On Double Counterpoint

Inversion at the Tenth

At present, double counterpoint at the tenth or third will be discussed, commencing with the usual rule, of the two rows in figures:

Counterpoint 1 2 3 4 5 6 7 8 9 10
Inversion 10 9 8 7 6 5 4 3 2 1

By these two series, it will be seen that two thirds (or two tenths) in succession must not be made; since there will then be two octaves (or two unisons). Neither must two sixths in succession by employed, because their inversion would produce two fifths. Nor must the fourth and the seventh be employed, except as passing tones (see I. in Example 166a), unless the fourth be resolved into a fifth or into a sixth (as in II. in Example 166b), and the seventh be resolved into a fifth (see III.* in Example 166c).

The ninth must be resolved either by the octave or by the fifth, in this manner:

From this analysis – with consideration, intelligence, and application – the pupil may acquire practice in this kind of double counterpoint, of which here is given an extended example:

This counterpoint may be inverted in several ways:

1st manner: By transposing the counterpoint a tenth below, while the theme remains in its place

2nd manner: By transposing the theme a third above, and the counterpoint an octave below

3rd manner: By transposing the counterpoint a third below, and the theme an octave below

4th manner: By transposing the counterpoint, and the theme, a third higher

In all the inversions and transpositions of this example, it will be perhaps necessary to add some accidentals, either to the theme, or to the counterpoint; and, sometimes, even a third part, in order to render the whole more correct: at the same time, nothing has been indicated of this, seeing that a counterpoint can be constructed in such a manner, as there need be no such alterations, nor any additional parts. The short examples set forth above have only been given to show in how many ways a double counterpoint at the tenth may be inverted. This counterpoint is one of those most used, as well as that at the octave.

  • cherubini_counterpoint_and_fugue/on_double_counterpoint/inversion_at_the_tenth.txt
  • Last modified: 2018/08/10 17:11
  • by brian