Jubilismic family - Revision history

FloraC: Canonicalize these obviously canonical extensions

2026-06-09T04:01:13Z

Canonicalize these obviously canonical extensions

← Older revision		Revision as of 04:01, 9 June 2026
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	Scales: [[jubilismic10]], [[jubilismic12]]		Scales: [[jubilismic10]], [[jubilismic12]]

	~~=== Jubilife ===~~
	~~There is a natural extension of jubilismic to the 2.3.5.7.17 subgroup, which tempers out [[85/84]] and [[120/119]], and identifies 7/5 with 10/7, 17/12 and 24/17 as the semioctave.~~

	~~Subgroup: 2.3.5.7.17~~

	~~Comma list: 50/49, 85/84~~

	~~Mapping: {{Mapping\| 2 0 0 1 5 \| 0 1 0 0 1 \| 0 0 1 1 0 }}~~

	~~Optimal tunings:~~
	* WE: ~7/5 = 599.8903{{c}}, ~3/2 = 702.6008{{c}}, ~5/4 = 379.6441{{c}}
	* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 702.5503{{c}}, ~5/4 = 379.4777{{c}}

	~~{{Optimal ET sequence\|legend=0\| 4, 8d, 10, 12, 22, 34d, 48 }}~~

	~~Badness (Sintel): 0.357~~

	== Undecimal jubilismic ==		== Undecimal jubilismic ==
	Formerly known as ''jubilee'', undecimal jubilismic tempers out [[99/98]] and [[100/99]], and is the most natural extension of jubilismic to the 11-limit. [[11/8]] is found by a stack of two [[7/6]]'s or two [[5/3]]'s octave reduced.		Formerly known as ''jubilee'', undecimal jubilismic tempers out [[99/98]] and [[100/99]], and is the most natural extension of jubilismic to the 11-limit. [[11/8]] is found by a stack of two [[7/6]]'s or two [[5/3]]'s octave reduced. This then extends naturally to the 2.3.5.7.11.17 subgroup, which tempers out [[85/84]] and [[120/119]], and adds [[17/12]] and [[24/17]] to the semioctave.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11
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	[[Badness]] (Sintel): 0.673		[[Badness]] (Sintel): 0.673

	=== ~~Jubilee~~ ===		=== 2.3.5.7.11.17 subgroup ===
	~~Jubilismic temperament works on the [[No-thirteens subgroup temperaments\|no-13s]] 17-limit subgroup very well, where the semioctave stands in for ~7/5, ~17/12, ~99/70 and their [[octave complement]]s.~~

	Subgroup: 2.3.5.7.11.17		Subgroup: 2.3.5.7.11.17

	Comma list: 50/49, 85/84, 99/98		Comma list: 50/49, 85/84, 99/98

	~~Mapping~~: {{Mapping\| 2 0 0 1 4 5 \| 0 1 0 0 -2 1 \| 0 0 1 1 2 0 }}		Subgroup-val mapping: {{Mapping\| 2 0 0 1 4 5 \| 0 1 0 0 -2 1 \| 0 0 1 1 2 0 }}

	Optimal tunings:		Optimal tunings:
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	* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9274{{c}}, ~5/4 = 379.2350{{c}}		* CWE: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9274{{c}}, ~5/4 = 379.2350{{c}}

	{{Optimal ET sequence\|legend=0\| 4, 8d, 10e, 12, 22, 34d, 48 }}		{{Optimal ET sequence\|legend=0\| 4, 8d, 10e, 12, 14c, 22, 34d, 48 }}

	Badness (Sintel): 0.578		Badness (Sintel): 0.578

Xenllium: Added 17-limit subgroup temperaments

2026-06-08T23:32:37Z

Added 17-limit subgroup temperaments

@@ Line 27: / Line 27: @@
 Scales: [[jubilismic10]], [[jubilismic12]]
 == Undecimal jubilismic ==
@@ Line 46: / Line 63: @@
 [[Badness]] (Sintel): 0.673
 == Festival ==

FloraC at 07:22, 28 January 2026

2026-01-28T07:22:29Z

← Older revision		Revision as of 07:22, 28 January 2026
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	== Undecimal jubilismic ==		== Undecimal jubilismic ==
	Formerly known as ''jubilee'', undecimal jubilismic tempers out [[99/98]] and [[100/99]], and is the most natural extension of jubilismic to the 11-limit. [[11/8]] is found by a stack of two [[5/4]]'s ~~minus two perfect fifths~~ octave reduced ~~(i.e. a whole tone)~~.		Formerly known as ''jubilee'', undecimal jubilismic tempers out [[99/98]] and [[100/99]], and is the most natural extension of jubilismic to the 11-limit. [[11/8]] is found by a stack of two [[7/6]]'s or two [[5/3]]'s octave reduced.

