4000/3969 - Revision history

FloraC: + a commatic identity. - edos (octagar family page contains better sequences). - see also

2026-03-13T14:18:37Z

+ a commatic identity. - edos (octagar family page contains better sequences). - see also

← Older revision		Revision as of 14:18, 13 March 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''octagar comma''' is a [[small comma\|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]'s and a stack of two [[7/6]]'s. It is also equal to ([[10/9]])/([[21/20]])<sup>2</sup>, with [[S-expression]] ~~S19 × S20~~<sup>2</sup>, making it a lopsided comma.		The '''octagar comma''' is a [[small comma\|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]'s and a stack of two [[7/6]]'s. It is also the difference between [[50/49]] and [[81/80]], and is equal to ([[10/9]])/([[21/20]])<sup>2</sup>, with [[S-expression]] S19⋅S20<sup>2</sup>, making it a lopsided comma.

	== Temperaments ==		== Temperaments ==
	Tempering out this comma alone in the 7-limit leads to the [[octagar]] temperament. See [[Octagar family]] for the family of rank-3 temperaments where it is tempered out. See [[Octagar temperaments]] for a collection of rank-2 temperaments where it is tempered out.		[[Tempering out]] this comma alone in the 7-limit leads to the [[octagar]] temperament. See [[Octagar family]] for the family of rank-3 temperaments where it is tempered out. See [[Octagar temperaments]] for a collection of rank-2 temperaments where it is tempered out.

	~~It is also tempered out in the following [[edo]]s (by [[simple map]]): {{EDOs\|3, 12, 15, 23, 26, 27, 29, 30, 38, 41, 42, 53, 56, 68, 71, 79, 80, 82, 83, 94, 95, 97}}..~~.

	== Etymology ==		== Etymology ==
	This comma was named as ''octagari'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[octacot]]'' and ''[[garibaldi]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group \| ''Seven limit comma names from pairs of temperament names'']</ref>. The last letter ''i'' was dropped by 2010, however<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_92281.html Yahoo! Tuning Group \| ''Octagar (4000/3969) planar temperament'']</ref>.		This comma was named as ''octagari'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[octacot]]'' and ''[[garibaldi]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group \| ''Seven limit comma names from pairs of temperament names'']</ref>. The last letter ''i'' was dropped by 2010, however<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_92281.html Yahoo! Tuning Group \| ''Octagar (4000/3969) planar temperament'']</ref>.

	~~== See also ==~~
	* [[Gallery of just intervals]]

	== References ==		== References ==

FloraC: + another reference

2025-11-25T12:21:51Z

+ another reference

← Older revision		Revision as of 12:21, 25 November 2025
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	== Etymology ==		== Etymology ==
	This comma was named as ''octagari'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[octacot]]'' and ''[[garibaldi]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group \| ''Seven limit comma names from pairs of temperament names'']</ref>. ~~It is not clear how it later dropped the~~ last letter ''i''.		This comma was named as ''octagari'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[octacot]]'' and ''[[garibaldi]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group \| ''Seven limit comma names from pairs of temperament names'']</ref>. The last letter ''i'' was dropped by 2010, however<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_92281.html Yahoo! Tuning Group \| ''Octagar (4000/3969) planar temperament'']</ref>.

	== See also ==		== See also ==
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

	== ~~Notes~~ ==		== References ==

	[[Category:Octagar]]		[[Category:Octagar]]
	[[Category:Commas named by combining multiple temperament names]]		[[Category:Commas named by combining multiple temperament names]]

FloraC: Readability

2025-11-25T12:18:53Z

Readability

← Older revision		Revision as of 12:18, 25 November 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
			The '''octagar comma''' is a [[small comma\|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]'s and a stack of two [[7/6]]'s. It is also equal to ([[10/9]])/([[21/20]])<sup>2</sup>, with [[S-expression]] S19 × S20<sup>2</sup>, making it a lopsided comma.
	The '''octagar comma''' is a [[small comma\|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]s and a stack of two [[7/6]]s. ~~[[Square_superparticular#Sk2_.2A_S.28k_.2B_1.29_and_S.28k_-_1.29_.2A_Sk2_.28lopsided_commas.29\|As per its S-expression of S20<sup>2</sup> * S19]], being a lopsided comma, it~~ is also equal to ([[10/9]])/([[21/20]])<sup>2</sup>.

