FA-81075 / Music interval and transposition theory / Member archive

Interval-class vector of a pitch-class set: self pairs and ordered pairs counted · case 05

Every interval is counted twice and each pitch class paired with itself lands in the tritone slot.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

Input a list of integers, reduced mod 12 and deduplicated. For each unordered pair count its interval class min(d, 12-d) in 1..6. Return the six counts [ic1..ic6]; non-integer input returns None.

Why this case matters

Interval vectors drive set-class similarity measures and Z-relation detection.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
oracle 0	`[2, 2, 2, 2, 2, 6]`	`[1, 1, 1, 1, 1, 1]`	Failed

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