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Chapter 1
Of Counterpoint, in the Composition of 2 Parts
Counterpoint is divided into simple and figurative. The former is a kind of composition in two or more parts, wherein the notes in the different parts are of the same value, and is called plain or simple from being note against note in concords 1) only. We may choose the subject either from our own fancy or from a church tune; in the latter case the subject is called in Italian canto fermo 2).
In figurative counterpoint the notes in the different parts may be of different value, and concords 3) intermixed with discords 4). When the cantus firmus or subject is placed in the lower parts, it is called in Italian contrapunto sopra il soggetto, and if in the upper parts, contrapunto sotto il soggetto.
Before we proceed, the following general rules in composition will be necessary to be observed with regard to the different motions in music: the regular, contrary, and oblique.
1. The contrary and oblique may be used in any progression; but the similar, only when we proceed from a perfect concord 5) to an imperfect, or from an imperfect to an imperfect: in this sense only the 8th and 5th are deemed perfect concords 6), but the 3rd and 6th imperfect.
The reason why the similar motion in the progression from a perfect and imperfect concord 7) to a perfect is not allowed is to avoid the wrong progression of successive fifths and eighths 8), whether open or hidden; the last may be discovered by the intermediate notes contained within the spaces, as may be seen in the following example.
2. We must avoid proceeding to an octave or unison by a skip, that is when the lower part ascends one degree and the upper descends by a skip, though it be in contrary motion.
3. An imperfect concord 9) is to be used preferably to a perfect, as the former is more harmonious than the latter.
4. The notes must be comfortable to the nature of the key.
5. The inharmonic relation in Mi against Fa is to be avoided as much as possible.
6. Regularity, variety, and good melody must continually be kept in view.
Now we proceed to the composition of plain counterpoint in two parts only. The principal points to be observed in this kind of composition are as follow:
a. Every note of the cantus firmus must have its particular concord 10). If it is in the lower part, the intervals must be taken upwards, and if in the upper part, then the intervals must be reckoned downwards. 11)
b. We must begin and end with a perfect concord 12).
c. If the cantus firmus is in the lower part, the last note but one requires the greater sixth, and if in the upper part, the lesser third. See the following example in D (La - Sol - Re).
Second Counterpoint
This is the kind of composition where two notes are set against one; it is used therefore in binary measure consisting of two equal parts: the first whereof is accented, and the other unaccented. Here the first minim 13) is to be a concord 14), and the second may be either a concord 15) or discord 16). The discord 17) therefore only is used in a gradual transition from concord 18) to concord 19); but in skips the concord 20) only can have place 21).
First Rule: If the cantus firmus is in the lower part, the two notes in the last bar but one must have a fifth for its first note and a greater sixth for its second note. But if in the upper part, then the first note requires a fifth and the other a lesser third.
Second Rule: Skips of thirds in a similar motion following one another must be avoided, as it would occasion a forbidden progression of fifths and octaves. See Ex. 1 - Greater skips as those of a fourth, fifth, and sixth are allowed, as it would not offend the ear so much. See Ex. 2.