Cluster MOS - Revision history

Lériendil at 14:55, 13 June 2025

2025-06-13T14:55:37Z

← Older revision		Revision as of 14:55, 13 June 2025
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	Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.		Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.

			{{todo\|add more detail\|inline=1}}

	== Examples of cluster MOSes ==		== Examples of cluster MOSes ==

Keenan Pepper: use table header rows

2024-04-20T22:26:49Z

use table header rows

← Older revision		Revision as of 22:26, 20 April 2024
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	{\| class="wikitable"		{\| class="wikitable"
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	\| \| Steps		! \| Steps
	\| \| "Diminished"		! \| "Diminished"
	\| \| "Minor"		! \| "Minor"
	\| \| "Major"		! \| "Major"
	\| \| "Augmented"		! \| "Augmented"
	\|-		\|-
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	{\| class="wikitable"		{\| class="wikitable"
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	\| \| Steps		! \| Steps
	\| \|		! \|
	\| \| "Diminished"		! \| "Diminished"
	\| \| "Minor"		! \| "Minor"
	\| \| "Major"		! \| "Major"
	\| \| "Augmented"		! \| "Augmented"
	\| \|		! \|
	\|-		\|-
	\| \| 1		\| \| 1
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	{\| class="wikitable"		{\| class="wikitable"
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	\| \|		! \|
	\| \| "Diminished"		! \| "Diminished"
	\| \| "Minor"		! \| "Minor"
	\| \| "Major"		! \| "Major"
	\| \| "Augmented"		! \| "Augmented"
	\| \|		! \|
	\| \|		! \|
	\|-		\|-
	\| \| 1		\| \| 1
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	{\| class="wikitable"		{\| class="wikitable"
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	\| \| "Diminished"		! \| "Diminished"
	\| \| "Minor"		! \| "Minor"
	\| \| "Major"		! \| "Major"
	\| \| "Augmented"		! \| "Augmented"
	\|-		\|-
	\| \| 1		\| \| 1
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	{\| class="wikitable"		{\| class="wikitable"
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	\| \| Steps		! \| Steps
	\| \|		! \|
	\| \| "Diminished"		! \| "Diminished"
	\| \| "Minor"		! \| "Minor"
	\| \| "Major"		! \| "Major"
	\| \| "Augmented"		! \| "Augmented"
	\| \|		! \|
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	\| \| Steps		! \| Steps
	\| \| "Diminished"		! \| "Diminished"
	\| \| "Minor"		! \| "Minor"
	\| \| "Major"		! \| "Major"
	\| \| "Augmented"		! \| "Augmented"
	\|-		\|-
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	{\| class="wikitable"		{\| class="wikitable"
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	\| \| Steps		! \| Steps
	\| \|		! \|
	\| \| "Diminished"		! \| "Diminished"
	\| \| "Minor"		! \| "Minor"
	\| \| "Major"		! \| "Major"
	\| \| "Augmented"		! \| "Augmented"
	\| \|		! \|
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	\| \| "Diminished"		! \| "Diminished"
	\| \| "Minor"		! \| "Minor"
	\| \| "Major"		! \| "Major"
	\| \| "Augmented"		! \| "Augmented"
	\| \|		! \|
	\|-		\|-
	\| \| 1		\| \| 1

BudjarnLambeth: Moved from category "MOS" to "MOS scales"

2023-04-28T09:39:07Z

Moved from category "MOS" to "MOS scales"

← Older revision		Revision as of 09:39, 28 April 2023
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	\| \| 9/5		\| \| 9/5
	\| \| 11/6		\| \| 11/6
	\|}		\|}

	=== Modus (of the tetracot family) ===		=== Modus (of the tetracot family) ===
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	[[Category:Rank 2]]		[[Category:Rank 2]]
	[[Category:MOS]]		[[Category:MOS scales]]

Xenllium at 09:40, 13 March 2022

2022-03-13T09:40:03Z

Show changes

Keenan Pepper: categories

2021-04-24T19:47:08Z

Inthar: /* Examples of cluster temperaments */

2021-04-01T04:07:11Z

Examples of cluster temperaments

← Older revision		Revision as of 04:07, 1 April 2021
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	Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.		Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.

			== Examples of cluster MOSes ==
			[[4L 3s#Parasoft\|Parasoft smitonic]] is a cluster MOS.
	== Examples of cluster temperaments ==		== Examples of cluster temperaments ==

Inthar at 04:06, 1 April 2021

2021-04-01T04:06:41Z

← Older revision		Revision as of 04:06, 1 April 2021
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	A '''cluster MOS''' or '''cluster scale''' is a very particular kind of [[MOS]]-based system (i.e. a system based on stacks of [[period]]s and [[generator]]s) whose generator is quite near a rational fraction of an octave. Therefore some MOS generated by the generator is quasi-equal (which should be reasonably sized for it to be a good cluster ~~temperament~~, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma ("diminished", "minor", "major", "augmented"...) include many nearby interval colors that are individually recognizable, yet conceptually grouped into the same category (or "cluster") because they're so close.		A '''cluster MOS''' or '''cluster scale''' is a very particular kind of [[MOS]]-based system (i.e. a system based on stacks of [[period]]s and [[generator]]s) whose generator is quite near a rational fraction of an octave. Therefore some MOS generated by the generator is quasi-equal (which should be reasonably sized for it to be a good cluster MOS, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma ("diminished", "minor", "major", "augmented"...) include many nearby interval colors that are individually recognizable, yet conceptually grouped into the same category (or "cluster") because they're so close.

