FA-81093 / Music interval and transposition theory / Member archive

Five-limit just ratio for a semitone interval: octave factor multiplied instead of exponentiated · case 03

Every interval smaller than an octave returns 0/1 and a twelfth returns 3/1 only by coincidence.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Input an integer semitone count (negative = descending). Ascending ratios use the table 1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 per pitch class, times 2 per octave. A descending interval is the reciprocal of the ascending one of the same size. Return "p/q" in lowest terms (always with a denominator); non-integers and booleans return None.

Why this case matters

Tuning tables and retuning tools convert interval sizes to exact frequency ratios.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
oracle 0	`"0/1"`	`"9/8"`	Failed

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