Breedsmic temperaments - Revision history

FloraC: - subneutral (more properly addressed in luna family)

2026-06-23T04:06:10Z

- subneutral (more properly addressed in luna family)

← Older revision		Revision as of 04:06, 23 June 2026
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	* ''[[Decoid]]'' (+67108864/66976875) → [[Quintosec family #Decoid\|Quintosec family]]		* ''[[Decoid]]'' (+67108864/66976875) → [[Quintosec family #Decoid\|Quintosec family]]
	* ''[[Quadritikleismic]]'' (+15625/15552) → [[Kleismic family #Quadritikleismic\|Kleismic family]]		* ''[[Quadritikleismic]]'' (+15625/15552) → [[Kleismic family #Quadritikleismic\|Kleismic family]]
			* ''[[Subneutral]]'' (+274877906944/274658203125) → [[Luna family #Subneutral\|Luna family]]
	* ''[[Neptune]]'' (+48828125/48771072) → [[Gammic family #Neptune\|Gammic family]]		* ''[[Neptune]]'' (+48828125/48771072) → [[Gammic family #Neptune\|Gammic family]]
	* ''[[Tertiseptisix]]'' (+390625000/387420489) → [[Quartonic family #Tertiseptisix\|Quartonic family]]		* ''[[Tertiseptisix]]'' (+390625000/387420489) → [[Quartonic family #Tertiseptisix\|Quartonic family]]
	* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Whitewood family #Greenwood\|Whitewood family]]		* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Whitewood family #Greenwood\|Whitewood family]]

	Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, septidiasemi~~, subneutral~~, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]].		Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, septidiasemi, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]].

	== Tertiaseptal ==		== Tertiaseptal ==
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	Badness (Sintel): 1.39		Badness (Sintel): 1.39

	~~== Subneutral ==~~
	~~{{See also\| Luna family }}~~

	~~[[Subgroup]]: 2.3.5.7~~

	~~[[Comma list]]: 2401/2400, 274877906944/274658203125~~

	~~{{Mapping\|legend=1\| 1 -41 8 -5 \| 0 60 -8 11 }}~~
	~~: mapping generators: ~2, ~46875/28672~~

	~~[[Optimal tuning]]s:~~
	* [[WE]]: ~2 = 1199.9998{{c}}, ~46875/28672 = 851.6994 (~57344/46875 = 348.3005{{c}})
	~~: [[error map]]: {{val\| -0.000 +0.013 +0.090 -0.132 }}~~
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~46875/28672 = 851.6995{{c}} (~57344/46875 = 348.3005{{c}})
	~~: error map: {{val\| 0.000 +0.014 +0.090 -0.132 }}~~

	~~{{Optimal ET sequence\|legend=1\| 31, …, 348, 379, 410, 441, 1354, 1795, 2236 }}~~

	~~[[Badness]] (Sintel): 1.16~~

	== Maviloid ==		== Maviloid ==

FloraC: /* Gorgik */ + intro

2026-05-28T10:21:19Z

Gorgik: + intro

← Older revision		Revision as of 10:21, 28 May 2026
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	== Gorgik ==		== Gorgik ==
			{{See also\| Llywelynsmic clan }}

			Gorgik may be described as the {{nowrap\| 21 & 37 }} temperament, with a [[ploidacot]] of 14-sheared 18-cot (or alpha-heptaseph due to a much simpler [[2.5.7 subgroup\|2.5.7-subgroup]] [[restriction]]). [[58edo]] makes for a strong tuning for this temperament.

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

FloraC: - newt (more properly addressed in the garischismic clan)

2026-05-20T09:40:27Z

- newt (more properly addressed in the garischismic clan)

@@ Line 6: / Line 6: @@
 Temperaments discussed elsewhere include:
 * ''[[Beatles]]'' (+64/63) → [[Archytas clan #Beatles|Archytas clan]]
 * [[Decimal]] (+25/24, 49/48 or 50/49) → [[Dicot family #Decimal|Dicot family]]
 * [[Squares]] (+81/80) → [[Meantone family #Squares|Meantone family]]
@@ Line 26: / Line 27: @@
 * ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Whitewood family #Greenwood|Whitewood family]]
-Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, newt, septidiasemi, subneutral, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]].
+Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, septidiasemi, subneutral, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]].
 == Tertiaseptal ==
@@ Line 596: / Line 597: @@
 [[Badness]] (Sintel): 0.945
 == Septidiasemi ==

