Aberschismic temperaments - Revision history

FloraC: Recategorize

2026-08-15T07:50:28Z

Recategorize

← Older revision		Revision as of 07:50, 15 August 2026
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	== References ==		== References ==

			[[Category:Aberschismic temperaments\| ]] <!-- main article -->
	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:~~Aberschismic temperaments\| ]] <!~~-~~- main article -->~~		[[Category:Catalogs of rank-2 temperaments]]
	~~[[Category:Rank~~ 2]]

FloraC at 10:04, 8 August 2026

2026-08-08T10:04:16Z

← Older revision		Revision as of 10:04, 8 August 2026
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	* ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter\|Escapade family]]		* ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter\|Escapade family]]

	Considered below are septiquarter, kwai, ketchup, undecental~~, leapday~~, mystery, hemidromeda, countriton, artoneutral, quanic and jorgensen, in the order of increasing [[TE logflat badness]].		Considered below are septiquarter, kwai, ketchup, undecental, mystery, hemidromeda, countriton, artoneutral, quanic and jorgensen, in the order of increasing [[TE logflat badness]].

	== Septiquarter ==		== Septiquarter ==

FloraC: - leapday (addressed in sengic temps)

2026-08-08T10:00:01Z

- leapday (addressed in sengic temps)

@@ Line 9: / Line 9: @@
 * [[Dominant (temperament)|Dominant]] (+36/35) → [[Meantone family #Dominant|Meantone family]]
 * [[Garibaldi]] (+225/224) → [[Schismatic family #Garibaldi|Schismatic family]]
 * [[Diaschismic]] (+126/125) → [[Diaschismic family #Septimal diaschismic|Diaschismic family]]
 * [[Hemififths]] (+2401/2400) → [[Breedsmic temperaments #Hemififths|Breedsmic temperaments]]
@@ Line 305: / Line 306: @@
 [[Badness]] (Sintel): 2.39
 == Mystery ==

FloraC: Recategorize (name change followup)

2026-06-06T12:45:42Z

Recategorize (name change followup)

← Older revision		Revision as of 12:45, 6 June 2026
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	[[Category:Temperament collections]]		[[Category:Temperament collections]]
	[[Category:~~Hemifamity~~ temperaments\| ]] <!-- main article -->		[[Category:Aberschismic temperaments\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

FloraC: FloraC moved page Hemifamity temperaments to Aberschismic temperaments

2026-06-06T12:32:53Z

FloraC moved page Hemifamity temperaments to Aberschismic temperaments

← Older revision	Revision as of 12:32, 6 June 2026
(No difference)

FloraC: Officialize the name aberschismic (see Talk: 5120/5103)

2026-06-06T12:31:50Z

Officialize the name aberschismic (see Talk: 5120/5103)

