Period: Difference between revisions

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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.

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.

~~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''<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.

~~== Scale types ==~~

* 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.

* A ''non-periodic scale'' is a scale whose step pattern does not systematically repeat, but that may have small repeating segments in its step pattern. 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 {{w|DTMF}} tones.

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

== Examples ==

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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.

== Footnotes ==

[[Category:Scale]]

[[Category:Generator]]

[[Category:Terms]]

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-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.
+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.
-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''<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.
-== Scale types ==
-* 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.
-* A ''non-periodic scale'' is a scale whose step pattern does not systematically repeat, but that may have small repeating segments in its step pattern. 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 {{w|DTMF}} tones.
-* An ''aperiodic scale'' is a scale whose step pattern never repeats. The [[harmonic series]] is an example of aperiodic scale.
 == Examples ==
@@ Line 16: / Line 13: @@
 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 ==
+<references group="note" />
 [[Category:Scale]]
 [[Category:Generator]]
 [[Category:Terms]]