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+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: ISO-8859-1
+
+*** 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°. 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° 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°,
+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 reënter. 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 reënters, 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. Lehmann
+
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+<pre>
+
+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: ISO-8859-1
+
+*** 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
+
+
+
+
+
+
+</pre>
+
+
+<div class="titlepage">
+
+<div class="docEdition">
+SEVENTH EDITION
+</div>
+
+<h1>
+<span style="font-size: 60%">A Treatise on</span><br />
+
+Simple Counterpoint<br />
+
+<span style="font-size: 60%">in<br />
+
+Forty Lessons</span>
+</h1>
+
+<div class="by">By</div>
+
+<div class="docAuthor">Friedrich J. Lehmann</div>
+
+<div class="docDesc">Instructor of Theory in the Oberlin Conservatory of Music
+Author of "Lessons in Harmony"</div>
+
+<div class="imprint">G. SCHIRMER, INC.<br />
+
+NEW YORK</div>
+</div>
+
+
+<div class="pagenum" id="page_iii">[iii]</div>
+
+<h2 id="PREFACE">PREFACE</h2>
+
+<hr style="width: 4em;" />
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>The use of the C-clefs is left optional with the teacher.</p>
+
+<p>A knowledge of harmony is presupposed, hence nothing is said
+pertaining to it.</p>
+
+<p>The author wishes to express his indebtedness to Professor A.E.
+Heacox for his help and advice.</p>
+
+<p class="signature">F.J. LEHMANN.</p>
+
+<p><span class="sc">Oberlin, Ohio</span>, <i>Jan. 6, 1907.</i></p>
+
+
+<div class="pagenum" id="page_v">[v]</div>
+
+<table id="TABLE_OF_CONTENTS" class="toc" summary="Table of Contents">
+
+<caption>TABLE OF CONTENTS</caption>
+
+<thead>
+  <tr>
+    <td></td>
+    <td class="tocpagehdr">PAGE</td>
+  </tr>
+</thead>
+
+<tbody>
+  <tr class="subheading"><th>SIMPLE COUNTERPOINT</th>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_I">I.</a> Definitions and Illustrations.</td>
+
+  <td class="page"><a href="#page_1">1-2</a></td>
+</tr>
+
+<tr class="subheading"><th>SIMPLE COUNTERPOINT IN TWO PARTS</th></tr>
+
+<tr>
+  <td style="text-indent: 0em;">First Species: Note against Note. Examples and Exercises.</td>
+  <td class="page"><a href="#page_3">3-5</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_II">II.</a> Second Species: Two Notes against One. Examples and
+Exercises.</td>
+  <td class="page"><a href="#page_6">6-9</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_III">III.</a> Second Species in Both Parts. Examples. Second Species
+Mixed in Both Parts. Examples and Exercises.</td>
+
+  <td class="page"><a href="#page_9">9-11</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_IV">IV.</a> Third Species: Four Notes against One. First Species
+against Six Notes. Second Species Continuously in Both Parts.
+Examples and Exercises.</td>
+  <td class="page"><a href="#page_11">11-15</a></td>
+</tr>
+
+<tr>
+
+  <td>LESSON <a href="#LESSON_V">V.</a> 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.</td>
+  <td class="page"><a href="#page_15">15-17</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_VI">VI.</a> 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.</td>
+  <td class="page"><a href="#page_17">17-19</a></td>
+
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_VII">VII.</a> Fourth Species (continued). Mixed, in Both Parts. Three
+Notes Syncopated against One. Examples and Exercises.</td>
+  <td class="page"><a href="#page_19">19-20</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_VIII">VIII.</a> Fourth Species (continued). Two Notes Syncopated
+against Two; Two against Four; Two against Six; Three against Six.
+Examples and Exercises.</td>
+
+  <td class="page"><a href="#page_20">20-22</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_IX">IX.</a> Fifth Species: Florid Counterpoint. Examples and Exercises.</td>
+  <td class="page"><a href="#page_22">22-24</a></td>
+</tr>
+
+<tr>
+
+  <td>LESSON <a href="#LESSON_X">X.</a> Florid Counterpoint (continued). Combining Fifth Species
+with Second; with Third; with Fourth; with Fifth. Examples and
+Exercises.</td>
+  <td class="page"><a href="#page_24">24-25</a></td>
+</tr>
+
+<tr class="subheading"><th>SIMPLE COUNTERPOINT IN THREE PARTS</th></tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XI">XI.</a> First Species in All Parts. Examples and Exercises.</td>
+
+  <td class="page"><a href="#page_26">26-28</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XII">XII.</a> Second Species in One Part. Examples and Exercises.</td>
+  <td class="page"><a href="#page_28">28-31</a></td>
+</tr>
+
+<tr>
+
+  <td>LESSON <a href="#LESSON_XIII">XIII.</a> Second Species in Two or More Parts. First and Second
+Species Mixed in All Parts. Second Species in All Parts. Examples
+and Exercises.</td>
+  <td class="page"><a href="#page_31">31-33</a></td>
+</tr>
+
+<tr>
+  <td><div class="pagenum" id="page_vi">[vi]</div>
+      LESSON <a href="#LESSON_XIV">XIV.</a> Third Species in One Part. Second Species in All Parts.
+Examples and Exercises.</td>
+  <td class="page"><a href="#page_33">33-34</a></td>
+
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XV">XV.</a> Third Species in Two or More Parts. First and Third
+Species Mixed in All Parts. Examples and Exercises.</td>
+  <td class="page"><a href="#page_34">34-36</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XVI">XVI.</a> Third Species (continued). Mixing First, Second, and
+Third Species in All Parts. Third Species in All Parts. Examples
+and Exercises.</td>
+
+  <td class="page"><a href="#page_36">36-37</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XVII">XVII.</a> Fourth Species in One Part. Three Notes Syncopated in
+One Part. Combining First, Second, and Third Species. Examples,
+and Exercises.</td>
+  <td class="page"><a href="#page_37">37-39</a></td>
+</tr>
+
+<tr>
+
+  <td>LESSON <a href="#LESSON_XVIII">XVIII.</a> Fourth Species (continued). Mixed in All Parts. Combining
+First, Second, and Fourth Species, and First, Third, and Fourth.
+Examples and Exercises.</td>
+  <td class="page"><a href="#page_40">40-41</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XIX">XIX.</a> Fifth Species in One Part. Examples and Exercises.</td>
+  <td class="page"><a href="#page_41">41</a></td>
+
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XX">XX.</a> Fifth Species (continued). Combining First, Second, and
+Fifth; First, Third, and Fifth; First, Fourth, and Fifth; Fifth in Two
+Parts. Example and Exercises.</td>
+  <td class="page"><a href="#page_42">42-43</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXI">XXI.</a> 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.</td>
+
+  <td class="page"><a href="#page_44">44-45</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXII">XXII.</a> Fifth Species in All Parts. Examples and Exercises.</td>
+  <td class="page"><a href="#page_45">45</a></td>
+</tr>
+
+
+<tr class="subheading"><th>SIMPLE COUNTERPOINT IN FOUR PARTS</th></tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXIII">XXIII.</a> First Species in All Parts. Examples and Exercises.</td>
+  <td class="page"><a href="#page_46">46</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXIV">XXIV.</a> Second Species in One Part. Examples and Exercises.</td>
+
+  <td class="page"><a href="#page_47">47</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXV">XXV.</a> Third Species in One Part. Second Species Mixed in
+Three Parts. Examples and Exercises.</td>
+  <td class="page"><a href="#page_47">47-48</a></td>
+</tr>
+
+<tr>
+
+  <td>LESSON <a href="#LESSON_XXVI">XXVI.</a> Third Species (continued). Mixed in Three Parts.
+Second Species Continuously in Two Parts. Examples and Exercises.</td>
+  <td class="page"><a href="#page_48">48-49</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXVII">XXVII.</a> Fourth Species in One Part. A Cantus Firmus with
+First, Second, and Third Species in the Other Three Parts. Examples
+and Exercises.</td>
+  <td class="page"><a href="#page_49">49-50</a></td>
+
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXVIII">XXVIII.</a> 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.</td>
+  <td class="page"><a href="#page_50">50-51</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXIX">XXIX.</a> Fifth Species in One Part. Examples and Exercises.</td>
+
+  <td class="page"><a href="#page_52">52</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXX">XXX.</a> Fifth Species in Two Parts. Mixing Second, Third, and
+Fourth Species in All Parts. Combining First, Second, Third, and
+Fourth Species. Examples and Exercises.</td>
+  <td class="page"><a href="#page_52">52-54</a></td>
+</tr>
+
+<tr>
+
+  <td>LESSON <a href="#LESSON_XXXI">XXXI.</a> Fifth Species in Three or Four Parts. Examples and
+Exercises.</td>
+  <td class="page"><a href="#page_54">54-55</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXXII">XXXII.</a> Fifth Species in All Parts, with Imitation. Examples
+and Exercises.</td>
+  <td class="page"><a href="#page_55">55</a></td>
+
+</tr>
+
+<tr class="subheading">
+<th>
+<div class="pagenum" id="page_vii">[vii]</div>
+FLORID MELODIES AS CANTI FIRMI</th></tr>
+
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXXIII">XXXIII.</a> Two-part Florid Counterpoint. Free Harmonization.
+Examples and Exercises.</td>
+  <td class="page"><a href="#page_55">55-58</a></td>
+</tr>
+
+<tr>
+  <td>LESSONS <a href="#LESSON_XXXIV">XXXIV</a> and <a href="#LESSON_XXXV">XXXV.</a> Three-part Florid Counterpoint. Free
+Harmonization. Examples and Exercises.</td>
+  <td class="page"><a href="#page_58">58-59</a></td>
+</tr>
+
+<tr>
+  <td>LESSON <a href="#LESSON_XXXVI">XXXVI.</a> Three-part Florid Counterpoint (continued). Exercise
+in Original Writing.</td>
+
+  <td class="page"><a href="#page_59">59</a></td>
+</tr>
+
+<tr>
+  <td>LESSONS <a href="#LESSON_XXXVII">XXXVII</a> to <a href="#LESSON_XL">XL.</a> Four-part Florid Counterpoint, Example and
+Exercises.</td>
+  <td class="page"><a href="#page_60">60</a></td>
+
+</tr>
+</tbody>
+</table>
+
+<div class="pagenum" id="page_1">[1]</div>
+
+<h2>SIMPLE COUNTERPOINT</h2>
+
+<h3 id="LESSON_I">LESSON I</h3>
+
+
+<p>Counterpoint is the art of combining two or more melodies of
+equal melodic individuality.</p>
+
+<p>In simple counterpoint all parts must remain in the same
+relative position to one another.</p>
+
+<p>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.</p>
+
+<p>The Counterpoint is any part other than the Cantus Firmus.</p>
+
+<p>Intervals are harmonic or melodic.</p>
+
+<p>An Harmonic interval is the difference in pitch between two
+tones sounding at the same time.</p>
+
+<p>A Melodic interval is the difference in pitch between two
+tones sounded in succession by the same voice. [<a href="#fig_1">Fig.&nbsp;1.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_1" summary="Figure 1">
+<tr><td class="caption">Fig.<br />1.</td>
+
+    <td class="figure"><img src="images/fig001.png" alt="Fig. 1." title="Fig. 1." /></td>
+</tr>
+</table>
+</div>
+
+<p>Harmonic intervals are divided into Consonances and Dissonances.</p>
+
+<p>Consonances are classed as perfect or imperfect.</p>
+
+<p>The Perfect consonances are the Unison, Fifth, and Octave.
