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Encyclopedia of Microtonal Music Theory

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[Joe Monzo]

A succession of musical pitches arranged in order of pitch-height, generally considered as a source set of pitches for musical composition.

Different types or families of scales are usually characterized by repeating patterns of intervals between the pitches.

As examples, the typical major and minor scales are diatonic, which means that they have characteristic interval patterns of "whole-tones" and semitones, usually called "whole-steps" and "half-steps" respectively. Pentatonic scales have characteristic interval patterns of "whole-steps" and "minor 3rds", etc. Note that in this latter example the so-called "minor-3rd" is still regarded as a step.

Scales are usually, but not necessarily, designated only for one octave and considered to be octave-invariant.

Alternatively (but rarely), an interval other than the octave may be used as the equivalence-interval. (For some examples of these, see Monzo, A stretched-'octave' scale of Charles Ives.)

Scales often, but not always, exhibit tetrachordal similarity, and other properties such as MOS, propriety, distributional evenness, etc.

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A comprehensive discussion of the definition of "scale" was begun with Yahoo tuning, message 58625.

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[Carl Lumma, Yahoo tuning message 73329 (Wed Sep 19, 2007 1:51 am PDT)]

A scale is a finite number of notes / pitches. Usually octave-equivalent, in which case it's a finite number of pitch classes.

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