Diatonic - Revision history

Unque: Deploying new navbox

2026-08-31T16:29:09Z

Deploying new navbox

← Older revision		Revision as of 16:29, 31 August 2026
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	\| Lydian \|\| LLLsLLs \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|A \|\| style="background-color:#66d"\|P \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|M		\| Lydian \|\| LLLsLLs \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|A \|\| style="background-color:#66d"\|P \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|M
	\|}		\|}
	[[File:The swry.png\|thumb\|362x362px\|The space of 4/3-spanning tetrachords, with Greek genera highlighted]]		{{Navbox MOS}}[[File:The swry.png\|thumb\|362x362px\|The space of 4/3-spanning tetrachords, with Greek genera highlighted]]

	== Greek diatonic scales ==		== Greek diatonic scales ==

Vector at 23:48, 26 March 2026

2026-03-26T23:48:02Z

← Older revision		Revision as of 23:48, 26 March 2026
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	[[File:Piano.png\|thumb\|417x417px\|A diatonic musical keyboard]]		[[File:Piano.png\|thumb\|417x417px\|A diatonic musical keyboard]]
	[[File:MOS diatonic.png\|thumb\|418x418px\|The generation of a MOS diatonic scale from the chain of fifths]]		[[File:MOS diatonic.png\|thumb\|418x418px\|The generation of a MOS diatonic scale from the chain of fifths]]
	'''Diatonic''' is a kind of scale characterized by the division of the [[octave]] into 5 large steps (''L'') and 2 small steps (''s'') in an ''LLsLLLs'' pattern, or any [[rotation]] thereof. The most widespread diatonic is the [[MOS]] form, ''5L 2s'', where the large steps are equally sized and the small steps are also equally sized. When ''diatonic'' is used as an adjective on the wiki to describe something other than a scale, the MOS is what it usually refers to (for example, the [[diatonic major third]] is the major third in the MOS diatonic scale). However, other similar scales may be called diatonic as well.		'''Diatonic''' is a kind of scale characterized by the division of the [[octave]] into 5 large steps (''L'') and 2 small steps (''s'') in an ''LLsLLLs'' pattern, or any [[rotation]] thereof. The most widespread diatonic is the [[MOS]] form, ''5L 2s'', where the large steps are equally sized and the small steps are also equally sized; in general, there can be multiple sizes of large or small step. When ''diatonic'' is used as an adjective on the wiki to describe something other than a scale, the MOS is what it usually refers to (for example, the [[diatonic major third]] is the major third in the MOS diatonic scale). However, other similar scales may be called diatonic as well.
	[[File:Diatonic scales high-rank.png\|thumb\|390x390px\|Various Greek diatonic scales.]]		[[File:Diatonic scales high-rank.png\|thumb\|390x390px\|Various Greek diatonic scales.]]

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	== Greek diatonic scales ==		== Greek diatonic scales ==
			''Main article: [[Tetrachord]]''

	Diatonic may be defined more broadly according to the Greek diatonic genus. In Greek music, a diatonic scale is constructed from identical [[tetrachord]]s spanning a [[perfect fourth]] each, and separated by a [[9/8\|Pythagorean major second]], such that		Diatonic may be defined more broadly according to the Greek diatonic genus. In Greek music, a diatonic scale is constructed from identical [[tetrachord]]s spanning a [[perfect fourth]] each, and separated by a [[9/8\|Pythagorean major second]], such that

Vector at 11:17, 26 March 2026

2026-03-26T11:17:32Z

← Older revision		Revision as of 11:17, 26 March 2026
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	\| Lydian \|\| LLLsLLs \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|A \|\| style="background-color:#66d"\|P \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|M		\| Lydian \|\| LLLsLLs \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|A \|\| style="background-color:#66d"\|P \|\| style="background-color:#66d"\|M \|\| style="background-color:#66d"\|M
	\|}		\|}
			[[File:The swry.png\|thumb\|362x362px\|The space of 4/3-spanning tetrachords, with Greek genera highlighted]]

	== Greek diatonic scales ==		== Greek diatonic scales ==
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	The simplest rank-3 diatonic tunings are those found in [[14edo]] (3-2-1-2-3-2-1) and [[15edo]] (3-2-1-3-2-3-1). Note that in both cases, the largest interval in the tetrachord is exactly half of its width. This is similar to the edge-case found with the tuning of MOS diatonic in 5edo or 7edo.		The simplest rank-3 diatonic tunings are those found in [[14edo]] (3-2-1-2-3-2-1) and [[15edo]] (3-2-1-3-2-3-1). Note that in both cases, the largest interval in the tetrachord is exactly half of its width. This is similar to the edge-case found with the tuning of MOS diatonic in 5edo or 7edo.

			Similarly, the MOS scales [[onyx]] and [[mosh]] with the large step between 4/3 and 3/2 are other edge cases of Greek diatonic scales.

