2.3.5.11 subgroup - Revision history

Overthink: /* Rank-2 temperaments */ mohaha; some other changes

2026-05-05T21:34:11Z

Rank-2 temperaments: mohaha; some other changes

← Older revision		Revision as of 21:34, 5 May 2026
Line 8:		Line 8:

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	[[~~Porcupine~~]] ~~(15 & 22)~~ provides a ~~simple yet high-damage~~ approximation to the ~~subgroup~~. ~~It is generated by a submajor second of around 163 cents, representing [[10/9]], [[11/10]], and [[12/11]], tempering out [[55/54]], [[100/99]], and [[121/120]]~~. ~~Two of these reach [[6/~~5~~]]~[[~~11~~/9]]~~, ~~and three of them reach~~ the ~~perfect fourth [[4/3]]. It finds 11/8 at~~ -~~4 generators and 5/4 at -5 generators. The interval at -7 generators represents several important ratios, such as [[25/24]], [[33/32]], [[45/44]], and [[81/80]]~~.		Since [[7edo]] provides a relatively accurate approximation of the 2.3.5.11 subgroup for its size, temperaments in this subgroup tend to work well with the 7-form.

	[[~~Schismic~~]] provides ~~two reasonable aproximations~~ to the ~~2.3.5~~.11 ~~subgroup~~, ~~one by finding~~ 11/~~8 at the triple-augmented second (+23 fifths) through the~~ [[~~cassandra~~]] ~~mapping~~, and ~~another by finding~~ 11/~~8 at the quadruple-diminished seventh (-30 fifths) through~~ the [[~~helenus~~]] ~~mapping~~. ~~Helenus~~, ~~{{nowrap\| 53 & 65 }}~~, ~~provides a much better approximation to the subgroup~~, ~~as both 5 and 11 are generated in the same direction~~, and ~~the optimal tuning for prime 11 tunes 5 much more accurately~~.		[[Porcupine]] (15 & 22) provides a simple yet high-damage approximation to the subgroup. It is generated by a submajor second of around 163 cents, representing [[10/9]], [[11/10]], and [[12/11]], tempering out [[55/54]], [[100/99]], and [[121/120]]. Two of these reach [[6/5]]~[[11/9]], and three of them reach the perfect fourth [[4/3]]. It finds 11/8 at –4 generators and 5/4 at –5 generators. The interval at –7 generators represents several important ratios, such as [[25/24]], [[33/32]], [[45/44]], and [[81/80]].

	[[Gravity]] also provides a very natural approximation to the 2.3.5.11 subgroup, having ~40/27 as the generator, and finding 3/2 at -6 gens, 5/4 at ~~-17~~ gens and 11/8 at ~~-15~~ gens. It is the unique temperament in the 2.3.5.11 subgroup equating [[81/80]] ({{S\|9}}), [[100/99]] ({{S\|10}}), and [[121/120]] ({{S\|11}}), thus [[tempering out]] [[243/242]], [[4000/3993]], and [[8019/8000]]. [[65edo]] is the unique intersection of schismic (helenus) and gravity, and thus has, for its size, great approximations to the subgroup.		[[Mohaha]] (24 & 31) can be considered an extension to [[meantone]] that adds neutral intervals, with the perfect fifth split into two neutral third generators, each representing [[11/9]]~[[27/22]], tempering out [[243/242]]. Here [[11/8]]~[[15/11]] is found as a semi-augmented fourth, and [[11/10]]~[[12/11]] is found as a neutral second, meaning [[121/120]] is also tempered out. The neutral third is very close to 11/9 as a result of the flat fifth, though this means the 11th harmonic is tuned considerably flat.

			[[Schismic]] provides two reasonable aproximations to the 2.3.5.11 subgroup, one by finding 11/8 at the triple-augmented second (+23 fifths) through the [[cassandra]] {{nowrap\| (41 & 53) }} mapping, tempering out [[2200/2187]], and another by finding 11/8 at the quadruple-diminished seventh (–30 fifths) through the [[helenus]] mapping, tempering out [[8019/8000]]. Helenus, {{nowrap\| 53 & 65 }}, provides a much better approximation to the subgroup, as both 5 and 11 are generated in the same direction, and the optimal tuning for prime 11 is closer to the optimal tuning for 5.