FloraC: /* Tertiaseptal */ rework into a no-19 29-limit temp, which is much more natural

2026-05-18T08:46:37Z

Tertiaseptal: rework into a no-19 29-limit temp, which is much more natural

← Older revision		Revision as of 08:46, 18 May 2026
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	=== Tertiaseptia ===		=== Tertiaseptia ===
	This extension was considered by [[Gene Ward Smith]] as a 41-limit temperament<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_9274.html Yahoo! Tuning Group \| ''A 41-limit temperament'']</ref>. It can be extended as such by tempering out 703/702 and 697/696, and mapping 37 and 41 to -81 and +10 steps, respectively.		This extension was considered by [[Gene Ward Smith]] as a 41-limit temperament<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_9274.html Yahoo! Tuning Group \| ''A 41-limit temperament'']</ref>. It can be extended as such by tempering out 875/874, 714/713, 703/702 and 697/696, and mapping 19, 31, 37 and 41 to 94, 105, -81 and +10 steps, respectively.

	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11
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	Badness (Sintel): 0.956		Badness (Sintel): 0.956

	==== ~~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: 595/594, 625/624, 833/832, 1156/1155~~, 1216/1215~~, 2200/2197		Comma list: 595/594, 625/624, 833/832, 1105/1104, 1156/1155, 2200/2197

	Mapping: {{mapping\| 1 -19 7 0 112 43 49 ~~-94~~ \| 0 22 -5 3 -116 -42 -48 ~~105~~ }}		Mapping: {{mapping\| 1 -19 7 0 112 43 49 114 \| 0 22 -5 3 -116 -42 -48 -117 }}

	Optimal tunings:		Optimal tunings:
	* WE: ~2 = 1200.~~0187~~{{c}}, ~65/34 = 1122.~~8489~~{{c}} (~68/65 = 77.~~1698~~{{c}})		* WE: ~2 = 1200.0047{{c}}, ~44/23 = 1122.8363{{c}} (~23/22 = 77.1684{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~65/34 = 1122.~~8313~~{{c}} (~68/65 = 77.~~1687~~{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8319{{c}} (~23/22 = 77.1681{{c}})

	{{Optimal ET sequence\|legend=0\| 140, 171, 311 }}		{{Optimal ET sequence\|legend=0\| 31ei, 140, 171, 311 }}

	Badness (Sintel): 1.07		Badness (Sintel): 0.944

	==== 23~~-limit~~ ====		==== 2.3.5.7.11.13.17.23.29 subgroup ====
	Subgroup: 2.3.5.7.11.13.17.19.23		Subgroup: 2.3.5.7.11.13.17.23.29

	Comma list: 595/594, 625/624, 833/832, ~~875~~/~~874~~, 1105/1104, 1156/1155~~, 1216/1215~~		Comma list: 595/594, 625/624, 784/783, 833/832, 1015/1014, 1105/1104, 1156/1155

	Mapping: {{mapping\| 1 -19 7 0 112 43 49 ~~-94~~ 114 \| 0 22 -5 3 -116 -42 -48 ~~105~~ -117 }}		Mapping: {{mapping\| 1 -19 7 0 112 43 49 114 61 \| 0 22 -5 3 -116 -42 -48 -117 -60 }}

	Optimal tunings:		Optimal tunings:
	* WE: ~2 = ~~1200~~.~~0101~~{{c}}, ~44/23 = 1122.~~8418~~{{c}} (~23/22 = 77.~~1683~~{{c}})		* WE: ~2 = 1199.9945{{c}}, ~44/23 = 1122.8270{{c}} (~23/22 = 77.1675{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.~~8323~~{{c}} (~23/22 = 77.~~1677~~{{c}})		* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8322{{c}} (~23/22 = 77.1678{{c}})

	{{Optimal ET sequence\|legend=0\| 140, 311, 762g }}		{{Optimal ET sequence\|legend=0\| 31ei, 140, 311, 762g }}

	Badness (Sintel): ~~1.08~~		Badness (Sintel): 0.858

	~~==== 29-limit ====~~
	~~Subgroup: 2.3.5.7.11.13.17.19.23.29~~

	~~Comma list: 595/594, 625/624, 784/783, 833/832, 875/874, 1015/1014, 1105/1104, 1156/1155~~