FloraC: + abergravity

2026-05-26T07:57:00Z

+ abergravity

← Older revision		Revision as of 07:57, 26 May 2026
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	* [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan\|Gamelismic clan]]		* [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan\|Gamelismic clan]]
	* ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot\|Alphatricot family]]		* ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot\|Alphatricot family]]
			* [[Misty]] (+3136/3125) → [[Misty family #Misty\|Misty family]]
	* [[Monkey]] (+875/864) → [[Tetracot family #Monkey\|Tetracot family]]		* [[Monkey]] (+875/864) → [[Tetracot family #Monkey\|Tetracot family]]
	* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]		* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]
	* [[Misty]] (+3136/3125) → [[Misty family #Misty\|Misty family]]
	* ''[[Supers]]'' (+118098/117649) → [[Stearnsmic clan #Supers\|Stearnsmic clan]]
	* ''[[Undim]]'' (+390625/388962) → [[Undim family #Septimal undim\|Undim family]]		* ''[[Undim]]'' (+390625/388962) → [[Undim family #Septimal undim\|Undim family]]
	* ''[[Quinticosiennic]]'' (+395136/390625) → [[Quintaleap family #Quinticosiennic\|Quintaleap family]]		* ''[[Quinticosiennic]]'' (+395136/390625) → [[Quintaleap family #Quinticosiennic\|Quintaleap family]]
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	* [[Amity]] (+4375/4374) → [[Amity family #Septimal amity\|Amity family]]		* [[Amity]] (+4375/4374) → [[Amity family #Septimal amity\|Amity family]]
	* ''[[Countercata]]'' (+15625/15552) → [[Kleismic family #Countercata\|Kleismic family]]		* ''[[Countercata]]'' (+15625/15552) → [[Kleismic family #Countercata\|Kleismic family]]
			* ''[[Abergravity]]'' (+177147/175000) → [[Gravity family #Abergravity\|Gravity family]]
			* ''[[Supers]]'' (+118098/117649) → [[Stearnsmic clan #Supers\|Stearnsmic clan]]
	* ''[[Warrior]]'' (+78732/78125) → [[Sensipent family #Warrior\|Sensipent family]]		* ''[[Warrior]]'' (+78732/78125) → [[Sensipent family #Warrior\|Sensipent family]]
	* ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter\|Escapade family]]		* ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter\|Escapade family]]

FloraC: /* Leapday */ replace 19- and 23-limit leapday and leapling with no-19 23-limit

2026-05-19T08:03:28Z

Leapday: replace 19- and 23-limit leapday and leapling with no-19 23-limit

@@ Line 377: / Line 377: @@
 Badness (Sintel): 0.910
-==== 19-limit ====
+=== 2.3.5.7.11.13.17.23 subgroup ===
-Subgroup: 2.3.5.7.11.13.17.19
+Subgroup: 2.3.5.7.11.13.17.23
-Comma list: 91/90, 121/120, 133/132, 136/135, 154/153, 169/168
+Comma list: 91/90, 121/120, 136/135, 154/153, 161/160, 169/168
-Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 9 | 0 1 21 15 11 8 24 -3 }}
+Mapping: {{mapping| 1 0 -31 -21 -14 -9 -34 -5 | 0 1 21 15 11 8 24 6 }}
 Optimal tunings:
-* WE: ~2 = 1201.0192{{c}}, ~3/2 = 704.7333{{c}}
+* WE: ~2 = 1200.5169{{c}}, ~3/2 = 704.5279{{c}}
-* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.1680{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 704.2450{{c}}
-{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 75dfgh, 121defgh }}
+{{Optimal ET sequence|legend=0| 17cg, 29g, 46, 121defg }}
-Badness (Sintel): 1.06
+Badness (Sintel): 0.872
 == Mystery ==

FloraC: /* Ketchup */ replace 19- and 23-limit with no-19 23-limit, which is more natural

2026-04-19T09:55:38Z

Ketchup: replace 19- and 23-limit with no-19 23-limit, which is more natural

← Older revision		Revision as of 09:55, 19 April 2026
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	== Ketchup ==		== Ketchup ==
	Ketchup may be described as the {{nowrap\| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its ploidacot is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament.		Ketchup may be described as the {{nowrap\| 46 & 94 }} temperament. It has a semi-octave period and a generator for a syntonic~septimal comma, four of which plus a period gives the perfect fifth; its [[ploidacot]] is diploid gamma-tetracot. [[140edo]] is an obvious tuning for this temperament.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

	Comma list: 289/288, 325/324, 352/351, 385/384, ~~561~~/~~560~~		Comma list: 289/288, 325/324, 352/351, 385/384, 442/441

	Mapping: {{mapping\| 2 3 4 6 7 8 8 \| 0 4 15 -9 -2 -14 4 }}		Mapping: {{mapping\| 2 3 4 6 7 8 8 \| 0 4 15 -9 -2 -14 4 }}
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	Badness (Sintel): 0.845		Badness (Sintel): 0.845