			[[Gravity]] (7 & 58) also provides a very natural approximation to the 2.3.5.11 subgroup, having ~40/27 as the generator, and finding 3/2 at –6 gens, 5/4 at –17 gens and 11/8 at –15 gens. It is the unique temperament in the 2.3.5.11 subgroup equating [[81/80]] ({{S\|9}}), [[100/99]] ({{S\|10}}), and [[121/120]] ({{S\|11}}), thus [[tempering out]] [[243/242]], [[4000/3993]], and [[8019/8000]]. [[65edo]] is the unique intersection of schismic (helenus) and gravity, and thus has, for its size, great approximations to the subgroup.

	=== Rank-3 temperaments ===		=== Rank-3 temperaments ===

Overthink: /* Rank-2 temperaments */ + porcupine

2026-05-05T21:20:07Z

Rank-2 temperaments: + porcupine

← Older revision		Revision as of 21:20, 5 May 2026
Line 8:		Line 8:

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	[[Schismic]] provides two reasonable aproximations to the 2.3.5.11 subgroup, one by finding 11/8 at the triple-augmented second (+23 fifths) through the [[cassandra]] mapping, and another by finding 11/8 at the quadruple-diminished seventh (-30 fifths) through the [[helenus]] mapping. Helenus, {{nowrap\| 53 & 65 }}, provides a much better approximation to the subgroup, as both 5 and 11 are generated in the same direction.		[[Porcupine]] (15 & 22) provides a simple yet high-damage approximation to the subgroup. It is generated by a submajor second of around 163 cents, representing [[10/9]], [[11/10]], and [[12/11]], tempering out [[55/54]], [[100/99]], and [[121/120]]. Two of these reach [[6/5]]~[[11/9]], and three of them reach the perfect fourth [[4/3]]. It finds 11/8 at -4 generators and 5/4 at -5 generators. The interval at -7 generators represents several important ratios, such as [[25/24]], [[33/32]], [[45/44]], and [[81/80]].

			[[Schismic]] provides two reasonable aproximations to the 2.3.5.11 subgroup, one by finding 11/8 at the triple-augmented second (+23 fifths) through the [[cassandra]] mapping, and another by finding 11/8 at the quadruple-diminished seventh (-30 fifths) through the [[helenus]] mapping. Helenus, {{nowrap\| 53 & 65 }}, provides a much better approximation to the subgroup, as both 5 and 11 are generated in the same direction, and the optimal tuning for prime 11 tunes 5 much more accurately.

	[[Gravity]] also provides a very natural approximation to the 2.3.5.11 subgroup, having ~40/27 as the generator, and finding 3/2 at -6 gens, 5/4 at -17 gens and 11/8 at -15 gens. It is the unique temperament in the 2.3.5.11 subgroup equating [[81/80]] ({{S\|9}}), [[100/99]] ({{S\|10}}), and [[121/120]] ({{S\|11}}), thus [[tempering out]] [[243/242]], [[4000/3993]], and [[8019/8000]]. [[65edo]] is the unique intersection of schismic (helenus) and gravity, and thus has, for its size, great approximations to the subgroup.		[[Gravity]] also provides a very natural approximation to the 2.3.5.11 subgroup, having ~40/27 as the generator, and finding 3/2 at -6 gens, 5/4 at -17 gens and 11/8 at -15 gens. It is the unique temperament in the 2.3.5.11 subgroup equating [[81/80]] ({{S\|9}}), [[100/99]] ({{S\|10}}), and [[121/120]] ({{S\|11}}), thus [[tempering out]] [[243/242]], [[4000/3993]], and [[8019/8000]]. [[65edo]] is the unique intersection of schismic (helenus) and gravity, and thus has, for its size, great approximations to the subgroup.

