Interval - Revision history

Overthink: grammar

2026-01-12T23:56:12Z

grammar

← Older revision		Revision as of 23:56, 12 January 2026
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	Human pitch perception is [[Wikipedia:Logarithm#Music\|logarithmic]], therefore an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.		Human pitch perception is [[Wikipedia:Logarithm#Music\|logarithmic]], therefore an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.

	A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its size in cents is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>, unless the interval happens to be an octave or some multiple of an octave. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its cents value may or may not be rational. An interval with rational cents is always irrational, unless it's an octave or some multiple of an octave. ~~But some~~ intervals have both irrational ratios and irrational cents.		A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its size in cents is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>, unless the interval happens to be an octave or some multiple of an octave. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its cents value may or may not be rational. An interval with rational cents is always irrational, unless it's an octave or some multiple of an octave. Some intervals have both irrational ratios and irrational cents.

	Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].		Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].

BudjarnLambeth: /* See also */ link to semi orphaned page

2025-04-30T07:35:23Z

FloraC: +interwiki

2024-12-18T08:31:35Z

+interwiki

← Older revision		Revision as of 08:31, 18 December 2024
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			{{Interwiki
			\| en = Interval
			\| ro = Interval (ro)
			}}
	{{Wikipedia\|Interval (music)}}		{{Wikipedia\|Interval (music)}}
	An '''interval''' is the difference in [[pitch]] between two notes.		An '''interval''' is the difference in [[pitch]] between two notes.

TallKite: corrected errors about irrational cents values. removed a misleading sentence about dyads.

2024-10-20T08:43:27Z

corrected errors about irrational cents values. removed a misleading sentence about dyads.

← Older revision		Revision as of 08:43, 20 October 2024
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	{{Wikipedia\|Interval (music)}}		{{Wikipedia\|Interval (music)}}
	An '''interval''' is the difference in [[pitch]] between two notes~~. Since two notes form a [[dyad]], the terms ''interval'' and ''dyad'' are sometimes used interchangeably~~.		An '''interval''' is the difference in [[pitch]] between two notes.

	Human pitch perception is [[Wikipedia:Logarithm#Music\|logarithmic]], therefore an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.		Human pitch perception is [[Wikipedia:Logarithm#Music\|logarithmic]], therefore an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.

	A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its ~~logarithmic measure~~ is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its ~~logarithmic measure~~ may or may not be rational. An interval with a rational ~~logarithmic measure~~ is always irrational, ~~but~~ some intervals have both irrational ratios and ~~logarithmic measures~~.		A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its size in cents is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>, unless the interval happens to be an octave or some multiple of an octave. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its cents value may or may not be rational. An interval with rational cents is always irrational, unless it's an octave or some multiple of an octave. But some intervals have both irrational ratios and irrational cents.

	Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].		Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].

Fredg999: Terms used interchangeably, link to Wikipedia for logarithmic pitch perception

2023-07-21T14:31:17Z

Terms used interchangeably, link to Wikipedia for logarithmic pitch perception

← Older revision		Revision as of 14:31, 21 July 2023
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	{{Wikipedia\|Interval (music)}}		{{Wikipedia\|Interval (music)}}
	An '''interval''' is the difference in [[pitch]] between two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.		An '''interval''' is the difference in [[pitch]] between two notes. Since two notes form a [[dyad]], the terms ''interval'' and ''dyad'' are sometimes used interchangeably.

			Human pitch perception is [[Wikipedia:Logarithm#Music\|logarithmic]], therefore an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.

	A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its logarithmic measure is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.		A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its logarithmic measure is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.
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	== See also ==		== See also ==
	* [[Dyad]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Interval size measure]]		* [[Interval size measure]]

Fredg999: Distinguish interval and dyad

2023-07-21T04:15:51Z

Distinguish interval and dyad

← Older revision		Revision as of 04:15, 21 July 2023
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	{{Wikipedia\|Interval (music)}}		{{Wikipedia\|Interval (music)}}
	~~{{Wikipedia\|Dyad (music)}}~~		An '''interval''' is the difference in [[pitch]] between two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.
	An '''interval''' ~~(or '''dyad'''; less commonly, '''diad''') is a [[chord]] of two different notes.~~

	~~The main property of an interval~~ is ~~its size, defined as~~ the difference in [[pitch]] between ~~its~~ two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s~~. Intervals are usually named after their size, which might explain why some dictionaries define the term ''interval'' as the size itself~~.