+[<a href="#fig_2">Fig.&nbsp;2<i>a</i></a>.]</p>
+
+<p>The Imperfect consonances are the Major and Minor Thirds
+and Sixths. [<a href="#fig_2">Fig.&nbsp;2<i>b</i></a>.]</p>
+
+<p>All other intervals are dissonances.</p>
+
+<div class="figure">
+<table class="figure" id="fig_2" summary="Figure 2">
+<tr><td class="caption">Fig.<br />2.</td>
+    <td class="figure"><img src="images/fig002.png" alt="Fig. 2." title="Fig. 2." /></td>
+</tr>
+</table>
+</div>
+
+<div class="pagenum" id="page2">[2]</div>
+
+<p>A Diatonic progression is one in which both name and pitch
+are changed. [<a href="#fig_3">Fig.&nbsp;3<i>a</i></a>.]</p>
+
+<p>A Chromatic progression is one in which the pitch is changed
+a semitone, while the name remains the same. [<a href="#fig_3">Fig.&nbsp;3<i>b</i></a>.]</p>
+
+<div class="figure">
+<table class="figure" id="fig_3" summary="Figure 3">
+<tr><td class="caption">Fig.<br />3.</td>
+    <td class="figure"><img src="images/fig003.png" alt="Fig. 3." title="Fig. 3." /></td>
+
+</tr>
+</table>
+</div>
+
+
+<p>Progression from one chord to another is called Harmonic progression;
+from one tone to another, Melodic progression.</p>
+
+<p>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 (<i>a</i>). [<a href="#fig_4">Fig.&nbsp;4.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_4" summary="Figure 4">
+<tr><td class="capnorm">Fig.<br />4.</td>
+    <td class="figure"><img src="images/fig004.png" alt="Fig. 4." title="Fig. 4." /></td>
+
+</tr>
+</table>
+</div>
+
+
+<p>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 (<i>a</i>); if it has two notes for each note of the
+cantus firmus, it is the Second Species (<i>b</i>); if four notes, the
+Third Species (<i>c</i>); if two notes syncopated, the Fourth Species (<i>d</i>);
+and a mixture of these species is the Fifth Species, or Florid
+Counterpoint (<i>e</i>). [<a href="#fig_5">Fig.&nbsp;5.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_5" summary="Figure 5">
+<tr><td class="capnorm">Fig.<br />5.</td>
+    <td class="figure"><img src="images/fig005.png" alt="Fig. 5." title="Fig. 5." /></td>
+</tr>
+</table>
+</div>
+
+<div class="pagenum" id="page_3">[3]</div>
+
+<h2>SIMPLE COUNTERPOINT IN TWO PARTS</h2>
+
+<h4>FIRST SPECIES</h4>
+
+
+<p>Two-part counterpoint comprises a cantus firmus and a counterpoint.
+[<a href="#fig_6">Fig.&nbsp;6.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_6" summary="Figure 6">
+<tr><td class="caption">Fig.<br />6.</td>
+    <td class="figure"><img src="images/fig006.png" alt="Fig. 6." title="Fig. 6." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>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. [<a href="#fig_7">Fig.&nbsp;7.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_7" summary="Figure 7">
+<tr><td class="caption">Fig.<br />7.</td>
+    <td class="figure"><img src="images/fig007.png" alt="Fig. 7." title="Fig. 7." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>The unison may be used in the first and last measures
+only. [<a href="#fig_7">Fig.&nbsp;7.</a>]</p>
+
+<p>All progressions must be diatonic, and parts should not cross.</p>
+
+<p>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.</p>
+
+<p>Do not use more than three thirds or sixths in succession.
+[<a href="#fig_8">Fig.&nbsp;8.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_8" summary="Figure 8">
+<tr><td class="caption">Fig.<br />8.</td>
+    <td class="figure"><img src="images/fig008.png" alt="Fig. 8." title="Fig. 8." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_4">[4]</div>
+
+<p>Successive similar skips, except the minor third (<i>a</i>), 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 <span class="sc">vii</span>°.
+The last tone should return one degree (<i>b</i>). [<a href="#fig_9">Fig.&nbsp;9.</a>]</p>
+
+<p>Do not move more than an octave in one direction in two
+skips. [<a href="#fig_9">Fig.&nbsp;9<i>c</i></a>.]</p>
+
+<div class="figure">
+<table class="figure" id="fig_9" summary="Figure 9">
+<tr><td class="capnorm">Fig.<br />9.</td>
+    <td class="figure"><img src="images/fig009.png" alt="Fig. 9." title="Fig. 9." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Covered fifths and octaves, except from I to V, or V to I, are
+forbidden. [<a href="#fig_10">Fig.&nbsp;10.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_10" summary="Figure 10">
+<tr><td class="caption">Fig.<br />10.</td>
+    <td class="figure"><img src="images/fig010.png" alt="Fig. 10." title="Fig. 10." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Both parts skipping in contrary motion to a fifth or octave
+should be avoided in two-part writing. [<a href="#fig_11">Fig.&nbsp;11.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_11" summary="Figure 11">
+<tr><td class="caption">Fig.<br />11.</td>
+    <td class="figure"><img src="images/fig011.png" alt="Fig. 11." title="Fig. 11." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Avoid consecutive perfect intervals. [<a href="#fig_12">Fig.&nbsp;12.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_12" summary="Figure 12">
+<tr><td class="caption">Fig.<br />12.</td>
+    <td class="figure"><img src="images/fig012.png" alt="Fig. 12." title="Fig. 12." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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 <a href="#fig_13">Fig.&nbsp;13<i>a</i></a>.
+This is shown by the fact, that if one part skips as at <i>b</i>, there is
+no unpleasant effect.</p>
+
+<div class="pagenum" id="page_5">[5]</div>
+
+<div class="figure">
+<table class="figure" id="fig_13" summary="Figure 13">
+<tr><td class="caption">Fig.<br />13.</td>
+    <td class="figure"><img src="images/fig013.png" alt="Fig. 13." title="Fig. 13." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Avoid consecutive major thirds in major keys. In minor keys
+they are good. [<a href="#fig_14">Fig.&nbsp;14.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_14" summary="Figure 14">
+<tr><td class="caption">Fig.<br />14.</td>
+    <td class="figure"><img src="images/fig014.png" alt="Fig. 14." title="Fig. 14." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Use adjacent voices in writing, and do not exceed the vocal
+compass of a voice.</p>
+
+<p>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.</p>
+
+<p>At the close parts should proceed stepwise to the unison, or
+octave. [<a href="#fig_15">Fig.&nbsp;15<i>a</i></a>.]</p>
+
+<p>A close as in <a href="#fig_15">Fig.&nbsp;15<i>b</i></a> may be used occasionally. In this case
+the leading-tone is better in the higher part.</p>
+
+<div class="figure">
+<table class="figure" id="fig_15" summary="Figure 15">
+<tr><td class="caption">Fig.<br />15.</td>
+    <td class="figure"><img src="images/fig015.png" alt="Fig. 15." title="Fig. 15." /></td>
+</tr>
+</table>
+</div>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To each of the following canti firmi write two counterpoints above, and
+two below.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_16" summary="Figure 16">
+<tr><td class="capnorm">Fig.<br />16.</td>
+    <td class="figure"><img src="images/fig016.png" alt="Fig. 16." title="Fig. 16." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_6">[6]</div>
+
+<h3 id="LESSON_II">LESSON II</h3>
+
+<h4>SECOND SPECIES</h4>
+
+
+<div class="figure">
+<table class="figure" id="fig_17" summary="Figure 17">
+<tr><td class="caption">Fig.<br />17.</td>
+    <td class="figure"><img src="images/fig017.png" alt="Fig. 17." title="Fig. 17." /></td>
+
+</tr>
+</table>
+</div>
+
+
+<p>All rules for the first species must be observed.</p>
+
+<p>Two notes are written in the counterpoint to one of the cantus
+firmus, except in the last measure. [<a href="#fig_18">Fig.&nbsp;18<i>a</i></a>.] In the last measure
+but one the first species may sometimes be used. [<a href="#fig_18">Fig.&nbsp;18<i>b</i></a>.]</p>
+
+<div class="figure">
+<table class="figure" id="fig_18" summary="Figure 18">
+<tr><td class="caption">Fig.<br />18.</td>
+    <td class="figure"><img src="images/fig018.png" alt="Fig. 18." title="Fig. 18." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Repetition of a note in any but the first species is forbidden.