FloraC: Style

2026-04-19T10:24:45Z

Style

← Older revision		Revision as of 10:24, 19 April 2026
Line 1:		Line 1:
	The '''2.3.5.11 subgroup''' (~~AKA~~ ''yala'' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 3, 5, and 11 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the [[octave]] include [[5/4]], [[3/2]], [[11/8]], [[11/9]], [[27/22]], and so on.		The '''2.3.5.11 subgroup''' (a.k.a. ''yala'' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 3, 5, and 11 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the [[octave]] include [[5/4]], [[3/2]], [[11/8]], [[11/9]], [[27/22]], and so on.

	In can be thought as either an extension of [[Alpharabian tuning]] with the familiar 5-limit chords and stuctures, or a retraction of the 11-limit by removing prime 7. It can be similar to the [[2.3.5.13 subgroup]], specially considering neutral interval pairs such as 39/32 ~ 11/9 and 16/13 ~ 27/22, which are connected by the small comma of [[352/351]].		In can be thought as either an extension of [[Alpharabian tuning]] with the familiar 5-limit chords and stuctures, or a retraction of the 11-limit by removing prime 7. It can be similar to the [[2.3.5.13 subgroup]], specially considering neutral interval pairs such as 39/32~11/9 and 16/13~27/22, which are connected by the small comma of [[352/351]].

	== Regular temperaments ==		== Regular temperaments ==
Line 10:		Line 10:
	[[Schismic]] provides two reasonable aproximations to the 2.3.5.11 subgroup, one by finding 11/8 at the triple-augmented second (+23 fifths) through the [[cassandra]] mapping, and another by finding 11/8 at the quadruple-diminished seventh (-30 fifths) through the [[helenus]] mapping. Helenus, {{nowrap\| 53 & 65 }}, provides a much better approximation to the subgroup, as both 5 and 11 are generated in the same direction.		[[Schismic]] provides two reasonable aproximations to the 2.3.5.11 subgroup, one by finding 11/8 at the triple-augmented second (+23 fifths) through the [[cassandra]] mapping, and another by finding 11/8 at the quadruple-diminished seventh (-30 fifths) through the [[helenus]] mapping. Helenus, {{nowrap\| 53 & 65 }}, provides a much better approximation to the subgroup, as both 5 and 11 are generated in the same direction.

	[[Gravity]] also provides a very natural approximation to the 2.3.5.11 subgroup, having ~40/27 as the generator, and finding 3/2 at -6 gens, 5/4 at -17 gens and 11/8 at -15 gens. It is the unique temperament in the 2.3.5.11 subgroup equating [[~~81/80\|S9 =~~ 81/80]], [[~~100/99\|S10 =~~ 100/99]], and [[~~121/120\|S11 =~~ 121/120]], thus tempering out [[243/242]], [[4000/3993]], and [[8019/8000]]. [[65edo]] is the unique intersection of schismic (helenus) and gravity, and thus has, for its size, great approximations to the subgroup.		[[Gravity]] also provides a very natural approximation to the 2.3.5.11 subgroup, having ~40/27 as the generator, and finding 3/2 at -6 gens, 5/4 at -17 gens and 11/8 at -15 gens. It is the unique temperament in the 2.3.5.11 subgroup equating [[81/80]] ({{S\|9}}), [[100/99]] ({{S\|10}}), and [[121/120]] ({{S\|11}}), thus [[tempering out]] [[243/242]], [[4000/3993]], and [[8019/8000]]. [[65edo]] is the unique intersection of schismic (helenus) and gravity, and thus has, for its size, great approximations to the subgroup.

	=== Rank-3 temperaments ===		=== Rank-3 temperaments ===
	[[Vishdel]] provides a low-complexity, accurate temperament, but for those searching a much higher accuracy system, [[tritomere]] is among the best rank-3 temperaments for this case, having tremendous accuracy with manageable complexity, tempering out the difference between three [[~~243/242\|rastmas~~]] and one [[~~81/80\|~~syntonic comma]] (0.08 cents). Its boundary of usability begins at [[152edo\|152]] and [[159edo]], the latter inheriting the marvelous fifths from 53edo, one that [[Aura]] has shown great interest in. Bigger edos that support this excellent temperament include [[342edo]], [[494edo]], [[677edo]], [[1171edo]], among others.		[[Vishdel]] provides a low-complexity, accurate temperament, but for those searching a much higher accuracy system, [[tritomere]] is among the best rank-3 temperaments for this case, having tremendous accuracy with manageable complexity, tempering out the difference between three [[rastma]]s and one [[syntonic comma]] (0.08 cents). Its boundary of usability begins at [[152edo\|152]] and [[159edo]], the latter inheriting the marvelous fifths from 53edo, one that [[Aura]] has shown great interest in. Bigger edos that support this excellent temperament include [[342edo]], [[494edo]], [[677edo]], [[1171edo]], among others.

