FA-81247 / Music interval and transposition theory / Member archive

Interval inversion by quality and number: inversion complement taken to eight · case 02

M3 inverts to m5 and P4 to P4: every inverted number is one too small.

Member previewVariant 2 · 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	`"m5"`	`"m6"`	Failed

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