On Double Counterpoint

When the inversion (or transposition) of a part takes place at the distance of an octave or a fifteenth, the counterpoint takes the denomination of double counterpoint at the octave.

In learning how to construct this counterpoint, it must be known what are the intervals to be avoided, that the inversion may be correct. For the acquirement of this knowledge, two rows of figures, not exceeding the number of eight, should be placed one row against the other, thus:

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

The figures of the upper row indicate the intervals of the counterpoint; those of the under row, the intervals which result from its inversion. It will be seen that the 1, or unison, changes into an octave; the second into a seventh; the third into a sixth; the fourth into a fifth, and so on, with the others.

The octave and the unison should not be too frequently employed, because they do not produce sufficient harmony; excepting, indeed, at the commencement and at the close of the theme, and when syncopation is employed.

The fifth should be avoided because it becomes a fourth. It can be employed only as a passing tone, or when it is used as a syncopation.

The fourth being open to the same objection, and to the same exceptions as the fifth, it should be avoided and admitted in the same way.

All the other intervals may be employed, by subjecting them to the laws which affect them. Placing the parts at a distance beyond the octave should also be avoided, as the intervals which exceed this limit undergo no change by inversion; that is to say, the third remains a third, the sixth remains a sixth, etc.

Here is an extended example of double counterpoint, by which it may now be seen how all the intervals should be employed, so as to obtain correct inversion.

Here are different ways of introducing inversions, with respect to Example 161.

1st manner: Invert the counterpoint an octave, from higher to lower

2nd manner: That the counterpoint may be at the fifteenth, it must be inverted thus, a fifteenth lower

3rd manner: Transpose the theme an octave higher, and the counterpoint an octave lower

4th manner: Transpose the theme an octave higher, while the counterpoint remains in its place

Before passing to another kind, it is essential to observe that the discord of the ninth cannot be employed in double counterpoint at the octave because it cannot be inverted. Double counterpoint at the octave is one of the counterpoints most used.

  • cherubini_counterpoint_and_fugue/on_double_counterpoint/inversion_at_the_octave.txt
  • Last modified: 2018/08/10 22:23
  • by brian