except the last of a choral may be either a
perfect (_a_) or imperfect consonance (_b_). [Fig. 156.]

[Illustration: Fig. 156.]

Modulation often occurs at the holds. If so, make it clear.

In this and in succeeding lessons set the cantus firmus in any part, and
transpose if necessary.


EXERCISES

To cantus firmus _b_ write two counterpoints above and two below.

To cantus firmus _a_ write one above and one below, with both parts resting
at the hold. Also do the same _with the counterpoint continuing at the
hold_. [Fig. 155_a, b._]


CANTI FIRMI

[Illustration: Fig. 157.]




LESSON XXXIV

FREE HARMONIZATION IN THREE-PART COUNTERPOINT


When writing in three or more parts, it is well to let a part rest
occasionally, and, when it reenters, have it imitate one of the other
parts. [Fig. 158.]

[Illustration: Fig. 158.]


EXERCISES

To cantus firmus _a_ write two counterpoints above and two below in
two-part counterpoint.

Write two original eight-measure phrases in two-part counterpoint.

To cantus firmus _b_ write one example in three-part counterpoint with
continuous movement at the hold. [Fig. 159.]

[Illustration: Fig. 159.]


CANTI FIRMI

[Illustration: Fig. 160.]




LESSON XXXV


To canti firmi _a_ and _b_ write two parts. Write each three times, setting
the cantus firmus in all parts in turn. Write one of the solutions of the
choral with continuous movement at the hold.


CANTI FIRMI

[Illustration: Fig. 161.]




LESSON XXXVI


Write two eight-measure phrases, and one sixteen-measure phrase, of
original counterpoint in three parts.




LESSON XXXVII

FREE HARMONIZATION IN FOUR-PART COUNTERPOINT


[Illustration: Fig. 162.]


EXERCISES

To the cantus firmus write three parts.

Write two sixteen-measure phrases of original four-part counterpoint, one
major and one minor.


CANTUS FIRMUS

[Illustration: Fig. 163.]




LESSON XXXVIII


In this and the following lessons have the parts in some of the exercises
begin one after the other in imitation. [Fig. 151.]


EXERCISES

Write two eight-measure phrases, and one sixteen-measure phrase, of
original four-part counterpoint.




LESSON XXXIX


Write two sixteen-measure phrases of original four-part counterpoint.




LESSON XL


Write an original exercise in four-part counterpoint, extended to
thirty-two measures.






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