Aberschismic temperaments - Revision history

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]]

FloraC: + more known naming history

2026-04-02T11:27:31Z

+ more known naming history

← Older revision		Revision as of 11:27, 2 April 2026
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	== Hemidromeda ==		== Hemidromeda ==
	Hemidromeda may be described as the {{nowrap\| 29 & 111 }} temperament. ~~The name~~ ''hemidromeda'' comes from "hemi-" (Ancient Greek for "one half") and ''[[andromeda]]'', because the generator is 1/2 of andromeda's perfect twelfth (~3/1, about 1902.4 cents); the ploidacot for this temperament is alpha-dicot.		Hemidromeda may be described as the {{nowrap\| 29 & 111 }} temperament. Named by [[Xenllium]] in 2023, ''hemidromeda'' comes from ''hemi-'' (Ancient Greek for "one half") and ''[[andromeda]]'', because the generator is 1/2 of andromeda's perfect twelfth (~3/1, about 1902.4 cents); the ploidacot for this temperament is alpha-dicot.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	Countriton may be described as the {{nowrap\| 51c & 53 }} temperament. It splits the [[24/1\|24th harmonic]] into nine tritone generators; its ploidacot is thus delta-enneacot. Among the possible tunings are [[157edo]] and [[210edo]], as well as [[104edo]] in the 104c val.		Countriton may be described as the {{nowrap\| 51c & 53 }} temperament. It splits the [[24/1\|24th harmonic]] into nine tritone generators; its ploidacot is thus delta-enneacot. Among the possible tunings are [[157edo]] and [[210edo]], as well as [[104edo]] in the 104c val.

			Countriton was named by [[Xenllium]] in 2022 as a counterpart of [[untriton]].

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7
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	== Artoneutral ==		== Artoneutral ==
	Artoneutral can be described as the {{nowrap\| 87 & 94 }} temperament. It is generated by an artoneutral third of ~11/9 (or a tendoneutral sixth of ~18/11), nine of which make the [[12/1\|12th harmonic]]; its ploidacot is thus beta-enneacot. [[181edo]] may be recommended as a tuning.		Artoneutral can be described as the {{nowrap\| 87 & 94 }} temperament. It is generated by an artoneutral third of ~11/9 (or a tendoneutral sixth of ~18/11), nine of which make the [[12/1\|12th harmonic]]; its ploidacot is thus beta-enneacot. [[181edo]] may be recommended as a tuning.

			Artoneutral was named by [[Flora Canou]] in 2023 for its generator's quality.

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

FloraC: Move kwai back cuz mirkwai clan is a no-2 clan, which doesn't explain its structure very well

2026-04-02T11:04:06Z

Move kwai back cuz mirkwai clan is a no-2 clan, which doesn't explain its structure very well

Show changes

Overthink: Undo revision 218064 by Overthink (talk) oops nvm

2025-11-28T00:35:13Z

Undo revision 218064 by Overthink (talk) oops nvm

← Older revision		Revision as of 00:35, 28 November 2025
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	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]] [[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]].

	Temperaments belonging to this category and generated by the fifth are dominant, garibaldi, kwai, 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.

	Diaschismic is generated by the fifth with a semi-octave period. Hemififths has the fifth sliced into two and 5/4 mapped to the hemififth + Pyth. comma. Hemidromeda has the fourth sliced into two and 5/4 mapped to the hemifourth + 3d4. Rodan has the fifth sliced into three as does slendric. Alphatrimot has the twelfth sliced into three as does alphatricot. Monkey has the fifth sliced into four as does tetracot. Buzzard has the twelfth sliced into four as does vulture. Misty is generated by the fifth with a 1/3-octave period. Supers has the fifth sliced into three with a semi-octave period. Undim is generated by the fifth with a 1/4-octave period. Quinticosiennic and quintakwai have the fourth sliced into five. Amity has the eleventh sliced into five. Countercata has the twelfth sliced into six as does hanson. Warrior has the 6th harmonic sliced into seven as does sensi. Finally, alphaquarter has the fourth sliced into nine as does escapade.		Diaschismic is generated by the fifth with a semi-octave period. Hemififths has the fifth sliced into two and 5/4 mapped to the hemififth + Pyth. comma. Hemidromeda has the fourth sliced into two and 5/4 mapped to the hemifourth + 3d4. Rodan has the fifth sliced into three as does slendric. Alphatrimot has the twelfth sliced into three as does alphatricot. Monkey has the fifth sliced into four as does tetracot. Buzzard has the twelfth sliced into four as does vulture. Misty is generated by the fifth with a 1/3-octave period. Supers has the fifth sliced into three with a semi-octave period. Undim is generated by the fifth with a 1/4-octave period. Quinticosiennic and quintakwai have the fourth sliced into five. Amity has the eleventh sliced into five. Countercata has the twelfth sliced into six as does hanson. Warrior has the 6th harmonic sliced into seven as does sensi. Finally, alphaquarter has the fourth sliced into nine as does escapade.

← 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>.