Kleisma - Revision history

FloraC: + reference

2026-07-14T14:57:08Z

+ reference

← Older revision		Revision as of 14:57, 14 July 2026
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	== As an interval region ==		== As an interval region ==
	As an interval region, the kleisma is an interval of about 1/3 of a [[comma #As an interval region\|comma]], roughly the size of the interval 15625/15552. In [[Sagittal notation]], a kleisma is specifically defined as between half of the 200-comma {{monzo\| 317 -200 }} and half of the [[Pythagorean comma]] {{monzo\| -19 12 }}, about 4.5{{c}} to 11.7{{c}}.		As an interval region, the kleisma is an interval of about 1/3 of a [[comma #As an interval region\|comma]], roughly the size of the interval 15625/15552. In [[Sagittal notation]], a kleisma is specifically defined as between half of the 200-comma {{monzo\| 317 -200 }} and half of the [[Pythagorean comma]] {{monzo\| -19 12 }}, about 4.5{{c}} to 11.7{{c}}<ref>[https://sagittal.org/sagittal.pdf ''Sagittal – A Microtonal Notation System''] by [[George Secor\|George D. Secor]] and [[Dave Keenan\|David C. Keenan]]</ref>.

	The kleisma is significant as it is a limit of intonational fidelity when playing on some physical instruments. That is, on free-pitch instruments, there is a level of precision to which one can be expected to play a note or interval "correctly": that level of precision is the kleisma.{{cn}}		The kleisma is significant as it is a limit of intonational fidelity when playing on some physical instruments. That is, on free-pitch instruments, there is a level of precision to which one can be expected to play a note or interval "correctly": that level of precision is the kleisma.{{cn}}
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	The [[19-comma]] is sometimes called ''Pythagorean kleisma'' for this reason.		The [[19-comma]] is sometimes called ''Pythagorean kleisma'' for this reason.

	The kleisma can be generalized to any [[mos scale]] as the '''moskleisma''', defined as \|2L - 3s\|, i.e. the distance between two large steps and three small steps.		The kleisma can be generalized to any [[mos scale]] as the '''moskleisma''', defined as \|2L - 3s\|, i.e. the distance between two large steps and three small steps.

			== References ==

	[[Category:Terms]]		[[Category:Terms]]
	[[Category:MOS scale]]		[[Category:MOS scale]]

FloraC: Un-disambiguate this page, following diesis

2026-07-12T13:02:37Z

Un-disambiguate this page, following diesis

← Older revision		Revision as of 13:02, 12 July 2026
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	~~"Kleisma" is a term with several related uses in music theory, to refer to small comma-sized intervals or intervals with a certain function in a scale.~~{{Wikipedia}}		{{Wikipedia}}
	~~The '''kleisma''' most commonly refers to:~~
	* The interval [[15625/15552]];
	* By extension, a melodic unit of about the size of 15625/15552 (≈ 8.1{{cent}}). See [[Kleisma (interval region)]];
	* In scale theory, the difference between a [[chroma]] and a [[Diesis (scale theory)\|diesis]], more precisely a '''moskleisma''', as used in [[extended meantone notation]].

	{{~~Disambiguation~~}}		The '''kleisma''' is an interval that has several related definitions. Most commonly, it refers to the [[just interval]] [[15625/15552]], but it can refer to other small comma-sized intervals or intervals with a certain function in a scale.

			== As an interval region ==
			As an interval region, the kleisma is an interval of about 1/3 of a [[comma #As an interval region\|comma]], roughly the size of the interval 15625/15552. In [[Sagittal notation]], a kleisma is specifically defined as between half of the 200-comma {{monzo\| 317 -200 }} and half of the [[Pythagorean comma]] {{monzo\| -19 12 }}, about 4.5{{c}} to 11.7{{c}}.

			The kleisma is significant as it is a limit of intonational fidelity when playing on some physical instruments. That is, on free-pitch instruments, there is a level of precision to which one can be expected to play a note or interval "correctly": that level of precision is the kleisma.{{cn}}

			Other just intervals that may be considered kleismas include [[225/224]], [[243/242]], [[1029/1024]], [[16875/16807]], and [[65536/65219]].

			== As a diatonic interval category ==
			In the [[5L 2s\|diatonic]] scale, the kleisma is the distance between the [[chroma]] and the [[diesis #As a diatonic interval category\|diesis]]. This usage is most relevant in [[meantone]] tunings, where it is small and functions similarly to the diesis. It spans nineteen perfect fifths and vanishes in [[19edo]]. It is used in [[extended meantone notation]].

