semitone

Removal test on accepted carves (Laws 2b/8b): semitone's accepted def fixes it as the distance between two adjacent pitch classes; pitch-class's accepted carve is a pitch's equivalence class under transposition by octaves, so the semitone's endpoints ARE pitches. Remove pitch now and the semitone loses the objects between which its distance is measured — it stops operating, not merely being sayable. Ladder check: interval DEPENDS_ON pitch is accepted; semitone is the nearest kind below interval on the same pitch-distance family, so this is the same rung, not a leap. The definition's parameters (qualities, cents in equal temperament) are measured against pitch and its mechanism (named distance between adjacent pitch classes) requires pitch to exist — no parameter-level import. Note pins the pitch-distance sense, not any temperament-specific sense.

Law 9 specific to nearest accepted kind; Law 11d pinned senses against both accepted defs. interval's accepted definition carves 'a named, categorized measure of the distance between two pitches within a given tuning system' with parameters step count, quality classification, and size in cents. semitone's own accepted definition declares it 'the smallest named interval of Western chromatic music — the distance between two adjacent pitch classes, named in two qualities' with parameters quality (diatonic/chromatic), size in cents (100 in equal temperament; ~112/~90 in just intonation), and notation. That is exactly interval's carve: a named, measured, quality-classified distance in cents. A competent speaker calls the semitone 'the smallest interval'. No nearer accepted kind exists on the board (no step or half-step entry; musical-interval unheld), so interval is the nearest rung.

Removal test (Law 8b): remove the semitone construct and equal-temperament stops operating. Its accepted definition IS 'the convention dividing the octave into twelve equal semitones' — the semitone is the unit the octave is divided into, and the 'equal' that names the system is the equality of those twelve semitone steps. Without the semitone construct there is no unit to divide the octave into, no way to state the equal spacing that defines the tuning, and no way to specify its consequences: the keyboard layout (adjacent keys one semitone apart) and the twelve equal keys it makes playable are both stated in semitone terms. The dependency is definitional-operational, not chronology and not mere sayability. Pinned sense: equal-temperament as the twelve-equal-semitone division of the octave.