15625/15552 - Revision history

Hstraub at 10:49, 16 February 2026

2026-02-16T10:49:35Z

← Older revision		Revision as of 10:49, 16 February 2026
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	{{interwiki		{{interwiki
	\| de = 15625		\| de = 15625/15552
	\| en = 15552		\| en = 15625/15552
	\| es =		\| es =
	\| ja =		\| ja =

Hstraub: Link to German

2026-02-16T10:49:04Z

Link to German

← Older revision		Revision as of 10:49, 16 February 2026
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			{{interwiki
			\| de = 15625
			\| en = 15552
			\| es =
			\| ja =
			}}
	{{Infobox Interval		{{Infobox Interval
	\| Ratio = 15625/15552		\| Ratio = 15625/15552

Lucius Chiaraviglio: Equates stack of three 25/24 to 9/8

2025-09-25T22:20:26Z

Equates stack of three 25/24 to 9/8

← Older revision		Revision as of 22:20, 25 September 2025
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	{{Wikipedia\|Kleisma}}		{{Wikipedia\|Kleisma}}

	'''15625/15552''', which is sometimes called the '''kleisma''', is the [[small comma\|small]] [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], or a stack of five 6/5s with [[5/2]]. It is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]), which is also known as the diminished comma. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[square superparticular #Glossary\|S-expression]] of S25<sup>2</sup> × S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).		'''15625/15552''', which is sometimes called the '''kleisma''', is the [[small comma\|small]] [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], or a stack of five 6/5s with [[5/2]], or a stack of three diptolemaic chromatic semitones ([[25/24]]) with the Pythagorean whole tone ([[9/8]]). It is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]), which is also known as the diminished comma. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[square superparticular #Glossary\|S-expression]] of S25<sup>2</sup> × S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).

	== Temperaments ==		== Temperaments ==

FloraC: Fix linking

2025-08-27T13:30:30Z

Fix linking

← Older revision		Revision as of 13:30, 27 August 2025
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	== Temperaments ==		== Temperaments ==
	This comma is tempered out in the [[kleismic]] temperament. See [[Kleismic family]] for the rank-2 temperament family where it is tempered out and [[~~Kleismic rank three family\|~~Kleismic rank-3 family]] for the rank-3 temperament family where it is tempered out.		This comma is tempered out in the [[kleismic]] temperament. See [[Kleismic family]] for the rank-2 temperament family where it is tempered out and [[Kleismic rank-3 family]] for the rank-3 temperament family where it is tempered out.

	== Etymology ==		== Etymology ==

Fitzgerald Lee: updated temperaments section; combined two clauses into one sentence

2025-08-05T07:53:15Z

updated temperaments section; combined two clauses into one sentence

← Older revision		Revision as of 07:53, 5 August 2025
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	== Temperaments ==		== Temperaments ==
	This comma is tempered out in the [[~~hanson~~]] temperament. See [[Kleismic family]] for the rank-2 temperament family where it is tempered out~~. See~~ [[Kleismic rank three family\|Kleismic rank-3 family]] for the rank-3 temperament family where it is tempered out.		This comma is tempered out in the [[kleismic]] temperament. See [[Kleismic family]] for the rank-2 temperament family where it is tempered out and [[Kleismic rank three family\|Kleismic rank-3 family]] for the rank-3 temperament family where it is tempered out.

	== Etymology ==		== Etymology ==

Fitzgerald Lee: Added comma interpretation, split lengthened sentence in two, added other name for 648/625

2025-08-05T01:42:33Z

Added comma interpretation, split lengthened sentence in two, added other name for 648/625

← Older revision		Revision as of 01:42, 5 August 2025
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	{{Wikipedia\|Kleisma}}		{{Wikipedia\|Kleisma}}

	'''15625/15552''', which is sometimes called the '''kleisma''', is the [[small comma\|small]] [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], ~~and~~ is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]). Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[square superparticular #Glossary\|S-expression]] of S25<sup>2</sup> × S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).		'''15625/15552''', which is sometimes called the '''kleisma''', is the [[small comma\|small]] [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], or a stack of five 6/5s with [[5/2]]. It is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]), which is also known as the diminished comma. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[square superparticular #Glossary\|S-expression]] of S25<sup>2</sup> × S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).

