FA-81323 / Music interval and transposition theory / Member archive

Triad and seventh inversion figures: first listed note taken as the bass · case 03

An unordered voicing such as [72,64,67] is reported in root position instead of first inversion.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Input 3 or 4 MIDI integers in any order. The pitch-class set must match a template relative to some root (triads 047 037 036 048; sevenths 047t 037t 047e 036t 0369, t=10 e=11); roots are tried in ascending pitch-class order. The bass is the lowest MIDI note. Return [root_pc, figure] with figures "", "6", "64" for triads and "7", "65", "43", "42" for sevenths by the bass position in the template; otherwise None.

Why this case matters

Figured-bass realisation and harmonic analysis depend on identifying chord root and inversion.

One recorded failure

Sample boundary fixture

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

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

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