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

FloraC: Promote jubilee to the canonical 11-limit jubilismic temp.

2026-01-28T07:21:06Z

Promote jubilee to the canonical 11-limit jubilismic temp.

← Older revision		Revision as of 07:21, 28 January 2026
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	Scales: [[jubilismic10]], [[jubilismic12]]		Scales: [[jubilismic10]], [[jubilismic12]]

	== ~~Jubilee~~ ==		== Undecimal jubilismic ==
			Formerly known as ''jubilee'', undecimal jubilismic tempers out [[99/98]] and [[100/99]], and is the most natural extension of jubilismic to the 11-limit. [[11/8]] is found by a stack of two [[5/4]]'s minus two perfect fifths octave reduced (i.e. a whole tone).

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

FloraC: - redundant category

2026-01-22T10:58:18Z

- redundant category

← Older revision		Revision as of 10:58, 22 January 2026
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Jubilismic family\| ]] <!-- main article -->		[[Category:Jubilismic family\| ]] <!-- main article -->
	~~[[Category:Jubilismic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-11-27T12:29:17Z

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

← Older revision		Revision as of 12:29, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Jubilismic family\| ]] <!-- main article -->		[[Category:Jubilismic family\| ]] <!-- main article -->
	[[Category:Jubilismic\| ]] <!-- key article -->		[[Category:Jubilismic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: - POTE tunings

2025-07-22T14:18:26Z

- POTE tunings

← Older revision		Revision as of 14:18, 22 July 2025
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	* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.4574{{c}}, ~5/4 = 380.0086{{c}}		* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.4574{{c}}, ~5/4 = 380.0086{{c}}
	: error map: {{val\| 0.000 +0.502 -6.305 +11.183 }}		: error map: {{val\| 0.000 +0.502 -6.305 +11.183 }}
	~~<!-- * [[POTE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9804{{c}}, ~5/4 = 380.8399{{c}} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9249{{c}}, ~5/4 = 379.6796{{c}}		* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9249{{c}}, ~5/4 = 379.6796{{c}}
	: error map: {{val\| 0.000 +0.970 -6.634 +10.854 +2.192 }}		: error map: {{val\| 0.000 +0.970 -6.634 +10.854 +2.192 }}
	~~<!-- * [[POTE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 703.4155{{c}}, ~5/4 = 380.6973{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 4, 8d, 10e, 12, 22, 34d, 48 }}		{{Optimal ET sequence\|legend=1\| 4, 8d, 10e, 12, 22, 34d, 48 }}
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	* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 694.5001{{c}}, ~5/4 = 372.9799{{c}}		* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 694.5001{{c}}, ~5/4 = 372.9799{{c}}
	: error map: {{val\| 0.000 -7.455 -13.334 +4.154 +10.662 }}		: error map: {{val\| 0.000 -7.455 -13.334 +4.154 +10.662 }}
	~~<!-- * [[POTE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 693.6257{{c}}, ~5/4 = 371.2658{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 10, 12, 22e, 26 }}		{{Optimal ET sequence\|legend=1\| 10, 12, 22e, 26 }}
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	* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 709.6819{{c}}, ~5/4 = 391.4911{{c}}		* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 709.6819{{c}}, ~5/4 = 391.4911{{c}}
	: error map: {{val\| 0.000 +7.727 +5.177 +22.665 +48.682 }}		: error map: {{val\| 0.000 +7.727 +5.177 +22.665 +48.682 }}
	~~<!-- * [[POTE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 713.5853{{c}}, ~5/4 = 397.6952{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 8d, 10, 12, 22e, 30dee, 42ddeee }}		{{Optimal ET sequence\|legend=1\| 8d, 10, 12, 22e, 30dee, 42ddeee }}
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	* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 706.7334{{c}}, ~5/4 = 376.9332{{c}}		* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 706.7334{{c}}, ~5/4 = 376.9332{{c}}
	: error map: {{val\| 0.000 +4.778 -9.381 +8.107 -8.051 }}		: error map: {{val\| 0.000 +4.778 -9.381 +8.107 -8.051 }}
	~~<!-- * [[POTE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 706.6559{{c}}, ~5/4 = 376.8308{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 8d, 10, 12e, 14c, 22, 58ce }}		{{Optimal ET sequence\|legend=1\| 8d, 10, 12e, 14c, 22, 58ce }}

