Two-Part Counterpoint

TWO-PART COUNTERPOINT (16th Century Style)

First Species (Note against note)

1) Melody * Available progressions: Seconds (major and minor) Thirds (major and minor) Fourth (perfect only) Fifths (perfect only) Sixths (minor only, ascending only) Octaves (perfest only) * The tritone (a melodic progression involving an augmented fourth or a diminished fifth) should be used only if it is continued stepwise. * The counterpoint must have one highest point, and should have one lowest point. * Sequences (consecutive repetitions of melodic elements) are to be avoided. The repetition of a tone is permitted occasionally; in such cases the two notes are tied together.

2) Counterpoint Available intervals between the two parts: Unison (first and last measures only) Thirds (major and minor) Fifths (perfect only) Sixths (major and minor) Octave (perfect only) Tenths, etc. * Unison, Fifth and Octave are called perfect consonances, Thirds and Sixths imperfect. * In general, the parts should not be farther apart than a tenth. One must begin and end with a perfect consonance. If the count- terpoint lies below the c.f. only actave or unison may be used for beginning and ending. * Fifths and octaves are not to be approached in parallel, or similar, motion. No more than three or four thirds or sixths should appear consecu- tively. * Crossing of the parts is permitted. *Rules valid in all species

Two-part Counterpoint

Second Species (Two notes against one)

1) Melody No more than two skips are available within an ascending, or descen- ding, portion of the melody. If two skips are used, the second skip has to follow the first one immediately. If the two skips are of unequal size, the larger skip has to be the lower of the two skips, in either direction. (Usually no dis- crimination is made between major and minor third, i.e. they are considered as of equal size.) Skips, following (in ascending motion), or preceding (in descending motion), a skip larger than a third, should be smaller than the skip which they follow, or precede. Descending skips may be preceded, ascending skips followed, by step- wise motion in the same direction, or the melody may turn back, by skip, or stepwise. After a skip of an octave the melody must turn back in the opposite direction. Immediate repetition of tones is not permitted.

2) Counterpoint On accented beats consonances only are available. On unaccented beats consonances as well as dissonances may be used. Dissonances must be introduced and left step wise in the same direction, i.e. dissonances must be passing notes. The counterpoint may begin on the first accented beat, or after a half note rest. In either case the first note of the counterpoint must form a perfect consonance with the c.f. If the counterpoint is below the c.f., octave or unison only may be used for begin- ning and ending. The last note of the counterpoint is always a whole note. In the next to the last measure one may use two half notes, or one whole note. In addition to its use in the first or last measure, the unison may appear occasionally on unaccented beats; it should be left in the direction opposite to that in which it was introduced. Fifts and octaves should be used but sparingly on consecutive ac- cented beats.

3) Cadence If the counterpoint ends on the final of the mode, the final has to be preceded by the lower, or the upper, leading tone, or by a skip from the fifth step of the mode ("dominant"). In the Phry- gian mode the leading tone approach only is available. The leading tones themselves should be approached stepwise (in either direc- tion), or by skip from the "dominant".

Two-part Counterpoint

Third Species (Four notes against one)

1) Melody No more than one skip is permitted within an ascending, or descending portion of the melody. (1) Ascending skips larger than a third should be followed by stepwise progression in the opposite direction. (2) Ascending skips are permitted only from unaccented quarter notes (2nd and 4th). (3) In ascending melodies skips are permitted only at the beginning, in descending melodies only at the end of the motion. (2), (4). Repetition of the tone of the first quarter beat on the third, or of the second on the fourth should be avoided as a rule, ex-cept if the third, respectively fourth, quarter note is introduced from below. (5)

2) Counterpoint The first and third quarter notes of each measure must be consonant. The second and fourth quarter notes may be consonant or dissonant; if dissonant, they must be introduced and left stepwise, in the same direction (passing note), or in the op- posite direction (auxiliary note); the latter, however, is available only below. (6) A dissonance on an unaccented quarter beat may be left by a skip down exceptionally in the case of the cambiata, a melodic figure consisting of five tones. After the skip the melody turns and ascends stepwise. (7) Fifths and octaves on accented beats should be separated by at least three quarter beats. (8) Unisons should not occur on the first beat of a measure, except in the first and the last measure. The counterpoint may begin on the first, or on the second (quarter) beat. In the former case only perfect consonances may be used (if the counterpoint is below the c.f., unison or octave only), in the latter imperfect consonances are permitted. The next to the last measure may have four quarter notes, or two half notes, or one whole note.

Two-part Counterpoint

Fourth Species (Dissonances on accented beats) Two half notes are placed against one note of the c.f. The accented half notes may form dissonances with the c.f., provided these dissonances are prepared and resolved properly, i.e. that the note which is dis- sonant with the c.f. is tied over from the preceding unaccented beat where it has to form a consonance with the c.f., and that the disso- nating note proceeds step wise down on the unaccented beat following the dissonance, where it has to form an imperfect consonance with the cf. Therefore, the following dissonances are available: a) if the counterpoint is above the c.f. 7, resolving to 6; 4, resolving to 3; b) if the counter point is below the c.f. 2, resolving to 3; 9, resolving to 10. Wherever a dissonance can not be placed according to the above rules, the rules of the second species will apply. They are also valid with respect to beginning and end of the c.f. Unisons may be used on both accented and unaccented beats.

