Escapade family - Revision history

Hkm: /* 2.3.5.11 subgroup */

2026-05-30T23:18:12Z

2.3.5.11 subgroup

← Older revision		Revision as of 23:18, 30 May 2026
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	=== 2.3.5.11 subgroup ===		=== 2.3.5.11 subgroup ===
	Since (an ideally slightly flat) 4/3 is split into 9 generators, it makes sense to equate ~~that~~ interval to [[11/10]] by tempering out 4000/3993, and therefore the generator to {{nowrap\|(11/10)/(16/15) {{=}} [[33/32]]}}; this does minimal damage to the temperament. This structure in 2.3.5.11 occurs in all extensions of escapade to include prime 7, and therefore will be considered the fount of all further extensions.		Since (an ideally slightly flat) 4/3 is split into 9 generators, it makes sense to equate the 3-generator interval to [[11/10]] by tempering out 4000/3993, and therefore the generator to {{nowrap\|(11/10)/(16/15) {{=}} [[33/32]]}}; this does minimal damage to the temperament. This structure in 2.3.5.11 occurs in all extensions of escapade to include prime 7, and therefore will be considered the fount of all further extensions.

	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

Pailiaq: /* 2.3.5.11 subgroup */

2026-05-30T23:09:53Z

2.3.5.11 subgroup

← Older revision		Revision as of 23:09, 30 May 2026
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	=== 2.3.5.11 subgroup ===		=== 2.3.5.11 subgroup ===
	Since (an ideally slightly flat) 4/3 is split ~~in three by the interval of 3~~ generators, it makes sense to equate that interval to [[11/10]] by tempering out 4000/3993, and therefore the generator to {{nowrap\|(11/10)/(16/15) {{=}} [[33/32]]}}; this does minimal damage to the temperament. This structure in 2.3.5.11 occurs in all extensions of escapade to include prime 7, and therefore will be considered the fount of all further extensions.		Since (an ideally slightly flat) 4/3 is split into 9 generators, it makes sense to equate that interval to [[11/10]] by tempering out 4000/3993, and therefore the generator to {{nowrap\|(11/10)/(16/15) {{=}} [[33/32]]}}; this does minimal damage to the temperament. This structure in 2.3.5.11 occurs in all extensions of escapade to include prime 7, and therefore will be considered the fount of all further extensions.

	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

Xenllium at 22:29, 9 March 2026

2026-03-09T22:29:40Z

Show changes

Lériendil: /* Escapade */

2026-02-09T16:13:38Z

Escapade

← Older revision		Revision as of 16:13, 9 February 2026
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	Optimal tuning (CTE): ~2 = 1200.0000, ~33/32 = 55.2760		Optimal tuning (CTE): ~2 = 1200.0000, ~33/32 = 55.2760

	{{Optimal ET sequence\|legend=1\| 21, 22, 43, 65, 87, 152, 369, 521e~~, 1194bcee, 1715bceeee~~ }}		{{Optimal ET sequence\|legend=1\| 21, 22, 43, 65, 87, 152, 369, 521e }}

	Badness: 0.0107		Badness: 0.0107
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	Optimal tuning (CTE): ~2 = 1200.000, ~32/31 = 55.276		Optimal tuning (CTE): ~2 = 1200.000, ~32/31 = 55.276

	{{Optimal ET sequence\|legend=0\| 21, 22, 43, 65, 87, 152, 369, 521e, 673e~~, 1194bcee, 1867bceeee~~ }}		{{Optimal ET sequence\|legend=0\| 21, 22, 43, 65, 87, 152, 369, 521e, 673e }}

	Badness (Sintel): 0.251		Badness (Sintel): 0.251

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

2025-11-27T12:27:24Z

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

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

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

2025-06-24T00:41:36Z

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

← Older revision		Revision as of 00:41, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Escapade family\| ]] <!-- main article -->		[[Category:Escapade family\| ]] <!-- main article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Lériendil at 02:22, 19 June 2025

2025-06-19T02:22:55Z

← Older revision		Revision as of 02:22, 19 June 2025
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	''[[#Strong extensions\|Return to the map]]''		''[[#Strong extensions\|Return to the map]]''

	Given the slightly sharp ~[[3/2]] in ideal tunings of escapade (between [[65edo]] and [[87edo]]), it does very little damage to temper out [[5120/5103]] to extend it to ~~the [[~~7~~-limit]]~~; the cost is that the harmonic 7 is exceedingly complex, located all the way at 61 generators up.		Given the slightly sharp ~[[3/2]] in ideal tunings of escapade (between [[65edo]] and [[87edo]]), it does very little damage to temper out [[5120/5103]] to extend it to prime 7; the cost is that the harmonic 7 is exceedingly complex, located all the way at 61 generators up.

