Invertible Counterpoint
Counterpoint in which two voices can swap above and below and still work
Related
Invertible counterpoint is counterpoint where two or more lines can exchange their vertical positions and still work. The upper goes below, the lower above, and every interval turns upside down: a third becomes a sixth, a fifth a fourth, a sixth a third. The composer must calculate the inverted intervals and avoid parallel fifths and octaves.
Inversion at the octave, tenth or twelfth is standard; the octave is commonest, letting subject and countersubject swap. Twelfth inversion turns a fifth into an octave and needs care. Bach's fugues, where subject and countersubject exchange, and canons with crossing voices, rest on this arithmetic.
It is not melodic inversion. Inversion reverses the direction of intervals; invertibility reverses the register of the voices, and both can operate at once. Listen for two lines swapping and still consonant, not a tune turned upside down.
Sources
- 可转位对位的音程计算、常见转位与赋格用法，参 The New Grove Dictionary of Music and Musicians, "Invertible counterpoint"；本文为原创表述
Used for fact-checking only; all prose is original.