Period: Difference between revisions

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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.

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''<ref group="note">The term ''non-periodic'' applied to scales is uncommon, but is consistent with the vocabulary of {{w|Tesselation|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.</ref>.

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

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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~~ ==

== Footnotes ==

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.

[[Category:Scale]]

[[Category:Generator]]

[[Category:Terms]]

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 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.
+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''<ref group="note">The term ''non-periodic'' applied to scales is uncommon, but is consistent with the vocabulary of {{w|Tesselation|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.</ref>.
 In [[regular temperament theory]], the period of a scale always coincides with one of its generators.
@@ Line 14: / Line 14: @@
 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 ==
+== Footnotes ==
-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.
+<references group="note" />
 [[Category:Scale]]
 [[Category:Generator]]
 [[Category:Terms]]