	A '''cluster temperament''' (named by [[Keenan_Pepper\|Keenan Pepper]]) is a rank-2 [[regular temperament]] interpretation of a cluster MOS. This means that in a cluster temperament, many different versions of each interval, differing by a chroma, these colors ''represent nearby JI intervals'' specifically (because a temperament is a JI interpretation of MOS generator chains separated by the period).		A '''cluster temperament''' (named by [[Keenan_Pepper\|Keenan Pepper]]) is a rank-2 [[regular temperament]] interpretation of a cluster MOS. This means that in a cluster temperament, many different versions of each interval, differing by a chroma, these colors ''represent nearby JI intervals'' specifically (because a temperament is a JI interpretation of MOS generator chains separated by the period).

Inthar at 00:56, 1 April 2021

2021-04-01T00:56:05Z

← Older revision		Revision as of 00:56, 1 April 2021
Line 1:		Line 1:
	A '''cluster MOS''' or '''cluster scale''' is a very particular kind of [[MOS]]-based system (i.e. a system based on stacks of [[period]]s and [[generator]]s) whose generator is quite near a rational fraction of an octave. Therefore some MOS generated by the generator is quasi-equal (which should be reasonably sized for it to be a good cluster temperament, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma ("diminished", "minor", "major", "augmented"...) include many nearby interval colors that are individually recognizable, yet conceptually grouped into the same category (or "cluster") because they're so close.		A '''cluster MOS''' or '''cluster scale''' is a very particular kind of [[MOS]]-based system (i.e. a system based on stacks of [[period]]s and [[generator]]s) whose generator is quite near a rational fraction of an octave. Therefore some MOS generated by the generator is quasi-equal (which should be reasonably sized for it to be a good cluster temperament, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma ("diminished", "minor", "major", "augmented"...) include many nearby interval colors that are individually recognizable, yet conceptually grouped into the same category (or "cluster") because they're so close.

	A '''cluster temperament''' (named by [[Keenan_Pepper\|Keenan Pepper]]) is a rank-2 [[regular temperament]] interpretation of a cluster MOS. ~~But not only~~ that; in a cluster temperament, many different versions of each interval, differing by a chroma, these colors ''represent nearby JI intervals'' specifically (because a ~~temmperament~~ is a JI interpretation of MOS generator chains separated by the period).		A '''cluster temperament''' (named by [[Keenan_Pepper\|Keenan Pepper]]) is a rank-2 [[regular temperament]] interpretation of a cluster MOS. This means that in a cluster temperament, many different versions of each interval, differing by a chroma, these colors ''represent nearby JI intervals'' specifically (because a temperament is a JI interpretation of MOS generator chains separated by the period).

	An example of something that is '''not''' a cluster temperament is [[Amity\|amity]], because although the amity generator is within 4 cents of 2\7, making amity[7] near equal, amity is too complex of a temperament and most of the intervals differing by a chroma do not represent simple JI intervals at all. For example, the list of amity "thirds" includes ...6/5 (339.5) (363.2) 5/4... where the intervals given in cents are not representable as simple JI intervals (243/200 and 100/81 are about as simple as you can get).		An example of something that is '''not''' a cluster temperament is [[Amity\|amity]], because although the amity generator is within 4 cents of 2\7, making amity[7] near equal, amity is too complex of a temperament and most of the intervals differing by a chroma do not represent simple JI intervals at all. For example, the list of amity "thirds" includes ...6/5 (339.5) (363.2) 5/4... where the intervals given in cents are not representable as simple JI intervals (243/200 and 100/81 are about as simple as you can get).

Inthar: /* Examples of cluster temperaments = */

2021-04-01T00:55:16Z

Examples of cluster temperaments =

← Older revision		Revision as of 00:55, 1 April 2021
Line 9:		Line 9:
	Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.		Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.

	== Examples of cluster temperaments ===		== Examples of cluster temperaments ==

	=== Slendric ===		=== Slendric ===

Inthar: /* Examples */

2021-04-01T00:55:05Z

Examples

← Older revision		Revision as of 00:55, 1 April 2021
Line 9:		Line 9:
	Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.		Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.