	~~Mapping: {{mapping\| 1 -19 7 0 112 43 49 -94 114 61 \| 0 22 -5 3 -116 -42 -48 105 -117 -60 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1200.0007{{c}}, ~44/23 = 1122.8332{{c}} (~23/22 = 77.1675{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8326{{c}} (~23/22 = 77.1674{{c}})

	~~{{Optimal ET sequence\|legend=0\| 140, 311, 762g }}~~

	~~Badness (Sintel): 1.02~~

	~~==== 31-limit ====~~
	~~Subgroup: 2.3.5.7.11.13.17.19.23.29.31~~

	~~Comma list: 595/594, 625/624, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014~~

	~~Mapping: {{mapping\| 1 -19 7 0 112 43 49 -94 114 61 -83 \| 0 22 -5 3 -116 -42 -48 105 -117 -60 94 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1199.9721{{c}}, ~44/23 = 1122.8047{{c}} (~23/22 = 77.1673{{c}})
	* CWE: ~2 = 1200.0000{{c}}, ~44/23 = 1122.8309{{c}} (~23/22 = 77.1691{{c}})

	~~{{Optimal ET sequence\|legend=~~0~~\| 140, 171, 311 }}~~

	~~Badness (Sintel): 1~~.18

	=== Hemitert ===		=== Hemitert ===

FloraC: Sort links by ploidacot

2026-05-17T16:07:34Z

Sort links by ploidacot

← Older revision		Revision as of 16:07, 17 May 2026
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	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
	* ''[[~~Decimal~~]]'' (+25/~~24, 49/48 or 50/49~~) → [[~~Dicot family~~ #~~Decimal~~\|~~Dicot family~~]]		* ''[[Beatles]]'' (+64/63) → [[Archytas clan #Beatles\|Archytas clan]]
	* ''[[~~Beatles~~]]'' (+64/63 or ~~686~~/~~675~~) → [[~~Archytas clan~~ #~~Beatles~~\|~~Archytas clan~~]]		* [[Decimal]] (+25/24, 49/48 or 50/49) → [[Dicot family #Decimal\|Dicot family]]
	* [[Squares]] (+81/80) → [[Meantone family #Squares\|Meantone family]]		* [[Squares]] (+81/80) → [[Meantone family #Squares\|Meantone family]]
	* [[~~Myna~~]] (+~~126~~/~~125~~) → [[~~Starling temperaments~~ #~~Myna~~\|~~Starling temperaments~~]]		* ''[[Sesquiquartififths]]'' (+32805/32768) → [[Schismatic family #Sesquiquartififths\|Schismatic family]]
	* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle\|Gamelismic clan]]		* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle\|Gamelismic clan]]
	* ''[[Octacot]]'' (+245/243) → [[Tetracot family #Octacot\|Tetracot family]]		* ''[[Octacot]]'' (+245/243) → [[Tetracot family #Octacot\|Tetracot family]]
	* ''[[~~Greenwood~~]]'' (+~~405~~/~~392 or 1323~~/~~1280~~) → [[~~Whitewood~~ family #~~Greenwood~~\|~~Whitewood~~ family]]		* ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta\|Diaschismic family]]
			* [[Myna]] (+126/125) → [[Starling temperaments #Myna\|Starling temperaments]]
			* [[Harry]] (+19683/19600) → [[Gravity family #Harry\|Gravity family]]
	* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp\|Keemic temperaments]]		* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp\|Keemic temperaments]]
	* ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta\|Diaschismic family]]
	* ''[[Quadrimage]]'' (+3125/3072) → [[Magic family #Quadrimage\|Magic family]]
	* ''[[Hemiwürschmidt]]'' (+3136/3125 or 6144/6125) → [[Hemimean clan #Hemiwürschmidt\|Hemimean clan]]		* ''[[Hemiwürschmidt]]'' (+3136/3125 or 6144/6125) → [[Hemimean clan #Hemiwürschmidt\|Hemimean clan]]
			* ''[[Eagle]]'' (+10485760000/10460353203) → [[Vulture family #Eagle\|Vulture family]]
	* [[Ennealimmal]] (+4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]		* [[Ennealimmal]] (+4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]
			* ''[[Quadrimage]]'' (+3125/3072) → [[Magic family #Quadrimage\|Magic family]]
			* ''[[Amicable]]'' (+1600000/1594323) → [[Amity family #Amicable\|Amity family]]
			* ''[[Decoid]]'' (+67108864/66976875) → [[Quintosec family #Decoid\|Quintosec family]]
	* ''[[Quadritikleismic]]'' (+15625/15552) → [[Kleismic family #Quadritikleismic\|Kleismic family]]		* ''[[Quadritikleismic]]'' (+15625/15552) → [[Kleismic family #Quadritikleismic\|Kleismic family]]
	* [[Harry]] (+19683/19600) → [[Gravity family #Harry\|Gravity family]]
	* ''[[Sesquiquartififths]]'' (+32805/32768) → [[Schismatic family #Sesquiquartififths\|Schismatic family]]
	* ''[[Amicable]]'' (+1600000/1594323) → [[Amity family #Amicable\|Amity family]]
	* ''[[Neptune]]'' (+48828125/48771072) → [[Gammic family #Neptune\|Gammic family]]		* ''[[Neptune]]'' (+48828125/48771072) → [[Gammic family #Neptune\|Gammic family]]
	* ''[[Decoid]]'' (+67108864/66976875) → [[Quintosec family #Decoid\|Quintosec family]]
	* ''[[Tertiseptisix]]'' (+390625000/387420489) → [[Quartonic family #Tertiseptisix\|Quartonic family]]		* ''[[Tertiseptisix]]'' (+390625000/387420489) → [[Quartonic family #Tertiseptisix\|Quartonic family]]
	* ''[[~~Eagle~~]]'' (+~~10485760000~~/~~10460353203~~) → [[~~Vulture~~ family #~~Eagle~~\|~~Vulture~~ family]]		* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Whitewood family #Greenwood\|Whitewood family]]

	Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, newt, septidiasemi, subneutral, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]].		Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, newt, septidiasemi, subneutral, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]].

FloraC: /* Lockerbie */ - extension beyond 31, already verbally addressed

2026-05-17T15:58:11Z

Lockerbie: - extension beyond 31, already verbally addressed

← Older revision		Revision as of 15:58, 17 May 2026
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	Lockerbie can be described as the {{nowrap\| 103 & 270 }} temperament. Its generator is [[~]][[77/60]] from the 11-limit onwards, and 74 generator steps give the interval class of [[3/1\|3]]; its [[ploidacot]] is 26-sheared 74-cot. An obvious tuning is given by 270edo, but [[373edo]] and especially [[643edo]] work as well.		Lockerbie can be described as the {{nowrap\| 103 & 270 }} temperament. Its generator is [[~]][[77/60]] from the 11-limit onwards, and 74 generator steps give the interval class of [[3/1\|3]]; its [[ploidacot]] is 26-sheared 74-cot. An obvious tuning is given by 270edo, but [[373edo]] and especially [[643edo]] work as well.

	The temperament derives its name from the {{w\|Lockerbie\|Scottish town}}, where a {{w\|Pan Am Flight 103\|flight numbered 103}} crashed with 270 casualties, and the temperament has a [[temperament merging\|join]] 103 & 270, hence the name. The name is proposed in 2022 by [[Eliora]], who favours it due to simplicity, ease of pronunciation and relation to numbers 103 and 270.		The temperament derives its name from the {{w\|Lockerbie\|Scottish town}}, where a {{w\|Pan Am Flight 103\|flight numbered 103}} crashed with 270 casualties, and the temperament has a [[temperament merging\|join]] 103 & 270, hence the name. The name was proposed in 2022 by [[Eliora]], who favours it due to simplicity, ease of pronunciation and relation to numbers 103 and 270.

	Lockerbie also has a unique extension that adds the [[41/1\|41st]] [[harmonic]] such that the generator is also on the same step in 103 or 270 as [[41/32]], which means that [[616/615]] is tempered out.		Lockerbie also has a unique extension that adds the [[41/1\|41st]] [[harmonic]] such that the generator is also on the same step in 103 or 270 as [[41/32]], which means that [[616/615]] is tempered out.
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	Badness (Sintel): 1.07		Badness (Sintel): 1.07

	~~=== 2.3.5.7.11.13.17.41 subgroup ===~~
	~~Subgroup: 2.3.5.7.11.13.17.41~~

	~~Comma list: 616/615, 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224~~

	~~Mapping: {{mapping\| 1 -25 -16 -13 -26 -6 -11 5 \| 0 74 51 44 82 27 42 1 }}~~

	~~Optimal tunings:~~
	* WE: ~2 = 1199.8693{{c}}, ~41/32 = 431.0650{{c}}
	* CWE: ~2 = 1200.000{{c}}, ~41/32 = 431.1109{{c}}

