FA-80908 / Music interval and transposition theory / Member archive
Interval quality and number naming: fourth handled as an imperfect interval · case 03
The perfect fourth C4-F4 is named M4 and the augmented fourth C4-F#4 becomes an A4 only by accident of offsets.
Case contract
Input [lower, upper] spelled pitches (letter, # or b accidentals, nonnegative octave). The generic number counts letter steps plus 7 per spelled octave plus one; quality compares the semitone span with the major/perfect reference (compounds add 12 per octave). Perfect class for simple numbers 1, 4, 5: P, A, d, AA, dd; others: M, m, A, d, AA, dd. Descending letter order or unrepresentable quality returns None.
Why this case matters
Pitch spelling and interval arithmetic decide the notes that notation, transposition and analysis tools display or play.
One recorded failure
Sample boundary fixtureThis sample comes from the broken implementation of a controlled reproducer.
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| oracle 7 | "M11" | "P11" | Failed |
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