	== Straddle-fifth diatonic scales ==		== Straddle-fifth diatonic scales ==

	A [[straddle-fifth]] system has a sharp and a flat fifth, which combine to create a 9/8 wholetone. So, in those systems, a diatonic scale analogous to the MOS diatonic may be generated by alternating the two fifths. This creates an ''LLmLLLs'' pattern, notably meaning there are multiple varieties of small step, rather than multiple varieties of large step. Again, there are fourteen modes, because, for example, there are again two Ionian modes: ''LLsLLLm'' and ''LLmLLLs''. Note that the perfect fourth is always based on one variety of fifth, and the perfect fifth is always the other.		A [[straddle-fifth]] system has a sharp and a flat fifth, which combine to create a 9/8 wholetone. So, in those systems, a diatonic scale analogous to the MOS diatonic may be generated by alternating the two fifths. This creates an ''LLmLLLs'' pattern, notably meaning there are multiple varieties of small step, rather than multiple varieties of large step. Again, there are fourteen modes, because, for example, there are again two Ionian modes: ''LLsLLLm'' and ''LLmLLLs''. Note that the perfect fourth is always based on one variety of fifth, and the perfect fifth is always the other.

Vector at 01:43, 8 February 2026

2026-02-08T01:43:09Z

← Older revision		Revision as of 01:43, 8 February 2026
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			[[File:Piano.png\|thumb\|417x417px\|A diatonic musical keyboard]]
			[[File:MOS diatonic.png\|thumb\|418x418px\|The generation of a MOS diatonic scale from the chain of fifths]]
	'''Diatonic''' is a kind of scale characterized by the division of the [[octave]] into 5 large steps (''L'') and 2 small steps (''s'') in an ''LLsLLLs'' pattern, or any [[rotation]] thereof. The most widespread diatonic is the [[MOS]] form, ''5L 2s'', where the large steps are equally sized and the small steps are also equally sized. When ''diatonic'' is used as an adjective on the wiki to describe something other than a scale, the MOS is what it usually refers to (for example, the [[diatonic major third]] is the major third in the MOS diatonic scale). However, other similar scales may be called diatonic as well.		'''Diatonic''' is a kind of scale characterized by the division of the [[octave]] into 5 large steps (''L'') and 2 small steps (''s'') in an ''LLsLLLs'' pattern, or any [[rotation]] thereof. The most widespread diatonic is the [[MOS]] form, ''5L 2s'', where the large steps are equally sized and the small steps are also equally sized. When ''diatonic'' is used as an adjective on the wiki to describe something other than a scale, the MOS is what it usually refers to (for example, the [[diatonic major third]] is the major third in the MOS diatonic scale). However, other similar scales may be called diatonic as well.
			[[File:Diatonic scales high-rank.png\|thumb\|390x390px\|Various Greek diatonic scales.]]

	== MOS diatonic ==		== MOS diatonic ==

Inthar: /* Intervals of MOS diatonic */

2025-12-30T21:11:44Z

Intervals of MOS diatonic

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 | Lydian || LLLsLLs || style="background-color:#66d"|M || style="background-color:#66d"|M || style="background-color:#66d"|A || style="background-color:#66d"|P || style="background-color:#66d"|M || style="background-color:#66d"|M
 |}
 == Greek diatonic scales ==

Inthar: /* Intervals of MOS diatonic */

2025-12-30T21:09:14Z

Intervals of MOS diatonic

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 === Intervals of MOS diatonic ===
 ==== Major second ====
 {{Infobox interval|9/8|names=Chromatic semitone, augmented unison|name=Chromatic semitone, augmented unison|Name=Diatonic major second}}

Inthar: /* MOS diatonic */

2025-12-30T21:07:54Z

MOS diatonic

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 | Lydian || LLLsLLs || style="background-color:#66d"|M || style="background-color:#66d"|M || style="background-color:#66d"|A || style="background-color:#66d"|P || style="background-color:#66d"|M || style="background-color:#66d"|M
 |}
 == Greek diatonic scales ==

Vector at 05:25, 27 December 2025

2025-12-27T05:25:37Z

← Older revision		Revision as of 05:25, 27 December 2025
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	'''Diatonic''' is a kind of scale characterized by the division of the [[octave]] into 5 large steps (''L'') and 2 small steps (''s'') in an ''LLsLLLs'' pattern, or any [[rotation]] thereof. The most widespread diatonic is the [[MOS]] form, ''5L 2s'', where the large steps are equally sized and the small steps are also equally sized. However, other similar scales may be called diatonic as well.		'''Diatonic''' is a kind of scale characterized by the division of the [[octave]] into 5 large steps (''L'') and 2 small steps (''s'') in an ''LLsLLLs'' pattern, or any [[rotation]] thereof. The most widespread diatonic is the [[MOS]] form, ''5L 2s'', where the large steps are equally sized and the small steps are also equally sized. When ''diatonic'' is used as an adjective on the wiki to describe something other than a scale, the MOS is what it usually refers to (for example, the [[diatonic major third]] is the major third in the MOS diatonic scale). However, other similar scales may be called diatonic as well.