	~~{{Optimal ET sequence\|legend=0\| 103, 167, 270 }}~~

	~~Badness (Sintel): 1.25~~

	== Unthirds ==		== Unthirds ==

FloraC: /* Tertiaseptal */ - extensions beyond 31

2026-05-17T15:55:44Z

Tertiaseptal: - extensions beyond 31

@@ Line 143: / Line 143: @@
 === Tertiaseptia ===
 Subgroup: 2.3.5.7.11
@@ Line 246: / Line 248: @@
 Badness (Sintel): 1.18
 === Hemitert ===

Overthink: /* Osiris */ - unexplained see also

2026-04-24T00:50:55Z

Osiris: - unexplained see also

← Older revision		Revision as of 00:50, 24 April 2026
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	== Osiris ==		== Osiris ==
	~~{{See also\| Metric microtemperaments #Geb }}~~

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

FloraC: /* Newt */ expand

2026-04-11T15:27:26Z

Newt: expand

← Older revision		Revision as of 15:27, 11 April 2026
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	== Newt ==		== Newt ==
	Newt tempers out the [[garischisma]] and can be described as the {{nowrap\| 41 & 270 }} temperament. It has a generator of a neutral third (0.2 cents flat of [[49/40]]) with a [[ploidacot]] signature of dicot. It extends into a strong [[13-limit]] temperament and eventually a no-17 [[19-limit]] temperament, a.k.a. '''neonewt'''. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] work even better.		Newt tempers out the [[garischisma]] and can be described as the {{nowrap\| 41 & 270 }} temperament. It has a generator of a neutral third (0.2 cents flat of [[49/40]]) with a [[ploidacot]] signature of dicot. 41 generator steps fall short of 12 octaves by a [[schisma]]~[[aberschisma]]. From there the intervals of 5 and 7 can be derived.

			Newt continues to be significant as an [[11-limit]] temperament. The commas it tempers out include the [[lehmerisma]] (3025/3024), the [[symbiotic comma]] (19712/19683), the [[argyria]] (41503/41472), and the [[olympia]] (131072/130977). This extends into a strong [[13-limit]] temperament and eventually a strong no-17 [[19-limit]] temperament, a.k.a. '''neonewt'''. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] work even better.

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

FloraC: /* Hemififths */ + 58 & 181 extension

2026-03-04T10:45:25Z

Hemififths: + 58 & 181 extension

← Older revision		Revision as of 10:45, 4 March 2026
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	Badness (Sintel): 1.29		Badness (Sintel): 1.29

			=== Cutefourths ===
			This extension splits the neutral third plus an octave in three, with a ploidacot signature of beta-hexacot. The generator is an acute fourth in size (but not representing [[27/20]]), hence the name.

			Subgroup: 2.3.5.7.11

			Comma list: 2401/2400, 4000/3993, 5120/5103

			Mapping: {{mapping\| 1 -1 -30 -14 -28 \| 0 6 75 39 73 }}
			: mapping generators: ~2, ~66/49

			Optimal tunings:
			* WE: ~2 = 1199.7345{{c}}, ~66/49 = 517.0436{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~66/49 = 517.1543{{c}}

			{{Optimal ET sequence\|legend=0\| 58, 181, 239, 1014bcee }}

			Badness (Sintel): 1.71

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

			Comma list: 352/351, 847/845, 1575/1573, 2401/2400

			Mapping: {{mapping\| 1 -1 -30 -14 -28 -20 \| 0 6 75 39 73 55 }}

			Optimal tunings:
			* WE: ~2 = 1199.6427{{c}}, ~66/49 = 517.0035{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~66/49 = 517.1524{{c}}