+[<a href="#fig_19">Fig.&nbsp;19.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_19" summary="Figure 19">
+<tr><td class="caption">Fig.<br />19.</td>
+    <td class="figure"><img src="images/fig019.png" alt="Fig. 19." title="Fig. 19." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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. [<a href="#fig_20">Fig.&nbsp;20.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_20" summary="Figure 20">
+<tr><td class="capnorm">Fig.<br />20.</td>
+    <td class="figure"><img src="images/fig020.png" alt="Fig. 20." title="Fig. 20." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>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 (<i>a</i>) or stepwise progression (<i>b</i>) unless
+dissonant with the cantus firmus; then avoid their use; if foreign
+
+<span class="pagenum" id="page_7">[7]</span>
+
+to it, whether consonant (<i>c</i>) with the C.F. or not (<i>d</i>), they
+must be treated as embellishments or passing-tones. [<a href="#fig_21">Fig.&nbsp;21.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_21" summary="Figure 21">
+<tr><td class="caption">Fig.<br />21.</td>
+    <td class="figure"><img src="images/fig021.png" alt="Fig. 21." title="Fig. 21." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The embellishment may be used as follows: when above the
+principal tone, it may be a semitone (<i>a</i>) or a whole tone (<i>b</i>) distant
+from it; and when below, a semitone (<i>c</i>). [<a href="#fig_22">Fig.&nbsp;22.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_22" summary="Figure 22">
+<tr><td class="caption">Fig.<br />22.</td>
+    <td class="figure"><img src="images/fig022.png" alt="Fig. 22." title="Fig. 22." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>An harmonic passing-tone is the second of three tones belonging
+to the same chord. [<a href="#fig_23">Fig.&nbsp;23<i>a</i></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 <a href="#fig_23">Fig.&nbsp;23<i>b</i></a>.</p>
+
+<p>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. [<a href="#fig_23">Fig.&nbsp;23<i>c</i></a>.]</p>
+
+<div class="figure">
+<table class="figure" id="fig_23" summary="Figure 23">
+<tr><td class="caption">Fig.<br />23.</td>
+    <td class="figure"><img src="images/fig023.png" alt="Fig. 23." title="Fig. 23." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The unison is permitted on the weak beat. [<a href="#fig_24">Fig.&nbsp;24.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_24" summary="Figure 24">
+<tr><td class="caption">Fig.<br />24.</td>
+
+    <td class="figure"><img src="images/fig024.png" alt="Fig. 24." title="Fig. 24." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_8">[8]</div>
+
+<p>Avoid broken-chord effects, that is, do not use more than three
+tones belonging to the same chord in succession. [<a href="#fig_25">Fig.&nbsp;25.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_25" summary="Figure 25">
+<tr><td class="caption">Fig.<br />25.</td>
+    <td class="figure"><img src="images/fig025.png" alt="Fig. 25." title="Fig. 25." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Avoid frequent skipping of parts. [<a href="#fig_26">Fig.&nbsp;26.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_26" summary="Figure 26">
+<tr><td class="caption">Fig.<br />26.</td>
+    <td class="figure"><img src="images/fig026.png" alt="Fig. 26." title="Fig. 26." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Parts may cross occasionally, but should return immediately
+[<a href="#fig_27">Fig.&nbsp;27.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_27" summary="Figure 27">
+<tr><td class="caption">Fig.<br />27.</td>
+    <td class="figure"><img src="images/fig027.png" alt="Fig. 27." title="Fig. 27." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Consecutive fifths or octaves on consecutive strong beats are
+bad; but they are good on the weak beats <i>if the second fifth or octave
+is approached in the opposite direction from the first</i>. [<a href="#fig_28">Fig.&nbsp;28.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_28" summary="Figure 28">
+<tr><td class="caption">Fig.<br />28.</td>
+    <td class="figure"><img src="images/fig028.png" alt="Fig. 28." title="Fig. 28." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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. [<a href="#fig_29">Fig.&nbsp;29.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_29" summary="Figure 29">
+<tr><td class="caption">Fig.<br />29.</td>
+    <td class="figure"><img src="images/fig029.png" alt="Fig. 29." title="Fig. 29." /></td>
+
+</tr>
+</table>
+</div>
+
+
+<p>In the last measure but one, both the supertonic and leading
+tone should appear. [<a href="#fig_30">Fig.&nbsp;30.</a>]</p>
+
+
+<div class="pagenum" id="page_9">[9]</div>
+
+<div class="figure">
+<table class="figure" id="fig_30" summary="Figure 30">
+<tr><td class="caption">Fig.<br />30.</td>
+    <td class="figure"><img src="images/fig030.png" alt="Fig. 30." title="Fig. 30." /></td>
+</tr>
+</table>
+</div>
+
+
+<p><i>Three</i> notes may be written to one of the cantus firmus, as in
+<a href="#fig_31">Fig.&nbsp;31.</a> For this no new rules are required.</p>
+
+<div class="figure">
+<table class="figure" id="fig_31" summary="Figure 31">
+<tr><td class="caption">Fig.<br />31.</td>
+    <td class="figure"><img src="images/fig031.png" alt="Fig. 31." title="Fig. 31." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The cadences in <a href="#fig_32">Fig.&nbsp;32</a> are good. It will be seen that the
+cadences of the first species may also be used.</p>
+
+<div class="figure">
+<table class="figure" id="fig_32" summary="Figure 32">
+<tr><td class="caption">Fig.<br />32.</td>
+    <td class="figure"><img src="images/fig032.png" alt="Fig. 32." title="Fig. 32." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write two counterpoints above and two below in the
+first species.</p>
+
+<p>To cantus firmus <i>b</i> write two above and two below in the second species.</p>
+
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_33" summary="Figure 33">
+<tr><td class="capnorm">Fig.<br />33.</td>
+    <td class="figure"><img src="images/fig033.png" alt="Fig. 33." title="Fig. 33." /></td>
+
+</tr>
+</table>
+</div>
+
+
+<h3 id="LESSON_III">LESSON III</h3>
+
+<h4>SECOND SPECIES IN BOTH PARTS<a id="FNanchor_A_1" href="#Footnote_A_1" class="fnanchor">[A]</a></h4>
+
+
+<div class="figure">
+<table class="figure" id="fig_34" summary="Figure 34">
+<tr><td class="caption">Fig.<br />34.</td>
+
+    <td class="figure"><img src="images/fig034.png" alt="Fig. 34." title="Fig. 34." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="footnote"><p id="Footnote_A_1"><a class="label" href="#FNanchor_A_1">[A]</a> 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.</p></div>
+
+<div class="pagenum" id="page_10">[10]</div>
+
+<p>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. [<a href="#fig_35">Fig.&nbsp;35.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_35" summary="Figure 35">
+<tr><td class="caption">Fig.<br />35.</td>
+
+    <td class="figure"><img src="images/fig035.png" alt="Fig. 35." title="Fig. 35." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>All tones not belonging to the harmony implied on the first
+beat, must be treated as dissonances. [<a href="#fig_36">Fig.&nbsp;36.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_36" summary="Figure 36">
+<tr><td class="caption">Fig.<br />36.</td>
+    <td class="figure"><img src="images/fig036.png" alt="Fig. 36." title="Fig. 36." /></td>
+
+</tr>
+</table>
+</div>
+
+
+<p>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. [<a href="#fig_37">Fig.&nbsp;37.</a>]</p>
+
+<p>The passing major seventh and its root may appear on the
+weak beat, even when approached in similar motion as in <a href="#fig_37">Fig.&nbsp;37<i>a</i></a>.
+The seventh must then be treated as a passing-tone.</p>
+
+<div class="figure">
+<table class="figure" id="fig_37" summary="Figure 37">
+<tr><td class="caption">Fig.<br />37.</td>
+    <td class="figure"><img src="images/fig037.png" alt="Fig. 37." title="Fig. 37." /></td>
+
+</tr>
+</table>
+</div>
+
+
+<p>The cadences in <a href="#fig_38">Fig.&nbsp;38</a> are good when writing second species
+in both parts. Those having the second species in one part only,
+may also be used.</p>
+
+<div class="pagenum" id="page_11">[11]</div>
+
+<div class="figure">
+<table class="figure" id="fig_38" summary="Figure 38">
+<tr><td class="caption">Fig.<br />38.</td>
+    <td class="figure"><img src="images/fig038.png" alt="Fig. 38." title="Fig. 38." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Writing the second species in both parts will, in this lesson, be
+confined to a mixture of the first and second species, as in <a href="#fig_39">Fig.&nbsp;39.</a></p>
+
+<p>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.</p>
+
+<div class="figure">
+<table class="figure" id="fig_39" summary="Figure 39">
+<tr><td class="caption">Fig.<br />39.</td>
+    <td class="figure"><img src="images/fig039.png" alt="Fig. 39." title="Fig. 39." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>Write two eight-measure phrases mixing the first and second species.
+[<a href="#fig_39">Fig.&nbsp;39.</a>]</p>
+
+<p>To cantus firmus <i>a</i> write one counterpoint above and one below, three
+notes to the measure. [<a href="#fig_31">Fig.&nbsp;31.</a>]</p>
+
+<p>To cantus firmus <i>b</i> write one above and one below, in the second species.</p>
+
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_40" summary="Figure 40">
+<tr><td class="capnorm">Fig.<br />40.</td>
+    <td class="figure"><img src="images/fig040.png" alt="Fig. 40." title="Fig. 40." /></td>
+</tr>
+</table>
+</div>
+
+<h3 id="LESSON_IV">LESSON IV</h3>
+
+<h4>THIRD SPECIES</h4>
+
+
+<div class="figure">
+<table class="figure" id="fig_41" summary="Figure 41">
+<tr><td class="capnorm">Fig.<br />41.</td>
+    <td class="figure"><img src="images/fig041.png" alt="Fig. 41." title="Fig. 41." /></td>
+</tr>
+</table>
+</div>
+
+<div class="pagenum" id="page_12">[12]</div>
+
+<p>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. [<a href="#fig_42">Fig.&nbsp;42.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_42" summary="Figure 42">
+<tr><td class="caption">Fig.<br />42.</td>
+    <td class="figure"><img src="images/fig042.png" alt="Fig. 42." title="Fig. 42." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The exercises should begin and end with tonic harmony.</p>
+
+<p>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.</p>
+
+<p>All previous rules are to be regarded, unless exceptions are
+made.</p>
+
+<p>At least one of the first three quarter-notes of a measure
+should be left degreewise. [<a href="#fig_43">Fig.&nbsp;43.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_43" summary="Figure 43">
+<tr><td class="caption">Fig.<br />43.</td>
+    <td class="figure"><img src="images/fig043.png" alt="Fig. 43." title="Fig. 43." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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 (<i>d</i>). [<a href="#fig_44">Fig.&nbsp;44.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_44" summary="Figure 44">
+<tr><td class="capnorm">Fig.<br />44.</td>
+    <td class="figure"><img src="images/fig044.png" alt="Fig. 44." title="Fig. 44." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Parts may cross occasionally.</p>
+
+<p>The use of non-harmonic tones, as in <a href="#fig_45">Fig.&nbsp;45</a>, is good in either
+part. At <i>a</i> 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
+
+<span class="pagenum" id="page_13">[13]</span>
+
+is most effective when the principal tone is the leading-tone, as
+at <i>b</i>. In both cases the counterpoint should continue degreewise
+through the chord-tone. [<a href="#fig_45">Fig.&nbsp;45.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_45" summary="Figure 45">
+<tr><td class="caption">Fig.<br />45.</td>
+    <td class="figure"><img src="images/fig045.png" alt="Fig. 45." title="Fig. 45." /></td>
+
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<div class="figure">
+<table class="figure" id="fig_46" summary="Figure 46">
+<tr><td class="caption">Fig.<br />46.</td>
+    <td class="figure"><img src="images/fig046.png" alt="Fig. 46." title="Fig. 46." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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. [<a href="#fig_47">Fig.&nbsp;47.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_47" summary="Figure 47">
+<tr><td class="capnorm">Fig.<br />47.</td>
+    <td class="figure"><img src="images/fig047.png" alt="Fig. 47." title="Fig. 47." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Oblique motion to the unison is bad. It is permitted if it continues
+in the same direction through the unison. [<a href="#fig_48">Fig.&nbsp;48.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_48" summary="Figure 28">
+<tr><td class="caption">Fig.<br />48.</td>
+    <td class="figure"><img src="images/fig048.png" alt="Fig. 48." title="Fig. 48." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The unison may be used on any but the first quarter of a
+measure.</p>
+
+<p>Frequent repetition of a figure as in <a href="#fig_49">Fig.&nbsp;49</a> is not good.</p>
+
+<div class="figure">
+<table class="figure" id="fig_49" summary="Figure 49">
+<tr><td class="caption">Fig.<br />49.</td>
+
+    <td class="figure"><img src="images/fig049.png" alt="Fig. 49." title="Fig. 49." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_14">[14]</div>
+
+<p>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. [<a href="#fig_50">Fig.&nbsp;50.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_50" summary="Figure 50">
+<tr><td class="caption">Fig.<br />50.</td>
+    <td class="figure"><img src="images/fig050.png" alt="Fig. 50." title="Fig. 50." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>The sixth or seventh degrees may be chromatically altered
+with only one note intervening. [<a href="#fig_51">Fig.&nbsp;51.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_51" summary="Figure 51">
+<tr><td class="caption">Fig.<br />51.</td>
+    <td class="figure"><img src="images/fig051.png" alt="Fig. 51." title="Fig. 51." /></td>
+</tr>
+</table>
+</div>
+
+<p>Six notes may be written to one of the cantus firmus, as in
+<a href="#fig_52">Fig.&nbsp;52.</a></p>
+
+<div class="figure">
+<table class="figure" id="fig_52" summary="Figure 52">
+<tr><td class="capnorm">Fig.<br />52.</td>
+    <td class="figure"><img src="images/fig052.png" alt="Fig. 52." title="Fig. 52." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The cadences in <a href="#fig_53">Fig.&nbsp;53</a> are good.</p>
+
+<div class="figure">
+<table class="figure" id="fig_53" summary="Figure 53">
+<tr><td class="capnorm">Fig.<br />53.</td>
+    <td class="figure"><img src="images/fig053.png" alt="Fig. 53." title="Fig. 53." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write three counterpoints above and three below, in the
+third species.</p>
+
+<p>Write two eight-measure phrases, using second species continuously in
+both parts. [<a href="#fig_34">Fig.&nbsp;<span class="sic" title="[sic]">34</span>.</a>]</p>
+
+<div class="pagenum" id="page_15">[15]</div>
+
+<h4 class="cf">Cantus Firmus</h4>
+
+<div class="figure">
+<table class="figure" id="fig_54" summary="Figure 54">
+<tr><td class="caption">Fig.<br />54.</td>
+    <td class="figure"><img src="images/fig054.png" alt="Fig. 54." title="Fig. 54." /></td>
+</tr>
+</table>
+</div>
+
+
+<h3 id="LESSON_V">LESSON V</h3>
+
+<h4>THIRD SPECIES IN BOTH PARTS</h4>
+
+<div class="figure">
+<table class="figure" id="fig_55" summary="Figure 55">
+<tr><td class="capnorm">Fig.<br />55.</td>
+    <td class="figure"><img src="images/fig055.png" alt="Fig. 55." title="Fig. 55." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>The augmented fourth, and diminished fifth and seventh, may
+be approached in similar motion. [<a href="#fig_56">Fig.&nbsp;56.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_56" summary="Figure 56">
+<tr><td class="caption">Fig.<br />56.</td>
+    <td class="figure"><img src="images/fig056.png" alt="Fig. 56." title="Fig. 56." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The augmented fourth following the perfect fourth, as in
+<a href="#fig_56">Fig.&nbsp;56<i>a</i></a>, is good.</p>
+
+<p>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. [<a href="#fig_57">Fig.&nbsp;57.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_57" summary="Figure 57">
+<tr><td class="caption">Fig.<br />57.</td>
+    <td class="figure"><img src="images/fig057.png" alt="Fig. 57." title="Fig. 57." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_16">[16]</div>
+
+<p>The first and third species may be mixed, as in <a href="#fig_58">Fig.&nbsp;58.</a></p>
+
+<div class="figure">
+<table class="figure" id="fig_58" summary="Figure 58">
+<tr><td class="caption">Fig.<br />58.</td>
+    <td class="figure"><img src="images/fig058.png" alt="Fig. 58." title="Fig. 58." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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. [<a href="#fig_59">Fig.&nbsp;59.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_59" summary="Figure 59">
+<tr><td class="capnorm">Fig.<br />59.</td>
+
+    <td class="figure"><img src="images/fig059.png" alt="Fig. 59." title="Fig. 59." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The cadences in <a href="#fig_60">Fig.&nbsp;60</a> are good, and will suggest others.</p>
+
+<div class="figure">
+<table class="figure" id="fig_60" summary="Figure 60">
+<tr><td class="caption">Fig.<br />60.</td>
+    <td class="figure"><img src="images/fig060.png" alt="Fig. 60." title="Fig. 60." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write one counterpoint above and one below, in the
+third species.</p>
+
+<p>To cantus firmus <i>b</i> write counterpoints in six notes, one above and one
+below. [<a href="#fig_52">Fig.&nbsp;52.</a>]</p>
+
+<p>Write one eight-measure phrase, mixing the first and third species.
