Scale

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A scale is a set of pitches which are chosen from in making music. Scales are usually periodic, i.e. the same pattern of intervals repeats at some interval called the equave. On the Xenharmonic Reference, scales are periodic or repeating unless stated otherwise. (Though of course, finite but nonrepeating pitch material may be useful to consider in some contexts like voicing and register, especially in harmonic series or spectralist music.) A periodic scale can be visualized as a set of points in the circle of equave-equivalent pitch classes.

Descriptions

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Scales are basically the same kind of object as chords, at least once an equave is chosen. There are a bunch of different equivalence relations between scales, which are somewhat confusingly all informally called things like "the same scale". The loosest such relation is step pattern equivalence, where "the same" means that two scales simply have the same step pattern (and often the same equave), and can vary in tuning, transposition, or rotation. This is the sense in which 5L 2s is "a scale". The strictest relation is wherein all three of these categories must be the same; in that two scales are only "the same" if they contain the exact same notes. This is the sense in which "C Ionian (12edo tuning)" is a scale.

Other categories lie in between these:

• "12edo diatonic" is a scale if only transposition and rotation may be varied;

• "Ionian" is a scale if only transposition and tuning may be varied;

• "C Ionian" is a scale if only tuning may be varied;

• "2-2-1-2-2-2-1" is a scale if only transposition may be varied.

"Scales" can, in practical music theory in certain cases, also have different forms to be used in different contexts. An example is melodic minor, which has a different ascending form and descending form.