FA-80934 / Music interval and transposition theory / Member archive
Spelled transposition by named interval: diminished imperfect interval equals minor · case 04
C4 up a diminished seventh returns Bb4 instead of Bbb4; diminished thirds and sixths collapse onto minor.
Case contract
Input [note, interval, direction]. note: letter, # or b accidentals, nonnegative octave. interval: quality letter (P, M, m, A, d) and generic number >= 1 with perfect-class numbers 1, 4, 5 (compounds reduce by 7). Direction up or down moves the letter by number-1 steps and the pitch by the interval size; the result is spelled with the moved letter, octave taken from the letter position. Results needing more than two accidentals, or a negative octave, return 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 0 | "Bb4" | "Bbb4" | Failed |
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