Unicorn family - Revision history

Xenllium at 04:18, 25 April 2026

2026-04-25T04:18:21Z

← Older revision		Revision as of 04:18, 25 April 2026
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	{{Optimal ET sequence\|legend=1\| 19, 39d, 58, 77, 135c, 212c }}		{{Optimal ET sequence\|legend=1\| 19, 39d, 58, 77, 135c, 212c }}

	Badness (Sintel): 1.035		[[Badness]] (Sintel): 1.035

	=== 2.3.5.7.13 subgroup ===		=== 2.3.5.7.13 subgroup ===
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	{{Optimal ET sequence\|legend=1\| 19, 39df, 58, 77, 212cf }}		{{Optimal ET sequence\|legend=1\| 19, 39df, 58, 77, 212cf }}

	Badness (Sintel): 0.590		[[Badness]] (Sintel): 0.590

	==== 2.3.5.7.13.29 subgroup ====		==== 2.3.5.7.13.29 subgroup ====
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	{{Mapping\|legend=1\| 1 2 3 4 5 6 \| 0 -8 -13 -23 -25 -22 }}		{{Mapping\|legend=1\| 1 2 3 4 5 6 \| 0 -8 -13 -23 -25 -22 }}

	[[Optimal tuning]] ([[~~CTE~~]]): 2 = ~~1\1~~, ~26/25 = 62.~~334~~		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.7715¢, ~26/25 = 62.2860¢
			* [[CWE]]: ~2 = 1200.0000¢, ~26/25 = 62.3141¢

	{{Optimal ET sequence\|legend=1\| 19, 39dfj, 58, 77, 212cf }}		{{Optimal ET sequence\|legend=1\| 19, 39dfj, 58, 77, 212cf }}

	Badness (Sintel): 0.487		[[Badness]] (Sintel): 0.487

	==== 2.3.5.7.13.29.43 subgroup ====		==== 2.3.5.7.13.29.43 subgroup ====
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	{{Mapping\|legend=1\| 1 2 3 4 5 6 6 \| 0 -8 -13 -23 -25 -22 -11 }}		{{Mapping\|legend=1\| 1 2 3 4 5 6 6 \| 0 -8 -13 -23 -25 -22 -11 }}

	[[Optimal tuning]] ([[~~CTE~~]]): 2 = ~~1\1~~, ~26/25 = 62.~~339~~		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.6269¢, ~26/25 = 62.2584¢
			* [[CWE]]: ~2 = 1200.0000¢, ~26/25 = 62.3008¢

	{{Optimal ET sequence\|legend=1\| 19, 39dfj, 58, 77, 135c, 212cfn }}		{{Optimal ET sequence\|legend=1\| 19, 39dfj, 58, 77, 135c, 212cfn }}

	Badness (Sintel): 0.514		[[Badness]] (Sintel): 0.514

	=== Alicorn ===		=== Alicorn ===
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	Mapping: {{mapping\| 2 4 6 8 9 10 \| 0 -8 -13 -23 -20 -25 }}		Mapping: {{mapping\| 2 4 6 8 9 10 \| 0 -8 -13 -23 -20 -25 }}

			Optimal tunings:
	* WE: ~55/39 = 599.8267¢, ~26/25 = 62.2833¢		* WE: ~55/39 = 599.8267¢, ~26/25 = 62.2833¢
	* CWE: ~55/39 = 600.0000¢, ~26/25 = 62.3262¢		* CWE: ~55/39 = 600.0000¢, ~26/25 = 62.3262¢
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	Mapping: {{mapping\| 2 4 6 8 9 10 9 \| 0 -8 -13 -23 -20 -25 -8 }}		Mapping: {{mapping\| 2 4 6 8 9 10 9 \| 0 -8 -13 -23 -20 -25 -8 }}

