Greater tendoneutralisma - Revision history

Lériendil at 16:04, 8 February 2026

2026-02-08T16:04:40Z

← Older revision		Revision as of 16:04, 8 February 2026
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	=== Greater Tendoneutralic ===		=== Greater Tendoneutralic ===
	Tempering out the greater tendoneutralisma in 2.3.13 leads to the highly notable 10 & 53 temperament, where [[10edo]] is the trivial tuning approximately equal to the pure-13's tuning and [[53edo]] is the tuning practically equal to the pure-3's tuning, although [[43edo]] is an interesting choice for combining this temperament with meantone and [[63edo]] is an interesting choice if you prefer slightly sharp fifths. [[Buzzardsmic clan #Demibuzzard]] is an extension of this which maps primes 5 and 7; [[Submajor (temperament)\|submajor]] and [[interpental]] map prime 11 and thus the full [[13-limit]].		Tempering out the greater tendoneutralisma in 2.3.13 leads to the highly notable 10 & 53 temperament, where [[10edo]] is the trivial tuning approximately equal to the pure-13's tuning and [[53edo]] is the tuning practically equal to the pure-3's tuning, although [[43edo]] is an interesting choice for combining this temperament with meantone and [[63edo]] is an interesting choice if you prefer slightly sharp fifths. [[Buzzardsmic clan #Demibuzzard\|Demibuzzard]] is an extension of this which maps primes 5 and 7; [[Submajor (temperament)\|submajor]] and [[interpental]] map prime 11 and thus the full [[13-limit]].

	[[Subgroup]]: 2.3.13		[[Subgroup]]: 2.3.13

Lériendil: submajor -> demibuzzard

2026-02-08T16:04:28Z

submajor -> demibuzzard

← Older revision		Revision as of 16:04, 8 February 2026
Line 11:		Line 11:

	=== Greater Tendoneutralic ===		=== Greater Tendoneutralic ===
	Tempering out the greater tendoneutralisma in 2.3.13 leads to the highly notable 10 & 53 temperament, where [[10edo]] is the trivial tuning approximately equal to the pure-13's tuning and [[53edo]] is the tuning practically equal to the pure-3's tuning, although [[43edo]] is an interesting choice for combining this temperament with meantone and [[63edo]] is an interesting choice if you prefer slightly sharp fifths. ~~This temperament~~ is ~~related to~~ [[~~submajor~~ (temperament)\|submajor]]~~, which extends it to~~ the full [[13-limit]].		Tempering out the greater tendoneutralisma in 2.3.13 leads to the highly notable 10 & 53 temperament, where [[10edo]] is the trivial tuning approximately equal to the pure-13's tuning and [[53edo]] is the tuning practically equal to the pure-3's tuning, although [[43edo]] is an interesting choice for combining this temperament with meantone and [[63edo]] is an interesting choice if you prefer slightly sharp fifths. [[Buzzardsmic clan #Demibuzzard]] is an extension of this which maps primes 5 and 7; [[Submajor (temperament)\|submajor]] and [[interpental]] map prime 11 and thus the full [[13-limit]].

	[[Subgroup]]: 2.3.13		[[Subgroup]]: 2.3.13

FloraC: Text replacement - "Badness (Dirichlet): " to "Badness (Sintel): "

2025-06-06T16:39:00Z

Text replacement - "Badness (Dirichlet): " to "Badness (Sintel): "

← Older revision		Revision as of 16:39, 6 June 2025
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	{{Optimal ET sequence\|legend=1\| 10, 33, 43, 53, 202, 255f, 308f, 361f }}		{{Optimal ET sequence\|legend=1\| 10, 33, 43, 53, 202, 255f, 308f, 361f }}

	[[Badness]] (~~Dirichlet~~): 3.037		[[Badness]] (Sintel): 3.037

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

BudjarnLambeth at 23:08, 15 November 2024

2024-11-15T23:08:18Z

← Older revision		Revision as of 23:08, 15 November 2024
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	* [[512/507]]		* [[512/507]]
	* [[Tridecapyth comma]]		* [[Tridecapyth comma]]

			[[Category:Commas with unknown etymology]]

BudjarnLambeth: BudjarnLambeth moved page 815730721/805306368 to Greater tendoneutralisma over redirect: Long comma number

2024-09-26T05:42:22Z

BudjarnLambeth moved page 815730721/805306368 to Greater tendoneutralisma over redirect: Long comma number

← Older revision	Revision as of 05:42, 26 September 2024
(No difference)

TallKite: add color name

2024-09-26T01:44:50Z

add color name

← Older revision		Revision as of 01:44, 26 September 2024
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	\| Ratio = 815730721/805306368		\| Ratio = 815730721/805306368
	\| Name = greater tendoneutralisma		\| Name = greater tendoneutralisma
			\| Color name = Laquadbitho comma
	\| Comma = yes		\| Comma = yes
	}}		}}