			The [[19-comma]] is sometimes called ''Pythagorean kleisma'' for this reason.

			The kleisma can be generalized to any [[mos scale]] as the '''moskleisma''', defined as \|2L - 3s\|, i.e. the distance between two large steps and three small steps.

			[[Category:Terms]]
			[[Category:MOS scale]]

VectorGraphics at 08:06, 16 April 2025

2025-04-16T08:06:38Z

← Older revision		Revision as of 08:06, 16 April 2025
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	"Kleisma" is a term with several related uses in music theory, to refer to intervals ~~of a certain size~~ or ~~that have~~ a certain function.{{Wikipedia}}		"Kleisma" is a term with several related uses in music theory, to refer to small comma-sized intervals or intervals with a certain function in a scale.{{Wikipedia}}
	The '''kleisma''' most commonly refers to:		The '''kleisma''' most commonly refers to:
	* The interval [[15625/15552]];		* The interval [[15625/15552]];

VectorGraphics at 08:06, 16 April 2025

2025-04-16T08:06:18Z

← Older revision		Revision as of 08:06, 16 April 2025
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	{{Wikipedia}}		"Kleisma" is a term with several related uses in music theory, to refer to intervals of a certain size or that have a certain function.{{Wikipedia}}
	The '''kleisma''' most commonly refers to:		The '''kleisma''' most commonly refers to:
	* The interval [[15625/15552]];		* The interval [[15625/15552]];

FloraC: Undo revision 192281 by VectorGraphics (talk). Sense 3 of the term has nothing to do with the size. diesis is also extremely unclear here

2025-04-15T21:00:59Z

Undo revision 192281 by VectorGraphics (talk). Sense 3 of the term has nothing to do with the size. *diesis* is also extremely unclear here

← Older revision		Revision as of 21:00, 15 April 2025
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	~~A '''kleisma''' is a kind of small [[comma]] or diesis.~~{{Wikipedia}}		{{Wikipedia}}
	The kleisma most commonly refers to:		The '''kleisma''' most commonly refers to:
	* The interval [[15625/15552]];		* The interval [[15625/15552]];
	* By extension, a melodic unit of about the size of 15625/15552 (≈ 8.1{{cent}}). See [[Kleisma (interval region)]];		* By extension, a melodic unit of about the size of 15625/15552 (≈ 8.1{{cent}}). See [[Kleisma (interval region)]];

VectorGraphics at 19:23, 15 April 2025

2025-04-15T19:23:21Z

← Older revision		Revision as of 19:23, 15 April 2025
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	{{Wikipedia}}		A '''kleisma''' is a kind of small [[comma]] or diesis.{{Wikipedia}}
	The ~~'''~~kleisma~~'''~~ most commonly refers to:		The kleisma most commonly refers to:
	* The interval [[15625/15552]];		* The interval [[15625/15552]];
	* By extension, a melodic unit of about the size of 15625/15552 (≈ 8.1{{cent}}). See [[Kleisma (interval region)]];		* By extension, a melodic unit of about the size of 15625/15552 (≈ 8.1{{cent}}). See [[Kleisma (interval region)]];

FloraC: Split the interval region sense to a separate page

2025-03-14T11:27:05Z

Split the interval region sense to a separate page

@@ Line 1: / Line 1: @@
-{{Infobox interval region
+{{Wikipedia}}
-|Name=Kleisma
+The '''kleisma''' most commonly refers to:
-|Cents lower=6
+* The interval [[15625/15552]];
-|Cents upper=9
+* By extension, a melodic unit of about the size of 15625/15552 (≈ 8.1{{cent}}). See [[Kleisma (interval region)]];
-|JI intervals=15625/15552, 243/242, 225/224, 1029/1024, 16875/16807, 65536/65219
+* In scale theory, the difference between a [[chroma]] and a [[Diesis (scale theory)|diesis]], more precisely a '''moskleisma''', as used in [[extended meantone notation]].
-As an interval region, the kleisma is significant as it is a limit of intonational fidelity when playing on some physical instruments. That is, on free-pitch instruments, there is a level of precision to which one can be expected to play a note or interval "correctly": that level of precision is the kleisma. Another significance is that a lot of commas are about 3-4 kleismas in size.
+{{Disambiguation}}