+[<a href="#fig_58">Fig.&nbsp;58.</a>]</p>
+
+<p>Write two eight-measure phrases, using third species in both parts.
+[<a href="#fig_55">Fig.&nbsp;55.</a>]</p>
+
+<div class="pagenum" id="page_17">[17]</div>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_61" summary="Figure 61">
+<tr><td class="caption">Fig.<br />61.</td>
+    <td class="figure"><img src="images/fig061.png" alt="Fig. 61." title="Fig. 61." /></td>
+</tr>
+
+</table>
+</div>
+
+
+
+<h3 id="LESSON_VI">LESSON VI</h3>
+
+<h4>FOURTH SPECIES</h4>
+
+<div class="figure">
+<table class="figure" id="fig_62" summary="Figure 62">
+<tr><td class="caption">Fig.<br />62.</td>
+    <td class="figure"><img src="images/fig062.png" alt="Fig. 62." title="Fig. 62." /></td>
+</tr>
+
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>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.</p>
+
+<p>After the first measure, the second half of the measure should
+contain a consonance (<a href="#fig_63">Fig.&nbsp;63<i>a</i></a>), the first half a consonance (<i>b</i>),
+or dissonance (<i>c</i>), 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&mdash;or
+ascend in retardation (<i>d</i>)&mdash;one degree to an imperfect
+consonance (<i>c</i>). When the first half is a consonance, it may
+be left by a skip to some other chord-tone (<i>e</i>), or by degreewise
+progression (<i>f</i>). In the latter case the second note is non-harmonic,
+and therefore should not be used to prepare a syncopation
+except as in <a href="#fig_63">Fig.&nbsp;63<i>d</i></a> (Retardation of the root in I<sub>6</sub>).</p>
+
+<div class="figure">
+<table class="figure" id="fig_63" summary="Figure 63">
+<tr><td class="caption">Fig.<br />63.</td>
+    <td class="figure"><img src="images/fig063.png" alt="Fig. 63." title="Fig. 63." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_18">[18]</div>
+
+<p>When writing three notes to one in the fourth species, the
+suspension may resolve on the second beat (<i>a</i>), or the third (<i>b</i>).
+In the latter case, the suspension skips (<i>c</i>) to some other chord-tone,
+before resolving. The resolution to the leading-tone (<i>d</i>)
+forms an important exception to this rule. [<a href="#fig_64">Fig.&nbsp;64.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_64" summary="Figure 64">
+<tr><td class="caption">Fig.<br />64.</td>
+    <td class="figure"><img src="images/fig064.png" alt="Fig. 64." title="Fig. 64." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The fifth may be used in the lower part if it becomes the preparation
+of a suspension (<a href="#fig_65">Fig.&nbsp;65<i>a</i></a>). It may also be used in the
+lower part, as in <a href="#fig_65">Fig.&nbsp;65<i>b</i></a>, provided it resolves by skipping to the
+third of the chord.</p>
+
+<p>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.</p>
+
+<div class="figure">
+<table class="figure" id="fig_65" summary="Figure 65">
+<tr><td class="caption">Fig.<br />65.</td>
+    <td class="figure"><img src="images/fig065.png" alt="Fig. 65." title="Fig. 65." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The retardation should be used only when prepared by the
+leading-tone. It rises a semitone in resolving. [<a href="#fig_66">Fig.&nbsp;66.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_66" summary="Figure 66">
+<tr><td class="caption">Fig.<br />66.</td>
+    <td class="figure"><img src="images/fig066.png" alt="Fig. 66." title="Fig. 66." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The following dissonant intervals may be used on the first half of
+the measure:&mdash;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. [<a href="#fig_67">Fig.&nbsp;67.</a>]</p>
+
+<div class="pagenum" id="page_19">[19]</div>
+
+<div class="figure">
+<table class="figure" id="fig_67" summary="Figure 67">
+<tr><td class="capnorm">Fig.<br />67.</td>
+
+    <td class="figure"><img src="images/fig067.png" alt="Fig. 67." title="Fig. 67." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Consecutive fifths on consecutive strong beats of the measure
+are good when one of the tones of the second fifth is prepared, as
+in <a href="#fig_68">Fig.&nbsp;68.</a></p>
+
+<div class="figure">
+<table class="figure" id="fig_68" summary="Figure 68">
+<tr><td class="caption">Fig.<br />68.</td>
+    <td class="figure"><img src="images/fig068.png" alt="Fig. 68." title="Fig. 68." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The following cadences are good:</p>
+
+<div class="figure">
+<table class="figure" id="fig_69" summary="Figure 69">
+<tr><td class="caption">Fig.<br />69.</td>
+    <td class="figure"><img src="images/fig069.png" alt="Fig. 69." title="Fig. 69." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>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. (<a href="#fig_59">Fig.&nbsp;59.</a>) In combining
+the species in this and succeeding lessons the student may place any
+species in any part.</p>
+
+<p>To the cantus firmus write two counterpoints above and two below, in the
+fourth species.</p>
+
+<h4 class="cf">Cantus Firmus</h4>
+
+<div class="figure">
+<table class="figure" id="fig_70" summary="Figure 70">
+<tr><td class="caption">Fig.<br />70.</td>
+    <td class="figure"><img src="images/fig070.png" alt="Fig. 70." title="Fig. 70." /></td>
+</tr>
+
+</table>
+</div>
+
+
+
+<h3 id="LESSON_VII">LESSON VII</h3>
+
+<h4>FOURTH SPECIES (Continued)</h4>
+
+<p>The first and fourth species may be mixed as in <a href="#fig_71">Fig.&nbsp;71.</a>
+Rules for writing other than the first species in both parts are to
+be regarded.</p>
+
+<div class="pagenum" id="page_20">[20]</div>
+
+<div class="figure">
+<table class="figure" id="fig_71" summary="Figure 71">
+<tr><td class="caption">Fig.<br />71.</td>
+
+    <td class="figure"><img src="images/fig071.png" alt="Fig. 71." title="Fig. 71." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write two counterpoints above and two below, in the
+fourth species.</p>
+
+<p>To cantus firmus <i>b</i> write two above and two below, three half-notes to the
+measure, with syncopations.</p>
+
+<p>Write two eight-measure phrases, mixing the first and fourth species.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_72" summary="Figure 72">
+<tr><td class="capnorm">Fig.<br />72.</td>
+    <td class="figure"><img src="images/fig072.png" alt="Fig. 72." title="Fig. 72." /></td>
+</tr>
+</table>
+</div>
+
+
+<h3 id="LESSON_VIII">LESSON VIII</h3>
+
+<h4>COMBINING THE FOURTH SPECIES WITH THE OTHERS</h4>
+
+<p>All previous rules for combining species still apply.</p>
+
+<p>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. [<a href="#fig_73">Fig.&nbsp;73.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_73" summary="Figure 73">
+<tr><td class="capnorm">Fig.<br />73.</td>
+
+    <td class="figure"><img src="images/fig073.png" alt="Fig. 73." title="Fig. 73." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_21">[21]</div>
+
+<p>The leading-tone may be doubled as in <a href="#fig_74">Fig.&nbsp;74.</a> Here the
+leading-tone that is prepared skips to some other chord-tone,
+while the new leading-tone remains stationary.</p>
+
+<div class="figure">
+<table class="figure" id="fig_74" summary="Figure 74">
+<tr><td class="caption">Fig.<br />74.</td>
+    <td class="figure"><img src="images/fig074.png" alt="Fig. 74." title="Fig. 74." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.
