Period

The period (or interval of repetition) of a scale is the interval at which the scale's step pattern eventually repeats, if it does at all. In practice, the period often corresponds to the equave (interval of equivalence) or to a fraction of the equave.

A periodic scale is a scale whose step pattern always repeats after a certain number of steps. The diatonic scale is an example of periodic scale.

An aperiodic scale is a scale whose step pattern never repeats. The harmonic series is an example of aperiodic scale.

In regular temperament theory, the period of a scale always coincides with one of its generators.

Examples

In mos scales, the period is one of the two defining intervals, the other being the generator. For example:

• The diatonic scale (LLsLLLs) has period equal to the octave.
• The diminished scale (sLsLsLsL) has period 1\4, since the mos pattern sL repeats at every 300 cents.

The same definition applies for a rank-2 temperament, when the temperament is seen as generating a mos. Every interval of a rank-2 temperament is a sum of some number of the period and some number of the generator of the temperament.

Special cases

A scale whose step pattern does not systematically repeat, but that may have small repeating segments in its step pattern, may be called a non-periodic scale. This type of scale is less common, but technically includes any scale with a finite number of notes and which is not expected to repeat at all, such as the sequence of DTMF tones. Aperiodic scales are a subset of non-periodic scales.