Rastmic rank-3 clan - Revision history

FloraC: - complexity spectra (relocated to the main article for it)

2026-09-26T13:47:38Z

- complexity spectra (relocated to the main article for it)

← Older revision		Revision as of 13:47, 26 September 2026
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	[[Badness]] (Sintel): 1.01		[[Badness]] (Sintel): 1.01

	~~[[Complexity spectrum]]: 11/9, 4/3, 12/11, 11/10, 10/9, 9/8, 11/8, 6/5, 5/4, 8/7, 7/6, 9/7, 14/11, 7/5~~

	Scales: [[urania24]]		Scales: [[urania24]]

FloraC: Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

2026-09-24T12:32:46Z

Text replacement - "Mapping: {{mapping| " to "{{Mapping|legend=0| "

← Older revision		Revision as of 12:32, 24 September 2026
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	Comma list: 225/224, 243/242, 351/350		Comma list: 225/224, 243/242, 351/350

	~~Mapping:~~ {{~~mapping~~\| 1 1 0 -3 2 -5 \| 0 2 0 4 5 -2 \| 0 0 1 2 0 4 }}		{{Mapping\|legend=0\| 1 1 0 -3 2 -5 \| 0 2 0 4 5 -2 \| 0 0 1 2 0 4 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 144/143, 176/175, 243/242		Comma list: 144/143, 176/175, 243/242

	~~Mapping:~~ {{~~mapping~~\| 1 1 0 6 2 4 \| 0 2 0 5 5 -1 \| 0 0 1 -2 0 0 }}		{{Mapping\|legend=0\| 1 1 0 6 2 4 \| 0 2 0 5 5 -1 \| 0 0 1 -2 0 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 126/125, 196/195, 243/242		Comma list: 126/125, 196/195, 243/242

	~~Mapping:~~ {{~~mapping~~\| 1 1 0 -3 2 -5 \| 0 2 0 -4 5 -10 \| 0 0 1 3 0 5 }}		{{Mapping\|legend=0\| 1 1 0 -3 2 -5 \| 0 2 0 -4 5 -10 \| 0 0 1 3 0 5 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 144/143, 243/242, 364/363		Comma list: 144/143, 243/242, 364/363

	~~Mapping:~~ {{~~mapping~~\| 1 1 0 -1 2 4 \| 0 2 0 13 5 -1 \| 0 0 1 0 0 0 }}		{{Mapping\|legend=0\| 1 1 0 -1 2 4 \| 0 2 0 13 5 -1 \| 0 0 1 0 0 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 729/728, 273/272, 153/152, 364/363, 1729/1728		Comma list: 729/728, 273/272, 153/152, 364/363, 1729/1728

	~~Mapping:~~ {{~~mapping~~\| 24 38 48 48 83 108 98 102 \| 0 0 1 0 0 0 0 0 \| 0 0 0 1 0 -1 0 0 }}		{{Mapping\|legend=0\| 24 38 48 48 83 108 98 102 \| 0 0 1 0 0 0 0 0 \| 0 0 0 1 0 -1 0 0 }}

	Optimal tunings:		Optimal tunings:
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	Comma list: 225/224, 243/242, 273/272, 385/384		Comma list: 225/224, 243/242, 273/272, 385/384

	~~Mapping:~~ {{~~mapping~~\| 1 1 3 3 2 0 0 \| 0 6 -7 -2 15 0 4 \| 0 0 0 0 0 1 1 }}		{{Mapping\|legend=0\| 1 1 3 3 2 0 0 \| 0 6 -7 -2 15 0 4 \| 0 0 0 0 0 1 1 }}

	Optimal tunings:		Optimal tunings:

FloraC: /* Mandos */ + link to 7-limit version

2026-09-16T07:46:21Z

Mandos: + link to 7-limit version

← Older revision		Revision as of 07:46, 16 September 2026
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	== Mandos ==		== Mandos ==
			: ''For the 7-limit version, see [[Miscellaneous 7-limit temperaments #Mandos]].''

	Mandos tempers out 176/175 and may be described as the {{nowrap\| 24 & 27e & 31 }} temperament.		Mandos tempers out 176/175 and may be described as the {{nowrap\| 24 & 27e & 31 }} temperament.

