chord

Removal test (Law 8b): remove the interval construct — the named, categorized distance between two pitches per its accepted definition — and chord stops operating as a unit of harmonic analysis. Chord's own accepted definition fixes its quality parameter in interval terms: major (root–major third–perfect fifth), minor (root–minor third–perfect fifth), diminished, augmented. Without the interval construct a chord is an undifferentiated mass of simultaneous pitches: major and minor can no longer be told apart, chord symbols can no longer be read, and harmonic analysis — the mechanism by which chord persists (theory, notation, pedagogy) — has nothing to name. A chord's identity is fixed by the intervallic structure among its members, so the dependency is operational, not mere sayability. Pinned sense: chord as a harmonic unit whose quality is determined by intervals, not chord as a bare simultaneous set of pitches.

Law 8d for-whose-sake: chord's accepted scope carves it as a fundamental unit of Western harmony, built to persist through theoretical analysis, performance practice, notation, and teaching - the designed sake is the harmonic system of which it is the unit. Nearest master: harmony (accepted v1: the structured combination of simultaneous pitches into chords and the principles governing chordal succession), not music - the board already seats harmony SERVES music (ACCEPTED), and the servant points at the nearest master; the same rung-skip logic that struck chord SERVES music applies. Not DEPENDS_ON: removing the harmony concept does not stop chords sounding or being counted in practice; harmony's own substrate is pitch per its accepted DEPENDS_ON pitch. Not CONTAINS: a chord is not a part of the dimension - I struck the pending harmony CONTAINS chord on those grounds; the unit-of-system relation is purpose, not part-whole. Pinned sense (Law 11d): chord as harmonic unit per its accepted definition. Servant (chord) -> master (harmony).

Pinned senses (Law 11d): harmony as its accepted v1 carve — 'the vertical dimension of music: the structured combination of simultaneous or near-simultaneous pitches into chords, and the principles governing chordal succession'; chord as its pending v1 carve filed in the same sitting — 'a set of two or more pitches sounded simultaneously, whose members bear harmonic relations to one another.' Part-of test: harmony is the whole structured out of its constituents — its accepted definition names chords as the objects of the structured combination and chordal succession as the governing principle, so the harmonic structure is composed of chords and their successions, exactly as the accepted bar CONTAINS beat composes the bar from its constituent temporal units. Remove the chord and there is nothing for harmony to combine or govern — the dimension collapses to a bare principle. Asymmetry holds: a chord (simultaneously sounded pitches) operates without the harmony concept — simultaneous pitch sets sound and persist as material of practice whether or not harmonic theory exists; the reverse fails the containment reading (a chord does not contain harmony). Not DEPENDS_ON: removing the harmony concept does not stop the chord operating (the chord is harmony's parameter, not its operational substrate; harmony's own substrate is pitch, per its accepted DEPENDS_ON pitch). Not INSTANCE_OF: a chord is not a kind of harmony — it is what harmony is composed of. Not SERVES: a constituent is not a servant built for its whole's sake. Direction: whole (harmony) -> part (chord), per the cluster's accepted part-whole pattern (sheet-music CONTAINS staff, note, barline, bar; bar CONTAINS beat).