MUS 311 Counterpoint
I. Invertible Counterpoint, Chapter 9
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Two-voice counterpoint is said to be "invertible" if
either voice can be used as an upper or lower part with good results
("double counterpoint").
-
The most common inversions are the 12th, or the
octave (15th).
- In two-voice counterpoint that is to be inverted at the octave,
the 5th should be avoided on the beat, as it would become a
4th when inverted, which is unusable as an essential interval.
- Accidentals are frequently introduced in the inverted voice to
achieve a better melodic line (in that the relationship of half and
whole steps is affected by the inversion).
- Inverted counterpoint at the 10th is rare and should be avoided
because the most frequently used intervals (3rd & 6th, e.g.),
when inverted, become octaves and fifths, often creating undesirable
parallelisms.
Inversion at the Octave:
| Original interval: |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
| Inverted interval: |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
Inversion at the 10th:
| Original interval: |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
| Inverted interval: |
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
Inversion at the 12th:
| Original interval: |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
| Inverted interval: |
12 |
11 |
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
-
Invertible three- and four-part counterpoint
("triple" and "quadruple" counterpoint) is
possible, but presents greater challenges.
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