	== Temperaments ==		== Temperaments ==

BudjarnLambeth at 12:59, 3 November 2024

2024-11-03T12:59:10Z

← Older revision		Revision as of 12:59, 3 November 2024
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	[[Category:Octagar]]		[[Category:Octagar]]
	[[Category:Commas named ~~for their regular~~ temperament ~~properties~~]]		[[Category:Commas named by combining multiple temperament names]]

BudjarnLambeth at 12:28, 3 November 2024

2024-11-03T12:28:16Z

← Older revision		Revision as of 12:28, 3 November 2024
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	[[Category:Octagar]]		[[Category:Octagar]]
			[[Category:Commas named for their regular temperament properties]]

Godtone: note the equivalence derivable from its S-expression

2024-05-09T15:38:11Z

note the equivalence derivable from its S-expression

← Older revision		Revision as of 15:38, 9 May 2024
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	}}		}}

	The '''octagar comma''' is a [[small comma\|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]s and a stack of two [[7/6]]s.		The '''octagar comma''' is a [[small comma\|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]s and a stack of two [[7/6]]s. [[Square_superparticular#Sk2_.2A_S.28k_.2B_1.29_and_S.28k_-_1.29_.2A_Sk2_.28lopsided_commas.29\|As per its S-expression of S20<sup>2</sup> * S19]], being a lopsided comma, it is also equal to ([[10/9]])/([[21/20]])<sup>2</sup>.

	== Temperaments ==		== Temperaments ==

FloraC: Expansion

2024-01-02T11:39:06Z

Expansion

← Older revision		Revision as of 11:39, 2 January 2024
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	== Temperaments ==		== Temperaments ==
	Tempering out this comma alone in the 7-limit leads to the [[octagar]] temperament. See [[~~octagar~~ family]] for the family of rank-3 temperaments where it is tempered out. See [[~~octagar~~ temperaments]] for a collection of rank-2 temperaments where it is tempered out.		Tempering out this comma alone in the 7-limit leads to the [[octagar]] temperament. See [[Octagar family]] for the family of rank-3 temperaments where it is tempered out. See [[Octagar temperaments]] for a collection of rank-2 temperaments where it is tempered out.

	It is also tempered out in the following [[edo]]s (by [[simple map]]): {{EDOs\|3, 12, 15, 23, 26, 27, 29, 30, 38, 41, 42, 53, 56, 68, 71, 79, 80, 82, 83, 94, 95, 97}}...		It is also tempered out in the following [[edo]]s (by [[simple map]]): {{EDOs\|3, 12, 15, 23, 26, 27, 29, 30, 38, 41, 42, 53, 56, 68, 71, 79, 80, 82, 83, 94, 95, 97}}...

			== Etymology ==
			This comma was named as ''octagari'' by [[Gene Ward Smith]] in 2005 as a contraction of ''[[octacot]]'' and ''[[garibaldi]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group \| ''Seven limit comma names from pairs of temperament names'']</ref>. It is not clear how it later dropped the last letter ''i''.

	== See also ==		== See also ==
	* [[Gallery of just intervals]]		* [[Gallery of just intervals]]

			== Notes ==

			[[Category:Octagar]]

Fredg999: Created page with "{{Infobox Interval | Ratio = 4000/3969 | Name = octagar comma | Color name = Rurutriyo comma | Comma = yes }} The '''octagar comma''' is a small 7-limit [..."

2023-05-22T19:32:53Z

Created page with "{{Infobox Interval | Ratio = 4000/3969 | Name = octagar comma | Color name = Rurutriyo comma | Comma = yes }} The '''octagar comma''' is a small 7-limit [..."

New page

{{Infobox Interval
| Ratio = 4000/3969
| Name = octagar comma
| Color name = Rurutriyo comma
| Comma = yes
}}

The '''octagar comma''' is a [[small comma|small]] [[7-limit]] [[comma]] with a [[ratio]] of 4000/3969. It is the difference between a stack of three [[10/9]]s and a stack of two [[7/6]]s.

== Temperaments ==
Tempering out this comma alone in the 7-limit leads to the [[octagar]] temperament. See [[octagar family]] for the family of rank-3 temperaments where it is tempered out. See [[octagar temperaments]] for a collection of rank-2 temperaments where it is tempered out.

It is also tempered out in the following [[edo]]s (by [[simple map]]): {{EDOs|3, 12, 15, 23, 26, 27, 29, 30, 38, 41, 42, 53, 56, 68, 71, 79, 80, 82, 83, 94, 95, 97}}...

== See also ==
* [[Gallery of just intervals]]