	[[Category:Just intonation subgroups\|#]]		[[Category:Just intonation subgroups\|#]]
	[[Category:Rank-4 temperaments\|#]]		[[Category:Rank-4 temperaments\|#]]
	[[Category:11-limit\|#]]		[[Category:11-limit\|#]]

Eufalesio at 09:54, 19 April 2026

2026-04-19T09:54:05Z

← Older revision		Revision as of 09:54, 19 April 2026
Line 1:		Line 1:
	The '''2.3.5.11 subgroup''' (AKA as ''yala'' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 3, 5, and 11 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the [[octave]] include [[5/4]], [[3/2]], [[11/8]], [[11/9]], [[27/22]], and so on.		The '''2.3.5.11 subgroup''' (AKA ''yala'' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 3, 5, and 11 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the [[octave]] include [[5/4]], [[3/2]], [[11/8]], [[11/9]], [[27/22]], and so on.

	In can be thought as either an extension of [[Alpharabian tuning]] with the familiar 5-limit chords and stuctures, or a retraction of the 11-limit by removing prime 7. It can be similar to the [[2.3.5.13 subgroup]], specially considering neutral interval pairs such as 39/32 ~ 11/9 and 16/13 ~ 27/22, which are connected by the small comma of [[352/351]].		In can be thought as either an extension of [[Alpharabian tuning]] with the familiar 5-limit chords and stuctures, or a retraction of the 11-limit by removing prime 7. It can be similar to the [[2.3.5.13 subgroup]], specially considering neutral interval pairs such as 39/32 ~ 11/9 and 16/13 ~ 27/22, which are connected by the small comma of [[352/351]].

Eufalesio: color notation

2026-04-19T09:53:36Z

color notation

← Older revision		Revision as of 09:53, 19 April 2026
Line 1:		Line 1:
	The '''2.3.5.11 subgroup''' is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 3, 5, and 11 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the [[octave]] include [[5/4]], [[3/2]], [[11/8]], [[11/9]], [[27/22]], and so on.		The '''2.3.5.11 subgroup''' (AKA as ''yala'' in [[color notation]]) is a [[just intonation subgroup]] consisting of [[rational interval]]s where 2, 3, 5, and 11 are the only allowable [[prime factor]]s, so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the [[octave]] include [[5/4]], [[3/2]], [[11/8]], [[11/9]], [[27/22]], and so on.

	In can be thought as either an extension of [[Alpharabian tuning]] with the familiar 5-limit chords and stuctures, or a retraction of the 11-limit by removing prime 7. It can be similar to the [[2.3.5.13 subgroup]], specially considering neutral interval pairs such as 39/32 ~ 11/9 and 16/13 ~ 27/22, which are connected by the small comma of [[352/351]].		In can be thought as either an extension of [[Alpharabian tuning]] with the familiar 5-limit chords and stuctures, or a retraction of the 11-limit by removing prime 7. It can be similar to the [[2.3.5.13 subgroup]], specially considering neutral interval pairs such as 39/32 ~ 11/9 and 16/13 ~ 27/22, which are connected by the small comma of [[352/351]].

