On Double Counterpoint

Triple and Quadruple Counterpoint at the Octave

There are two ways of composing these counterpoints; the first and most easy, consists in adding a double counterpoint, one or two parts proceeding in thirds, either with the lower part, or with the upper part.

Double counterpoint, in order to be susceptible of receiving these two parts in thirds, or even a single one, must be constructed according to certain conditions:

  • Firstly, it should not contain – throughout – either two thirds, or two sixths in succession, and consequently, it should be written entirely in contrary movement or in oblique movement.
  • Secondly, it should contain no discord, except passing tones.
Example of a double counterpoint at the octave

In order first to transform this double counterpoint into triple counterpoint, no more need be done, than to add a third part, either a third above the upper part, or a third above the lower part. 1)

Triple counterpoint: Adding a third above the lower part

To convert the same double counterpoint into quadruple counterpoint, there must be joined to the two principal parts, the two parts just added; the one, a third above the upper part, and the other, a third above the lower part.

Then the parts of this counterpoint may be inverted in several ways, as the following example shows:

The other way of introducing triple and quadruple counterpoint at the octave consists of combining the parts in such a manner, as that they may be inverted; that is to say, so that each part can be placed above or below, without changing the melody at all, and without there arising the least-objectionable point, or the least infringement of the strictest rules. It is indispensable, to ensure this, that the parts shall never form between each other either a fourth or a fifth; excepting in the case where the melody proceeds by conjunct movement, or in that where only discords prepared by the second, the fourth, and the seventh are employed. The discord of the prepared ninth is impracticable in this kind of counterpoint, as has already been said with regard to double counterpoint at the octave.

Examples of triple counterpoint of this kind

Examples of quadruple counterpoint of the same kind (media player is above Example 181)

This kind of counterpoint, by its nature and its regularity of inversions, may be applied to counter-subjects of a fugue; as will be seen when that sort of composition comes under discussion in the next chapter.


1)
Editor's note: Despite these instructions, in Example 179b, Cherubini adds a third below the upper part. In Example 179c, the upper part becomes this added third-below line.
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