Period - Revision history

Fredg999: Moved all the borderline superflous non-periodic scale stuff into a footnote

2025-02-23T07:24:21Z

Moved all the borderline superflous non-periodic scale stuff into a footnote

← Older revision		Revision as of 07:24, 23 February 2025
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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.		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.		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.		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:Scale]]
	[[Category:Generator]]		[[Category:Generator]]
	[[Category:Terms]]		[[Category:Terms]]

Fredg999: Move non-periodic scales at the bottom of the page, rephrase its definition to lessen the impression that the term is common.

2025-02-23T06:43:42Z

Move non-periodic scales at the bottom of the page, rephrase its definition to lessen the impression that the term is common.

← Older revision		Revision as of 06:43, 23 February 2025
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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.

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

	[[Category:Scale]]		[[Category:Scale]]
	[[Category:Generator]]		[[Category:Generator]]
	[[Category:Terms]]		[[Category:Terms]]

Fredg999: Improve lead section, add "Scale types" section (not sure about the title, good enough for now), enclose last part into an "Examples" section, categories

2025-02-23T06:16:50Z

Improve lead section, add "Scale types" section (not sure about the title, good enough for now), enclose last part into an "Examples" section, categories

← Older revision		Revision as of 06:16, 23 February 2025
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	The '''period''' ~~of a [[scale]] is the interval at which the scale pattern repeats. Another word for the period is the~~ '''interval of repetition'''~~. A scale with a period is known as~~ a [[~~periodic~~ scale]]~~. The period~~ is ~~usually~~ the ~~same size as~~ the [[~~equave~~]] ~~(interval of equivalence) or a fraction thereof~~.		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 [[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 ==
	In [[mos scale]]s, the period is one of the two defining intervals, the other being the [[generator]]. For example:		In [[mos scale]]s, 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 diatonic scale (LLsLLLs) has period equal to the octave.
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	[[Category:Scale]]		[[Category:Scale]]
	[[Category:~~Rank 2~~]]		[[Category:Generator]]
	[[Category:Terms]]		[[Category:Terms]]

FloraC: This isn't limited to mos scales

2022-12-12T01:31:11Z

This isn't limited to mos scales

← Older revision		Revision as of 01:31, 12 December 2022
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	The '''period''' of a [[~~MOS~~ scale]] is the interval at which the ~~MOS~~ pattern repeats. Another word for the period is the '''interval of repetition'''. It is usually the same size as the [[equave]] (interval of equivalence) or a fraction thereof. ~~Along with the~~ [[~~generator~~]], it is one of the two defining intervals ~~of a MOS~~. For example:		The '''period''' of a [[scale]] is the interval at which the scale pattern repeats. Another word for the period is the '''interval of repetition'''. A scale with a period is known as a [[periodic scale]]. The period is usually the same size as the [[equave]] (interval of equivalence) or a fraction thereof.

			In [[mos scale]]s, 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 diatonic scale (LLsLLLs) has period equal to the octave.
	* The diminished scale (sLsLsLsL) has period 1\4, ~~because~~ the ~~MOS~~ pattern sL repeats at every 300 cents.		* 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.
			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.

	[[Category:~~MOS~~]]		[[Category:Scale]]
	[[Category:Rank 2]]		[[Category:Rank 2]]
	[[Category:Terms]]		[[Category:Terms]]

Fredg999: Minor rephrasing + added to Terms category

2021-08-01T14:24:55Z

Minor rephrasing + added to Terms category

← Older revision		Revision as of 14:24, 1 August 2021
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	The '''period''' of a [[MOS]] is the interval at which the MOS pattern repeats. Another word for the period is the '''interval of repetition'''. It is usually ~~also~~ the [[interval of equivalence~~]]. Its size is usually an octave~~ or a fraction thereof. Along with the [[generator]], it is one of the two defining intervals of a MOS. For example:		The '''period''' of a [[MOS scale]] is the interval at which the MOS pattern repeats. Another word for the period is the '''interval of repetition'''. It is usually the same size as the [[equave]] (interval of equivalence) or a fraction thereof. Along with the [[generator]], it is one of the two defining intervals of a MOS. For example:
	* The diatonic scale (LLsLLLs) has period equal to the octave.		* The diatonic scale (LLsLLLs) has period equal to the octave.
	* The diminished scale (sLsLsLsL) has period 1\4, because the MOS pattern sL repeats at every 300 cents.		* The diminished scale (sLsLsLsL) has period 1\4, because the MOS pattern sL repeats at every 300 cents.
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	[[Category:MOS]]		[[Category:MOS]]
	[[Category:Rank 2]]		[[Category:Rank 2]]
			[[Category:Terms]]

