Schismatic family - Revision history

Godtone: /* Nestoria (2.3.5.19) */ missing info

2026-06-05T14:58:54Z

Nestoria (2.3.5.19): missing info

← Older revision		Revision as of 14:58, 5 June 2026
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	: ''See also: [[No-elevens subgroup temperaments #Garibaldia]] and [[No-elevens subgroup temperaments #Pontia\|#Pontia]]''		: ''See also: [[No-elevens subgroup temperaments #Garibaldia]] and [[No-elevens subgroup temperaments #Pontia\|#Pontia]]''

	Nestoria is notable for having one of the lowest-badness subgroup extensions of schismic. Note that despite prime [[19/1\|19]] being optimized by a flatter fifth, the fifth in optimal tunings of nestoria is generally not flatter than the fifth in optimal schismic due to its optimization considering intervals like [[19/10]] and [[19/15]].		Nestoria is notable for having one of the lowest-badness subgroup extensions of schismic. Note that despite prime [[19/1\|19]] being optimized by a flatter fifth, the fifth in optimal tunings of nestoria is generally not flatter than the fifth in optimal schismic due to its optimization considering intervals like [[19/10]] and [[19/15]]. However, the dyadic tuning sensitivity of [[19/16]] suggests using tunings like [[65edo]] and [[77edo]] to optimize in favour of prime 19, as [[53edo]] is already arguably undertempered for it despite being the flattest tuning appearing in the optimal ET sequence.

	[[Subgroup]]: 2.3.5.19		[[Subgroup]]: 2.3.5.19

Godtone: /* Tridecaschismic (2.3.5.13) */ "thus also" feels weird to use if theres no explanation for how it follows

2026-05-06T18:05:38Z

Tridecaschismic (2.3.5.13): "thus also" feels weird to use if theres no explanation for how it follows

← Older revision		Revision as of 18:05, 6 May 2026
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	=== Tridecaschismic (2.3.5.13) ===		=== Tridecaschismic (2.3.5.13) ===
	Proposed by [[Eufalesio]] in 2026, tridecaschismic adds the [[325/324\|marveltwin comma]] to the comma list, ~~thus also tempering out~~ the [[tridecapyth comma]]. It benefits from a fifth that is just, or practically indistinguishable from just, like in 53edo. It is one of the lowest badness schismic extensions. It is also equivalent to the 2.3.5.13 [[restriction]] of 13-limit [[cassandra]].		Proposed by [[Eufalesio]] in 2026, tridecaschismic adds the [[325/324\|marveltwin comma]] to the comma list, or equivalently, the [[tridecapyth comma]]. It benefits from a fifth that is just, or practically indistinguishable from just, like in 53edo. It is one of the lowest badness schismic extensions. It is also equivalent to the 2.3.5.13 [[restriction]] of 13-limit [[cassandra]].

	Subgroup: 2.3.5.13		Subgroup: 2.3.5.13

Godtone: /* Tridecaschismic (2.3.5.13) */ grammar

2026-05-06T17:30:19Z

Tridecaschismic (2.3.5.13): grammar

← Older revision		Revision as of 17:30, 6 May 2026
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	=== Tridecaschismic (2.3.5.13) ===		=== Tridecaschismic (2.3.5.13) ===
	Proposed by [[Eufalesio]] in 2026, tridecaschismic adds the [[325/324\|marveltwin comma]] to the comma list, thus also tempering out the [[tridecapyth comma]]. It benefits from a fifth that is just, or practically indistinguishable from just, like in 53edo. It is ~~has among~~ the lowest badness of schismic extensions. It is also equivalent to the 2.3.5.13 [[restriction]] of 13-limit [[cassandra]].		Proposed by [[Eufalesio]] in 2026, tridecaschismic adds the [[325/324\|marveltwin comma]] to the comma list, thus also tempering out the [[tridecapyth comma]]. It benefits from a fifth that is just, or practically indistinguishable from just, like in 53edo. It is one of the lowest badness schismic extensions. It is also equivalent to the 2.3.5.13 [[restriction]] of 13-limit [[cassandra]].

	Subgroup: 2.3.5.13		Subgroup: 2.3.5.13

Hotcrystal0: mention tridecapyth comma for tridecaschismic

2026-04-21T20:25:31Z

mention tridecapyth comma for tridecaschismic

← Older revision		Revision as of 20:25, 21 April 2026
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	=== Tridecaschismic (2.3.5.13) ===		=== Tridecaschismic (2.3.5.13) ===
	Proposed by [[Eufalesio]] in 2026, tridecaschismic adds the [[325/324\|marveltwin comma]] to the comma list, ~~benefitting~~ from a fifth that is just, or practically indistinguishable from just, like in 53edo. It is has among the lowest badness of schismic extensions. It is also equivalent to the 2.3.5.13 [[restriction]] of 13-limit [[cassandra]].		Proposed by [[Eufalesio]] in 2026, tridecaschismic adds the [[325/324\|marveltwin comma]] to the comma list, thus also tempering out the [[tridecapyth comma]]. It benefits from a fifth that is just, or practically indistinguishable from just, like in 53edo. It is has among the lowest badness of schismic extensions. It is also equivalent to the 2.3.5.13 [[restriction]] of 13-limit [[cassandra]].

