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").

  1. The most common inversions are the 12th, or the octave (15th).

  1. 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.
  1. 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).
  1. 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
  1. Invertible three- and four-part counterpoint ("triple" and "quadruple" counterpoint) is possible, but presents greater challenges.

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