VectorGraphics at 09:26, 14 March 2025

2025-03-14T09:26:13Z

← Older revision		Revision as of 09:26, 14 March 2025
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	\|Cents lower=6		\|Cents lower=6
	\|Cents upper=9		\|Cents upper=9
	\|JI intervals=15625/15552, 225/224, 1029/1024, 16875/16807, 65536/65219		\|JI intervals=15625/15552, 243/242, 225/224, 1029/1024, 16875/16807, 65536/65219
	\|Lower region=[[Unnoticeable comma]]		\|Lower region=[[Unnoticeable comma]]
	\|Superregions=[[Small comma]] <br> [[Comma (interval region)\|Comma]] <br> [[Comma and diesis]]		\|Superregions=[[Small comma]] <br> [[Comma (interval region)\|Comma]] <br> [[Comma and diesis]]

VectorGraphics at 07:29, 14 March 2025

2025-03-14T07:29:23Z

← Older revision		Revision as of 07:29, 14 March 2025
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	\|JI intervals=15625/15552, 225/224, 1029/1024, 16875/16807, 65536/65219		\|JI intervals=15625/15552, 225/224, 1029/1024, 16875/16807, 65536/65219
	\|Lower region=[[Unnoticeable comma]]		\|Lower region=[[Unnoticeable comma]]
	\|Superregions=[[Comma (interval region)\|Comma]] <br> [[Comma and diesis]]		\|Superregions=[[Small comma]] <br> [[Comma (interval region)\|Comma]] <br> [[Comma and diesis]]
	\|Higher region=[[Small comma]]}}{{Wikipedia}}		\|Higher region=[[Small comma]]}}{{Wikipedia}}
	A '''kleisma''' is an interval of about 8.1 cents, roughly the size of the interval [[15625/15552]], which is called a kleisma in just intonation.		A '''kleisma''' is an interval of about 8.1 cents, roughly the size of the interval [[15625/15552]], which is called a kleisma in just intonation.

VectorGraphics at 07:29, 14 March 2025

2025-03-14T07:29:02Z

← Older revision		Revision as of 07:29, 14 March 2025
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	\|Superregions=[[Comma (interval region)\|Comma]] <br> [[Comma and diesis]]		\|Superregions=[[Comma (interval region)\|Comma]] <br> [[Comma and diesis]]
	\|Higher region=[[Small comma]]}}{{Wikipedia}}		\|Higher region=[[Small comma]]}}{{Wikipedia}}
	A '''kleisma''' is an interval of about 8.1 cents, roughly the size of the interval [[15625/15552]], which is called a kleisma in just intonation.\		A '''kleisma''' is an interval of about 8.1 cents, roughly the size of the interval [[15625/15552]], which is called a kleisma in just intonation.

	As an interval region, the kleisma is significant as it is a limit of intonational fidelity when playing on some physical instruments. That is, on free-pitch instruments, there is a level of precision to which one can be expected to play a note or interval "correctly": that level of precision is the kleisma.		As an interval region, the kleisma is significant as it is a limit of intonational fidelity when playing on some physical instruments. That is, on free-pitch instruments, there is a level of precision to which one can be expected to play a note or interval "correctly": that level of precision is the kleisma. Another significance is that a lot of commas are about 3-4 kleismas in size.

	Kleismas belong to the larger interval region of [[Comma (interval region)\|commas]], which are part of the [[Comma and diesis\|"comma and diesis"]] category.		Kleismas belong to the larger interval region of [[Comma (interval region)\|commas]], which are part of the [[Comma and diesis\|"comma and diesis"]] category.

Kleisma - Revision history

FloraC: + reference

FloraC: Un-disambiguate this page, following diesis

VectorGraphics at 08:06, 16 April 2025

VectorGraphics at 08:06, 16 April 2025

FloraC: Undo revision 192281 by VectorGraphics (talk). Sense 3 of the term has nothing to do with the size. *diesis* is also extremely unclear here

VectorGraphics at 19:23, 15 April 2025

FloraC: Split the interval region sense to a separate page

VectorGraphics at 09:26, 14 March 2025

VectorGraphics at 07:29, 14 March 2025

VectorGraphics at 07:29, 14 March 2025

FloraC: Undo revision 192281 by VectorGraphics (talk). Sense 3 of the term has nothing to do with the size. diesis is also extremely unclear here