FA-81034 / Music interval and transposition theory / Member archive
Pitch-class set normal form (right-packed): span ties broken from the left · case 04
Sets such as [0,1,5,6,8] and [0,1,3,5,8,9] get the left-packed normal form instead of the stipulated right-packed one.
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 0 | [5, 6, 8, 0, 1] | [0, 1, 5, 6, 8] | Failed |
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