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.]
| Fig. 42. |
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.]
| Fig. 43. |
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.]
| Fig. 44. |
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.]
| Fig. 45. |
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.
| Fig. 46. |
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.]
| Fig. 47. |
Fig. 47. |
Oblique motion to the unison is bad. It is permitted if it continues in the same direction through the unison. [Fig. 48.]
| Fig. 48. |
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.
| Fig. 49. |
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.]
| Fig. 50. |
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.]
| Fig. 51. |
Fig. 51. |
Six notes may be written to one of the cantus firmus, as in Fig. 52.
| Fig. 52. |
Fig. 52. |
The cadences in Fig. 53 are good.
| Fig. 53. |
Fig. 53. |
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.]
| Fig. 54. |
Fig. 54. |
| Fig. 55. |
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.]
| Fig. 56. |
Fig. 56. |
The augmented fourth following the perfect fourth, as in Fig. 56a, 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.]
| Fig. 57. |
Fig. 57. |
The first and third species may be mixed, as in Fig. 58.
| Fig. 58. |
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.]
| Fig. 59. |
Fig. 59. |
The cadences in Fig. 60 are good, and will suggest others.
| Fig. 60. |
Fig. 60. |
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.]
| Fig. 61. |
Fig. 61. |
| Fig. 62. |
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. 63a), 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. 63d (Retardation of the root in I6).
| Fig. 63. |
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.]
| Fig. 64. |
Fig. 64. |
The fifth may be used in the lower part if it becomes the preparation of a suspension (Fig. 65a). It may also be used in the lower part, as in Fig. 65b, 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.
| Fig. 65. |
Fig. 65. |
The retardation should be used only when prepared by the leading-tone. It rises a semitone in resolving. [Fig. 66.]
| Fig. 66. |
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.]
| Fig. 67. |
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.
| Fig. 68. |
Fig. 68. |
The following cadences are good:
| Fig. 69. |
Fig. 69. |
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.
| Fig. 70. |
Fig. 70. |
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.
| Fig. 71. |
Fig. 71. |
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.
| Fig. 72. |
Fig. 72. |
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.]
| Fig. 73. |
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.
| Fig. 74. |
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.]
| Fig. 75. |
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.]
| Fig. 76. |
Fig. 76. |
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.]
| Fig. 77. |
Fig. 77. |
| Fig. 78. |
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.]
| Fig. 79. |
Fig. 79. |
Not more than one and one-half measures of any one species should be used continuously in one part. [Fig. 80.]
| Fig. 80. |
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.]
| Fig. 81. |
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.
| Fig. 82. |
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.
To canti firmi a and b write two counterpoints above and two below, in the fifth species
| Fig. 83. |
Fig. 83. |
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.]
| Fig. 84. |
Fig. 84. |
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.]
| Fig. 85. |
Fig. 85. |
| Fig. 86. |
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.
| Fig. 87. |
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.]
| Fig. 88. |
Fig. 88. |
The dominant seventh may be used in any but its second inversion, the fifth being omitted.[A] 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 V7 is used. [Fig. 89.]
| Fig. 89. |
Fig. 89. |
Consecutive major thirds may be used when three or more parts are employed. [Fig. 90.]
| Fig. 90. |
Fig. 90. |
A note may now be repeated in the lowest part when it becomes the seventh of a dominant seventh-chord. [Fig. 91.]
| Fig. 91. |
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. 92a, b.]
[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.
The perfect fifth following the diminished fifth is good when taken in an upward direction stepwise in the higher parts. [Fig. 92c.]
| Fig. 92. |
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.
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.
| Fig. 93. |
Fig. 93. |
| Fig. 94. |
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 V43 or the cadencing tonic six-four chord.
The V43 chord may be used on the weak beat, necessitating the omission of the third. [Fig. 95a.]
The third may be omitted (b), or doubled (c), on the weak beat in this and succeeding species. [Fig. 95.]
| Fig. 95. |
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.]
| Fig. 96. |
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.
| Fig. 97. |
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.]
| Fig. 98. |
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.
| Fig. 99. |
Fig. 99. |
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.
| Fig. 100. |
Fig. 100. |
| Fig. 101. |
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.]
| Fig. 102. |
Fig. 102. |
At Fig. 102a, 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.]