	=== ~~19-limit~~ ===		=== 2.3.5.7.11.13.17.23 subgroup ===
	Subgroup: 2.3.5.7.11.13.17.19		Subgroup: 2.3.5.7.11.13.17.23

	Comma list: ~~190~~/~~189~~, ~~209~~/~~208~~, ~~289~~/~~288~~, 352/351, 385/384, ~~561~~/~~560~~		Comma list: 253/252, 289/288, 325/324, 352/351, 385/384, 391/390

	Mapping: {{mapping\| 2 3 4 6 7 8 8 9 \| 0 4 15 -9 -2 -14 4 ~~-12~~ }}		Mapping: {{mapping\| 2 3 4 6 7 8 8 9 \| 0 4 15 -9 -2 -14 4 1 }}

	Optimal tunings:		Optimal tunings:
	* WE: ~17/12 = 600.~~1639~~{{c}}, ~66/65 = 25.~~6669~~{{c}}		* WE: ~17/12 = 600.1139{{c}}, ~66/65 = 25.7053{{c}}
	* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.~~6597~~{{c}}		* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.7013{{c}}

	{{Optimal ET sequence\|legend=0\| 46, 94, ~~140h }}~~		{{Optimal ET sequence\|legend=0\| 46, 94, 140 }}

	~~Badness (Sintel): 1.11~~

	~~=== 23-limit ===~~
	~~Subgroup: 2.3.5.7.11.13.17.19.23~~

	~~Comma list: 190/189, 209/208, 253/252, 289/288, 323/322, 352/351, 385/384~~

	~~Mapping: {{mapping\| 2 3 4 6 7 8 8 9 9 \| 0 4 15 -9 -2 -14 4 -12 1 }}~~

	~~Optimal tunings:~~
	* WE: ~17/12 = 600.1777{{c}}, ~66/65 = 25.6682{{c}}
	* CWE: ~17/12 = 600.0000{{c}}, ~66/65 = 25.6605{{c}}

	~~{{Optimal ET sequence\|legend=0\| 46, 94, 140h~~ }}

	Badness (Sintel): 1.00		Badness (Sintel): 0.772

	== Undecental ==		== Undecental ==

FloraC: Status update

2026-04-15T17:59:41Z

Status update

← Older revision		Revision as of 17:59, 15 April 2026
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	* [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan\|Gamelismic clan]]		* [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan\|Gamelismic clan]]
	* ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot\|Alphatricot family]]		* ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot\|Alphatricot family]]
	* ''[[Monkey]]'' (+875/864) → [[Tetracot family #Monkey\|Tetracot family]]		* [[Monkey]] (+875/864) → [[Tetracot family #Monkey\|Tetracot family]]
	* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]		* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]
	* [[Misty]] (+3136/3125) → [[Misty family #Misty\|Misty family]]		* [[Misty]] (+3136/3125) → [[Misty family #Misty\|Misty family]]