FloraC: - no-19 23-limit mirage (no need). Request completion of data

2026-08-15T08:49:28Z

- no-19 23-limit mirage (no need). Request completion of data

← Older revision		Revision as of 08:49, 15 August 2026
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	=== Gunn ===		=== Gunn ===
	~~[[Subgroup]]: 2~~.3.5.~~7.11~~.13.17.19		{{Todo\|inline=1\|complete section\|unify precision\|comment= Sort the comma basis. Normalize the mapping. Unify the cent values in optimal tunings to 4 decimal places. Add the optimal ET sequence. <br>Add the data for the 13- and 17-limit versions. }}

	~~[[Comma list]]: 729/728, 273/272, 153/152, 364/363, 1729/1728~~		==== 19-limit ====
			Subgroup: 2.3.5.7.11.13.17.19
	~~{{Mapping\|24 38 48 48 83 108 98 102\|0 0 1 0 0 0 0 0\|0 0 0 1 0~~ -~~1 0 0\|legend~~=~~1}}~~

	~~[[Optimal tuning\|Optimal tunings]]~~:

	* [[WE]]: ~33/32 = 50.~~030{{c}}, ~~~5~~/4 = 384~~.~~859{{c}}, ~~~7~~/4 = 965~~.~~679{{c}}~~

	: ~~[[error map]]: {{val\|+0.724 -0.809 -0.007 -1.700 +1.185 -2.949 -2.000 +5.563}}~~		Comma list: 729/728, 273/272, 153/152, 364/363, 1729/1728

	* [[CWE]]: ~~~33/32 = 50.000~~{{~~c}}, ~5/4 = 384.837{{c}}, ~7/4 = 965.136{{c~~}}		Mapping: {{mapping\| 24 38 48 48 83 108 98 102 \| 0 0 1 0 0 0 0 0 \| 0 0 0 1 0 -1 0 0 }}

	: error map: {{val\|-0.000 -1.955 -1.476 -3.690 -1.318 -5.663 -4.955 2.487}}		Optimal tunings:
			* WE: ~33/32 = 50.030{{c}}, ~5/4 = 384.859{{c}}, ~7/4 = 965.679{{c}}
			: error map: {{val\| +0.724 -0.809 -0.007 -1.700 +1.185 -2.949 -2.000 +5.563 }}
			* CWE: ~33/32 = 50.000{{c}}, ~5/4 = 384.837{{c}}, ~7/4 = 965.136{{c}}
			: error map: {{val\| -0.000 -1.955 -1.476 -3.690 -1.318 -5.663 -4.955 2.487 }}

	Supporting ETs: {{Edos\|24p, 72, 48f, 24c, 24df, 48cf, 48d, 96d, 48cd, 24cdf}}		Supporting ETs: {{Edos\| 24p, 72, 48f, 24c, 24df, 48cf, 48d, 96d, 48cd, 24cdf }}

	[[Badness]] (Sintel): 3.285		Badness (Sintel): 3.285

	== Mirage ==		== Mirage ==
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	{{Todo\|complete temperament data\|inline=1}}		{{Todo\|complete temperament data\|inline=1}}

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

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	{{Todo\|complete temperament data\|inline=1}}		{{Todo\|complete temperament data\|inline=1}}

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

	Comma list: 225/224, 243/242, 273/272, 300/299, 324/323, 385/384		Comma list: 225/224, 243/242, 273/272, 300/299, 324/323, 385/384

	~~{{Todo\|complete temperament data\|inline=1}}~~

	~~=== No-19 23-limit ===~~
	~~Subgroup: 2.3.5.7.11.13.17.23~~

	~~Comma list: 225/224, 243/242, 273/272, 300/299, 385/384~~

	{{Todo\|complete temperament data\|inline=1}}		{{Todo\|complete temperament data\|inline=1}}

FloraC: Recategorize

2026-08-15T07:40:42Z

Recategorize

← Older revision		Revision as of 07:40, 15 August 2026
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	== References ==		== References ==