Godtone: pls keep these. these are related as they are different ways of achieving prime 3 by stacking prime 13; keeping them only in the exposition makes them a lot less visible and harder to find if one is looking for them; also "lesser tendoneutralisma" is especially important as being related naming-wise to this comma

2024-06-04T15:13:22Z

pls keep these. these are related as they are different ways of achieving prime 3 by stacking prime 13; keeping them only in the exposition makes them a lot less visible and harder to find if one is looking for them; also "lesser tendoneutralisma" is especially important as being related naming-wise to this comma

← Older revision		Revision as of 15:13, 4 June 2024
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	== See also ==		== See also ==
			* [[Lesser tendoneutralisma]]
			* [[512/507]]
	* [[Tridecapyth comma]]		* [[Tridecapyth comma]]

FloraC: Move the discussion about temps to the right section. This covers the lesser tendoneutralisma and the tridecimal neutral thirds comma so they don't need to appear again in the "see also" section.

2024-06-04T06:13:54Z

Move the discussion about temps to the right section. This covers the lesser tendoneutralisma and the tridecimal neutral thirds comma so they don't need to appear again in the "see also" section.

← Older revision		Revision as of 06:13, 4 June 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''greater tendoneutralisma''' is a [[small comma]] of the 2.3.13 [[subgroup]] which is the amount by which a stack of eight [[16/13]]'s minus two [[octave]]s falls short of [[4/3]]; that is, it is equal to ([[16/3]])/([[16/13]])<sup>8</sup> and so equivalently also to ([[13/3]])/([[16/13]])<sup>7</sup>. Although the comma is similar in size to something like 81/80, it is quite accurate because the error can be split evenly over eight 16/13's, so that the pure-3's tuning (very close to [[53edo]]) has 13 off by only 2.78{{cent}}. A more accurate (lower damage) way of achieving the same (finding 3 by stacking 13's) is by tempering the [[lesser tendoneutralisma]]. Very importantly, both are distinct ways of mapping 2.3.13, so that you cannot combine them unless you want to use the trivial tuning of [[10edo]], so that edos > 10 which have a good 3 and 13 will usually pick between one of these two mappings. (A much simpler but relatively much higher error way of mapping 3 for those that prefer sharp fifths is by tempering ([[16/13]])<sup>2</sup>/([[3/2]]) = [[512/507]].)		The '''greater tendoneutralisma''' is a [[small comma]] of the 2.3.13 [[subgroup]] which is the amount by which a stack of eight [[16/13]]'s minus two [[octave]]s falls short of [[4/3]]; that is, it is equal to ([[16/3]])/([[16/13]])<sup>8</sup> and so equivalently also to ([[13/3]])/([[16/13]])<sup>7</sup>.

	== Temperaments ==		== Temperaments ==
			Although the comma is similar in size to something like 81/80, the corresponding temperament is quite accurate because the error can be split evenly over eight 16/13's, so that the pure-3's tuning (very close to [[53edo]]) has 13 off by only 2.78{{cent}}. A more accurate (lower damage) way of achieving the same (finding 3 by stacking 13's) is by tempering the [[lesser tendoneutralisma]]. Very importantly, both are distinct ways of mapping 2.3.13, so that you cannot combine them unless you want to use the trivial tuning of [[10edo]], so that edos > 10 which have a good 3 and 13 will usually pick between one of these two mappings. A much simpler but relatively much higher error way of mapping 3 for those that prefer sharp fifths is by tempering ([[16/13]])<sup>2</sup>/([[3/2]]) = [[512/507]].

	=== Greater Tendoneutralic ===		=== Greater Tendoneutralic ===
	Tempering out the greater tendoneutralisma in 2.3.13 leads to the highly notable 10 & 53 temperament, where [[10edo]] is the trivial tuning approximately equal to the pure-13's tuning and [[53edo]] is the tuning practically equal to the pure-3's tuning, although [[43edo]] is an interesting choice for combining this temperament with meantone and [[63edo]] is an interesting choice if you prefer slightly sharp fifths. This temperament is related to [[submajor (temperament)\|submajor]], which extends it to the full [[13-limit]].		Tempering out the greater tendoneutralisma in 2.3.13 leads to the highly notable 10 & 53 temperament, where [[10edo]] is the trivial tuning approximately equal to the pure-13's tuning and [[53edo]] is the tuning practically equal to the pure-3's tuning, although [[43edo]] is an interesting choice for combining this temperament with meantone and [[63edo]] is an interesting choice if you prefer slightly sharp fifths. This temperament is related to [[submajor (temperament)\|submajor]], which extends it to the full [[13-limit]].
Line 23:		Line 25:

