Rastmic clan - Revision history

FloraC: - redundant category

2026-03-22T14:25:47Z

- redundant category

← Older revision		Revision as of 14:25, 22 March 2026
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	[[Category:Rastmic clan\| ]] <!-- main article -->		[[Category:Rastmic clan\| ]] <!-- main article -->
	~~[[Category:Rastmic\| ]] <!-- key article -->~~
	[[Category:Rank 2]]		[[Category:Rank 2]]

Overthink: /* Mohoho */ fix error

2026-01-11T00:24:11Z

Mohoho: fix error

← Older revision		Revision as of 00:24, 11 January 2026
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	{{Optimal ET sequence\|legend=0\| 7, 17c, 24, 31, 55 }}		{{Optimal ET sequence\|legend=0\| 7, 17c, 24, 31, 55 }}

	[[Badness]] (Sintel): 0.~~401~~		[[Badness]] (Sintel): 0.545

	Scales: [[mohaha7]], [[mohaha10]]		Scales: [[mohaha7]], [[mohaha10]]

FloraC: Text replacement - "Category:Temperament clans↵Category:Pages with mostly numerical content" to "Category:Temperament clans"

2025-11-27T12:22:38Z

Text replacement - "Category:Temperament clans↵Category:Pages with mostly numerical content" to "Category:Temperament clans"

← Older revision		Revision as of 12:22, 27 November 2025
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Rastmic clan\| ]] <!-- main article -->		[[Category:Rastmic clan\| ]] <!-- main article -->
	[[Category:Rastmic\| ]] <!-- key article -->		[[Category:Rastmic\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Overthink: /* Suhajira */ Added brief description

2025-11-04T06:47:23Z

Suhajira: Added brief description

← Older revision		Revision as of 06:47, 4 November 2025
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	== Suhajira ==		== Suhajira ==
			Suhajira can be thought of as "superpyth with quartertones", adding neutral intervals onto the existing pythagorean and septimal ones. Due to the sharper generator, it is now much more natural to add prime 13, with the neutral intervals generally closer to simple intervals of 13 than simple intervals of 11.

	[[Subgroup]]: 2.3.7.11		[[Subgroup]]: 2.3.7.11

FloraC: Another pass on neutrality, explaining what actually happens with CTE/CWE and giving an alternative that bypasses their mechanics

2025-08-24T16:07:18Z

Another pass on neutrality, explaining what actually happens with CTE/CWE and giving an alternative that bypasses their mechanics

← Older revision		Revision as of 16:07, 24 August 2025
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	=== Namo ===		=== Namo ===
	Namo adds [[144/143]] to the comma list and finds ~[[16/13]] at the same neutral third. With 11/9~16/13, it requires a slightly flat ~[[27/22]] as the tuning of the neutral third. [[58edo]] is the largest [[patent val]] tuning for it in the [[optimal ET sequence]], with a tuning between that of [[17edo]] and [[41edo]], so that ~11 and ~13 are practically equally sharp, given that [[29edo]] forms a [[consistent circle]] of [[13/11]]'s with a [[closing error]] of 31.2%. It might be recommended as a tuning for this reason, as having the neutral third much sharper to optimize plausibility of ~~~16/~~13 implies that the 11 is extremely sharp because 11/9 must be tuned sharp so that 11 must be sharper than 9, which is ~~thus~~ four times as sharp as however sharp of the (3/2)<sup>1/2</sup> neutral third is, while tuning it much flatter means ~~that you increase~~ the error of ~~16/~~13, which in 58edo is already as almost 8{{cent}} off and in [[99edo\|99ef]] it is only slightly worse. ~~For these reasons, Godtone is not fond of the recommendations by the various~~ [[~~optimal tuning~~]]~~s to tune flat~~ of ~~58edo~~, ~~although it~~ is ~~clear that~~ in ~~an optimal tuning nothing much sharper than 58edo should be used~~, as ~~making 11~~ more ~~off than 13 would imply damaging 3~~ and 11/9 more than necessary. ~~Curiously, [[POTE]]~~ (351.~~488~~{{c}}) ~~recommends a sharper tuning than [[CWE]] here~~, ~~but~~ still flat of 58edo.		Namo adds [[144/143]] to the comma list and finds ~[[16/13]] at the same neutral third. With 11/9~16/13, it requires a slightly flat ~[[27/22]] as the tuning of the neutral third. [[58edo]] is the largest [[patent val]] tuning for it in the [[optimal ET sequence]], with a tuning between that of [[17edo]] and [[41edo]], so that ~11 and ~13 are practically equally sharp, given that [[29edo]] forms a [[consistent circle]] of [[13/11]]'s with a [[closing error]] of 31.2%. It might be recommended as a tuning for this reason, as having the neutral third tuned much sharper to optimize the plausibility of prime 13 implies that the 11 is extremely sharp because 11/9 must be tuned sharp so that 11 must be sharper than 9, which is four times as sharp as however sharp of just the (3/2)<sup>1/2</sup> neutral third is, while tuning it much flatter means increasing the error of prime 13, which in 58edo is already almost 8{{cent}} off and in [[99edo\|99ef-edo]] it is only slightly worse.

