Syntonic–kleismic equivalence continuum - Revision history

Xenllium at 09:57, 14 May 2026

2026-05-14T09:57:05Z

← Older revision		Revision as of 09:57, 14 May 2026
Line 249:		Line 249:
	[[Badness]] (Sintel): 10.8		[[Badness]] (Sintel): 10.8

	== Parakleismic ~~(5-limit)~~ ==		== Parakleismic ==
	{{Main\| Parakleismic }}		{{Main\| Parakleismic }}
	: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]].''		: ''For extensions, see [[Ragismic microtemperaments #Parakleismic]] and [[Starling temperaments #Paraguay]].''

	The 5-limit version of parakleismic tempers out the [[parakleisma]]. It corresponds to {{nowrap\| ''n'' {{=}} 13/2 }}, and 13 generator steps give the interval class of [[3/1\|3]].		The 5-limit version of parakleismic tempers out the [[parakleisma]]. It corresponds to {{nowrap\| ''n'' {{=}} 13/2 }}, and 13 generator steps give the interval class of [[3/1\|3]].

2026-05-02T06:28:42Z

← Older revision		Revision as of 06:28, 2 May 2026
Line 190:		Line 190:

	== Xenial ==		== Xenial ==
	Xenial splits the [[8/3\|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. It corresponds to {{nowrap\| ''n'' {{=}} 9 }}. Its [[ploidacot]] is zeta-enneacot, and from this it derives its name.		: ''For extensions, see [[Starling temperaments #Xenial]] and [[Sensamagic clan #Xenia]].''

			Named by [[User:Xenllium\|Xenllium]] in 2026, xenial splits the [[8/3\|perfect eleventh]] into nine equal parts, each for ~[[10/9]]. It corresponds to {{nowrap\| ''n'' {{=}} 9 }}. Its [[ploidacot]] is zeta-enneacot, and from this it derives its name.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
Line 196:		Line 198:
	[[Comma list]]: 129140163/125000000		[[Comma list]]: 129140163/125000000

	{{Mapping\|legend=1\| 1 ~~3 5~~ \| 0 -9 -17 }}		{{Mapping\|legend=1\| 1 -6 -12 \| 0 9 17 }}
			: mapping generators: ~2, ~9/5

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1200.2802{{c}}, ~10/9 = ~~188~~.~~9887~~{{c}}		* [[WE]]: ~2 = 1200.2802{{c}}, ~9/5 = 1011.2914{{c}}
	: [[error map]]: {{val\| +0.~~2802,~~ -2.~~0133,~~ +2.~~2783~~ }}		: [[error map]]: {{val\| +0.280 -2.013 +2.278 }}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = ~~188~~.~~9238~~{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~9/5 = 1011.0762{{c}}
	: error map: {{val\| 0.000 -2.~~2688,~~ +1.~~9824~~ }}		: error map: {{val\| 0.000 -2.269 +1.982 }}

	{{Optimal ET sequence\|legend=1\| 19, 70, 89, 108, 127 }}		{{Optimal ET sequence\|legend=1\| 19, 70, 89, 108, 127 }}

2026-05-02T02:48:33Z

@@ Line 62: / Line 62: @@
 |-
 | 9
-| 19 & 51c
+| [[Xenial]]
 | [[129140163/125000000]]
 | {{Monzo| -6 17 -9 }}
@@ Line 188: / Line 188: @@
 [[Badness]] (Sintel): 2.04
 == Lalasepyo (8c & 11) ==

2026-03-24T15:00:53Z

Restore the optimal GPV sequence with explanation

← Older revision		Revision as of 15:00, 24 March 2026
Line 104:		Line 104:

	== Graywood ==		== Graywood ==
	Named by [[CompactStar]] in 2024, graywood tempers out the [[19-comma]], corresponding to {{nowrap\| ''n'' {{=}} 0 }}.		Named by [[CompactStar]] in 2024, graywood tempers out the [[19-comma]], corresponding to {{nowrap\| ''n'' {{=}} 0 }}. It takes [[19edo]]'s closed [[circle of fifths]], but adds an independent generator for [[prime interval\|prime]] [[5/1\|5]]. 19 is the only equal temperament that makes it to the optimal ET sequence as all the small edo tunings, e.g. [[38edo\|38c-edo]] or [[57edo\|57c-edo]], are not nearly as accurate as 19 itself.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
Line 119:		Line 119:
	: error map: {{val\| 0.000 -7.218 -3.525 }}		: error map: {{val\| 0.000 -7.218 -3.525 }}

	~~[[Support]]ing [[ET]]s:~~ {{~~EDOs~~\|19~~, 38c, 57c, 76c, 95bcc~~ }}		{{Optimal ET sequence\|legend=1\| 19 }}

	[[Badness]] (Sintel): 32.4		[[Badness]] (Sintel): 32.4

2026-03-23T20:47:04Z

2026-03-23T12:55:37Z

Move graywood and 5-limit enneadecal here

@@ Line 17: / Line 17: @@
 |-
 | 0
-| 19 & 19c
+| [[Graywood]]
 | [[19-comma|1162261467/1073741824]]
 | {{Monzo| -30 19 }}
@@ Line 102: / Line 102: @@
 | [[Mowgli]] || 15/2 = 7.5 || {{monzo| 0 22 -15 }}
 |}
 == Hogzilla ==
@@ Line 251: / Line 271: @@
 [[Badness]] (Sintel): 15.3
 == Countermeantone ==

2026-03-16T11:47:53Z

Move hogzilla, stump, and unsmate here

@@ Line 102: / Line 102: @@
 | [[Mowgli]] || 15/2 = 7.5 || {{monzo| 0 22 -15 }}
 |}
 == Negri (5-limit) ==
@@ Line 145: / Line 188: @@
 [http://x31eq.com/cgi-bin/rt.cgi?ets=19_8c&limit=5 The temperament finder - 5-limit 19 & 8c]
 == Parakleismic (5-limit) ==

2026-03-14T10:31:30Z

Linking

← Older revision		Revision as of 10:31, 14 March 2026
Line 103:		Line 103:
	\|}		\|}

	== Negri ==		== Negri (5-limit) ==
			{{Main\| Negri }}
	: ''For extensions, see [[Semaphoresmic clan #Negri]].''		: ''For extensions, see [[Semaphoresmic clan #Negri]].''

2026-03-14T10:29:41Z

Sort by ploidacot

2026-03-14T10:26:43Z

Normalize mapping