key

Pinned sense: a key as a FUNCTIONALIZED scale. The accepted key definition carves it as 'an organized set of pitches whose members bear functional roles defined by their relation to a central pitch, the tonic' — that is a scale (an organized set of pitches) plus a functional hierarchy with a designated center. A key is therefore a specific kind of scale: the kind whose members carry tonal functions. Law 9 nearest kind: no intermediate rung is accepted between key and a pitch-set framework — 'pitch' is a quantity, not a kind of framework, and no scale node existed before this filing. A competent speaker would call the key of C major 'the C major scale with its tonic and functional roles'. The complementary equal-temperament SERVES key edge is unaffected; this INST claim is a distinct kind-membership.

Law 8b removal test, grounded in the target's own accepted definition: key carves itself as 'an organized set of pitches whose members bear functional roles defined by their relation to a central pitch, the tonic', and its first parameter is 'tonic — the central pitch class of the framework, the point of departure and resolution'. Remove the tonic construct now and the key stops operating as a key: the pitches' functional roles are defined by their relation to the tonic, so without it the framework collapses to a bare musical-scale (a pitch set with no center) — which is exactly the residual rung the board already seats as key INSTANCE_OF musical-scale. Not a sayability claim: the key's identity (C major vs. the chromatic set) is fixed by its tonic, and harmonic analysis — the mechanism by which the key persists — names keys by their tonics. Pinned sense (Law 11d): key as a tonal framework organized around a central pitch per its accepted definition. Not DERIVED_FROM: this is a present-tense structural dependency (the key operates around the tonic now), not a historical origin.

Directional test (Law 2b): remove the mode construct (the named interval patterns — major, minor, the modes of major) now. The key's own definition fixes its quality as 'the intervallic pattern above the tonic fixing the major or minor mode' — without the mode, that parameter has no content: the key signature (its persistence mechanism, 'the sharps or flats that name the framework') loses the pattern it names, the functional hierarchy (tonic/dominant/subdominant functions) loses the mode-specific structure that distinguishes D major from D minor, and 'D major' becomes unnameable. What remains is an anchored pitch collection — a center plus a set, not a key. The key stops operating. Pinned sense (Law 11d): this is the mechanism edge — the pattern by which the collection is fixed — distinct from the already-accepted kind edge key INSTANCE_OF musical-scale, in the same shape as musical-scale DEPENDS_ON pitch.

Law 8b removal test on the defined sense: key's accepted carve organizes 'a set of pitches whose members bear functional roles defined by their relation to a central pitch, the tonic' — parameters (1) tonic, (2) quality as intervallic pattern above the tonic, (3) diatonic pitch set, (4) transposition across the twelve pitch classes. Every parameter is a pitch-class parameter. Remove pitch now and the key stops operating: there is no tonic to center the framework on, no pitch classes to organize into functions, no twelve pitch classes to transpose across — not merely unsayable, but without the objects the framework operates on. Same accepted pattern as interval DEPENDS_ON pitch (already accepted on the board): both are pitch-relation frameworks at the same rung; not a ladder leap. Not chronology or identity — the removal consequence is in the definition's own parameters.

Law 8d for-whose-sake: equal-temperament's accepted carve states the purpose explicitly — parameter (4) 'interval compromise — the octave and tritone remain exact while the perfect fifth ... and the major and minor thirds are slightly tempered, the price that makes transposition and modulation to all twelve keys possible without retuning.' The compromise is built FOR whose sake? So that the twelve keys stand as equally playable tonal frameworks — the key is the beneficiary, the temperament is the servant. This is purpose, which Law 8c assigns to SERVES, never DEPENDS_ON (keys of other temperaments have existed without this one; removing equal temperament now leaves the key framework standing, retuned). Pinned senses: equal-temperament as the 12-equal-step division whose compromise parameter exists for the keys; key as the tonal framework of organized pitches centered on a tonic, twelve of which the temperament makes playable.