			Optimal tunings:
	* WE: ~17/12 = 600.0715¢, ~26/25 = 62.3767¢		* WE: ~17/12 = 600.0715¢, ~26/25 = 62.3767¢
	* CWE: ~17/12 = 600.0000¢, ~26/25 = 62.3605¢		* CWE: ~17/12 = 600.0000¢, ~26/25 = 62.3605¢

Xenllium at 04:09, 25 April 2026

2026-04-25T04:09:16Z

Show changes

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

2025-11-27T12:32:03Z

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

← Older revision		Revision as of 12:32, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Unicorn family\| ]] <!-- main article -->		[[Category:Unicorn family\| ]] <!-- main article -->
	[[Category:Unicorn\| ]] <!-- key article -->		[[Category:Unicorn\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

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

2025-06-24T00:34:36Z

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

← Older revision		Revision as of 00:34, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Unicorn family\| ]] <!-- main article -->		[[Category:Unicorn family\| ]] <!-- main article -->
	[[Category:Unicorn\| ]] <!-- key article -->		[[Category:Unicorn\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 04:53, 12 June 2025

2025-06-12T04:53:58Z

← Older revision		Revision as of 04:53, 12 June 2025
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	{{Mapping\|legend=1\| 1 2 3 4 \| 0 -8 -13 -23 }}		{{Mapping\|legend=1\| 1 2 3 4 \| 0 -8 -13 -23 }}

	~~{{Multival\|legend=1\| 8 13 23 2 14 17 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
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	{{Mapping\|legend=1\| 1 2 3 3 \| 0 -8 -13 -4 }}		{{Mapping\|legend=1\| 1 2 3 3 \| 0 -8 -13 -4 }}

	~~{{Multival\|legend=1\| 8 13 4 2 -16 -27 }}~~

	[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 62.920		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 62.920

FloraC: Text replacement - "Badness (Dirichlet): " to "Badness (Sintel): "

2025-06-06T16:38:31Z

Text replacement - "Badness (Dirichlet): " to "Badness (Sintel): "

← Older revision		Revision as of 16:38, 6 June 2025
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	{{Optimal ET sequence\|legend=1\| 19, 39df, 58, 77, 212cf }}		{{Optimal ET sequence\|legend=1\| 19, 39df, 58, 77, 212cf }}

	Badness (~~Dirichlet~~): 0.590		Badness (Sintel): 0.590

	==== 2.3.5.7.13.29 subgroup ====		==== 2.3.5.7.13.29 subgroup ====
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	{{Optimal ET sequence\|legend=1\| 19, 39dfj, 58, 77, 212cfn }}		{{Optimal ET sequence\|legend=1\| 19, 39dfj, 58, 77, 212cfn }}

	Badness (~~Dirichlet~~): 0.487		Badness (Sintel): 0.487

	==== 2.3.5.7.13.29.43 subgroup ====		==== 2.3.5.7.13.29.43 subgroup ====
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	{{Optimal ET sequence\|legend=1\| 19, 39dfj, 58, 77, 135c, 212cfn }}		{{Optimal ET sequence\|legend=1\| 19, 39dfj, 58, 77, 135c, 212cfn }}

	Badness (~~Dirichlet~~): 0.514		Badness (Sintel): 0.514

	=== Alicorn ===		=== Alicorn ===

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:44:44Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:44, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''unicorn family''' tempers out the [[unicorn comma]], 1594323/1562500 = {{monzo\| -2 13 -8 }}. The canonical extension to the 7-limit is by interpreting the generator as a slightly flattened [[~]][[28/27]] so that a flat [[~]][[6/5]] is found at 5 generators, corresponding to tempering [[126/125]], the [[octaphore]] and the [[hemimage comma]].		The '''unicorn family''' tempers out the [[unicorn comma]], 1594323/1562500 = {{monzo\| -2 13 -8 }}. The canonical extension to the 7-limit is by interpreting the generator as a slightly flattened [[~]][[28/27]] so that a flat [[~]][[6/5]] is found at 5 generators, corresponding to tempering [[126/125]], the [[octaphore]] and the [[hemimage comma]].

