FA-81293 / Music interval and transposition theory / Member archive

Staff position and ledger lines for a clef: lower ledger count rounded the wrong way · case 03

B3 in treble clef (just below middle C) reports two ledger lines instead of one.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Input [note, clef] where note is a letter, accidentals (# b x, ignored for placement) and a nonnegative octave, and clef is treble (bottom line E4), bass (G2), alto (F3) or tenor (D3). Position counts diatonic steps above the bottom line (lines are even positions 0..8). Ledger lines: below the staff (-position)//2 for negative positions, above (position-8)//2 for positions over 8, else 0. Return [position, ledgers] or None when invalid.

Why this case matters

Engraving and notation-rendering code places noteheads and ledger lines from pitch spellings.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
oracle 0	`[-1, 1]`	`[-1, 0]`	Failed

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