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

2025-07-22T14:18:06Z

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

← Older revision		Revision as of 14:18, 22 July 2025
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	: mapping generators: ~7/5, ~3, ~5		: mapping generators: ~7/5, ~3, ~5

	[[Optimal tuning]] ([[POTE]]): ~7/5 = ~~1\2~~, ~3/2 = 702.9804, ~5/4 = 380.8399		[[Optimal tuning]]s:
			* [[WE]]: ~7/5 = 599.6673{{c}}, ~3/2 = 702.5906{{c}}, ~5/4 = 380.6287{{c}}
			: [[error map]]: {{val\| -0.665 -0.030 -7.016 +10.139 }}
			* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.4574{{c}}, ~5/4 = 380.0086{{c}}
			: error map: {{val\| 0.000 +0.502 -6.305 +11.183 }}
			<!-- * [[POTE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9804{{c}}, ~5/4 = 380.8399{{c}} -->

	[[Minimax tuning]]:		[[Minimax tuning]]:
	* 7- and [[9-odd-limit]]		* 7- and [[9-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| -1/4 0 1/2 1/2 \| 1/4 0 1/2 1/2 }}		: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| -1/4 0 1/2 1/2 \| 1/4 0 1/2 1/2 }}
	: [[~~Eigenmonzo~~ basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.35		: [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.35

	{{Optimal ET sequence\|legend=1\| 4, 8d, 10, 12, 22, 34d, 48 }}		{{Optimal ET sequence\|legend=1\| 4, 8d, 10, 12, 22, 34d, 48, 60d }}

			[[Badness]] (Sintel): 0.561

	Scales: [[jubilismic10]], [[jubilismic12]]		Scales: [[jubilismic10]], [[jubilismic12]]

	== Jubilee ==		== Jubilee ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	{{Mapping\|legend=1\| 2 0 0 1 4 \| 0 1 0 0 -2 \| 0 0 1 1 2 }}		{{Mapping\|legend=1\| 2 0 0 1 4 \| 0 1 0 0 -2 \| 0 0 1 1 2 }}

	[[Optimal tuning]] ([[POTE]]): ~7/5 = ~~1\2~~, ~3/2 = 703.4155, ~5/4 = 380.6973		[[Optimal tuning]]s:
			* [[WE]]: ~7/5 = 599.6219{{c}}, ~3/2 = 702.9722{{c}}, ~5/4 = 380.4574{{c}}
			: [[error map]]: {{val\| -0.756 +0.261 -7.369 +9.741 +0.628 }}
			* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 702.9249{{c}}, ~5/4 = 379.6796{{c}}
			: error map: {{val\| 0.000 +0.970 -6.634 +10.854 +2.192 }}
			<!-- * [[POTE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 703.4155{{c}}, ~5/4 = 380.6973{{c}} -->

	{{Optimal ET sequence\|legend=1\| 4, 8d, 10e, 12, 22, 34d, 48 }}		{{Optimal ET sequence\|legend=1\| 4, 8d, 10e, 12, 22, 34d, 48 }}

	[[Badness]]: 0.~~600 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.673

	== Festival ==		== Festival ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	{{Mapping\|legend=1\| 2 0 0 1 -4 \| 0 1 0 0 2 \| 0 0 1 1 1 }}		{{Mapping\|legend=1\| 2 0 0 1 -4 \| 0 1 0 0 2 \| 0 0 1 1 1 }}

	[[Optimal tuning]] ([[~~POTE~~]]): ~7/5 = 1\2, ~3/2 = 693.6257, ~5/4 = 371.2658		[[Optimal tuning]]s:
			* [[WE]]: ~7/5 = 600.8501{{c}}, ~3/2 = 694.6084{{c}}, ~5/4 = 371.7918{{c}}
			: [[error map]]: {{val\| +1.700 -5.646 -11.121 +7.216 +13.091 }}
			* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 694.5001{{c}}, ~5/4 = 372.9799{{c}}
			: error map: {{val\| 0.000 -7.455 -13.334 +4.154 +10.662 }}
			<!-- * [[POTE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 693.6257{{c}}, ~5/4 = 371.2658{{c}} -->