	== See also ==		== See also ==
	* [[Lesser tendoneutralisma]]
	* [[512/507]]
	* [[Tridecapyth comma]]		* [[Tridecapyth comma]]

FloraC: Corrections; update links; style

2024-06-04T06:10:21Z

Corrections; update links; style

← Older revision		Revision as of 06:10, 4 June 2024
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''greater tendoneutralisma''' is a [[small comma]] of the 2.3.13 subgroup which is the amount by which a stack of eight [[16/13]]'s minus two [[octave]]s falls short of [[4/3]]; that is, it is equal to ([[16/3]])/([[16/13]])<sup>8</sup> and so equivalently also to ([[13/3]])/([[16/13]])<sup>7</sup>. Although the comma is similar in size to something like 81/80, it is quite accurate because the error can be split evenly over eight 16/13's, so that the pure-3's tuning (very close to [[53edo]]) has 13 off by only 2.78{{cent}}. A more accurate (lower damage) way of achieving the same (finding 3 by stacking 13's) is by tempering the [[lesser tendoneutralisma]]. Very importantly, both are distinct ways of mapping 2.3.13, so that you ~~can't~~ combine them unless you want to use the trivial tuning of [[10edo]], so that edos > 10 which have a good 3 and 13 will usually pick between one of these two mappings. (A much simpler but (relatively) much higher error way of mapping 3 for those that prefer sharp fifths is by tempering ([[16/13]])<sup>2</sup>/([[3/2]]) = [[512/507]].)		The '''greater tendoneutralisma''' is a [[small comma]] of the 2.3.13 [[subgroup]] which is the amount by which a stack of eight [[16/13]]'s minus two [[octave]]s falls short of [[4/3]]; that is, it is equal to ([[16/3]])/([[16/13]])<sup>8</sup> and so equivalently also to ([[13/3]])/([[16/13]])<sup>7</sup>. Although the comma is similar in size to something like 81/80, it is quite accurate because the error can be split evenly over eight 16/13's, so that the pure-3's tuning (very close to [[53edo]]) has 13 off by only 2.78{{cent}}. A more accurate (lower damage) way of achieving the same (finding 3 by stacking 13's) is by tempering the [[lesser tendoneutralisma]]. Very importantly, both are distinct ways of mapping 2.3.13, so that you cannot combine them unless you want to use the trivial tuning of [[10edo]], so that edos > 10 which have a good 3 and 13 will usually pick between one of these two mappings. (A much simpler but relatively much higher error way of mapping 3 for those that prefer sharp fifths is by tempering ([[16/13]])<sup>2</sup>/([[3/2]]) = [[512/507]].)

	== Temperaments ==		== Temperaments ==
	=== Greater Tendoneutralic ===		=== Greater Tendoneutralic ===
	Tempering the greater tendoneutralisma in 2.3.13 leads to the highly notable 10 & 53 temperament, where [[10edo]] is the trivial tuning approximately equal to the pure-13's tuning and [[53edo]] is the tuning practically equal to the pure-3's tuning, although [[43edo]] is an interesting choice for combining this temperament with meantone and [[63edo]] is an interesting choice if you prefer slightly sharp fifths. This temperament is related to [[submajor temperament]], which extends it to the full [[13-limit]].		Tempering out the greater tendoneutralisma in 2.3.13 leads to the highly notable 10 & 53 temperament, where [[10edo]] is the trivial tuning approximately equal to the pure-13's tuning and [[53edo]] is the tuning practically equal to the pure-3's tuning, although [[43edo]] is an interesting choice for combining this temperament with meantone and [[63edo]] is an interesting choice if you prefer slightly sharp fifths. This temperament is related to [[submajor (temperament)\|submajor]], which extends it to the full [[13-limit]].

	[[Subgroup]]: 2.3.13		[[Subgroup]]: 2.3.13
Line 21:		Line 21:

	[[Badness]] (Dirichlet): 3.037		[[Badness]] (Dirichlet): 3.037

	~~Related temperaments: [[Submajor temperament]]~~

	== See also ==		== See also ==
	* [[Submajor temperament]]
	* [[Lesser tendoneutralisma]]		* [[Lesser tendoneutralisma]]
	* [[512/507]]		* [[512/507]]
	* [[Tridecapyth comma]]		* [[Tridecapyth comma]]

Godtone: /* See also */ add submajor temperament in the "see also" section

2024-05-29T20:01:54Z

See also: add submajor temperament in the "see also" section

← Older revision		Revision as of 20:01, 29 May 2024
Line 25:		Line 25:

	== See also ==		== See also ==
			* [[Submajor temperament]]
	* [[Lesser tendoneutralisma]]		* [[Lesser tendoneutralisma]]
	* [[512/507]]		* [[512/507]]
	* [[Tridecapyth comma]]		* [[Tridecapyth comma]]