harmony

SERVES: for whose sake? Harmony is built and maintained for the sake of music — its designed purpose is to create the vertical dimension of musical sound (simultaneous pitches, chords, progressions). The note shows the teleological direction: harmony points at music as its master. Harmony doesn't need music to operate (that would be DEPENDS_ON), but it exists for the sake of musical composition and experience.

Harmony combines simultaneous pitches into chordal structures. Remove pitch and harmony has no operational element — there are no pitches to harmonize. The concept collapses entirely without pitch. Constitutive dependency.

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).

An arpeggio is designed and maintained for the sake of harmony — it articulates vertical chordal structure as sequential linear motion. Law 8d: servant(arpeggio)→master(harmony). The technique exists to realize and express harmonic content.

An arpeggio IS the sequential playing of chord notes — it needs the concept of harmony (chords) to operate NOW (Law 8 removal test). Remove harmony/chords and the arpeggio has nothing to arpeggiate. Arpeggio SERVES harmony (already accepted) and DEPENDS_ON harmony (constitutive prerequisite — the technique extracts from the harmonic structure).

Dissonance is maintained for the sake of harmony — in music and perception, dissonance creates tension that makes harmony perceptible and meaningful. Law 8d: servant (dissonance) points at master (harmony). The designed purpose of dissonance in musical practice is to serve harmonic resolution.

Consonance IS a specific kind of harmony — the partial or full acoustic harmony where simultaneous sounds blend without perceptual clash. A competent speaker would call consonance 'a kind of harmony' (specifically acoustic harmony). Law 9: specific→general.

Cadence is a harmonic progression that establishes or temporarily rejects tonal resolution. Remove the concept of harmony and cadence has nothing to measure — it ceases to operate (Law 8 removal test). Harmony is the system of pitches that cadence navigates; cadence operates as a moment within that system. This is an operational dependency, not a shared condition of conceptuality (Law 2b).

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).