	{{Optimal ET sequence\|legend=1\| 10, 12, 22e, 26 }}		{{Optimal ET sequence\|legend=1\| 10, 12, 22e, 26 }}

	[[Badness]]: 0.~~689 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.827

	== Fiesta ==		== Fiesta ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	{{Mapping\|legend=1\| 2 0 0 1 7 \| 0 1 0 0 0 \| 0 0 1 1 0 }}		{{Mapping\|legend=1\| 2 0 0 1 7 \| 0 1 0 0 0 \| 0 0 1 1 0 }}

	[[Optimal tuning]] ([[POTE]]): ~7/5 = ~~1\2~~, ~3/2 = 713.5853, ~5/4 = 397.6952		[[Optimal tuning]]:
			* [[WE]]: ~7/5 = 596.3068{{c}}, ~3/2 = 709.1930{{c}}, ~5/4 = 395.2472{{c}}
			: [[error map]]: {{val\| -7.386 -0.148 -5.839 +7.955 +22.830 }}
			* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 709.6819{{c}}, ~5/4 = 391.4911{{c}}
			: error map: {{val\| 0.000 +7.727 +5.177 +22.665 +48.682 }}
			<!-- * [[POTE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 713.5853{{c}}, ~5/4 = 397.6952{{c}} -->

	{{Optimal ET sequence\|legend=1\| 8d, 10, 12, 22e }}		{{Optimal ET sequence\|legend=1\| 8d, 10, 12, 22e, 30dee, 42ddeee }}

	[[Badness]]: 0.~~717 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.861

	== Jamboree ==		== Jamboree ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	{{Mapping\|legend=1\| 2 0 0 1 2 \| 0 1 0 0 3 \| 0 0 1 1 -1 }}		{{Mapping\|legend=1\| 2 0 0 1 2 \| 0 1 0 0 3 \| 0 0 1 1 -1 }}

	[[Optimal tuning]] ([[POTE]]): ~7/5 = ~~1\2~~, ~3/2 = 706.6559, ~5/4 = 376.8308		[[Optimal tuning]]s:
			* [[WE]]: ~7/5 = 600.0436{{c}}, ~3/2 = 706.7073{{c}}, ~5/4 = 376.8582{{c}}
			: [[error map]]: {{val\| +0.087 +4.839 -9.281 +8.250 -7.880 }}
			* [[CWE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 706.7334{{c}}, ~5/4 = 376.9332{{c}}
			: error map: {{val\| 0.000 +4.778 -9.381 +8.107 -8.051 }}
			<!-- * [[POTE]]: ~7/5 = 600.0000{{c}}, ~3/2 = 706.6559{{c}}, ~5/4 = 376.8308{{c}} -->

	{{Optimal ET sequence\|legend=1\| 8d, 10, 12e, 14c, 22 }}		{{Optimal ET sequence\|legend=1\| 8d, 10, 12e, 14c, 22, 58ce }}

	[[Badness]]: 0.~~781 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.938

	[[Category:Temperament families]]		[[Category:Temperament families]]

FloraC: Intro

2025-07-22T13:09:06Z

Intro

← Older revision		Revision as of 13:09, 22 July 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''jubilismic family''' ~~contains~~ temperaments ~~that temper~~ out ~~the~~ [[~~jubilisma\|jubilisma (~~50/49)]] ~~(also called tritonic diesis, or septimal sixth~~-~~tone)~~. It therefore identifies the two septimal tritones [[7/5]] and [[10/7]], an identification familiar from [[12edo]]. While ~~most~~ rank-~~three~~ temperaments are planar, a jubilismic temperament divides the octave in two.		The '''jubilismic family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] [[50/49]] in the full [[7-limit]]. It therefore identifies the two septimal tritones [[7/5]] and [[10/7]], an identification familiar from [[12edo]]. While many rank-3 temperaments are planar, a jubilismic temperament divides the [[2/1\|octave]] in two. Related to this is the 2.5.7-subgroup {50/49} temperament [[jubilic]].

	== Jubilismic ==		== Jubilismic ==

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

2025-06-24T00:30:02Z

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

← Older revision		Revision as of 00:30, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Jubilismic family\| ]] <!-- main article -->		[[Category:Jubilismic family\| ]] <!-- main article -->
	[[Category:Jubilismic\| ]] <!-- key article -->		[[Category:Jubilismic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]