	== Temperaments ==		== Temperaments ==

FloraC: +etymology; +external link

2024-11-07T14:18:13Z

+etymology; +external link

← Older revision		Revision as of 14:18, 7 November 2024
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	== Temperaments ==		== Temperaments ==
	This comma is tempered out in the [[hanson]] temperament. See [[Kleismic family]] for the rank-2 temperament family where it is tempered out. See [[Kleismic rank three family\|Kleismic rank-3 family]] for the rank-3 temperament family where it is tempered out.		This comma is tempered out in the [[hanson]] temperament. See [[Kleismic family]] for the rank-2 temperament family where it is tempered out. See [[Kleismic rank three family\|Kleismic rank-3 family]] for the rank-3 temperament family where it is tempered out.

			== Etymology ==
			This comma was named by {{w\|Shohé Tanaka}} in 1890.

	== See also ==		== See also ==
	* [[Kleisma]] (disambiguation page)		* [[Kleisma]] (disambiguation page)

			== External links ==
			* [http://tonalsoft.com/enc/k/kleisma.aspx Tonalsoft Encyclopedia \| ''Kleisma'']

	[[Category:Kleismic]]		[[Category:Kleismic]]
	[[Category:Commas named by translating something into another language]]		[[Category:Commas named by translating something into another language]]

FloraC: +temperaments section

2024-11-07T13:44:41Z

+temperaments section

← Older revision		Revision as of 13:44, 7 November 2024
Line 7:		Line 7:
	{{Wikipedia\|Kleisma}}		{{Wikipedia\|Kleisma}}

	'''15625/15552''', which is sometimes called the '''kleisma''', is the [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], and is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]])~~. It is tempered out in [[Hanson\|Hanson temperament]] and the [[kleismic family]]~~. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[~~Square_superparticular~~#Glossary\|S-expression]] of S25<sup>2</sup> * S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).		'''15625/15552''', which is sometimes called the '''kleisma''', is the [[small comma\|small]] [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], and is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]). Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[square superparticular #Glossary\|S-expression]] of S25<sup>2</sup> × S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).

			== Temperaments ==
			This comma is tempered out in the [[hanson]] temperament. See [[Kleismic family]] for the rank-2 temperament family where it is tempered out. See [[Kleismic rank three family\|Kleismic rank-3 family]] for the rank-3 temperament family where it is tempered out.

	== See also ==		== See also ==
	* [[Small comma]]
	* [[Kleismic family]], the rank-2 temperament family where it is tempered out
	* [[Kleismic rank three family]], the rank-3 temperament family where it is tempered out
	* [[Kleisma]] (disambiguation page)		* [[Kleisma]] (disambiguation page)

	[[Category:Kleismic]]		[[Category:Kleismic]]
	[[Category:Commas named by translating something into another language]]		[[Category:Commas named by translating something into another language]]

BudjarnLambeth at 12:12, 3 November 2024

2024-11-03T12:12:43Z

← Older revision		Revision as of 12:12, 3 November 2024
Line 16:		Line 16:

	[[Category:Kleismic]]		[[Category:Kleismic]]
			[[Category:Commas named by translating something into another language]]

Lériendil at 02:58, 21 October 2024

2024-10-21T02:58:35Z

← Older revision		Revision as of 02:58, 21 October 2024
Line 7:		Line 7:
	{{Wikipedia\|Kleisma}}		{{Wikipedia\|Kleisma}}

	'''15625/15552''', which is sometimes called the '''kleisma''', is the [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], and is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]). It is tempered out in [[Hanson\|Hanson temperament]] and the kleismic family. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[Square_superparticular#Glossary\|S-expression]] of S25<sup>2</sup> * S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).		'''15625/15552''', which is sometimes called the '''kleisma''', is the [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], and is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]). It is tempered out in [[Hanson\|Hanson temperament]] and the [[kleismic family]]. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[Square_superparticular#Glossary\|S-expression]] of S25<sup>2</sup> * S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).

	== See also ==		== See also ==