FA-81244 / Music interval and transposition theory / Member archive

Interval inversion by quality and number: octave reduced to unison before inverting · case 04

P8 inverts to P8 instead of P1 because the octave is first reduced to a unison.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

Input an interval string: quality from P, M, m, A, d, AA, dd followed by a positive integer. Compound numbers above 8 reduce by 7 until <= 8. P is valid only for 1, 4, 5, 8; M and m only for 2, 3, 6, 7. Inversion maps M<->m, A<->d, AA<->dd, P->P and number n -> 9-n. Invalid input returns None.

Why this case matters

Pitch spelling and interval arithmetic decide the notes that notation, transposition and analysis tools display or play.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
oracle 0	`"P8"`	`"P1"`	Failed

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