← Older revision		Revision as of 07:57, 26 May 2026
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	* [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan\|Gamelismic clan]]		* [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan\|Gamelismic clan]]
	* ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot\|Alphatricot family]]		* ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot\|Alphatricot family]]
			* [[Misty]] (+3136/3125) → [[Misty family #Misty\|Misty family]]
	* [[Monkey]] (+875/864) → [[Tetracot family #Monkey\|Tetracot family]]		* [[Monkey]] (+875/864) → [[Tetracot family #Monkey\|Tetracot family]]
	* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]		* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]
	* [[Misty]] (+3136/3125) → [[Misty family #Misty\|Misty family]]
	* ''[[Supers]]'' (+118098/117649) → [[Stearnsmic clan #Supers\|Stearnsmic clan]]
	* ''[[Undim]]'' (+390625/388962) → [[Undim family #Septimal undim\|Undim family]]		* ''[[Undim]]'' (+390625/388962) → [[Undim family #Septimal undim\|Undim family]]
	* ''[[Quinticosiennic]]'' (+395136/390625) → [[Quintaleap family #Quinticosiennic\|Quintaleap family]]		* ''[[Quinticosiennic]]'' (+395136/390625) → [[Quintaleap family #Quinticosiennic\|Quintaleap family]]
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	* [[Amity]] (+4375/4374) → [[Amity family #Septimal amity\|Amity family]]		* [[Amity]] (+4375/4374) → [[Amity family #Septimal amity\|Amity family]]
	* ''[[Countercata]]'' (+15625/15552) → [[Kleismic family #Countercata\|Kleismic family]]		* ''[[Countercata]]'' (+15625/15552) → [[Kleismic family #Countercata\|Kleismic family]]
			* ''[[Abergravity]]'' (+177147/175000) → [[Gravity family #Abergravity\|Gravity family]]
			* ''[[Supers]]'' (+118098/117649) → [[Stearnsmic clan #Supers\|Stearnsmic clan]]
	* ''[[Warrior]]'' (+78732/78125) → [[Sensipent family #Warrior\|Sensipent family]]		* ''[[Warrior]]'' (+78732/78125) → [[Sensipent family #Warrior\|Sensipent family]]
	* ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter\|Escapade family]]		* ''[[Alphaquarter]]'' (+29360128/29296875) → [[Escapade family #Alphaquarter\|Escapade family]]

← Older revision		Revision as of 17:59, 15 April 2026
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	* [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan\|Gamelismic clan]]		* [[Rodan]] (+245/243) → [[Gamelismic clan #Rodan\|Gamelismic clan]]
	* ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot\|Alphatricot family]]		* ''[[Alphatrimot]]'' (+2430/2401) → [[Alphatricot family #Alphatrimot\|Alphatricot family]]
	* ''[[Monkey]]'' (+875/864) → [[Tetracot family #Monkey\|Tetracot family]]		* [[Monkey]] (+875/864) → [[Tetracot family #Monkey\|Tetracot family]]
	* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]		* [[Buzzard]] (+1728/1715) → [[Buzzardsmic clan #Buzzard\|Buzzardsmic clan]]
	* [[Misty]] (+3136/3125) → [[Misty family #Misty\|Misty family]]		* [[Misty]] (+3136/3125) → [[Misty family #Misty\|Misty family]]

← Older revision		Revision as of 12:31, 6 June 2026
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	{{Technical data page}}		{{Technical data page}}
	This is a collection of [[rank-2 temperament\|rank-2]] ~~[[regular temperament\|~~temperaments]] [[tempering out]] the [[~~hemifamity comma~~]] ({{monzo\|legend=1\| 10 -6 1 -1 }}, [[ratio]]: 5120/5103). These temperaments divide an exact or approximate septimal quartertone, [[36/35]] into two equal steps, each representing [[81/80]][[~]][[64/63]], the syntonic comma or the septimal comma. Therefore, classical and septimal intervals are found by the same [[chain of fifths]] inflected by the syntonic~septimal comma to the opposite sides. In addition we may identify [[10/7]] by the augmented fourth and [[50/49]] by the [[Pythagorean comma]].		This is a collection of [[rank-2 temperament\|rank-2]] '''aberschismic temperaments''', which [[tempering out\|temper out]] the [[aberschisma]] ({{monzo\|legend=1\| 10 -6 1 -1 }}, [[ratio]]: 5120/5103). These temperaments divide an exact or approximate septimal quartertone, [[36/35]] into two equal steps, each representing [[81/80]][[~]][[64/63]], the syntonic comma or the septimal comma. Therefore, classical and septimal intervals are found by the same [[chain of fifths]] inflected by the syntonic~septimal comma to the opposite sides. In addition we may identify [[10/7]] by the augmented fourth and [[50/49]] by the [[Pythagorean comma]].