	A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its logarithmic measure is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.		A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its logarithmic measure is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.
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	== See also ==		== See also ==
			* [[Dyad]]
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Interval size measure]]		* [[Interval size measure]]
			* [[:Category:Interval naming]]

	== References ==		== References ==

Fredg999: Reworked the rational/irrational paragraph, misc. edits

2022-08-03T02:50:58Z

Reworked the rational/irrational paragraph, misc. edits

← Older revision		Revision as of 02:50, 3 August 2022
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	{{Wikipedia\|Interval (music)}}		{{Wikipedia\|Interval (music)}}
	{{Wikipedia\|Dyad (music)}}		{{Wikipedia\|Dyad (music)}}
	An '''interval''' or '''dyad''' (less commonly, '''diad''') is a [[chord]] of two different notes.		An '''interval''' (or '''dyad'''; less commonly, '''diad''') is a [[chord]] of two different notes.

	The main property of an interval is its size, defined as the difference in [[pitch]] between its two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s. Intervals are usually named after their size, which might explain why some dictionaries define the term ''interval'' as the size itself.		The main property of an interval is its size, defined as the difference in [[pitch]] between its two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s. Intervals are usually named after their size, which might explain why some dictionaries define the term ''interval'' as the size itself.

	An interval is ~~rational if its~~ ratio is a rational number~~, and its~~ logarithmic measure is then necessarily irrational. Conversely, an interval is ~~irrational if its~~ frequency ratio is an irrational number~~; in~~ that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.		A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its logarithmic measure is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.

	Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].		Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].
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	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Interval size measure]]		* [[Interval size measure]]

			== References ==
			<references/>

	[[Category:Interval\| ]] <!-- main article -->		[[Category:Interval\| ]] <!-- main article -->

Godtone: minor correction

2021-09-04T21:48:57Z

minor correction

← Older revision		Revision as of 21:48, 4 September 2021
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	The main property of an interval is its size, defined as the difference in [[pitch]] between its two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s. Intervals are usually named after their size, which might explain why some dictionaries define the term ''interval'' as the size itself.		The main property of an interval is its size, defined as the difference in [[pitch]] between its two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s. Intervals are usually named after their size, which might explain why some dictionaries define the term ''interval'' as the size itself.

	An interval is rational if its ratio is a rational number, and its logarithmic measure is necessarily irrational. Conversely, an interval is irrational if its frequency ratio is an irrational number; in that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.		An interval is rational if its ratio is a rational number, and its logarithmic measure is then necessarily irrational. Conversely, an interval is irrational if its frequency ratio is an irrational number; in that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.

	Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].		Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].

Fredg999: Full rewrite

2021-09-04T21:15:32Z

Full rewrite

← Older revision		Revision as of 21:15, 4 September 2021
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	In music, ~~the term~~ '''~~interval~~''' is ~~used to characterize the relation between simultaneous or successive tones~~.		{{Wikipedia\|Interval (music)}}
			{{Wikipedia\|Dyad (music)}}
			An '''interval''' or '''dyad''' (less commonly, '''diad''') is a [[chord]] of two different notes.

	~~If the name "~~interval" is ~~taken~~ as ~~a starting point, the term initially aims to determine~~ the [[pitch ~~difference~~]] between ~~the~~ two ~~sound phenomena involved~~. ~~At the same time (~~with ~~otherwise relatively stable~~ [[~~timbre~~]]s) a ~~specific character~~ of the ~~joint sound results from~~ a ~~given distance between the participating tones~~, ~~which~~ is (in ~~classic Western music theory) often graduated between~~ [[~~consonance~~]] ~~and~~ [[dissonance]]).		The main property of an interval is its size, defined as the difference in [[pitch]] between its two notes. Since pitch perception is logarithmic, an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s. Intervals are usually named after their size, which might explain why some dictionaries define the term ''interval'' as the size itself.