Two-part Counterpoint

Fifth Species (mixed, or florid, counterpoint)

1) Melody and Rhythm If an ascending portion of the melody contains different rhythmic values, shorter values usually precede longer values. (1) If a descending portion of the melody contains different rhythmic values, longer values usually precede shorter values. (2) Sequences of quarter notes begin in descending motion preferably on unaccented beats (3) in ascending motion on both kinds of beats (4) (in both directions with good effect after a skip in the opposite direction); end on a fully accented beat (first beat of a measure); if they end on a relatively accented beat (second half note of a measure), it is advisable to tie the half note over to the next fully accented beat. (5) In general, there should not appear more than 9 quarter notes in continuous sequence. Groups of two quarter notes ("isolated" quarter notes) are to be avoided on fully accented beats, unless the following half note is tied over to the next accented beat, preferably by forming a dissonance there. (6) Groups of two quarter notes on relatively accented beats (second half of a measure) are correct. (7) Within a section occupied by quarter notes the rules of the third species apply. Eighth notes: in groups of two only; on unaccented quarter beats only; stepwise only: as passing notes, as alternating notes, below only. (8) Only whole notes and half notes can be tied to subsequent notes. The second of the two notes tied together may be of the same value as the first one, or half as long. (9)

Two-part Counterpoint

Fifth Species (continued)

2) Counterpoint A dissonance can not be resolved on an unaccented quarter beat, but must always be resolved on the following relatively accented beat. the resolving note itself may be of any rhythmic value (except eighth notes). (1). On the unaccented quarter beat between a dissonance and its resolution one may interpolate either a quarter note which is a third below the preceding dissona- ting note, provided that this interpolated quarter note is consonant with the other part, (2) or a group of two alternating eight notes (below only). (3) Alternating quarter notes above are permitted before longer rhythmic values. (4) The cambiata may appear in different various rhythmic combinations (see ex. 5). The second, dissonant note must always be an unac- cented quarter note. If the fourth note is a consonant half note, the fifth note does not need to be one step above the fourth note. When an accented note is approached stepwise from above, it may be anti- cipated on the immediately preceding unaccented quarter beat, regard- less of whether this anticipated note is consonant or dissonant. Anticipations from below are unusual and only occasionally used in final cadences. (6) When an accented half note is followed by two quarter notes in stepwise descending motion, the first of these quarter notes may be dissonant in spite of its staying on a relatively accented beat ("accented passing tone"). (7)

Two-part Counterpoint

Free Counterpoint (without Cantus Firmus)

Additional rules and modifications of former rules: Quarter notes may dissonate with each other on unaccented beats, provided the dissonances are treated correctly in each part. (1) The part against which the other part forms an accented dissonance (see fourth species) may move on before the dissonance is resolved, provided an im- perfect consonance is formed when the resolution takes place. Dissonan- ces which would resolve into perfect consonances if the other part would not move on are now available provided the motion in the other part leads to an imperfect consonance. When the part against which the dis- sonance is formed moves in half notes, its progression is subject only to the general rules concerning melody. If this part moves in smaller rhythmic values, the progression must be stepwise (passing, or altern.) (2) In a figure of four quarter notes, beginning on a fully accented beat, de- scending stepwise, and the last one followed by its upper second, the third quarter note may dissonate with the other part, if this dissonance is tied over and repeated on the strong beat following the last of the four quarter notes and then resolved regularly ("Anticipated dissonance") (3) Stepwise parallel motion in half notes, in both directions, may be modified so that in one of the parts the tone destined for the relatively unac- cented beat does not enter before the unaccented quarter beat following the relatively unaccented beat, even if the delay causes a dissonance on that beat ("Delayed parallel motion"). (4) Parallel motion in quarter note sections may occasionally comprise more than four consecutive notes. The rule concerning the distance of the parts from each other is applied less rigidly than heretofore, if the flow of the melodies requires an exception.

Two-part Counterpoint

Double Counterpoint

Both parts shall be written in such a way that each of them can function both as an upper part or a lower part in relation to the other part. If one of the two parts remains in its place, one calls the double counterpoint, according to the interval by which the other part is transposed in order to change its relation to the fixed part, "double counterpoint of" (or "to") "the octave","the tenth", "the twelfth", etc. In order to insure correct procedure, one has to examine in what inter- vals the original intervals are transformed by the transposition of the movable part. For the double counterpoint of the octave the transformation of the intervals gives the following results: 1 2 3 4 5 6 7 8 becomes 8 7 6 5 4 3 2 1 For the double counterpoint of the tenth the results are: 1 2 3 4 5 6 7 8 9 10 becomes 10 9 8 7 6 5 4 3 2 1 The intervals of the original version must be treated with a view of what becomes of them after the transposition. For example, in the double counterpoint of the octave the fifth must be treated as a dissonance, because it become a fourth after the transposition. In the double counterpoint of the tenth parallel thirds and sixths must be avoided, because they result in parallel octaves and fifths after the transposition, etc.