	Temperaments belonging to this category and generated by the fifth are dominant, garibaldi, kwai, undecental, and leapday. Dominant has 5/4 mapped to M3. Garibaldi has 5/4 mapped to d4. Kwai has 5/4 mapped to 4A7. Undecental has 5/4 mapped to 5d7. Leapday has 5/4 mapped to 3A1.		Temperaments belonging to this category and generated by the fifth are dominant, garibaldi, kwai, undecental, and leapday. Dominant has 5/4 mapped to M3. Garibaldi has 5/4 mapped to d4. Kwai has 5/4 mapped to 4A7. Undecental has 5/4 mapped to 5d7. Leapday has 5/4 mapped to 3A1.
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	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Leapday]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Leapday]].''

	Leapday tempers out [[686/675]], the senga, in addition to the ~~hemifamity comma~~, and may be described as the {{nowrap\| 29 & 46 }} temperament. It extends [[leapfrog]], such that [[7/4]] is found by 15 generators up, as a double-augmented fifth (a major sixth and a diesis). 5/4 is found by a tritone above that, as a triple-augmented unison (a minor third and two dieses). [[46edo]] itself is an excellent tuning for this.		Leapday tempers out [[686/675]], the senga, in addition to the aberschisma, and may be described as the {{nowrap\| 29 & 46 }} temperament. It extends [[leapfrog]], such that [[7/4]] is found by 15 generators up, as a double-augmented fifth (a major sixth and a diesis). 5/4 is found by a tritone above that, as a triple-augmented unison (a minor third and two dieses). [[46edo]] itself is an excellent tuning for this.

	Leapday is more notable in the higher limits than the lower, as it nails the 13-limit pretty well from identifying [[14/11]] by a major third and [[13/11]] by a minor third, tempering out not only [[352/351]] and [[364/363]] but [[91/90]], [[121/120]], [[169/168]] and [[196/195]]. It can be further extended to include the [[17/1\|17th]] and [[23/1\|23rd]] [[harmonic]]s. Adding 17 would fix the valid diamond monotone tuning to 46edo, however.		Leapday is more notable in the higher limits than the lower, as it nails the 13-limit pretty well from identifying [[14/11]] by a major third and [[13/11]] by a minor third, tempering out not only [[352/351]] and [[364/363]] but [[91/90]], [[121/120]], [[169/168]] and [[196/195]]. It can be further extended to include the [[17/1\|17th]] and [[23/1\|23rd]] [[harmonic]]s. Adding 17 would fix the valid diamond monotone tuning to 46edo, however.

	Leapday has an alternative extension called [[porwell temperaments #Polypyth\|polypyth]], which tempers out the same 5-limit comma as leapday, but with the porwell ([[6144/6125]]) rather than the ~~hemifamity comma~~ tempered out.		Leapday has an alternative extension called [[porwell temperaments #Polypyth\|polypyth]], which tempers out the same 5-limit comma as leapday, but with the porwell comma ([[6144/6125]]) rather than the aberschisma tempered out.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Jorgensen]].''		: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Jorgensen]].''

	Jorgensen tempers out the [[linus comma]] in addition to the ~~hemifamity comma~~, and may be described as the {{nowrap\| 70 & 140 }} temperament, with a 70th-octave period. Its ploidacot is 70-ploid acot.		Jorgensen tempers out the [[linus comma]] in addition to the aberschisma, and may be described as the {{nowrap\| 70 & 140 }} temperament, with a 70th-octave period. Its ploidacot is 70-ploid acot.

	It is the natural 7-limit extension of the 5-limit temperament tempering out the 70-comma, named by [[Mike Battaglia]] in 2012 for historical interests<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103982.html Yahoo! Tuning Group \| ''Jorgensen Temperament'']</ref>.		It is the natural 7-limit extension of the 5-limit temperament tempering out the 70-comma, named by [[Mike Battaglia]] in 2012 for historical interests<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_103982.html Yahoo! Tuning Group \| ''Jorgensen Temperament'']</ref>.