FA-81105 / Music interval and transposition theory / Member archive

Pythagorean ratio for a chain of fifths: flatward chains lifted by a single octave · case 05

Two fifths down returns 8/9 (below unison) instead of 16/9.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

Input an integer k with |k| <= 24 (booleans rejected). Return (3/2)**k octave-reduced into [1, 2) as [numerator, denominator]; out-of-range or non-integer input returns None.

Why this case matters

Pythagorean and meantone tuning tools stack fifths and octave-reduce the result.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
oracle 1	`[8, 9]`	`[16, 9]`	Failed

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