	== MOS diatonic ==		== MOS diatonic ==

Inthar: /* Dual-fifth diatonic scales */ dual/split -> straddle

2025-12-11T01:01:11Z

Dual-fifth diatonic scales: dual/split -> straddle

← Older revision		Revision as of 01:01, 11 December 2025
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	The simplest rank-3 diatonic tunings are those found in [[14edo]] (3-2-1-2-3-2-1) and [[15edo]] (3-2-1-3-2-3-1). Note that in both cases, the largest interval in the tetrachord is exactly half of its width. This is similar to the edge-case found with the tuning of MOS diatonic in 5edo or 7edo.		The simplest rank-3 diatonic tunings are those found in [[14edo]] (3-2-1-2-3-2-1) and [[15edo]] (3-2-1-3-2-3-1). Note that in both cases, the largest interval in the tetrachord is exactly half of its width. This is similar to the edge-case found with the tuning of MOS diatonic in 5edo or 7edo.

	== ~~Dual~~-fifth diatonic scales ==		== Straddle-fifth diatonic scales ==

	A [[~~dual~~-fifth]] system has a sharp and a flat fifth, which combine to create a 9/8 wholetone. So, in those systems, a diatonic scale analogous to the MOS diatonic may be generated by alternating the two fifths. This creates an ''LLmLLLs'' pattern, notably meaning there are multiple varieties of small step, rather than multiple varieties of large step. Again, there are fourteen modes, because, for example, there are again two Ionian modes: ''LLsLLLm'' and ''LLmLLLs''. Note that the perfect fourth is always based on one variety of fifth, and the perfect fifth is always the other.		A [[straddle-fifth]] system has a sharp and a flat fifth, which combine to create a 9/8 wholetone. So, in those systems, a diatonic scale analogous to the MOS diatonic may be generated by alternating the two fifths. This creates an ''LLmLLLs'' pattern, notably meaning there are multiple varieties of small step, rather than multiple varieties of large step. Again, there are fourteen modes, because, for example, there are again two Ionian modes: ''LLsLLLm'' and ''LLmLLLs''. Note that the perfect fourth is always based on one variety of fifth, and the perfect fifth is always the other.

Vector at 00:46, 11 December 2025

2025-12-11T00:46:40Z

← Older revision		Revision as of 00:46, 11 December 2025
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	Diatonic may be defined more broadly according to the Greek diatonic genus. In Greek music, a diatonic scale is constructed from identical [[tetrachord]]s spanning a [[perfect fourth]] each, and separated by a [[9/8\|Pythagorean major second]], such that		Diatonic may be defined more broadly according to the Greek diatonic genus. In Greek music, a diatonic scale is constructed from identical [[tetrachord]]s spanning a [[perfect fourth]] each, and separated by a [[9/8\|Pythagorean major second]], such that

	a) the largest interval in the tetrachord is ~~less than~~ half of its total span		a) the largest interval in the tetrachord is at most half of its total span

	b) the middle interval in the tetrachord is not the smallest.		b) the middle interval in the tetrachord is not the smallest.
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	Another example of a Greek diatonic is the equable diatonic, which is a tuning where ''C'' is 9/8, ''B'' is 10/9, ''A'' is 11/10, and ''s'' is 12/11. This has the property of being easily expressible as a [[Otonality and utonality\|utonal]] sequence 1/(18:20:22:24:27:30:33:36).		Another example of a Greek diatonic is the equable diatonic, which is a tuning where ''C'' is 9/8, ''B'' is 10/9, ''A'' is 11/10, and ''s'' is 12/11. This has the property of being easily expressible as a [[Otonality and utonality\|utonal]] sequence 1/(18:20:22:24:27:30:33:36).

			The simplest rank-3 diatonic tunings are those found in [[14edo]] (3-2-1-2-3-2-1) and [[15edo]] (3-2-1-3-2-3-1). Note that in both cases, the largest interval in the tetrachord is exactly half of its width. This is similar to the edge-case found with the tuning of MOS diatonic in 5edo or 7edo.

	== Dual-fifth diatonic scales ==		== Dual-fifth diatonic scales ==

	A [[dual-fifth]] system has a sharp and a flat fifth, which combine to create a 9/8 wholetone. So, in those systems, a diatonic scale analogous to the MOS diatonic may be generated by alternating the two fifths. This creates an ''LLmLLLs'' pattern, notably meaning there are multiple varieties of small step, rather than multiple varieties of large step. Again, there are fourteen modes, because, for example, there are again two Ionian modes: ''LLsLLLm'' and ''LLmLLLs''. Note that the perfect fourth is always based on one variety of fifth, and the perfect fifth is always the other.		A [[dual-fifth]] system has a sharp and a flat fifth, which combine to create a 9/8 wholetone. So, in those systems, a diatonic scale analogous to the MOS diatonic may be generated by alternating the two fifths. This creates an ''LLmLLLs'' pattern, notably meaning there are multiple varieties of small step, rather than multiple varieties of large step. Again, there are fourteen modes, because, for example, there are again two Ionian modes: ''LLsLLLm'' and ''LLmLLLs''. Note that the perfect fourth is always based on one variety of fifth, and the perfect fifth is always the other.