BudjarnLambeth: {{Technical data page}}

2025-04-13T05:07:47Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 05:07, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''unicorn family''' tempers out the [[unicorn comma]], 1594323/1562500 = {{monzo\| -2 13 -8 }}. The canonical extension to the 7-limit is by interpreting the generator as a slightly flattened [[~]][[28/27]] so that a flat [[~]][[6/5]] is found at 5 generators, corresponding to tempering [[126/125]], the [[octaphore]] and the [[hemimage comma]].		The '''unicorn family''' tempers out the [[unicorn comma]], 1594323/1562500 = {{monzo\| -2 13 -8 }}. The canonical extension to the 7-limit is by interpreting the generator as a slightly flattened [[~]][[28/27]] so that a flat [[~]][[6/5]] is found at 5 generators, corresponding to tempering [[126/125]], the [[octaphore]] and the [[hemimage comma]].

Recentlymaterialized: /* 2.3.5.7.13.29.43 subgroup */

2025-04-13T02:50:30Z

2.3.5.7.13.29.43 subgroup

← Older revision		Revision as of 02:50, 13 April 2025
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	==== 2.3.5.7.13.29.43 subgroup ====		==== 2.3.5.7.13.29.43 subgroup ====
	A notable tuning of unicorn not appearing in the [[optimal ET sequence]] here is [[96edo]] using the 96d val (~~meaning accepting~~ [[~~16edo~~]]'s [[~]][[7/4]] of ~~975{{cent}}~~), ~~which serves as a nice~~ alternative to [[77edo]] that sacrifices the accuracy of prime 7 in favour of more accurate ~~other primes usually not found accurately in good rank 1 unicorn tunings~~.		A notable tuning of unicorn not appearing in the [[optimal ET sequence]] here is [[96edo]] using the 96d val (with a 963[[cent\|¢]] [[~]][[7/4]] similar to that of [[meanpop]]), an alternative to [[77edo]] that sacrifices the accuracy of prime 7 in favour of a more accurate [[5/4]] and [[43/32]].

	[[Subgroup]]: 2.3.5.7.13.29.43		[[Subgroup]]: 2.3.5.7.13.29.43

Godtone: link

2025-01-25T17:25:18Z

link

← Older revision		Revision as of 17:25, 25 January 2025
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	== Unicorn ==		== Unicorn ==
	By noticing that the generator is very close to [[28/27]] we find the extension to the 7-limit by tempering the [[octaphore]] (which finds [[~]][[9/7]] at 7 gens and [[~]][[4/3]] at 8 gens, hence its name) and [[126/125]] (finding [[~]][[6/5]] at 5 gens). From this we can observe that the most natural extension is by equating adjacent [[superparticular interval]]s, by tempering the [[square-particular]]s between them, leading to its S-expression-based comma list of {[[676/675\|S26]], [[729/728\|S27]], [[784/783\|S28]], [[841/840\|S29]]}, to which experimentation shows we can find a reasonable mapping for prime 43 at -11 gens while all other primes require either quite complex mappings (being significantly positive rather than negative) or require high error or both.		By noticing that the generator is very close to [[28/27]] we find the extension to the 7-limit by tempering the [[octaphore]] (which finds [[~]][[9/7]] at 7 gens and [[~]][[4/3]] at 8 gens, hence its name) and [[126/125]] (finding [[~]][[6/5]] at 5 gens). From this we can observe that the most natural extension is by equating adjacent [[superparticular interval]]s, by tempering the [[square-particular]]s between them, leading to its [[S-expression]]-based comma list of {[[676/675\|S26]], [[729/728\|S27]], [[784/783\|S28]], [[841/840\|S29]]}, to which experimentation shows we can find a reasonable mapping for prime 43 at -11 gens while all other primes require either quite complex mappings (being significantly positive rather than negative) or require high error or both.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5