Cmloegcmluin: bold alternate term

2021-05-23T23:28:05Z

bold alternate term

← Older revision		Revision as of 23:28, 23 May 2021
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	The '''period''' of a [[MOS]] is the interval at which the MOS pattern repeats. Another word for the period is the interval of repetition. It is usually also the [[interval of equivalence]]. Its size is usually an octave or a fraction thereof. Along with the [[generator]], it is one of the two defining intervals of a MOS. For example:		The '''period''' of a [[MOS]] is the interval at which the MOS pattern repeats. Another word for the period is the '''interval of repetition'''. It is usually also the [[interval of equivalence]]. Its size is usually an octave or a fraction thereof. Along with the [[generator]], it is one of the two defining intervals of a MOS. For example:
	* The diatonic scale (LLsLLLs) has period equal to the octave.		* The diatonic scale (LLsLLLs) has period equal to the octave.
	* The diminished scale (sLsLsLsL) has period 1\4, because the MOS pattern sL repeats at every 300 cents.		* The diminished scale (sLsLsLsL) has period 1\4, because the MOS pattern sL repeats at every 300 cents.

Cmloegcmluin at 18:49, 9 April 2021

2021-04-09T18:49:29Z

← Older revision		Revision as of 18:49, 9 April 2021
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	The '''period''' of a [[MOS]] is the interval at which the MOS pattern repeats~~; it~~ is the [[interval of equivalence]] (usually ~~the~~ octave) or a fraction ~~of it~~. Along with the [[generator]], it is one of the two defining intervals of a MOS. For example:		The '''period''' of a [[MOS]] is the interval at which the MOS pattern repeats. Another word for the period is the interval of repetition. It is usually also the [[interval of equivalence]]. Its size is usually an octave or a fraction thereof. Along with the [[generator]], it is one of the two defining intervals of a MOS. For example:
	* The diatonic scale (LLsLLLs) has period equal to the octave.		* The diatonic scale (LLsLLLs) has period equal to the octave.
	* The diminished scale (sLsLsLsL) has period 1\4, because the MOS pattern sL repeats at every 300 cents.		* The diminished scale (sLsLsLsL) has period 1\4, because the MOS pattern sL repeats at every 300 cents.

Xenwolf: separate categories from text by an empty line, place each one on their own line

2021-01-15T20:00:29Z

separate categories from text by an empty line, place each one on their own line

← Older revision		Revision as of 20:00, 15 January 2021
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	* The diminished scale (sLsLsLsL) has period 1\4, because the MOS pattern sL repeats at every 300 cents.		* The diminished scale (sLsLsLsL) has period 1\4, because 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.		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.
	[[Category:MOS]][[Category:Rank 2]]
			[[Category:MOS]]
			[[Category:Rank 2]]

Inthar at 19:28, 15 January 2021

2021-01-15T19:28:01Z

← Older revision		Revision as of 19:28, 15 January 2021
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	* The diatonic scale (LLsLLLs) has period equal to the octave.		* The diatonic scale (LLsLLLs) has period equal to the octave.
	* The diminished scale (sLsLsLsL) has period 1\4, because the MOS pattern sL repeats at every 300 cents.		* The diminished scale (sLsLsLsL) has period 1\4, because 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.		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.
	[[Category:MOS]][[Category:Rank 2]]		[[Category:MOS]][[Category:Rank 2]]

Inthar at 19:26, 15 January 2021

2021-01-15T19:26:16Z

← Older revision		Revision as of 19:26, 15 January 2021
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	The '''period''' of a [[MOS]] is the interval at which the MOS pattern repeats; it is the interval of equivalence (usually the octave) or a fraction of it. Along with the [[generator]], it is one of the two defining intervals of a MOS. For example:		The '''period''' of a [[MOS]] is the interval at which the MOS pattern repeats; it is the [[interval of equivalence]] (usually the octave) or a fraction of it. Along with the [[generator]], it is one of the two defining intervals of a MOS. For example:
	* The diatonic scale (LLsLLLs) has period equal to the octave.		* The diatonic scale (LLsLLLs) has period equal to the octave.
	* The diminished scale (sLsLsLsL) has period 1\4, because the MOS pattern sL repeats at every 300 cents.		* The diminished scale (sLsLsLsL) has period 1\4, because 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.		The same definition applies for a [[rank]]-2 temperament, when the temperament is seen as generating a MOS.
	[[Category:MOS]][[Category:Rank 2]]		[[Category:MOS]][[Category:Rank 2]]