			The [[CWE]] tuning given below takes account of how optimizational resource is best used. As such, the optimum is not raised much in the introduction of prime 13, as each unit increment in the generator implies four and five times more error in the harmonics 9 and 11, respectively, damaging them more than necessary. A sharper pure-octave tuning would be given by CTOP (~351.7142{{c}}), which is still flat of 58edo.

	[[Subgroup]]: 2.3.11.13		[[Subgroup]]: 2.3.11.13

FloraC: - CTE & POTE tunings

2025-08-24T14:24:44Z

- CTE & POTE tunings

← Older revision		Revision as of 14:24, 24 August 2025
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	* [[WE]]: ~2 = 1200.0635{{c}}, ~11/9 = 350.5439{{c}}		* [[WE]]: ~2 = 1200.0635{{c}}, ~11/9 = 350.5439{{c}}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 350.5486{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 350.5486{{c}}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.572{{c}}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.525{{c}} -->

	{{Optimal ET sequence\|legend=1\| 7, 17, 24, 65, 89, 202, 291, 380 }}		{{Optimal ET sequence\|legend=1\| 7, 17, 24, 65, 89, 202, 291, 380 }}
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	* [[WE]]: ~2 = 1198.8553{{c}}, ~11/9 = 351.1523{{c}}		* [[WE]]: ~2 = 1198.8553{{c}}, ~11/9 = 351.1523{{c}}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 351.2700{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 351.2700{{c}}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.746{{c}}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~11/9 = 351.488{{c}} -->

	{{Optimal ET sequence\|legend=1\| 7, 10, 17, 41, 58, 99ef, 239eefff, 338eeeffff }}		{{Optimal ET sequence\|legend=1\| 7, 10, 17, 41, 58, 99ef, 239eefff, 338eeeffff }}
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	* [[WE]]: ~2 = 1196.3496{{c}}, ~11/9 = 352.8809{{c}}		* [[WE]]: ~2 = 1196.3496{{c}}, ~11/9 = 352.8809{{c}}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 353.7832{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 353.7832{{c}}
	~~<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 353.139{{c}}~~
	* [[POTE]]: ~2 = 1200.000{{c}}, ~11/9 = 353.958{{c}} -->

	{{Optimal ET sequence\|legend=1\| 7, 10, 17, 44e, 61de, 78ddee, 139bdddeeee }}		{{Optimal ET sequence\|legend=1\| 7, 10, 17, 44e, 61de, 78ddee, 139bdddeeee }}
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	* WE: ~2 = 1196.8114{{c}}, ~11/9 = 352.8351{{c}}		* WE: ~2 = 1196.8114{{c}}, ~11/9 = 352.8351{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 353.6791{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 353.6791{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~11/9 = 352.219{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~11/9 = 353.775{{c}} -->

	{{Optimal ET sequence\|legend=0\| 7, 10, 17, 44e, 61de, 78ddee }}		{{Optimal ET sequence\|legend=0\| 7, 10, 17, 44e, 61de, 78ddee }}
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	* [[WE]]: ~2 = 1201.8548{{c}}, ~11/9 = 348.6318{{c}}		* [[WE]]: ~2 = 1201.8548{{c}}, ~11/9 = 348.6318{{c}}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 348.3793{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 348.3793{{c}}
	~~<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~11/9 = 348.8296{{c}}~~
	* [[POTE]]: ~2 = 1200.0000{{c}}, ~11/9 = 348.0938{{c}} -->

	{{Optimal ET sequence\|legend=1\| 7, 17c, 24, 31, 69e, 100e, 131bee }}		{{Optimal ET sequence\|legend=1\| 7, 17c, 24, 31, 69e, 100e, 131bee }}
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	* [[WE]]: ~2 = 1199.8846{{c}}, ~11/9 = 348.8820{{c}}		* [[WE]]: ~2 = 1199.8846{{c}}, ~11/9 = 348.8820{{c}}
	* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 348.9040{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 348.9040{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~11/9 = 348.8794{{c}}~~
	* POTE: ~2 = 1200.0000{{c}}, ~11/9 = 348.9155{{c}} -->

	{{Optimal ET sequence\|legend=0\| 7, 17c, 24, 31, 55 }}		{{Optimal ET sequence\|legend=0\| 7, 17c, 24, 31, 55 }}
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	* WE: ~2 = 1201.7423{{c}}, ~11/9 = 348.6879{{c}}		* WE: ~2 = 1201.7423{{c}}, ~11/9 = 348.6879{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 348.2867{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 348.2867{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~11/9 = 348.5324{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~11/9 = 348.182{{c}} -->

	{{Optimal ET sequence\|legend=0\| 7d, 24d, 31, 100de, 131bdee, 162bdee }}		{{Optimal ET sequence\|legend=0\| 7d, 24d, 31, 100de, 131bdee, 162bdee }}
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	* WE: ~2 = 1200.2590{{c}}, ~11/9 = 348.5648{{c}}		* WE: ~2 = 1200.2590{{c}}, ~11/9 = 348.5648{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 348.5009{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 348.5009{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~11/9 = 348.5444{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~11/9 = 348.490{{c}} -->