+[<a href="#fig_75">Fig.&nbsp;75.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_75" summary="Figure 75">
+<tr><td class="capnorm">Fig.<br />75.</td>
+    <td class="figure"><img src="images/fig075.png" alt="Fig. 75." title="Fig. 75." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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. [<a href="#fig_76">Fig.&nbsp;76.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_76" summary="Figure 76">
+<tr><td class="capnorm">Fig.<br />76.</td>
+    <td class="figure"><img src="images/fig076.png" alt="Fig. 76." title="Fig. 76." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_22">[22]</div>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To the cantus firmus write one counterpoint above and one below, in the
+fourth species.</p>
+
+<p>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. [<a href="#fig_76">Fig.&nbsp;76.</a>]</p>
+
+<h4 class="cf">Cantus Firmus</h4>
+
+<div class="figure">
+<table class="figure" id="fig_77" summary="Figure 77">
+<tr><td class="caption">Fig.<br />77.</td>
+    <td class="figure"><img src="images/fig077.png" alt="Fig. 77." title="Fig. 77." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_IX">LESSON IX</h3>
+
+<h4>FIFTH SPECIES: FLORID COUNTERPOINT</h4>
+
+<div class="figure">
+<table class="figure" id="fig_78" summary="Figure 78">
+<tr><td class="caption">Fig.<br />78.</td>
+    <td class="figure"><img src="images/fig078.png" alt="Fig. 78." title="Fig. 78." /></td>
+</tr>
+</table>
+</div>
+
+<p>Florid counterpoint is a mixture of the second, third and fourth
+species.</p>
+
+<p>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. [<a href="#fig_79">Fig.&nbsp;79.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_79" summary="Figure 79">
+<tr><td class="capnorm">Fig.<br />79.</td>
+    <td class="figure"><img src="images/fig079.png" alt="Fig. 79." title="Fig. 79." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Not more than one and one-half measures of any one species
+should be used continuously in one part. [<a href="#fig_80">Fig.&nbsp;80.</a>]</p>
+
+<div class="pagenum" id="page_23">[23]</div>
+
+<div class="figure">
+<table class="figure" id="fig_80" summary="Figure 80">
+<tr><td class="capnorm">Fig.<br />80.</td>
+    <td class="figure"><img src="images/fig080.png" alt="Fig. 80." title="Fig. 80." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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. [<a href="#fig_81">Fig.&nbsp;81.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_81" summary="Figure 81">
+<tr><td class="capnorm">Fig.<br />81.</td>
+    <td class="figure"><img src="images/fig081.png" alt="Fig. 81." title="Fig. 81." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>For the present the suspension should not be less than a half-note
+or its rhythmic equivalent in the ornamental resolution.</p>
+
+<p>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. [<a href="#fig_82">Fig.&nbsp;82.</a>]</p>
+
+<p>When the suspension is left by a leap, the note skipped to
+should be consonant with the other part (<i>b</i>). When eighth-notes
+are used, as at <i>a</i>, they must be approached and left stepwise.</p>
+
+<p>The suspension, instead of being sustained as a half-note, may
+be repeated on the second quarter, as at <i>c</i>. In this case it is
+best to continue stepwise through the tone of resolution.</p>
+
+<p>At <i>d</i> the resolution, instead of coming on the second half,
+appears on the quarters on either side. This is good.</p>
+
+<div class="pagenum" id="page_24">[24]</div>
+
+<div class="figure">
+<table class="figure" id="fig_82" summary="Figure 82">
+<tr><td class="capnorm">Fig.<br />82.</td>
+    <td class="figure"><img src="images/fig082.png" alt="Fig. 82." title="Fig. 82." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The ornamental resolution may be used in either part.</p>
+
+<p>Use the suspension freely.</p>
+
+<p>The solutions should be musical, and are to be written over
+and over again until such are secured.</p>
+
+<p>All cadences of the second, third and fourth species, or any
+combination of these, may be used.</p>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To canti firmi <i>a</i> and <i>b</i> write two counterpoints above and two below, in
+the fifth species</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_83" summary="Figure 83">
+<tr><td class="capnorm">Fig.<br />83.</td>
+    <td class="figure"><img src="images/fig083.png" alt="Fig. 83." title="Fig. 83." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_X">LESSON X</h3>
+
+<h4>FLORID COUNTERPOINT (Continued)</h4>
+
+<p>When florid counterpoint is combined with other than first
+species, the dotted half followed by a quarter-note (<i>a</i>), or two
+
+<span class="pagenum" id="page_25">[25]</span>
+
+eighth-notes (<i>b</i>), is good. Also, a rhythmic figure, as at <i>c</i>, where
+a half-note occupies the second and third quarters, may be used.
+[<a href="#fig_84">Fig.&nbsp;84.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_84" summary="Figure 84">
+<tr><td class="caption">Fig.<br />84.</td>
+    <td class="figure"><img src="images/fig084.png" alt="Fig. 84." title="Fig. 84." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>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. [<a href="#fig_85">Fig.&nbsp;85.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_85" summary="Figure 85">
+<tr><td class="capnorm">Fig.<br />85.</td>
+    <td class="figure"><img src="images/fig085.png" alt="Fig. 85." title="Fig. 85." /></td>
+</tr>
+</table>
+</div>
+
+<div class="pagenum" id="page_26">[26]</div>
+
+<h2>SIMPLE COUNTERPOINT IN THREE PARTS</h2>
+
+<h3 id="LESSON_XI">LESSON XI</h3>
+
+<h4>FIRST SPECIES</h4>
+
+<div class="figure">
+<table class="figure" id="fig_86" summary="Figure 86">
+<tr><td class="caption">Fig.<br />86.</td>
+    <td class="figure"><img src="images/fig086.png" alt="Fig. 86." title="Fig. 86." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Regard all rules for two-part counterpoint, unless otherwise
+mentioned.</p>
+
+<p>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 (<a href="#fig_87">Fig.&nbsp;87</a>). The
+doubling of the fifth is, of course, impossible, since it necessitates
+the omission of the third.</p>
+
+<div class="figure">
+<table class="figure" id="fig_87" summary="Figure 87">
+<tr><td class="caption">Fig.<br />87.</td>
+    <td class="figure"><img src="images/fig087.png" alt="Fig. 87." title="Fig. 87." /></td>
+
+</tr>
+</table>
+</div>
+
+
+<p>All triads may be used in their first inversion.</p>
+
+<p>Diminished and augmented triads, however, are best used in
+their first inversion.</p>
+
+<p>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 <i>b</i>. [<a href="#fig_88">Fig.&nbsp;88.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_88" summary="Figure 88">
+<tr><td class="caption">Fig.<br />88.</td>
+
+    <td class="figure"><img src="images/fig088.png" alt="Fig. 88." title="Fig. 88." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_27">[27]</div>
+
+<p>The dominant seventh may be used in any but its second inversion,
+the fifth being omitted.<a id="FNanchor_A_2" href="#Footnote_A_2" class="fnanchor">[A]</a> The seventh requires no preparation.
+Other chords of the seventh are better not used until
+second species and later.</p>
+
+<p>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<sub>7</sub> is used. [<a href="#fig_89">Fig.&nbsp;89.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_89" summary="Figure 89">
+<tr><td class="caption">Fig.<br />89.</td>
+    <td class="figure"><img src="images/fig089.png" alt="Fig. 89." title="Fig. 89." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Consecutive major thirds may be used when three or more
+parts are employed. [<a href="#fig_90">Fig.&nbsp;90.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_90" summary="Figure 90">
+<tr><td class="caption">Fig.<br />90.</td>
+
+    <td class="figure"><img src="images/fig090.png" alt="Fig. 90." title="Fig. 90." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>A note may now be repeated in the lowest part when it becomes
+the seventh of a dominant seventh-chord. [<a href="#fig_91">Fig.&nbsp;91.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_91" summary="Figure 91">
+<tr><td class="caption">Fig.<br />91.</td>
+    <td class="figure"><img src="images/fig091.png" alt="Fig. 91." title="Fig. 91." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>All hidden fifths and octaves are bad, except between I and V
+and V and I. [<a href="#fig_92">Fig.&nbsp;92<i>a</i></a>, <i>b</i>.]</p>
+
+<div class="footnote"><p id="Footnote_A_2"><a href="#FNanchor_A_2" class="label">[A]</a> 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.</p></div>
+
+<div class="pagenum" id="page_28">[28]</div>
+
+<p>The perfect fifth following the diminished fifth is good when
+taken in an upward direction stepwise in the higher parts.
+[<a href="#fig_92">Fig.&nbsp;92<i>c</i></a>.]</p>
+
+<div class="figure">
+<table class="figure" id="fig_92" summary="Figure 92">
+<tr><td class="caption">Fig.<br />92.</td>
+    <td class="figure"><img src="images/fig092.png" alt="Fig. 92." title="Fig. 92." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>All cadences used in harmony are good.</p>
+
+<p>Unless otherwise mentioned, put the cantus firmus in any part,
+but avoid its continued use in the same part.</p>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To canti firmi <i>a</i> and <i>b</i> 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.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_93" summary="Figure 93">
+<tr><td class="capnorm">Fig.<br />93.</td>
+    <td class="figure"><img src="images/fig093.png" alt="Fig. 93." title="Fig. 93." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XII">LESSON XII</h3>
+
+<h4>THE SECOND SPECIES</h4>
+
+<div class="figure">
+<table class="figure" id="fig_94" summary="Figure 94">
+<tr><td class="caption">Fig.<br />94.</td>
+    <td class="figure"><img src="images/fig094.png" alt="Fig. 94." title="Fig. 94." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The second species is written in one part and the first in the
+other two.</p>
+
+<div class="pagenum" id="page_29">[29]</div>
+
+<p>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.</p>
+
+<p>The fifth, when in the lowest voice, should be used as in two-part
+counterpoint, except when used in V<sup class="vertical">4</sup><sub class="vertical">3</sub> or the cadencing tonic
+six-four chord.</p>
+
+<p>The V<sup class="vertical">4</sup><sub class="vertical">3</sub> chord may be used on the weak beat, necessitating
+the omission of the third. [<a href="#fig_95">Fig.&nbsp;95<i>a</i></a>.]</p>
+
+<p>The third may be omitted (<i>b</i>), or doubled (<i>c</i>), on the weak
+beat in this and succeeding species. [<a href="#fig_95">Fig.&nbsp;95.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_95" summary="Figure 95">
+<tr><td class="caption">Fig.<br />95.</td>
+    <td class="figure"><img src="images/fig095.png" alt="Fig. 95." title="Fig. 95." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>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. [<a href="#fig_96">Fig.&nbsp;96.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_96" summary="Figure 96">
+<tr><td class="capnorm">Fig.<br />96.</td>
+    <td class="figure"><img src="images/fig096.png" alt="Fig. 96." title="Fig. 96." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_30">[30]</div>
+
+<p>The progression from <span class="sc">vii</span>°<sub class="vertical">6</sub> to V in root-position or any inversion
+in the same measure, is good. [<a href="#fig_97">Fig.&nbsp;97.</a>] Use <i>b</i> and <i>c</i> only
+when using other than first species in two or more parts.</p>
+
+<div class="figure">
+<table class="figure" id="fig_97" summary="Figure 97">
+<tr><td class="caption">Fig.<br />97.</td>
+    <td class="figure"><img src="images/fig097.png" alt="Fig. 97." title="Fig. 97." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Each measure should usually contain a complete chord. If not
+complete on the first beat, bring the missing interval in on the
+second. [<a href="#fig_98">Fig.&nbsp;98.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_98" summary="Figure 98">
+<tr><td class="caption">Fig.<br />98.</td>
+
+    <td class="figure"><img src="images/fig098.png" alt="Fig. 98." title="Fig. 98." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The cadences in <a href="#fig_99">Fig.&nbsp;99</a> are good, and will suggest others.
