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diff --git a/16342.txt b/16342.txt new file mode 100644 index 0000000..3dd8ac4 --- /dev/null +++ b/16342.txt @@ -0,0 +1,2324 @@ +The Project Gutenberg EBook of A Treatise on Simple Counterpoint in Forty +Lessons, by Friedrich J. Lehmann + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: A Treatise on Simple Counterpoint in Forty Lessons + +Author: Friedrich J. Lehmann + +Release Date: July 21, 2005 [EBook #16342] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK A TREATISE ON SIMPLE *** + + + + +Produced by David Newman, Dainis Millers and the Online +Distributed Proofreading Team at https://www.pgdp.net + + + + + + +_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. + + + + + + +End of the Project Gutenberg EBook of A Treatise on Simple Counterpoint in +Forty Lessons, by Friedrich J. 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