			{{Optimal ET sequence\|legend=0\| 58, 181, 239f }}

			Badness (Sintel): 1.45

	== Osiris ==		== Osiris ==

← Older revision		Revision as of 16:07, 17 May 2026
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	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
	* ''[[~~Decimal~~]]'' (+25/~~24, 49/48 or 50/49~~) → [[~~Dicot family~~ #~~Decimal~~\|~~Dicot family~~]]		* ''[[Beatles]]'' (+64/63) → [[Archytas clan #Beatles\|Archytas clan]]
	* ''[[~~Beatles~~]]'' (+64/63 or ~~686~~/~~675~~) → [[~~Archytas clan~~ #~~Beatles~~\|~~Archytas clan~~]]		* [[Decimal]] (+25/24, 49/48 or 50/49) → [[Dicot family #Decimal\|Dicot family]]
	* [[Squares]] (+81/80) → [[Meantone family #Squares\|Meantone family]]		* [[Squares]] (+81/80) → [[Meantone family #Squares\|Meantone family]]
	* [[~~Myna~~]] (+~~126~~/~~125~~) → [[~~Starling temperaments~~ #~~Myna~~\|~~Starling temperaments~~]]		* ''[[Sesquiquartififths]]'' (+32805/32768) → [[Schismatic family #Sesquiquartififths\|Schismatic family]]
	* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle\|Gamelismic clan]]		* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle\|Gamelismic clan]]
	* ''[[Octacot]]'' (+245/243) → [[Tetracot family #Octacot\|Tetracot family]]		* ''[[Octacot]]'' (+245/243) → [[Tetracot family #Octacot\|Tetracot family]]
	* ''[[~~Greenwood~~]]'' (+~~405~~/~~392 or 1323~~/~~1280~~) → [[~~Whitewood~~ family #~~Greenwood~~\|~~Whitewood~~ family]]		* ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta\|Diaschismic family]]
			* [[Myna]] (+126/125) → [[Starling temperaments #Myna\|Starling temperaments]]
			* [[Harry]] (+19683/19600) → [[Gravity family #Harry\|Gravity family]]
	* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp\|Keemic temperaments]]		* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp\|Keemic temperaments]]
	* ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta\|Diaschismic family]]
	* ''[[Quadrimage]]'' (+3125/3072) → [[Magic family #Quadrimage\|Magic family]]
	* ''[[Hemiwürschmidt]]'' (+3136/3125 or 6144/6125) → [[Hemimean clan #Hemiwürschmidt\|Hemimean clan]]		* ''[[Hemiwürschmidt]]'' (+3136/3125 or 6144/6125) → [[Hemimean clan #Hemiwürschmidt\|Hemimean clan]]
			* ''[[Eagle]]'' (+10485760000/10460353203) → [[Vulture family #Eagle\|Vulture family]]
	* [[Ennealimmal]] (+4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]		* [[Ennealimmal]] (+4375/4374) → [[Septiennealimmal clan #Ennealimmal\|Septiennealimmal clan]]
			* ''[[Quadrimage]]'' (+3125/3072) → [[Magic family #Quadrimage\|Magic family]]
			* ''[[Amicable]]'' (+1600000/1594323) → [[Amity family #Amicable\|Amity family]]
			* ''[[Decoid]]'' (+67108864/66976875) → [[Quintosec family #Decoid\|Quintosec family]]
	* ''[[Quadritikleismic]]'' (+15625/15552) → [[Kleismic family #Quadritikleismic\|Kleismic family]]		* ''[[Quadritikleismic]]'' (+15625/15552) → [[Kleismic family #Quadritikleismic\|Kleismic family]]
	* [[Harry]] (+19683/19600) → [[Gravity family #Harry\|Gravity family]]
	* ''[[Sesquiquartififths]]'' (+32805/32768) → [[Schismatic family #Sesquiquartififths\|Schismatic family]]
	* ''[[Amicable]]'' (+1600000/1594323) → [[Amity family #Amicable\|Amity family]]
	* ''[[Neptune]]'' (+48828125/48771072) → [[Gammic family #Neptune\|Gammic family]]		* ''[[Neptune]]'' (+48828125/48771072) → [[Gammic family #Neptune\|Gammic family]]
	* ''[[Decoid]]'' (+67108864/66976875) → [[Quintosec family #Decoid\|Quintosec family]]
	* ''[[Tertiseptisix]]'' (+390625000/387420489) → [[Quartonic family #Tertiseptisix\|Quartonic family]]		* ''[[Tertiseptisix]]'' (+390625000/387420489) → [[Quartonic family #Tertiseptisix\|Quartonic family]]
	* ''[[~~Eagle~~]]'' (+~~10485760000~~/~~10460353203~~) → [[~~Vulture~~ family #~~Eagle~~\|~~Vulture~~ family]]		* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Whitewood family #Greenwood\|Whitewood family]]

	Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, newt, septidiasemi, subneutral, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]].		Considered below are tertiaseptal, emmthird, hemififths, osiris, quasiorwell, quinmite, newt, septidiasemi, subneutral, maviloid, lockerbie, unthirds, neominor, catafourth, cotritone, fibo, quasimoha, mintone, gorgik, hemigoldis, and surmarvelpyth, in the order of increasing [[badness]].