+The use of the fourth species is permitted as at <i>a</i>. A note may
+be repeated in the final cadence in all species as at <i>b</i>.</p>
+
+<div class="figure">
+<table class="figure" id="fig_99" summary="Figure 99">
+<tr><td class="capnorm">Fig.<br />99.</td>
+
+    <td class="figure"><img src="images/fig099.png" alt="Fig. 99." title="Fig. 99." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_31">[31]</div>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write the first species in all parts, as previously
+directed.</p>
+
+<p>To cantus firmus <i>b</i> 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.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_100" summary="Figure 100">
+<tr><td class="capnorm">Fig.<br />100.</td>
+    <td class="figure"><img src="images/fig100.png" alt="Fig. 100." title="Fig. 100." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XIII">LESSON XIII</h3>
+
+<h4>SECOND SPECIES IN TWO PARTS</h4>
+
+<div class="figure">
+<table class="figure" id="fig_101" summary="Figure 101">
+<tr><td class="caption">Fig.<br />101.</td>
+    <td class="figure"><img src="images/fig101.png" alt="Fig. 101." title="Fig. 101." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>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. [<a href="#fig_102">Fig.&nbsp;102.</a>]</p>
+
+<div class="pagenum" id="page_32">[32]</div>
+
+<div class="figure">
+<table class="figure" id="fig_102" summary="Figure 102">
+<tr><td class="caption">Fig.<br />102.</td>
+    <td class="figure"><img src="images/fig102.png" alt="Fig. 102." title="Fig. 102." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>At <a href="#fig_102">Fig.&nbsp;102<i>a</i></a>, the accidental harmony <i>f-a-c</i> is on the weak
+beat. The <i>f</i> and <i>a</i>, being foreign to the chord <i>c-e-g</i> on the strong
+beat, are correctly treated as dissonances. At <i>b</i>, the <i>f</i> and <i>a</i> are
+left by skip, which is not permitted.</p>
+
+<p>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. [<a href="#fig_103">Fig.&nbsp;103.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_103" summary="Figure 103">
+<tr><td class="caption">Fig.<br />103.</td>
+    <td class="figure"><img src="images/fig103.png" alt="Fig. 103." title="Fig. 103." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The first and second species may be mixed, as in <a href="#fig_104">Fig.&nbsp;104.</a></p>
+
+<div class="figure">
+<table class="figure" id="fig_104" summary="Figure 104">
+<tr><td class="caption">Fig.<br />104.</td>
+    <td class="figure"><img src="images/fig104.png" alt="Fig. 104." title="Fig. 104." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The cadences in <a href="#fig_105">Fig.&nbsp;105</a> are good, and will suggest others.
+Those with first species in all parts may also be used.</p>
+
+<div class="figure">
+<table class="figure" id="fig_105" summary="Figure 105">
+<tr><td class="caption">Fig.<br />105.</td>
+
+    <td class="figure"><img src="images/fig105.png" alt="Fig. 105." title="Fig. 105." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_33">[33]</div>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write a counterpoint in the second species in one part.
+Write three settings, as directed in the previous lesson.</p>
+
+<p>Write two eight-measure phrases mixing the first and second species in all
+parts.</p>
+
+<p>To cantus firmus <i>b</i> write counterpoints in the second species in the other
+two parts. Write two settings, with the cantus firmus in different parts.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_106" summary="Figure 106">
+<tr><td class="capnorm">Fig.<br />106.</td>
+    <td class="figure"><img src="images/fig106.png" alt="Fig. 106." title="Fig. 106." /></td>
+</tr>
+
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XIV">LESSON XIV</h3>
+
+<h4>THIRD SPECIES</h4>
+
+<div class="figure">
+<table class="figure" id="fig_107" summary="Figure 107">
+<tr><td class="capnorm">Fig.<br />107.</td>
+    <td class="figure"><img src="images/fig107.png" alt="Fig. 107." title="Fig. 107." /></td>
+</tr>
+
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>The cadences at <a href="#fig_108">Fig.&nbsp;108</a> are good, and will suggest others.</p>
+
+<div class="figure">
+<table class="figure" id="fig_108" summary="Figure 108">
+<tr><td class="caption">Fig.<br />108.</td>
+    <td class="figure"><img src="images/fig108.png" alt="Fig. 108." title="Fig. 108." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_34">[34]</div>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write third species in one part. Write three settings
+as previously directed.</p>
+
+<p>To cantus firmus <i>b</i> write second species in two parts, as previously
+directed.</p>
+
+<p>Write one eight-measure phrase, using second species in all parts.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_109" summary="Figure 109">
+<tr><td class="capnorm">Fig.<br />109.</td>
+    <td class="figure"><img src="images/fig109.png" alt="Fig. 109." title="Fig. 109." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XV">LESSON XV</h3>
+
+<h4>THIRD SPECIES IN TWO OR MORE PARTS</h4>
+
+<div class="figure">
+<table class="figure" id="fig_110" summary="Figure 110">
+<tr><td class="capnorm">Fig.<br />110.</td>
+    <td class="figure"><img src="images/fig110.png" alt="Fig. 110." title="Fig. 110." /></td>
+</tr>
+</table>
+</div>
+
+<div class="pagenum" id="page_35">[35]</div>
+
+<p>Previous suggestions when two or more parts have other than
+first species, apply here.</p>
+
+<p>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]). [<a href="#fig_111">Fig.&nbsp;111.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_111" summary="Figure 111">
+<tr><td class="capnorm">Fig.<br />111.</td>
+    <td class="figure"><img src="images/fig111.png" alt="Fig. 111." title="Fig. 111." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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.</p>
+
+<p>The cadences in <a href="#fig_112">Fig.&nbsp;112</a> are good.</p>
+
+<div class="figure">
+<table class="figure" id="fig_112" summary="Figure 112">
+<tr><td class="capnorm">Fig.<br />112.</td>
+    <td class="figure"><img src="images/fig112.png" alt="Fig. 112." title="Fig. 112." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_36">[36]</div>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write third species in one part, as previously directed.</p>
+
+<p>To cantus firmus <i>b</i> write third species in two parts, as in <a href="#fig_110">Fig.&nbsp;110<i>b</i></a>.
+Write twice, changing the cantus firmus about.</p>
+
+<p>Write one eight-measure phrase, mixing first and third species as in <a href="#fig_110">Fig.&nbsp;110<i>a</i></a>.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_113" summary="Figure 113">
+<tr><td class="capnorm">Fig.<br />113.</td>
+    <td class="figure"><img src="images/fig113.png" alt="Fig. 113." title="Fig. 113." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XVI">LESSON XVI</h3>
+
+<h4>THIRD SPECIES (Continued)</h4>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To the cantus firmus write third species in one part, as previously directed.</p>
+
+<p>Write one eight-measure phrase, mixing first and third species; also one
+mixing first, second and third. [<a href="#fig_114">Fig.&nbsp;114.</a>]</p>
+
+<p>Write one eight-measure phrase, using third species in all parts. [<a href="#fig_110">Fig.&nbsp;110<i>c</i></a>.]</p>
+
+<div class="figure">
+<table class="figure" id="fig_114" summary="Figure 114">
+<tr><td class="capnorm">Fig.<br />114.</td>
+    <td class="figure"><img src="images/fig114.png" alt="Fig. 114." title="Fig. 114." /></td>
+</tr>
+</table>
+</div>
+
+<div class="pagenum" id="page_37">[37]</div>
+
+<h4 class="cf">Cantus Firmus</h4>
+
+<div class="figure">
+<table class="figure" id="fig_115" summary="Figure 115">
+<tr><td class="caption">Fig.<br />115.</td>
+    <td class="figure"><img src="images/fig115.png" alt="Fig. 115." title="Fig. 115." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XVII">LESSON XVII</h3>
+
+<h4>FOURTH SPECIES</h4>
+
+<div class="figure">
+<table class="figure" id="fig_116" summary="Figure 116">
+<tr><td class="caption">Fig.<br />116.</td>
+    <td class="figure"><img src="images/fig116.png" alt="Fig. 116." title="Fig. 116." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>When the syncopation is a suspension or retardation, it is
+treated the same as in harmony.</p>
+
+<p>The retardation should always be prepared by the leading-tone.</p>
+
+<p>When the syncopated note belongs to the harmony of the measure,
+it may be left by a skip or stepwise progression. [<a href="#fig_117">Fig.&nbsp;117.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_117" summary="Figure 117">
+<tr><td class="caption">Fig.<br />117.</td>
+    <td class="figure"><img src="images/fig117.png" alt="Fig. 117." title="Fig. 117." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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 <a href="#fig_117">Fig.&nbsp;117<i>a</i></a>.</p>
+
+<p>Consecutive fifths, but not octaves, are saved by the suspension.
+Whenever they occur, do not use the note of resolution as
+
+<span class="pagenum" id="page_38">[38]</span>
+
+preparation of a suspension, or tie it into the next measure (<i>a</i>),
+since it is really the passing seventh, and that does not lend itself
+well to either of the above, except in sequence as at <i>b</i>. [<a href="#fig_118">Fig.&nbsp;118.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_118" summary="Figure 118">
+<tr><td class="capnorm">Fig.<br />118.</td>
+    <td class="figure"><img src="images/fig118.png" alt="Fig. 118." title="Fig. 118." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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 <a href="#fig_119">Fig. 119</a>.</p>
+
+<div class="figure">
+<table class="figure" id="fig_119" summary="Figure 119">
+<tr><td class="caption">Fig.<br />119.</td>
+    <td class="figure"><img src="images/fig119.png" alt="Fig. 119." title="Fig. 119." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>This species may also be written in triple rhythm. [<a href="#fig_120">Fig.&nbsp;120.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_120" summary="Figure 120">
+<tr><td class="caption">Fig.<br />120.</td>
+    <td class="figure"><img src="images/fig120.png" alt="Fig. 120." title="Fig. 120." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_39">[39]</div>
+
+<p>The cadences in <a href="#fig_121">Fig.&nbsp;121</a> are good, as well as those of the
+second species.</p>
+
+<div class="figure">
+<table class="figure" id="fig_121" summary="Figure 121">
+<tr><td class="capnorm">Fig.<br />121.</td>
+    <td class="figure"><img src="images/fig121.png" alt="Fig. 121." title="Fig. 121." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write fourth species in one part. Write three settings,
+as usual.</p>
+
+<p>To cantus firmus <i>b</i> write fourth species in one part in triple rhythm.
+Write three settings, as above.</p>
+
+<p>To cantus firmus <i>b</i> write second species in one part and third in the other.
+[<a href="#fig_122">Fig.&nbsp;122.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_122" summary="Figure 122">
+<tr><td class="caption">Fig.<br />122.</td>
+    <td class="figure"><img src="images/fig122.png" alt="Fig. 122." title="Fig. 122." /></td>
+</tr>
+</table>
+</div>
+
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_123" summary="Figure 123">
+<tr><td class="capnorm">Fig.<br />123.</td>
+    <td class="figure"><img src="images/fig123.png" alt="Fig. 123." title="Fig. 123." /></td>
+</tr>
+</table>
+</div>
+
+<div class="pagenum" id="page_40">[40]</div>
+
+<h3 id="LESSON_XVIII">LESSON XVIII</h3>
+
+
+<h4>FOURTH SPECIES (Continued)</h4>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>Write two eight-measure phrases, using the fourth species mixed in all
+parts. [<a href="#fig_124">Fig.&nbsp;124<i>a</i></a>.]</p>
+
+<p>To cantus firmus <i>a</i> write second species in one part and fourth in the
+other. [<a href="#fig_124">Fig.&nbsp;124<i>b</i></a>.]</p>
+
+<p>To cantus firmus <i>b</i> write third species in one part and fourth in the other.
