pitch

Per Law 8 removal test: pitch is a perceptual attribute OF sound. Remove the concept of sound and the concept of pitch literally ceases to operate — pitch has no domain without sound. This is a genuine object-level dependency (Law 2b), not a meta-level sayability issue.

The concept of pitch (as a musical/perceptual correlate of frequency) needs the concept of frequency to operate. Without the frequency concept — cycles per unit time — the pitch concept loses its quantitative framework and cannot be precisely defined or compared. Law 8 removal test: remove frequency and pitch stops operating as a defined musical concept.

An overtone is defined as a frequency component above a fundamental pitch. Remove the concept of pitch and overtone loses its operative framework — it cannot specify what frequency it is above. Per Law 8 removal test: X stops operating without Y.

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.

Melody is a sequence of pitched notes organized temporally. Remove pitch as a concept and melody has nothing to be a sequence of — it collapses entirely. Pitch is the fundamental element from which melody is constructed; the removal test passes clearly.

Tuning is the practice of adjusting instruments or voices to correct pitch. Remove the concept of pitch and tuning has no target — it ceases to operate. Per Law 8 removal test: X needs Y operating now. Tuning NEEDS pitch to function as a concept.

An interval names the distance between two pitches. Remove the concept of pitch and an interval has nothing to measure — it ceases to operate. The removal test passes: intervals need pitch as their constitutive referent.

The mel scale (1937, Stevens-Volkmann-Newman) was developed from the concept of pitch perception to create a scale where equal steps are perceived as equal pitch intervals. Pitch as a perceptual concept existed before the mel frequency scale was created to quantify it.

pitch-class needs pitch to operate: it categorizes pitches by their equivalence classes. Remove the concept of pitch (the perceptual attribute of how high or low a sound is) and pitch-class loses its operative basis — you cannot group by pitch name without the concept of pitch itself. The removal test passes: without pitch, pitch-class cannot function.

Tonality organizes musical pitches around a central reference. Remove pitch and tonality has nothing to organize — its entire structure of pitch hierarchies collapses. Pitch as a perceptual attribute exists independently of tonality, but tonality as a musical system requires pitch to operate.

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.

Removal test (Law 8): remove pitch — the musical quantity of perceived frequency — and a musical scale stops OPERATING: a scale is an ordered set of PITCH CLASSES, so without pitch there is no content to order, no interval pattern to instantiate, nothing to notate or perform. Pitch is the substance the framework organizes, not a historical association (no chronology argued) and not a mere naming loss (Law 8b): the framework's own operation collapses, it does not merely stop being sayable. Analogous to the accepted version-control DEPENDS_ON source-code, where the framework's managed content is its dependency. Direction: scale needs pitch, not the reverse — pitch operates without any scale.

octave is defined by the 2:1 frequency ratio between two pitches. Per Law 8 removal test: remove the concept of pitch and octave ceases to operate — an octave is literally the relationship between two pitches. This is object-level dependency, not meta-level (Law 2b).

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.