FA-81040 / Music interval and transposition theory / Member archive

Pitch-class set normal form (right-packed): symmetric sets start on the highest pitch class · case 05

The augmented triad [0,4,8] returns [8,0,4] and the diminished seventh starts on 9.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

Input a list of integers (reduced mod 12, duplicates removed). Return the normal form: among all rotations of the ascending set, choose the one with the smallest span first-to-last, then smallest span first-to-penultimate, and so on toward the second element; a full tie picks the rotation starting on the lowest pitch class. Empty input returns []; non-integer input returns None.

Why this case matters

Post-tonal analysis tools use normal form to compare and catalogue pitch-class sets.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
oracle 5	`[11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]`	`[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]`	Failed

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