Overthink: /* Rank-2 temperaments */ note commas and structure for gravity

2026-03-16T05:05:49Z

Rank-2 temperaments: note commas and structure for gravity

← Older revision		Revision as of 05:05, 16 March 2026
Line 10:		Line 10:
	[[Schismic]] provides two reasonable aproximations to the 2.3.5.11 subgroup, one by finding 11/8 at the triple-augmented second (+23 fifths) through the [[cassandra]] mapping, and another by finding 11/8 at the quadruple-diminished seventh (-30 fifths) through the [[helenus]] mapping. Helenus, {{nowrap\| 53 & 65 }}, provides a much better approximation to the subgroup, as both 5 and 11 are generated in the same direction.		[[Schismic]] provides two reasonable aproximations to the 2.3.5.11 subgroup, one by finding 11/8 at the triple-augmented second (+23 fifths) through the [[cassandra]] mapping, and another by finding 11/8 at the quadruple-diminished seventh (-30 fifths) through the [[helenus]] mapping. Helenus, {{nowrap\| 53 & 65 }}, provides a much better approximation to the subgroup, as both 5 and 11 are generated in the same direction.

	[[Gravity]] also provides a very natural approximation to the 2.3.5.11 subgroup, having ~40/27 as the generator, and finding 3/2 at -6 gens, 5/4 at -17 gens and 11/8 at -15 gens. [[65edo]] is the intersection of schismic (helenus) and gravity, and thus has, for its size, great approximations to the subgroup.		[[Gravity]] also provides a very natural approximation to the 2.3.5.11 subgroup, having ~40/27 as the generator, and finding 3/2 at -6 gens, 5/4 at -17 gens and 11/8 at -15 gens. It is the unique temperament in the 2.3.5.11 subgroup equating [[81/80\|S9 = 81/80]], [[100/99\|S10 = 100/99]], and [[121/120\|S11 = 121/120]], thus tempering out [[243/242]], [[4000/3993]], and [[8019/8000]]. [[65edo]] is the unique intersection of schismic (helenus) and gravity, and thus has, for its size, great approximations to the subgroup.

	=== Rank-3 temperaments ===		=== Rank-3 temperaments ===

FloraC: /* Regular temperaments */ review list

2026-02-13T09:42:01Z

Regular temperaments: review list

← Older revision		Revision as of 09:42, 13 February 2026
Line 5:		Line 5:
	== Regular temperaments ==		== Regular temperaments ==
	=== Rank-1 temperaments (edos) ===		=== Rank-1 temperaments (edos) ===
	It is relatively well approximated by the following edos (bold ones do particularly well in this subgroup): ~~[[7edo\|7]], [[15edo\|15]], [[22edo\|22]], [[24edo~~\|'''24''']], ~~[[31edo\|~~31]], ~~[[38edo\|38]]~~, ~~[[41edo\|~~41]], ~~[[46edo\|~~46]], ~~[[65edo\|~~'''65'''~~]], [[72edo\|'''72''']], [[80edo\|80]]~~, ~~[[87edo\|'''~~87~~''']]~~, ~~[[94edo\|94]], [[96edo\|96]], [[118edo\|'''~~118~~''']], [[130edo\|130]]~~, ~~[[137edo\|137]], [[159edo\|~~'''~~159~~''']], ~~[[183edo\|183]]~~, ~~[[217edo\|217]]~~, ~~[[224edo\|224]]~~, ~~[[270edo\|~~'''~~270~~'''~~]], [[311edo\|311]]~~, …		The 2.3.5.11 subgroup is relatively well approximated by the following edos (decreasing [[TE error]], bold ones do particularly well in this subgroup): {{EDOs\| '''7''', 12, 15, 19, 22, 31, 34, 41, 46, 53, '''65''', 87, 118, '''152''', 224, 270, 335, '''342''', … }}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===