+[<a href="#fig_124">Fig.&nbsp;124<i>c</i></a>.]</p>
+
+<div class="figure">
+<table class="figure" id="fig_124" summary="Figure 124">
+<tr><td class="capnorm">Fig.<br />124.</td>
+    <td class="figure"><img src="images/fig124a.png" alt="Fig. 124., part 1" title="Fig. 124." /></td>
+</tr>
+<tr>
+  <td colspan="2" style="padding-top: 30px; text-align:right">
+    <img src="images/fig124b.png" alt="Fig. 124, part 2" />
+  </td>
+</tr>
+</table>
+</div>
+
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_125" summary="Figure 125">
+<tr><td class="capnorm">Fig.<br />125.</td>
+    <td class="figure"><img src="images/fig125.png" alt="Fig. 125." title="Fig. 125." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<div class="pagenum" id="page_41">[41]</div>
+
+<h3 id="LESSON_XIX">LESSON XIX</h3>
+
+<h4>FIFTH SPECIES</h4>
+
+<div class="figure">
+<table class="figure" id="fig_126" summary="Figure 126">
+<tr><td class="capnorm">Fig.<br />126.</td>
+    <td class="figure"><img src="images/fig126.png" alt="Fig. 126." title="Fig. 126." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>No suggestions other than have already been given for two- and
+three-part counterpoint are necessary for this species.</p>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To canti firmi <i>a</i> and <i>b</i> write fifth species in one part. Write each three
+times, as usual.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_127" summary="Figure 127">
+<tr><td class="capnorm">Fig.<br />127.</td>
+    <td class="figure"><img src="images/fig127.png" alt="Fig. 127." title="Fig. 127." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_42">[42]</div>
+
+<h3 id="LESSON_XX">LESSON XX</h3>
+
+<h4>FIFTH SPECIES (Continued)</h4>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write second species in one part and fifth in the other.
+[<a href="#fig_128">Fig.&nbsp;128<i>a</i></a>.]</p>
+
+<p>To cantus firmus <i>b</i> write third species in one part and fifth in the
+other. [<i>b</i>.]</p>
+
+<p>To cantus firmus <i>c</i> write fourth species in one part and fifth in the
+other. [<i>c</i>].</p>
+
+<p>To cantus firmus <i>d</i> write fifth species in two parts. [<i>d</i>.]</p>
+
+<div class="figure">
+<table class="figure" id="fig_128" summary="Figure 128">
+<tr><td class="capnorm">Fig.<br />128.</td>
+    <td class="figure"><img src="images/fig128a.png" alt="Fig. 128. part 1." title="Fig. 128." /></td>
+</tr>
+<tr>
+  <td>
+    <div class="pagenum" id="page_43">[43]</div>
+  </td>
+  <td colspan="2" style="padding-top: 30px; text-align:right">
+    <img src="images/fig128b.png" alt="Fig. 128. part 2." title="Fig. 128." />
+  </td>
+</tr>
+</table>
+</div>
+
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_129" summary="Figure 129">
+<tr><td class="capnorm">Fig.<br />129.</td>
+    <td class="figure"><img src="images/fig129.png" alt="Fig. 129." title="Fig. 129." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_44">[44]</div>
+
+<h3 id="LESSON_XXI">LESSON XXI</h3>
+
+<h4>COMBINING THE VARIOUS SPECIES</h4>
+
+<h4 class="ex">EXERCISES</h4>
+
+
+<p>Write one eight-measure phrase each, of the following combinations:
+(1) 2nd, 3rd and 4th species (<a href="#fig_130">Fig.&nbsp;130<i>a</i></a>); (2) 2nd, 3rd and fifth species (<i>b</i>)
+(3) 3rd, 5th and 5th species (<i>c</i>); (4) 2nd, 4th and 5th species (<i>d</i>); (5) 4th,
+5th and 5th species (<i>e</i>).</p>
+
+<div class="figure">
+<table class="figure" id="fig_130" summary="Figure 130">
+<tr><td class="capnorm">Fig.<br />130.</td>
+    <td class="figure"><img src="images/fig130a.png" alt="Fig. 130. part 1." title="Fig. 130." /></td>
+</tr>
+<tr>
+  <td>
+    <div class="pagenum" id="page_45">[45]</div>
+  </td>
+  <td style="padding-top: 30px" class="figure">
+    <img src="images/fig130b.png" alt="Fig. 130. part 2" title="Fig. 130." />
+  </td>
+</tr>
+</table>
+</div>
+
+
+<h3 id="LESSON_XXII">LESSON XXII</h3>
+
+<h4>FIFTH SPECIES IN ALL PARTS</h4>
+
+<h4 class="ex">EXERCISES</h4>
+
+
+<p>Write five eight-measure phrases with fifth species in all parts, making
+use of imitation at the beginning as in <a href="#fig_131">Fig.&nbsp;131.</a> 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.</p>
+
+<div class="figure">
+<table class="figure" id="fig_131" summary="Figure 131">
+<tr><td class="capnorm">Fig.<br />131.</td>
+
+    <td class="figure"><img src="images/fig131.png" alt="Fig. 131." title="Fig. 131." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_46">[46]</div>
+
+<h2>SIMPLE COUNTERPOINT IN FOUR PARTS</h2>
+
+
+<h3 id="LESSON_XXIII">LESSON XXIII</h3>
+
+<div class="figure">
+<table class="figure" id="fig_132" summary="Figure 132">
+<tr><td class="caption">Fig.<br />132.</td>
+
+    <td class="figure"><img src="images/fig132.png" alt="Fig. 132." title="Fig. 132." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>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 V<sup class="vertical">4</sup><sub class="vertical">3</sub> or <span class="sc">vii</span>°<sub class="vertical">6</sub>, use the latter, as in <a href="#fig_133">Fig.&nbsp;133.</a></p>
+
+<div class="figure">
+<table class="figure" id="fig_133" summary="Figure 133">
+<tr><td class="caption">Fig.<br />133.</td>
+
+    <td class="figure"><img src="images/fig133.png" alt="Fig. 133." title="Fig. 133." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To canti firmi <i>a</i> and <i>b</i> write the first species in the other parts. Write
+each four times, setting the cantus firmus in each part in turn.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_134" summary="Figure 134">
+<tr><td class="capnorm">Fig.<br />134.</td>
+    <td class="figure"><img src="images/fig134.png" alt="Fig. 134." title="Fig. 134." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_47">[47]</div>
+
+<h3 id="LESSON_XXIV">LESSON XXIV</h3>
+
+<div class="figure">
+<table class="figure" id="fig_135" summary="Figure 135">
+<tr><td class="caption">Fig.<br />135.</td>
+    <td class="figure"><img src="images/fig135.png" alt="Fig. 135." title="Fig. 135." /></td>
+</tr>
+</table>
+</div>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+
+<p>To cantus firmus <i>a</i> write the first species in all parts, as in the previous
+lesson.</p>
+
+<p>To cantus firmus <i>b</i> 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. [<a href="#fig_135">Fig.&nbsp;135.</a>]</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_136" summary="Figure 136">
+<tr><td class="capnorm">Fig.<br />136.</td>
+    <td class="figure"><img src="images/fig136.png" alt="Fig. 136." title="Fig. 136." /></td>
+</tr>
+
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XXV">LESSON XXV</h3>
+
+<div class="figure">
+<table class="figure" id="fig_137" summary="Figure 137">
+<tr><td class="capnorm">Fig.<br />137.</td>
+    <td class="figure"><img src="images/fig137.png" alt="Fig. 137." title="Fig. 137." /></td>
+</tr>
+</table>
+</div>
+
+<div class="pagenum" id="page_48">[48]</div>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write second species in one part as previously directed.</p>
+
+<p>To cantus firmus <i>b</i> write the first and second species mixed in the other
+three parts. [<a href="#fig_137">Fig.&nbsp;137<i>a</i></a>.]</p>
+
+<p>To cantus firmus <i>c</i> write third species in one part, as directed for the
+second species (<i>b</i>).</p>
+
+
+<div class="figure">
+<table class="figure" id="fig_138" summary="Figure 138">
+<tr><td class="capnorm">Fig.<br />138.</td>
+    <td class="figure"><img src="images/fig138.png" alt="Fig. 138." title="Fig. 138." /></td>
+</tr>
+</table>
+</div>
+
+
+<h3 id="LESSON_XXVI">LESSON XXVI</h3>
+
+<div class="figure">
+<table class="figure" id="fig_139" summary="Figure 139">
+<tr><td class="capnorm">Fig.<br />139.</td>
+    <td class="figure"><img src="images/fig139.png" alt="Fig. 139." title="Fig. 139." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_49">[49]</div>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write the second species in two parts and the first in
+the others. Write twice, changing the parts about. [<a href="#fig_139">Fig.&nbsp;139<i>a</i></a>.]</p>
+
+<p>To cantus firmus <i>b</i> write third species in one part as previously directed.</p>
+
+<p>To cantus firmus <i>c</i> write third species mixed in the other three parts, as
+at <a href="#fig_139">Fig.&nbsp;139<i>b</i></a>.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_140" summary="Figure 140">
+<tr><td class="capnorm">Fig.<br />140.</td>
+    <td class="figure"><img src="images/fig140.png" alt="Fig. 140." title="Fig. 140." /></td>
+</tr>
+</table>
+</div>
+
+
+<h3 id="LESSON_XXVII">LESSON XXVII</h3>
+
+<div class="figure">
+<table class="figure" id="fig_141" summary="Figure 141">
+<tr><td class="capnorm">Fig.<br />141.</td>
+    <td class="figure"><img src="images/fig141.png" alt="Fig. 141." title="Fig. 141." /></td>
+</tr>
+</table>
+</div>
+
+<div class="pagenum" id="page_50">[50]</div>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write the first, second and third species in the other
+three parts. Write twice, changing the parts about [<a href="#fig_141">Fig.&nbsp;141<i>a</i></a>.]</p>
+
+<p>To cantus firmus <i>b</i> write fourth species in one part, as directed in previous
+lessons. [<a href="#fig_141">Fig.&nbsp;141<i>b</i></a>.]</p>
+
+<p>To cantus firmus <i>c</i> write third species mixed in the other three parts.
