Symbiotic comma - Revision history

FloraC: Note an important consequence of the temp

2026-10-23T12:08:41Z

Note an important consequence of the temp

← Older revision		Revision as of 12:08, 23 October 2026
Line 10:		Line 10:

	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic''' temperament (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), or in the 2.3.7.11 subgroup, the '''symbiotian''' temperament. In either case, ~~it identifies~~ [[11/8]] by an apotome over [[9/7]], [[11/6]] by an apotome over [[12/7]], and [[11/9]] by an apotome over [[8/7]]. Finally, ~~it identifies~~ 11/9 by a [[256/243\|limma]] below 9/7.		[[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic''' temperament (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), or in the 2.3.7.11 subgroup, the '''symbiotian''' temperament. In either case, 28/27 and 33/32 become apotome complements, and [[11/8]] is identified with an apotome over [[9/7]], [[11/6]] with an apotome over [[12/7]], and [[11/9]] with an apotome over [[8/7]]. Finally, 11/9 is identified with a [[256/243\|limma]] below 9/7.

	=== Symbiotian ===		=== Symbiotian ===

FloraC: The factorizations were not arbitrary. They were either simpler, superparticular or in the same subgroup

2026-10-23T12:05:23Z

The factorizations were not arbitrary. They were either simpler, superparticular or in the same subgroup

← Older revision		Revision as of 12:05, 23 October 2026
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27~~]]. It is also the difference between a [[septischisma]] and a [[olympia~~]].		'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between a [[2187/2048\|Pythagorean apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]].

	~~It factors into~~ the ~~following commas:~~		In terms of other commas, it is the difference between a [[septischisma]] and an [[olympia]]. It is also the sum of an [[argyria]] and an olympia, as well as the sum of a [[quartisma]] and a [[nexus comma]]. In the full 11-limit, it factors into simpler commas as ([[4375/4374]])⋅([[5632/5625]]), and in the 19-limit, ([[1216/1215]])⋅([[1540/1539]]).

	*[[~~2.3.7.11 subgroup~~]]:
	~~:* (~~[[olympia]]~~)⋅(~~[[argyria]])
	~~:* (~~[[quartisma]]~~)⋅(~~[[nexus comma]])
	* [[11-limit~~]]:~~
	~~:* ([[3025/3024]])⋅([[reef comma]])~~
	:*([[4375/4374]])⋅([[5632/5625]])
	* [[13-limit]]
	~~:* ([[676/675]])⋅([[chalmersia]])~~
	~~:* ([[1001/1000]])⋅([[phaotic comma]])~~
	~~:* ([[4096/4095]])⋅([[35035/34992]])~~
	* [[2.3.5.7.11.13.19 subgroup]]
	:* ([[1216/1215]])⋅([[1540/1539]])

	== Temperaments ==		== Temperaments ==

FloraC: Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

2026-09-30T17:38:51Z

Text replacement - "{{Mapping|legend=2| " to "{{Mapping|legend=3| "

← Older revision		Revision as of 17:38, 30 September 2026
Line 30:		Line 30:
	[[Comma list]]: 19712/19683		[[Comma list]]: 19712/19683

	{{Mapping\|legend=2\| 1 0 0 -8 \| 0 1 0 9 \| 0 0 1 -1 }}		{{Mapping\|legend=3\| 1 0 0 -8 \| 0 1 0 9 \| 0 0 1 -1 }}
	: mapping generators: ~2, ~3, ~7		: mapping generators: ~2, ~3, ~7

Eufalesio: Order it better

2026-09-28T07:36:04Z

Order it better

← Older revision		Revision as of 07:36, 28 September 2026
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 ~~subgroup\|2.3.7.11-~~subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]]. It is also the difference between a [[septischisma]] and a [[olympia]].		'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]]. It is also the difference between a [[septischisma]] and a [[olympia]].