			[[Category:Rastmic rank-3 clan\| ]] <!-- main article -->
	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:~~Rastmic~~ rank-3 ~~clan\| ]] <!-- main article -->~~		[[Category:Catalogs of rank-3 temperaments]]
	~~[[Category:Rank 3~~]]

Zeta Function: /* Rabic */ Move technical temperament data

2026-08-10T16:05:03Z

Rabic: Move technical temperament data

← Older revision		Revision as of 16:05, 10 August 2026
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	[[Badness]] (Sintel): 7.30		[[Badness]] (Sintel): 7.30

			=== Gunn ===
			[[Subgroup]]: 2.3.5.7.11.13.17.19

			[[Comma list]]: 729/728, 273/272, 153/152, 364/363, 1729/1728

			{{Mapping\|24 38 48 48 83 108 98 102\|0 0 1 0 0 0 0 0\|0 0 0 1 0 -1 0 0\|legend=1}}

			[[Optimal tuning\|Optimal tunings]]:

			* [[WE]]: ~33/32 = 50.030{{c}}, ~5/4 = 384.859{{c}}, ~7/4 = 965.679{{c}}

			: [[error map]]: {{val\|+0.724 -0.809 -0.007 -1.700 +1.185 -2.949 -2.000 +5.563}}

			* [[CWE]]: ~33/32 = 50.000{{c}}, ~5/4 = 384.837{{c}}, ~7/4 = 965.136{{c}}

			: error map: {{val\|-0.000 -1.955 -1.476 -3.690 -1.318 -5.663 -4.955 2.487}}

			Supporting ETs: {{Edos\|24p, 72, 48f, 24c, 24df, 48cf, 48d, 96d, 48cd, 24cdf}}

			[[Badness]] (Sintel): 3.285

	== Mirage ==		== Mirage ==

FloraC: Move rabic here

2026-05-15T11:04:12Z

Move rabic here

@@ Line 5: / Line 5: @@
 * [[Jove]] (+441/440 or 540/539) → [[Breed family #Jove|Breed family]]
 * ''[[Hagrid]]'' (+9801/9800) → [[Cataharry family #Hagrid|Cataharry family]]
-Considered below are spectacle, mirwomo, mandos, cuckoo, parahemif, urania, and mirage.
+Considered below are spectacle, mirwomo, mandos, cuckoo, parahemif, urania, rabic, and mirage.
 == Spectacle ==
@@ Line 216: / Line 215: @@
 Scales: [[urania24]]
 == Mirage ==

FloraC: - redundant category

2026-03-22T14:26:18Z

- redundant category

← Older revision		Revision as of 14:26, 22 March 2026
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Rastmic rank-3 clan\| ]] <!-- main article -->		[[Category:Rastmic rank-3 clan\| ]] <!-- main article -->
	~~[[Category:Rastmic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

Squib: /* 19-limit */

2026-03-19T01:28:18Z

19-limit

← Older revision		Revision as of 01:28, 19 March 2026
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	Subgroup: 2.3.5.7.11.13.17.19		Subgroup: 2.3.5.7.11.13.17.19

	Comma list: 210/209, 225/224, 243/242, 273/272, ~~385~~/~~384~~		Comma list: 210/209, 225/224, 243/242, 273/272, 343/342

	{{Todo\|complete temperament data\|inline=1}}		{{Todo\|complete temperament data\|inline=1}}

Squib: /* 17-limit */

2026-03-19T00:57:10Z

17-limit

← Older revision		Revision as of 00:57, 19 March 2026
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	=== 17-limit ===		=== 17-limit ===
	Mirage is very naturally a 17-limit temperament, relating 13 and 17 by tempering out [[273/272]], [[715/714]], [[833/832]], and [[936/935]]. Instead of 13/8, the second generator can also be the small comma ~~representing 105/104~120/119~144/143~154/153~189/187~196/195. (Tempering this comma~~ out ~~gives~~ [[miraculous]].)		Mirage is very naturally a 17-limit temperament, relating 13 and 17 by tempering out [[273/272]], [[715/714]], [[833/832]], and [[936/935]]. Instead of 13/8, the second generator can also be the small comma tempered out by [[miraculous]].

	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17