+[<a href="#fig_139">Fig.&nbsp;139<i>b</i></a>.]</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_142" summary="Figure 142">
+<tr><td class="capnorm">Fig.<br />142.</td>
+    <td class="figure"><img src="images/fig142.png" alt="Fig. 142." title="Fig. 142." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XXVIII">LESSON XXVIII</h3>
+
+<div class="figure">
+<table class="figure" id="fig_143" summary="Figure 143">
+<tr><td class="capnorm">Fig.<br />143.</td>
+    <td class="figure"><img src="images/fig143a.png" alt="Fig. 143, part 1." title="Fig. 143." /></td>
+</tr>
+<tr>
+  <td>
+    <div class="pagenum" id="page_51">[51]</div>
+  </td>
+  <td style="padding-top: 30px" class="figure"><img src="images/fig143b.png" alt="Fig. 143, part 2." title="Fig. 143." /></td>
+</tr>
+</table>
+</div>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write the fourth species in one part, as usual.</p>
+
+<p>To cantus firmus <i>b</i> write first, second and fourth species in the other
+three parts. [<a href="#fig_143">Fig.&nbsp;143<i>a</i></a>.]</p>
+
+<p>To cantus firmus <i>c</i> write the first, third and fourth species in the other
+three parts. [<a href="#fig_143">Fig.&nbsp;143<i>b</i></a>.]</p>
+
+<p>To cantus firmus <i>c</i> write fourth species mixed in the other parts. [<a href="#fig_143">Fig.&nbsp;143<i>c</i></a>.]</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_144" summary="Figure 144">
+<tr><td class="capnorm">Fig.<br />144.</td>
+    <td class="figure"><img src="images/fig144.png" alt="Fig. 144." title="Fig. 144." /></td>
+
+</tr>
+</table>
+</div>
+
+<div class="pagenum" id="page_52">[52]</div>
+
+
+<h3 id="LESSON_XXIX">LESSON XXIX</h3>
+
+<div class="figure">
+<table class="figure" id="fig_145" summary="Figure 145">
+<tr><td class="capnorm">Fig.<br />145.</td>
+    <td class="figure"><img src="images/fig145.png" alt="Fig. 145." title="Fig. 145." /></td>
+</tr>
+</table>
+</div>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To canti firmi <i>a</i> and <i>b</i> write fifth species in one part, as before.</p>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_146" summary="Figure 146">
+<tr><td class="capnorm">Fig.<br />146.</td>
+    <td class="figure"><img src="images/fig146.png" alt="Fig. 146." title="Fig. 146." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XXX">LESSON XXX</h3>
+
+<div class="figure">
+<table class="figure" id="fig_147" summary="Figure 147">
+<tr><td class="capnorm">Fig.<br />147.</td>
+    <td class="figure"><img src="images/fig147a.png" alt="Fig. 147. part 1." title="Fig. 147." /></td>
+</tr>
+<tr>
+  <td>
+    <div class="pagenum" id="page_53">[53]</div>
+  </td>
+  <td style="padding-top: 50px"><img src="images/fig147b.png" alt="Fig. 147. part 2" title="Fig. 147." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_54">[54]</div>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To the cantus firmus write the fifth species in two parts. Write four times,
+changing the cantus firmus into every part. [<a href="#fig_147">Fig.&nbsp;147<i>a</i></a>.]</p>
+
+<p>Write one eight-measure phrase mixing the second, third and fourth
+species (<i>b</i>). Also write one exercise combining the first, second, third and
+fourth species (<i>c</i>).</p>
+
+<h4 class="cf">Cantus Firmus</h4>
+
+<div class="figure">
+<table class="figure" id="fig_148" summary="Figure 148">
+<tr><td class="caption">Fig.<br />148.</td>
+    <td class="figure"><img src="images/fig148.png" alt="Fig. 148." title="Fig. 148." /></td>
+</tr>
+
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XXXI">LESSON XXXI</h3>
+
+<div class="figure">
+<table class="figure" id="fig_149" summary="Figure 149">
+<tr><td class="capnorm">Fig.<br />149.</td>
+    <td class="figure"><img src="images/fig149.png" alt="Fig. 149." title="Fig. 149." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_55">[55]</div>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To the cantus firmus write the fifth species in all of the other parts.
+[<a href="#fig_149">Fig.&nbsp;149<i>a</i></a>.]</p>
+
+<p>Write four eight-measure phrases with the fifth species in all parts.
+[<a href="#fig_149">Fig.&nbsp;149<i>b</i></a>.]</p>
+
+<h4 class="cf">Cantus Firmus</h4>
+
+
+<div class="figure">
+<table class="figure" id="fig_150" summary="Figure 150">
+<tr><td class="caption">Fig.<br />150.</td>
+    <td class="figure"><img src="images/fig150.png" alt="Fig. 150." title="Fig. 150." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XXXII">LESSON XXXII</h3>
+
+<div class="figure">
+<table class="figure" id="fig_151" summary="Figure 151">
+<tr><td class="capnorm">Fig.<br />151.</td>
+    <td class="figure"><img src="images/fig151.png" alt="Fig. 151." title="Fig. 151." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>Write six eight-measure phrases, using the fifth species in all the parts.
+Let the parts begin one after the other in imitation. [<a href="#fig_151">Fig.&nbsp;151.</a>]</p>
+
+
+<h3 id="LESSON_XXXIII">LESSON XXXIII</h3>
+
+<h4>FLORID MELODIES AS CANTI FIRMI<br />
+FREE HARMONIZATION IN TWO-PART COUNTERPOINT</h4>
+
+<div class="figure">
+<table class="figure" id="fig_152" summary="Figure 152">
+<tr><td class="caption">Fig.<br />152.</td>
+    <td class="figure"><img src="images/fig152.png" alt="Fig. 152." title="Fig. 152." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_56">[56]</div>
+
+<p>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. [<a href="#fig_152">Fig.&nbsp;152.</a>]</p>
+
+<p>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.</p>
+
+<p>The suspension may now be a quarter-note, or its rhythmic
+equivalent. It then comes on the first (<i>a</i>) or third (<i>b</i>) quarter
+of the measure, and the resolution on the quarter following. The
+preparation should be as long as, or longer than, the suspension.
+[<a href="#fig_153">Fig.&nbsp;153.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_153" summary="Figure 153">
+<tr><td class="caption">Fig.<br />153.</td>
+    <td class="figure"><img src="images/fig153.png" alt="Fig. 153." title="Fig. 153." /></td>
+</tr>
+</table>
+</div>
+
+<p>The eighth-note as in <a href="#fig_154">Fig.&nbsp;154<i>a</i></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. [<a href="#fig_154">Fig.&nbsp;154<i>b</i></a>.]</p>
+
+<div class="figure">
+<table class="figure" id="fig_154" summary="Figure 154">
+<tr><td class="caption">Fig.<br />154.</td>
+    <td class="figure"><img src="images/fig154.png" alt="Fig. 154." title="Fig. 154." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The first species may be employed occasionally in the course
+of an exercise.</p>
+
+<p>Make plentiful use of imitation.</p>
+
+<p>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 <i>a</i>, or
+letting them rest, as at <i>b</i>. [<a href="#fig_155">Fig.&nbsp;155.</a>]</p>
+
+<p>When, in place of the hold, the movement continues, it is
+necessary to interpolate a full measure in place of the hold.
+[<a href="#fig_155">Fig.&nbsp;155</a> and <a href="#fig_159">Fig.&nbsp;159.</a>]</p>
+
+<div class="pagenum" id="page_57">[57]</div>
+
+<div class="figure">
+<table class="figure" id="fig_155" summary="Figure 155">
+<tr><td class="capnorm">Fig.<br />155.</td>
+    <td class="figure"><img src="images/fig155.png" alt="Fig. 155." title="Fig. 155." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>The note under the hold may be continued the extra measure,
+or the part may rest and then reënter. 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.</p>
+
+<p>The interval at any hold except the last of a choral may be
+either a perfect (<i>a</i>) or imperfect consonance (<i>b</i>). [<a href="#fig_156">Fig.&nbsp;156.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_156" summary="Figure 156">
+<tr><td class="capnorm">Fig.<br />156.</td>
+    <td class="figure"><img src="images/fig156.png" alt="Fig. 156." title="Fig. 156." /></td>
+</tr>
+</table>
+</div>
+
+
+<p>Modulation often occurs at the holds. If so, make it clear.</p>
+
+<p>In this and in succeeding lessons set the cantus firmus in any
+part, and transpose if necessary.</p>
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>b</i> write two counterpoints above and two below.</p>
+
+<p>To cantus firmus <i>a</i> write one above and one below, with both parts resting
+at the hold. Also do the same <i>with the counterpoint continuing at the
+hold</i>. [<a href="#fig_155">Fig.&nbsp;155<i>a</i></a>, <i>b</i>.]</p>
+
+<div class="pagenum" id="page_58">[58]</div>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_157" summary="Figure 157">
+<tr><td class="capnorm">Fig.<br />157.</td>
+    <td class="figure"><img src="images/fig157.png" alt="Fig. 157." title="Fig. 157." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XXXIV">LESSON XXXIV</h3>
+
+<h4>FREE HARMONIZATION IN THREE-PART COUNTERPOINT</h4>
+
+
+<p>When writing in three or more parts, it is well to let a part
+rest occasionally, and, when it reënters, have it imitate one of the
+other parts. [<a href="#fig_158">Fig.&nbsp;158.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_158" summary="Figure 158">
+<tr><td class="caption">Fig.<br />158.</td>
+    <td class="figure"><img src="images/fig158.png" alt="Fig. 158." title="Fig. 158." /></td>
+</tr>
+</table>
+</div>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+<p>To cantus firmus <i>a</i> write two counterpoints above and two below in two-part
+counterpoint.</p>
+
+<p>Write two original eight-measure phrases in two-part counterpoint.</p>
+
+<p>To cantus firmus <i>b</i> write one example in three-part counterpoint with continuous
+movement at the hold. [<a href="#fig_159">Fig.&nbsp;159.</a>]</p>
+
+<div class="figure">
+<table class="figure" id="fig_159" summary="Figure 159">
+<tr><td class="capnorm">Fig.<br />159.</td>
+    <td class="figure"><img src="images/fig159.png" alt="Fig. 159." title="Fig. 159." /></td>
+</tr>
+</table>
+</div>
+
+
+<div class="pagenum" id="page_59">[59]</div>
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_160" summary="Figure 160">
+<tr><td class="capnorm">Fig.<br />160.</td>
+    <td class="figure"><img src="images/fig160.png" alt="Fig. 160." title="Fig. 160." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XXXV">LESSON XXXV</h3>
+
+
+<p>To canti firmi <i>a</i> and <i>b</i> 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.</p>
+
+
+<h4 class="cf">Canti Firmi</h4>
+
+<div class="figure">
+<table class="figure" id="fig_161" summary="Figure 161">
+<tr><td class="capnorm">Fig.<br />161.</td>
+    <td class="figure"><img src="images/fig161.png" alt="Fig. 161." title="Fig. 161." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XXXVI">LESSON XXXVI</h3>
+
+
+<p>Write two eight-measure phrases, and one sixteen-measure
+phrase, of original counterpoint in three parts.</p>
+
+<div class="pagenum" id="page_60">[60]</div>
+
+<h3 id="LESSON_XXXVII">LESSON XXXVII</h3>
+
+<h4>FREE HARMONIZATION IN FOUR-PART COUNTERPOINT</h4>
+
+
+<div class="figure">
+<table class="figure" id="fig_162" summary="Figure 162">
+<tr><td class="caption">Fig.<br />162.</td>
+    <td class="figure"><img src="images/fig162.png" alt="Fig. 162." title="Fig. 162." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h4 class="ex">EXERCISES</h4>
+
+
+<p>To the cantus firmus write three parts.</p>
+
+<p>Write two sixteen-measure phrases of original four-part counterpoint, one
+major and one minor.</p>
+
+
+<h4 class="cf">Cantus Firmus</h4>
+
+
+<div class="figure">
+<table class="figure" id="fig_163" summary="Figure 163">
+<tr><td class="caption">Fig.<br />163.</td>
+    <td class="figure"><img src="images/fig163.png" alt="Fig. 163." title="Fig. 163." /></td>
+</tr>
+</table>
+</div>
+
+
+
+<h3 id="LESSON_XXXVIII">LESSON XXXVIII</h3>
+
+
+<p>In this and the following lessons have the parts in some of the
+exercises begin one after the other in imitation. [<a href="#fig_151">Fig.&nbsp;151.</a>]</p>
+
+
+<h4 class="ex">EXERCISES</h4>
+
+
+<p>Write two eight-measure phrases, and one sixteen-measure phrase, of
+original four-part counterpoint.</p>
+
+
+<h3 id="LESSON_XXXIX">LESSON XXXIX</h3>
+
+
+<p>Write two sixteen-measure phrases of original four-part counterpoint.</p>
+
+<h3 id="LESSON_XL">LESSON XL</h3>
+
+
+<p>Write an original exercise in four-part counterpoint, extended
+to thirty-two measures.</p>
+
+
+
+
+
+
+
+
+<pre>
+
+
+
+
+
+End of the Project Gutenberg EBook of A Treatise on Simple Counterpoint in
+Forty Lessons, by Friedrich J. Lehmann
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@@ -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. Lehmann
+
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