	It factors into the following:		It factors into the following commas:

	* ([[olympia]])⋅([[argyria]])		*[[2.3.7.11 subgroup]]:
	* ([[~~676/675~~]])⋅([[~~chalmersia~~]])		:* ([[olympia]])⋅([[argyria]])
	* ([[~~1001/1000]])⋅([[phaotic comma~~]])		:* ([[quartisma]])⋅([[nexus comma]])
	* ([[3025/3024]])⋅([[reef comma]])		* [[11-limit]]:
	* ([[~~4096~~/~~4095~~]])⋅([[~~35035~~/~~34992~~]])		:* ([[3025/3024]])⋅([[reef comma]])
	* ([[~~4375~~/~~4374~~]])⋅([[~~5632/5625~~]])		:*([[4375/4374]])⋅([[5632/5625]])
	* ([[~~quartisma~~]])⋅([[~~nexus~~ comma]])		* [[13-limit]]
	* ([[~~1216~~/~~1215~~]])⋅([[~~1540~~/~~1539~~]]) ~~[<nowiki/>~~[[2.3.5.7.11.13.19 subgroup]]]		:* ([[676/675]])⋅([[chalmersia]])
			:* ([[1001/1000]])⋅([[phaotic comma]])
			:* ([[4096/4095]])⋅([[35035/34992]])
			* [[2.3.5.7.11.13.19 subgroup]]
			:* ([[1216/1215]])⋅([[1540/1539]])

	== Temperaments ==		== Temperaments ==

Eufalesio: More equivalences!

2026-09-28T07:30:40Z

More equivalences!

← Older revision		Revision as of 07:30, 28 September 2026
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup\|2.3.7.11-subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]].		'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup\|2.3.7.11-subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]]. It is also the difference between a [[septischisma]] and a [[olympia]].

	It factors into ([[4375/4374]])⋅([[5632/5625]])~~, and moreover, into the~~ [[quartisma]] ~~and the~~ [[nexus comma]]~~. In the [[19-limit]], it factors neatly into~~ ([[1216/1215]])⋅([[1540/1539]]).		It factors into the following:

			* ([[olympia]])⋅([[argyria]])
			* ([[676/675]])⋅([[chalmersia]])
			* ([[1001/1000]])⋅([[phaotic comma]])
			* ([[3025/3024]])⋅([[reef comma]])
			* ([[4096/4095]])⋅([[35035/34992]])
			* ([[4375/4374]])⋅([[5632/5625]])
			* ([[quartisma]])⋅([[nexus comma]])
			* ([[1216/1215]])⋅([[1540/1539]]) [<nowiki/>[[2.3.5.7.11.13.19 subgroup]]]

	== Temperaments ==		== Temperaments ==

FloraC: + data for symbiotian

2026-09-01T16:02:38Z

+ data for symbiotian

@@ Line 11: / Line 11: @@
 == Temperaments ==
 [[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic''' temperament (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), or in the 2.3.7.11 subgroup, the '''symbiotian''' temperament. In either case, it identifies [[11/8]] by an apotome over [[9/7]], [[11/6]] by an apotome over [[12/7]], and [[11/9]] by an apotome over [[8/7]]. Finally, it identifies 11/9 by a [[256/243|limma]] below 9/7.
 == Etymology ==

FloraC: Update name

2026-09-01T16:01:49Z

Update name

← Older revision		Revision as of 16:01, 1 September 2026
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}

	'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup\|2.3.7.11-subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]].		'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup\|2.3.7.11-subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]].

Line 14:		Line 13:

	== Etymology ==		== Etymology ==
	This comma was named by [[Aura]] in 2020, from the fact that it is tempered out in such notable temperaments as [[vishnu]], [[newt]], [[kwai]], [[supers]], [[guiron]] and [[amity]], and, from the fact that it also makes a good extension to a number of other temperaments such as [[~~canou family\|canou~~]].		This comma was named by [[Aura]] in 2020, from the fact that it is tempered out in such notable temperaments as [[vishnu]], [[newt]], [[kwai]], [[supers]], [[guiron]] and [[amity]], and, from the fact that it also makes a good extension to a number of other temperaments such as [[cathartic]].

	[[Category:Symbiotic]]		[[Category:Symbiotic]]
	[[Category:Commas named for their regular temperament properties]]		[[Category:Commas named for their regular temperament properties]]

FloraC: Mention the no-5 temp's name. Re-organize

2026-05-19T10:10:03Z

Mention the no-5 temp's name. Re-organize

← Older revision		Revision as of 10:10, 19 May 2026
Line 6:		Line 6:
	}}		}}

	'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 2.55 [[cent]]s. It gets its names from the fact that it is tempered out in such notable temperaments as [[vishnu]], [[newt]], [[kwai]], [[supers]], [[guiron]] and [[amity]], and, from the fact that it also makes a good extension to a number of other temperaments such as [[canou family\|canou]]. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]].		'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup\|2.3.7.11-subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]].