	=== 7-limit ===		=== 7-limit ===

VectorGraphics at 04:57, 12 June 2025

2025-06-12T04:57:59Z

← Older revision		Revision as of 04:57, 12 June 2025
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	{{Mapping\|legend=1\| 1 2 2 4 \| 0 -9 7 -26 }}		{{Mapping\|legend=1\| 1 2 2 4 \| 0 -9 7 -26 }}

	~~{{Multival\|legend=1\| 9 -7 26 -32 16 80 }}~~

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~28/27 = 55.122		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~28/27 = 55.122
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	{{Mapping\|legend=1\| 1 2 2 0 \| 0 -9 7 61 }}		{{Mapping\|legend=1\| 1 2 2 0 \| 0 -9 7 61 }}

	~~{{Multival\|legend=1\| 9 -7 -61 -32 -122 -122 }}~~

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~16128/15625 = 55.243		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~16128/15625 = 55.243
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	{{Mapping\|legend=1\| 1 2 2 3 \| 0 -9 7 -4 }}		{{Mapping\|legend=1\| 1 2 2 3 \| 0 -9 7 -4 }}

	~~{{Multival\|legend=1\| 9 -7 4 -32 -19 29 }}~~

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~49/48 = 55.327		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~49/48 = 55.327
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	: mapping generators: ~343/243, ~16875/16384		: mapping generators: ~343/243, ~16875/16384

	~~{{Multival\|legend=1\| 18 -14 30 -64 -3 109 }}~~

	[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~16875/16384 = 55.320		[[Optimal tuning]] ([[POTE]]): ~343/243 = 1\2, ~16875/16384 = 55.320
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	: mapping generators: ~2, ~64/63		: mapping generators: ~2, ~64/63

	~~{{Multival\|legend=1\| 18 -14 -35 -64 -106 -42 }}~~

	[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~64/63 = 27.668		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~64/63 = 27.668

Lériendil at 13:04, 11 June 2025

2025-06-11T13:04:33Z

← Older revision		Revision as of 13:04, 11 June 2025
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	== Escapade ==		== Escapade ==
			For intervals along the chain of generators in the 2.3.5.11.31 subgroup temperament, out to 22 generators up, see the third column of [[16ed5/3#Intervals]].

	=== 5-limit ===		=== 5-limit ===
	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	=== 2.3.5.11 subgroup ===		=== 2.3.5.11 subgroup ===
	Since (an ideally slightly flat) 4/3 is split in three by the interval of 3 generators, it makes sense to equate that interval to [[11/10]] by tempering out 4000/3993, and therefore the generator to {{nowrap\|(11/10)/(16/15) {{=}} [[33/32]]}}; this does minimal damage to the temperament. This structure in 2.3.5.11 occurs in all extensions of escapade to include prime 7, and therefore will be considered the fount of all further extensions~~. For intervals along the chain of generators in the 2.3.5.11.31 subgroup temperament, out to 22 generators up, see the third column of [[16ed5/3#Intervals]]~~.		Since (an ideally slightly flat) 4/3 is split in three by the interval of 3 generators, it makes sense to equate that interval to [[11/10]] by tempering out 4000/3993, and therefore the generator to {{nowrap\|(11/10)/(16/15) {{=}} [[33/32]]}}; this does minimal damage to the temperament. This structure in 2.3.5.11 occurs in all extensions of escapade to include prime 7, and therefore will be considered the fount of all further extensions.

	Subgroup: 2.3.5.11		Subgroup: 2.3.5.11

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

2025-06-06T16:38:10Z

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=0\| 21, 22, 43, 65, 87, 152, 369, 521e, 673e, 1194bcee, 1867bceeee }}		{{Optimal ET sequence\|legend=0\| 21, 22, 43, 65, 87, 152, 369, 521e, 673e, 1194bcee, 1867bceeee }}

	Badness (~~Dirichlet~~): 0.251		Badness (Sintel): 0.251

	{\| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"		{\| class="wikitable center-1 center-2 center-3 center-4 mw-collapsible mw-collapsed"