	Subgroup: 2.3.5.13		Subgroup: 2.3.5.13

Overthink: /* Overview to extensions */ here as well

2026-04-07T21:03:22Z

Overview to extensions: here as well

← Older revision		Revision as of 21:03, 7 April 2026
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	[[#Bischismic\|Bischismic]] adds {{monzo\| -69 40 0 2 }} and has a fifth generator with a half-octave period. [[#Salsa\|Salsa]] adds [[parahemif comma\|{{monzo\| 15 -13 0 2 }}]] and has a hemififth generator. [[#Hemischis\|Hemischis]] adds {{monzo\| -34 25 0 -2 }} and has a hemitwelfth generator. [[Gamelismic clan #Guiron\|Guiron]] adds [[1029/1024\|{{monzo\| -10 1 0 3 }}]], with an ~8/7 generator, three of which give the fifth. [[#Term\|Term]] adds {{monzo\| -94 54 0 3 }} with a 1/3-octave period. [[#Squirrel\|Squirrel]], [[#Tertiaschis\|tertiaschis]], and [[#Countertertiaschis\|countertertiaschis]] each has a generator that is 1/3 of the fourth. [[#Quadrant\|Quadrant]] adds {{monzo\| -119 68 0 4 }} with a 1/4-octave period. [[#Kleischismic\|Kleischismic]] adds {{monzo\| 49 -38 0 4 }} with a half-octave period and also a bisect generator. [[#Sesquiquartififths\|Sesquiquartififths]] adds {{monzo\| -35 15 0 4 }} and slices the fifth in four.		[[#Bischismic\|Bischismic]] adds {{monzo\| -69 40 0 2 }} and has a fifth generator with a half-octave period. [[#Salsa\|Salsa]] adds [[parahemif comma\|{{monzo\| 15 -13 0 2 }}]] and has a hemififth generator. [[#Hemischis\|Hemischis]] adds {{monzo\| -34 25 0 -2 }} and has a hemitwelfth generator. [[Gamelismic clan #Guiron\|Guiron]] adds [[1029/1024\|{{monzo\| -10 1 0 3 }}]], with an ~8/7 generator, three of which give the fifth. [[#Term\|Term]] adds {{monzo\| -94 54 0 3 }} with a 1/3-octave period. [[#Squirrel\|Squirrel]], [[#Tertiaschis\|tertiaschis]], and [[#Countertertiaschis\|countertertiaschis]] each has a generator that is 1/3 of the fourth. [[#Quadrant\|Quadrant]] adds {{monzo\| -119 68 0 4 }} with a 1/4-octave period. [[#Kleischismic\|Kleischismic]] adds {{monzo\| 49 -38 0 4 }} with a half-octave period and also a bisect generator. [[#Sesquiquartififths\|Sesquiquartififths]] adds {{monzo\| -35 15 0 4 }} and slices the fifth in four.

	Temperaments involving larger splits include [[#Tsaharuk\|tsaharuk]], [[#Quanharuk\|quanharuk]], [[#Quintilipyth\|quintilipyth]], [[#Quintaschis\|quintaschis]], [[#Altinex\|altinex]], [[Stearnsmic clan #Pogo\|pogo]], [[#Sextilifourths\|sextilifourths]], [[#~~Octant~~\|~~octant~~]], [[#~~Nonant~~\|~~nonant~~]], [[#~~Septant~~\|~~septant~~]], [[#Septiquarschis\|septiquarschis]], and [[#Tridecafifths\|tridecafifths]]. Those split the schismic structure into five to thirteen parts.		Temperaments involving larger splits include [[#Tsaharuk\|tsaharuk]], [[#Quanharuk\|quanharuk]], [[#Quintilipyth\|quintilipyth]], [[#Quintaschis\|quintaschis]], [[#Altinex\|altinex]], [[Stearnsmic clan #Pogo\|pogo]], [[#Sextilifourths\|sextilifourths]], [[#Septant\|septant]], [[#Octant\|octant]], [[#Nonant\|nonant]], [[#Septiquarschis\|septiquarschis]], and [[#Tridecafifths\|tridecafifths]]. Those split the schismic structure into five to thirteen parts.

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:

Overthink: better ordering

2026-04-07T21:02:48Z

better ordering

Show changes

Aura: /* Hemiterm */Corrected wrong information

2026-04-05T09:00:23Z

Hemiterm: Corrected wrong information

← Older revision		Revision as of 09:00, 5 April 2026
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	=== Hemiterm ===		=== Hemiterm ===
	The hemiterm temperament tempers out [[3025/3024]] (lehmerisma), and may be described as {{nowrap\| 159 & 183 }}. Its ploidacot is triploid ~~beta~~-dicot.		The hemiterm temperament tempers out [[3025/3024]] (lehmerisma), and may be described as {{nowrap\| 159 & 183 }}. Its ploidacot is triploid alpha-dicot.