Two-part Counterpoint

Imitation

The second part enters, after the first part has set forth a characteristic motif of at least one measure and not more than two measures length, by repeating the same motif, at any desired interval. Unison, octave, upper fifth, or lower fourth are more frequently used. The first part goes on with a counterpoint, and the piece develops and ends like the previous exercises in free counterpoint. The imitating part may enter at either a perfect, or an imperfect, consonance, or producing a syn- copated dissonance against the other part. (5) The imitation may be strict (all intervals imitated exactly) (1), or free (minor intervals may be represented by major intervals, or vice verse, or other alter- ations may occur, provided the characteristics of the original motif remain recognizable) (2) tonal (in the imitation special attention is given to reproducing characteristic final-dominant, or dominant-final, progressions by correspon- ding dominant-final, or final-dominant, pro- gressions; adjustments of the motif will be necessary, so that tonal imitation usually is a case of free imitation) (3) real (if the principle of tonal imitation is not applied) (4)

Two-part Counterpoint

Inversion The imitation in the second part answers the opening motif of the first part by inversion, i.e. ascending intervals are transformed into equivalent descending ones, and vice versa (with the adjustments necessary for staying within the chosen mode). In the original motif one has to avoid everything that would be inadmissible in the opposite direction (see rules on sixth skips, skips in quarter note motion, alternating notes, etc.)

Augmentation The imitation in the second part answers the opening motif of the first part in twice as long rhythmic values.

Diminution The imitation presents the opening motif in rhythmic values half as long as those of the original motif. In the original motif one has to avoid everything that would be inadmissible in the smaller rhythmic values. In treating half notes, or quarter notes, one has to keep in mind that they will be transformed into quarter notes, or eight notes, respectively.

Canon Imitation not confined to the opening motif, but carried through the whole length of the composition, except for the last measures where arrangements for the simultaneous ending of both parts must be made. The devices of inversion, augmentation and diminution can be used si- multaneously in various combinations.

Treatment of Text

Any note longer than a quarter note may carry a syllable. Several notes of any value may carry a syllable. (1) A quarter note may carry a syllable if it is preceded and followed by larger values, or by groups of several quarter notes carrying one syllable. (2) Notes may be repeated on new syllables. (3) Linguistic accents coincide with the accents of the musical phrase. Phrases of the text, or parts thereof, may be repeated. New phrases of the text should be introduced by new musical motifs. Especially in two-part writing each new section of the music should begin with imita- tion. The two parts should not cadence simultaneously, except at the end of the piece. Each section of the composition should end with a clearly articulated melo- dic cadence in each part, preferably on a fully accented beat. Any interval may occur between the last tone of a section of the melody and the first tone of the next one, especially if these tones are separated by rests, which should always be the case between sections of the text. (4)

Three-part Counterpoint

Additional Rules for Three-part Writing

1. Consonant three-tone combinations: Major and minor triads in root position and first inversion. Diminished triad in first inversion. Major and minor sixth-four chord exceptionally, on unaccented half-beats, provided the fourth is tied over into another dissonance which is to be resolved regularly.

2. "Borrowed" dissonance: If a dissonance is in normal progress between two parts as a tied-over syncopation, the third part may, on an unaccented quarter beat jump into this dissonance and again out of it.

3. Half notes on relatively unaccented beats may form passing dissonances against a second part with larger rhythmic values (according to second species rules), even if the third part has quarter notes. These quarter notes, however, must be correct in regard to both parts. Generally speaking, each part must agree with all other parts carrying larger rhythmic values than itself does at any particular place.

4. Quarter notes on unaccented beats may dissonate with each other provided the dis- sonances are treated correctly in each part and/or with respect to any part carrying larger rhythmic values.

5. The "anticipated" dissonance may be used whenever the third and fourth notes of the four-note figure explained earlier are introduced stepwise from above, by no matter what rhythmic value.

6. Fifths and octaves may be approached in similar motion except between outer parts (crossing of parts makes the middle part frequently an outer part!). They are particularly acceptable if accompanied by contrary motion in the third part.

7. The distance between the upper parts should not exceed an octave, as a rule.

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Two Part Counterpoint

Text for the Christmas Motet Rorate, caeli, desuper, et nubes pluant justum: aperiatur terra, et germinet Salvatorem. (Isai. 45,8) Caeli enarrant gloriam Dei: et opera manuum ejus annuntiat firmamentum. (Ps. 18,2) Tollite portas, principes, vestras: et introibit Rex gloriae. (Ps. 23, 7,3,4)

in English: Drop down, ye heavens, from above and let the skies pour down righteousness: let the earth open, that they may bring forth salvation. The heavens declare the glory of God; and the firmament sheweth his handywork. Lift up your heads, O ye gates: And the King of glory shall come in. 46.

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