FA-81028 / Music interval and transposition theory / Member archive
Pitch-class set normal form (right-packed): wrapped members not lifted an octave · case 03
Rotations that wrap past 11 produce negative spans, so a wrapped rotation such as [11,0,4] is never chosen correctly.
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 fixtureThis sample comes from the broken implementation of a controlled reproducer.
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| oracle 1 | [5, 6, 8, 0, 1] | [0, 1, 5, 6, 8] | Failed |
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