	{{Optimal ET sequence\|legend=0\| 7d, 24d, 31 }}		{{Optimal ET sequence\|legend=0\| 7d, 24d, 31 }}
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	* WE: ~2 = 1203.8812{{c}}, ~11/9 = 348.0444{{c}}		* WE: ~2 = 1203.8812{{c}}, ~11/9 = 348.0444{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 346.9194{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 346.9194{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~11/9 = 346.905{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~11/9 = 346.922{{c}} -->

	{{Optimal ET sequence\|legend=0\| 7, 31dd, 38d, 45e, 83bcddee }}		{{Optimal ET sequence\|legend=0\| 7, 31dd, 38d, 45e, 83bcddee }}
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	* WE: ~2 = 1203.9456{{c}}, ~11/9 = 348.0510{{c}}		* WE: ~2 = 1203.9456{{c}}, ~11/9 = 348.0510{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 346.8878{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 346.8878{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~11/9 = 346.754{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~11/9 = 346.910{{c}} -->

	{{Optimal ET sequence\|legend=0\| 7, 31ddf, 38df, 45ef, 83bcddeeff, 128bccddeeefff }}		{{Optimal ET sequence\|legend=0\| 7, 31ddf, 38df, 45ef, 83bcddeeff, 128bccddeeefff }}
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	* WE: ~2 = 1195.9529{{c}}, ~11/9 = 349.7505{{c}}		* WE: ~2 = 1195.9529{{c}}, ~11/9 = 349.7505{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.7031{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.7031{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~11/9 = 349.865{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~11/9 = 350.934{{c}} -->

	{{Optimal ET sequence\|legend=0\| 7, 17c, 24d, 41cd }}		{{Optimal ET sequence\|legend=0\| 7, 17c, 24d, 41cd }}
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	* WE: ~2 = 1196.3143{{c}}, ~11/9 = 349.7387{{c}}		* WE: ~2 = 1196.3143{{c}}, ~11/9 = 349.7387{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.6573{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~11/9 = 350.6573{{c}}
	~~<!-- * CTE: ~2 = 1200.000{{c}}, ~11/9 = 349.904{{c}}~~
	* POTE: ~2 = 1200.000{{c}}, ~11/9 = 350.816{{c}} -->

	{{Optimal ET sequence\|legend=0\| 7, 17c, 24d, 41cd }}		{{Optimal ET sequence\|legend=0\| 7, 17c, 24d, 41cd }}
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	* [[WE]]: ~2 = 601.5167{{c}}, ~7/4 = 951.1267{{c}}		* [[WE]]: ~2 = 601.5167{{c}}, ~7/4 = 951.1267{{c}}
	* [[CWE]]: ~2 = 600.0000{{c}}, ~7/4 = 949.6883{{c}}		* [[CWE]]: ~2 = 600.0000{{c}}, ~7/4 = 949.6883{{c}}
	~~<!-- * CTE: ~77/54 = 600.000{{c}}, ~7/4 = 951.181{{c}}~~
	* POTE: ~77/54 = 600.000{{c}}, ~7/4 = 948.728{{c}} -->

	{{Optimal ET sequence\|legend=1\| 10, 14, 24, 62dd }}		{{Optimal ET sequence\|legend=1\| 10, 14, 24, 62dd }}

FloraC: (For the first entry)

2025-08-24T14:24:08Z

(For the first entry)

← Older revision		Revision as of 14:24, 24 August 2025
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.572{{c}}		* [[WE]]: ~2 = 1200.0635{{c}}, ~11/9 = 350.5439{{c}}
	* [[POTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.525{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 350.5486{{c}}
			<!-- * [[CTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.572{{c}}
			* [[POTE]]: ~2 = 1200.000{{c}}, ~11/9 = 350.525{{c}} -->

	{{Optimal ET sequence\|legend=1\| 7, 17, 24, 65, 89, 202, 291, 380 }}		{{Optimal ET sequence\|legend=1\| 7, 17, 24, 65, 89, 202, 291, 380 }}

FloraC: Switch to Sintel's badness, WE & CWE tunings, per community consensus

2025-08-24T14:22:59Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus

Show changes

FloraC: Cleanup. - gencom (trivial)

2025-08-24T13:45:08Z

Cleanup. - gencom (trivial)

Show changes

Lériendil: Text replacement - "Category:Temperament clans" to "Category:Temperament clans Category:Pages with mostly numerical content"

2025-06-24T00:35:21Z

Text replacement - "Category:Temperament clans" to "Category:Temperament clans Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:35, 24 June 2025
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	[[Category:Temperament clans]]		[[Category:Temperament clans]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Rastmic clan\| ]] <!-- main article -->		[[Category:Rastmic clan\| ]] <!-- main article -->
	[[Category:Rastmic\| ]] <!-- key article -->		[[Category:Rastmic\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]