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. More generally, any scale whose step pattern does not repeat may be called a non-periodic scale[note 1].
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.
Footnotes
- ↑ The term non-periodic applied to scales is uncommon, but is consistent with the vocabulary of geometric tilings, which have a similar structure. Non-periodic scales 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, whereas aperiodic scales are assumed to have notes above and below any given note in the scale.