	It factors into ([[4375/4374]])⋅([[5632/5625]]), and moreover, into the [[quartisma]] and the [[nexus comma]]. In the [[19-limit]], it factors neatly into ([[1216/1215]])⋅([[1540/1539]]).		It factors into ([[4375/4374]])⋅([[5632/5625]]), and moreover, into the [[quartisma]] and the [[nexus comma]]. In the [[19-limit]], it factors neatly into ([[1216/1215]])⋅([[1540/1539]]).

	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic ~~temperament~~''' (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]). ~~This~~ temperament identifies [[11/8]] by an apotome over [[9/7]], [[11/6]] by an apotome over [[12/7]], and [[11/9]] by an apotome over [[8/7]]. Finally, it identifies 11/9 by a [[256/243\|limma]] below 9/7.		[[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic''' temperament (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), or in the 2.3.7.11 subgroup, the '''symbiotian''' temperament. In either case, it identifies [[11/8]] by an apotome over [[9/7]], [[11/6]] by an apotome over [[12/7]], and [[11/9]] by an apotome over [[8/7]]. Finally, it identifies 11/9 by a [[256/243\|limma]] below 9/7.

			== Etymology ==
			This comma was named by [[Aura]] in 2020, from the fact that it is tempered out in such notable temperaments as [[vishnu]], [[newt]], [[kwai]], [[supers]], [[guiron]] and [[amity]], and, from the fact that it also makes a good extension to a number of other temperaments such as [[canou family\|canou]].

	[[Category:Symbiotic]]		[[Category:Symbiotic]]
	[[Category:Commas named for their regular temperament properties]]		[[Category:Commas named for their regular temperament properties]]

FloraC: Expand

2025-02-20T08:18:05Z

Expand

← Older revision		Revision as of 08:18, 20 February 2025
Line 6:		Line 6:
	}}		}}

	'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[11-limit]] [[~~unnoticeable~~ comma]] measuring about 2.55 [[cent]]s. It gets its names from the fact that it is tempered out in such notable temperaments as [[vishnu]], [[newt]], [[kwai]], [[supers]], [[guiron]] and [[amity]], and, from the fact that it also makes a good extension to a number of other temperaments such as [[~~Canou~~ family\|canou]]. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a [[33/32]] ~~quartertone~~ stacked on top of [[28/27]]. ~~Alternatively stated, it identifies [[11/8]] by an apotome over [[9/7]].~~ It factors into ([[4375/4374]])([[5632/5625]]), and moreover, into the [[quartisma]] and the [[nexus comma]].		'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma\|unnoticeable]] [[11-limit]] [[comma]] measuring about 2.55 [[cent]]s. It gets its names from the fact that it is tempered out in such notable temperaments as [[vishnu]], [[newt]], [[kwai]], [[supers]], [[guiron]] and [[amity]], and, from the fact that it also makes a good extension to a number of other temperaments such as [[canou family\|canou]]. It is the difference between an [[2187/2048\|apotome (2187/2048)]] and an [[77/72\|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]].

			It factors into ([[4375/4374]])⋅([[5632/5625]]), and moreover, into the [[quartisma]] and the [[nexus comma]]. In the [[19-limit]], it factors neatly into ([[1216/1215]])⋅([[1540/1539]]).

	== Temperaments ==		== Temperaments ==
	Tempering out this comma in the 11-limit results in the rank-4 '''symbiotic temperament''' (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]).		[[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic temperament''' (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]). This temperament identifies [[11/8]] by an apotome over [[9/7]], [[11/6]] by an apotome over [[12/7]], and [[11/9]] by an apotome over [[8/7]]. Finally, it identifies 11/9 by a [[256/243\|limma]] below 9/7.

	~~== See also ==~~
	* [[~~Unnoticeable comma~~]]

	[[Category:Symbiotic]]		[[Category:Symbiotic]]
	[[Category:Commas named for their regular temperament properties]]		[[Category:Commas named for their regular temperament properties]]

BudjarnLambeth at 23:45, 3 November 2024

2024-11-03T23:45:42Z

← Older revision		Revision as of 23:45, 3 November 2024
Line 15:		Line 15:

	[[Category:Symbiotic]]		[[Category:Symbiotic]]
			[[Category:Commas named for their regular temperament properties]]