			An interval is rational if its ratio is a rational number, and its logarithmic measure is necessarily irrational. Conversely, an interval is irrational if its frequency ratio is an irrational number; in that case, however, its logarithmic measure may or may not be rational. An interval with a rational logarithmic measure is always irrational, but some intervals have both irrational ratios and logarithmic measures.

			Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].

	== See also ==		== See also ==
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]
	* [[Interval size measure]]		* [[Interval size measure]]
	* [[Sonance]]

	~~== External links ==~~
	* [[Wikipedia: Interval (music)]]

			[[Category:Interval\| ]] <!-- main article -->
	[[Category:Terms]]		[[Category:Terms]]
	~~[[Category:Interval\| ]] <!-- main article -->~~

	{{todo\| review }}		{{todo\| review }}

Fredg999: Moved Wikipedia link to new External links section

2021-07-17T17:37:53Z

Moved Wikipedia link to new External links section

← Older revision		Revision as of 17:37, 17 July 2021
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	* [[Interval size measure]]		* [[Interval size measure]]
	* [[Sonance]]		* [[Sonance]]

			== External links ==
	* [[Wikipedia: Interval (music)]]		* [[Wikipedia: Interval (music)]]

← Older revision		Revision as of 23:56, 12 January 2026
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	Human pitch perception is [[Wikipedia:Logarithm#Music\|logarithmic]], therefore an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.		Human pitch perception is [[Wikipedia:Logarithm#Music\|logarithmic]], therefore an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.

	A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its size in cents is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>, unless the interval happens to be an octave or some multiple of an octave. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its cents value may or may not be rational. An interval with rational cents is always irrational, unless it's an octave or some multiple of an octave. ~~But some~~ intervals have both irrational ratios and irrational cents.		A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its size in cents is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>, unless the interval happens to be an octave or some multiple of an octave. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its cents value may or may not be rational. An interval with rational cents is always irrational, unless it's an octave or some multiple of an octave. Some intervals have both irrational ratios and irrational cents.

	Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].		Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].

← Older revision		Revision as of 08:43, 20 October 2024
Line 1:		Line 1:
	{{Wikipedia\|Interval (music)}}		{{Wikipedia\|Interval (music)}}
	An '''interval''' is the difference in [[pitch]] between two notes~~. Since two notes form a [[dyad]], the terms ''interval'' and ''dyad'' are sometimes used interchangeably~~.		An '''interval''' is the difference in [[pitch]] between two notes.

	Human pitch perception is [[Wikipedia:Logarithm#Music\|logarithmic]], therefore an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.		Human pitch perception is [[Wikipedia:Logarithm#Music\|logarithmic]], therefore an interval can be described with a [[ratio\|frequency ratio]] or a logarithmic measure of that ratio, such as [[cent]]s.

	A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its ~~logarithmic measure~~ is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its ~~logarithmic measure~~ may or may not be rational. An interval with a rational ~~logarithmic measure~~ is always irrational, ~~but~~ some intervals have both irrational ratios and ~~logarithmic measures~~.		A '''rational interval''' is an interval whose frequency ratio is a [[Wikipedia:Rational number\|rational number]]. Its size in cents is then necessarily irrational<ref>See example on [[Wikipedia: Irrational number#Logarithms]]. A full proof would rely on the [[Wikipedia: Fundamental theorem of arithmetic\|fundamental theorem of arithmetic]] to generalize the results to all pairs of coprime natural numbers.</ref>, unless the interval happens to be an octave or some multiple of an octave. A [[tuning system]] based exclusively on rational intervals is said to be in [[just intonation]]. Conversely, an '''irrational interval''' is an interval whose frequency ratio is an [[Wikipedia:Irrational number\|irrational number]]. In that case, however, its cents value may or may not be rational. An interval with rational cents is always irrational, unless it's an octave or some multiple of an octave. But some intervals have both irrational ratios and irrational cents.

	Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].		Another property is [[harmonic entropy]], a measure of concordance, which is usually associated with [[sonance\|consonance and dissonance]].

← Older revision		Revision as of 07:35, 30 April 2025
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	* [[Interval size measure]]		* [[Interval size measure]]
	* [[:Category:Interval naming]]		* [[:Category:Interval naming]]
			* [[Negative interval]]

	== References ==		== References ==