FloraC at 10:24, 11 February 2026

2026-02-11T10:24:54Z

← Older revision		Revision as of 10:24, 11 February 2026
Line 15:		Line 15:
	[[Vishdel]] provides a low-complexity, accurate temperament, but for those searching a much higher accuracy system, [[tritomere]] is among the best rank-3 temperaments for this case, having tremendous accuracy with manageable complexity, tempering out the difference between three [[243/242\|rastmas]] and one [[81/80\|syntonic comma]] (0.08 cents). Its boundary of usability begins at [[152edo\|152]] and [[159edo]], the latter inheriting the marvelous fifths from 53edo, one that [[Aura]] has shown great interest in. Bigger edos that support this excellent temperament include [[342edo]], [[494edo]], [[677edo]], [[1171edo]], among others.		[[Vishdel]] provides a low-complexity, accurate temperament, but for those searching a much higher accuracy system, [[tritomere]] is among the best rank-3 temperaments for this case, having tremendous accuracy with manageable complexity, tempering out the difference between three [[243/242\|rastmas]] and one [[81/80\|syntonic comma]] (0.08 cents). Its boundary of usability begins at [[152edo\|152]] and [[159edo]], the latter inheriting the marvelous fifths from 53edo, one that [[Aura]] has shown great interest in. Bigger edos that support this excellent temperament include [[342edo]], [[494edo]], [[677edo]], [[1171edo]], among others.

	[[Category:Just intonation subgroups]]		[[Category:Just intonation subgroups\|#]]
	[[Category:Rank-4 temperaments]]		[[Category:Rank-4 temperaments\|#]]
			[[Category:11-limit\|#]]

FloraC: Recategorize

2026-02-11T10:10:09Z

Recategorize

← Older revision		Revision as of 10:10, 11 February 2026
Line 15:		Line 15:
	[[Vishdel]] provides a low-complexity, accurate temperament, but for those searching a much higher accuracy system, [[tritomere]] is among the best rank-3 temperaments for this case, having tremendous accuracy with manageable complexity, tempering out the difference between three [[243/242\|rastmas]] and one [[81/80\|syntonic comma]] (0.08 cents). Its boundary of usability begins at [[152edo\|152]] and [[159edo]], the latter inheriting the marvelous fifths from 53edo, one that [[Aura]] has shown great interest in. Bigger edos that support this excellent temperament include [[342edo]], [[494edo]], [[677edo]], [[1171edo]], among others.		[[Vishdel]] provides a low-complexity, accurate temperament, but for those searching a much higher accuracy system, [[tritomere]] is among the best rank-3 temperaments for this case, having tremendous accuracy with manageable complexity, tempering out the difference between three [[243/242\|rastmas]] and one [[81/80\|syntonic comma]] (0.08 cents). Its boundary of usability begins at [[152edo\|152]] and [[159edo]], the latter inheriting the marvelous fifths from 53edo, one that [[Aura]] has shown great interest in. Bigger edos that support this excellent temperament include [[342edo]], [[494edo]], [[677edo]], [[1171edo]], among others.

	[[Category:~~Subgroup~~]]		[[Category:Just intonation subgroups]]
			[[Category:Rank-4 temperaments]]

Overthink: a category for that already exists

2026-01-15T09:12:35Z

a category for that already exists

← Older revision		Revision as of 09:12, 15 January 2026
Line 15:		Line 15:
	[[Vishdel]] provides a low-complexity, accurate temperament, but for those searching a much higher accuracy system, [[tritomere]] is among the best rank-3 temperaments for this case, having tremendous accuracy with manageable complexity, tempering out the difference between three [[243/242\|rastmas]] and one [[81/80\|syntonic comma]] (0.08 cents). Its boundary of usability begins at [[152edo\|152]] and [[159edo]], the latter inheriting the marvelous fifths from 53edo, one that [[Aura]] has shown great interest in. Bigger edos that support this excellent temperament include [[342edo]], [[494edo]], [[677edo]], [[1171edo]], among others.		[[Vishdel]] provides a low-complexity, accurate temperament, but for those searching a much higher accuracy system, [[tritomere]] is among the best rank-3 temperaments for this case, having tremendous accuracy with manageable complexity, tempering out the difference between three [[243/242\|rastmas]] and one [[81/80\|syntonic comma]] (0.08 cents). Its boundary of usability begins at [[152edo\|152]] and [[159edo]], the latter inheriting the marvelous fifths from 53edo, one that [[Aura]] has shown great interest in. Bigger edos that support this excellent temperament include [[342edo]], [[494edo]], [[677edo]], [[1171edo]], among others.

	[[Category:~~Just intonation subgroups~~]]		[[Category:Subgroup]]