On Double Counterpoint
First Section: Double Counterpoint in Two Parts
Inversion at the Twelfth
These are the two rows of figures which should be compared together for obtaining the inversions of double counterpoint at the twelfth:
| Counterpoint | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Inversion | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
It will be seen that the unison or octave changes, in counterpoint of this kind, into a twelfth, the second into an eleventh, etc.
The sixth, which by inversion becomes a seventh, should be prepared either in the upper part, or the lower; and the bass should then descend one note or degree.
Examples from Marpurg
This is an extended example of double counterpoint at the twelfth:
1st manner of inverting: Transpose the counterpoint a fourth below, while the theme remains in its place
2nd manner of inverting: Transpose the theme a twelfth below, while the counterpoint remains in its place
3rd manner of inverting: Transpose the theme an octave below, and the counterpoint a fifth below
4th manner of inverting: Transpose the theme a fifth above, and the counterpoint an octave below
This counterpoint is one of the most used, and one of the most fertile in resources.