	=Examples=		== Examples of cluster temperaments ===

	==Slendric==		=== Slendric ===
	Main article: [[Slendric\|Slendric]]		Main article: [[Slendric\|Slendric]]

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	Slendric has two quite different extensions that are both also cluster scales:		Slendric has two quite different extensions that are both also cluster scales:

	===Mothra===		====Mothra====
	Main article: [[Mothra\|Mothra]]		Main article: [[Mothra\|Mothra]]

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	*[http://sevish.com/scaleworkshop/index.htm?name=31edo%20mothra&data=38.70967741935484%0A77.41935483870968%0A116.12903225806451%0A154.83870967741936%0A193.5483870967742%0A232.25806451612902%0A270.9677419354839%0A309.6774193548387%0A348.38709677419354%0A387.0967741935484%0A425.80645161290323%0A464.51612903225805%0A503.2258064516129%0A541.9354838709678%0A580.6451612903226%0A619.3548387096774%0A658.0645161290323%0A696.7741935483871%0A735.483870967742%0A774.1935483870968%0A812.9032258064516%0A851.6129032258065%0A890.3225806451613%0A929.0322580645161%0A967.741935483871%0A1006.4516129032259%0A1045.1612903225807%0A1083.8709677419356%0A1122.5806451612902%0A1161.2903225806451%0A1200.&vert=-5&horiz=6&midi=16 Play Mothra in 31edo]		*[http://sevish.com/scaleworkshop/index.htm?name=31edo%20mothra&data=38.70967741935484%0A77.41935483870968%0A116.12903225806451%0A154.83870967741936%0A193.5483870967742%0A232.25806451612902%0A270.9677419354839%0A309.6774193548387%0A348.38709677419354%0A387.0967741935484%0A425.80645161290323%0A464.51612903225805%0A503.2258064516129%0A541.9354838709678%0A580.6451612903226%0A619.3548387096774%0A658.0645161290323%0A696.7741935483871%0A735.483870967742%0A774.1935483870968%0A812.9032258064516%0A851.6129032258065%0A890.3225806451613%0A929.0322580645161%0A967.741935483871%0A1006.4516129032259%0A1045.1612903225807%0A1083.8709677419356%0A1122.5806451612902%0A1161.2903225806451%0A1200.&vert=-5&horiz=6&midi=16 Play Mothra in 31edo]

	===Rodan===		====Rodan====
	Main article: [[Rodan\|Rodan]]		Main article: [[Rodan\|Rodan]]

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	\|}		\|}

	==Modus (of the tetracot family)==		=== Modus (of the tetracot family) ===
	Main article: [[Modus\|Modus]]		Main article: [[Modus\|Modus]]

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	* [http://sevish.com/scaleworkshop/index.htm?name=34edo%20modus&data=35.294117647058826%0A70.58823529411765%0A105.88235294117648%0A141.1764705882353%0A176.47058823529414%0A211.76470588235296%0A247.05882352941177%0A282.3529411764706%0A317.64705882352945%0A352.9411764705883%0A388.2352941176471%0A423.5294117647059%0A458.82352941176475%0A494.11764705882354%0A529.4117647058824%0A564.7058823529412%0A600.%0A635.2941176470589%0A670.5882352941177%0A705.8823529411766%0A741.1764705882354%0A776.4705882352941%0A811.764705882353%0A847.0588235294118%0A882.3529411764706%0A917.6470588235295%0A952.9411764705883%0A988.2352941176471%0A1023.529411764706%0A1058.8235294117649%0A1094.1176470588236%0A1129.4117647058824%0A1164.7058823529412%0A1200.&vert=-4&horiz=5 Play Modus in 34edo]		* [http://sevish.com/scaleworkshop/index.htm?name=34edo%20modus&data=35.294117647058826%0A70.58823529411765%0A105.88235294117648%0A141.1764705882353%0A176.47058823529414%0A211.76470588235296%0A247.05882352941177%0A282.3529411764706%0A317.64705882352945%0A352.9411764705883%0A388.2352941176471%0A423.5294117647059%0A458.82352941176475%0A494.11764705882354%0A529.4117647058824%0A564.7058823529412%0A600.%0A635.2941176470589%0A670.5882352941177%0A705.8823529411766%0A741.1764705882354%0A776.4705882352941%0A811.764705882353%0A847.0588235294118%0A882.3529411764706%0A917.6470588235295%0A952.9411764705883%0A988.2352941176471%0A1023.529411764706%0A1058.8235294117649%0A1094.1176470588236%0A1129.4117647058824%0A1164.7058823529412%0A1200.&vert=-4&horiz=5 Play Modus in 34edo]

	==Miracle==		=== Miracle ===
	Main article: [[Miracle\|Miracle]]		Main article: [[Miracle\|Miracle]]

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	\|}		\|}

	==Porcupine(fish)==		=== Porcupine(fish) ===
	Main article: [[Porcupine\|Porcupine]]		Main article: [[Porcupine\|Porcupine]]

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	\|}		\|}

	==17-limit valentino==		=== 17-limit valentino ===
	Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150		Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150

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	\|}		\|}

	==2.3.5.11.13 hitchcock==		=== 2.3.5.11.13 hitchcock ===
	Unlike amity itself, this 2.3.5.11.13 amity extension is a cluster temperament because the intervals between 6/5 and 5/4 are mapped to 11/9 and 16/13.		Unlike amity itself, this 2.3.5.11.13 amity extension is a cluster temperament because the intervals between 6/5 and 5/4 are mapped to 11/9 and 16/13.

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			[[Category:Rank 2]]
			[[Category:MOS]]