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

FloraC: Review

2026-02-26T11:21:56Z

Review

← Older revision		Revision as of 11:21, 26 February 2026
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	== Quasipyth ==		== Quasipyth ==
	~~Quasipyth~~ tempers out {{monzo\|109 -67 0 -1}}, the [[nanisma]], as well as the [[catasyc comma]], 390625/387072. The 7/4 is found at −67 fifths, represented by the nonuple-diminished ~~13th~~.		Named by [[Xenllium]] in 2026, quasipyth tempers out {{monzo\| 109 -67 0 -1 }}, the [[nanisma]], as well as the [[catasyc comma]], 390625/387072. The 7/4 is found at −67 fifths, represented by the nonuple-diminished thirteenth.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	: error map: {{val\| 0.0000 +0.0065 -2.0054 -0.2437 }}		: error map: {{val\| 0.0000 +0.0065 -2.0054 -0.2437 }}

	{{Optimal ET sequence\|legend=1\| 53, 147d, 200, 253, 306c }}		{{Optimal ET sequence\|legend=1\| 53, 147d, 200, 253, 306c, 559c }}

	[[Badness]] (Sintel): 5.~~041~~		[[Badness]] (Sintel): 5.04

	=== 11-limit ===		=== 11-limit ===
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	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9713{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9713{{c}}

	{{Optimal ET sequence\|legend=0\| 53~~, 147d~~, 200, 253, ~~306ce~~ }}		{{Optimal ET sequence\|legend=0\| 53, 200, 253, 559ce }}

	Badness (Sintel): 3.83		Badness (Sintel): 3.83
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	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9714{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9714{{c}}

	{{Optimal ET sequence\|legend=0\| 53~~, 147d~~, 200, 253, ~~306ce~~ }}		{{Optimal ET sequence\|legend=0\| 53, 200, 253, 559ce }}

	Badness (Sintel): 2.13		Badness (Sintel): 2.13

Xenllium at 03:30, 26 February 2026

2026-02-26T03:30:59Z

← Older revision		Revision as of 03:30, 26 February 2026
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1200.~~257~~{{c}}, ~3/2 = 702.~~115~~{{c}}		* [[WE]]: ~2 = 1200.2569{{c}}, ~3/2 = 702.1149{{c}}
	: [[error map]]: {{val\| +0.~~257~~ +0.~~417~~ -1.~~434~~ +0.~~268~~ }}		: [[error map]]: {{val\| +0.2569 +0.4168 -1.4342 +0.2685 }}
	* [[CWE]]: ~2 = 1200.~~000~~{{c}}, ~3/2 = 701.~~961~~{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9615{{c}}
	: error map: {{val\| 0.~~000~~ +0.~~006~~ -2.~~005~~ -0.~~244~~ }}		: error map: {{val\| 0.0000 +0.0065 -2.0054 -0.2437 }}

	{{Optimal ET sequence\|legend=1\| 53, 200, 253, 306c }}		{{Optimal ET sequence\|legend=1\| 53, 147d, 200, 253, 306c }}

	[[Badness]] (Sintel): 5.041		[[Badness]] (Sintel): 5.041

			=== 11-limit ===
			Subgroup: 2.3.5.7.11

			Comma list: 385/384, 19712/19683, 78125/77616

			Mapping: {{mapping\| 1 0 15 109 -117 \| 0 1 -8 -67 76 }}

			Optimal tunings:
			* WE: ~2 = 1200.3283{{c}}, ~3/2 = 702.1636{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9713{{c}}

			{{Optimal ET sequence\|legend=0\| 53, 147d, 200, 253, 306ce }}

			Badness (Sintel): 3.83

			=== 13-limit ===
			Subgroup: 2.3.5.7.11.13

			Comma list: 325/324, 385/384, 2200/2197, 19712/19683

			Mapping: {{mapping\| 1 0 15 109 -117 -28 \| 0 1 -8 -67 76 20 }}

			Optimal tunings:
			* WE: ~2 = 1200.3229{{c}}, ~3/2 = 702.1603{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.9714{{c}}

			{{Optimal ET sequence\|legend=0\| 53, 147d, 200, 253, 306ce }}

			Badness (Sintel): 2.13

	== Schism ==		== Schism ==
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	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1199.9362{c}}, ~11/9 = 351.0061{{c}}		* WE: ~2 = 1199.9362{{c}}, ~11/9 = 351.0061{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.0247{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 351.0247{{c}}

Xenllium: /* Quasipyth */

2026-02-11T01:44:38Z

Quasipyth

← Older revision		Revision as of 01:44, 11 February 2026
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	== Quasipyth ==		== Quasipyth ==
	Quasipyth tempers out the [[nanisma]], ~~and~~ the 7/4 is found at −67 fifths, represented by the nonuple-diminished 13th.		Quasipyth tempers out {{monzo\|109 -67 0 -1}}, the [[nanisma]], as well as the [[catasyc comma]], 390625/387072. The 7/4 is found at −67 fifths, represented by the nonuple-diminished 13th.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7