FA-81090 / Music interval and transposition theory / Member archive

Five-limit just ratio for a semitone interval: descending intervals looked up by floor modulo · case 05

A descending whole tone returns 9/10 instead of 8/9 and a descending tritone 45/64 instead of 32/45.

Member previewVariant 5 · 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 5	`"9/10"`	`"8/9"`	Failed

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