19th-octave temperaments - Revision history

Hotcrystal0: Graywood notice

2026-03-23T20:48:43Z

Graywood notice

← Older revision		Revision as of 20:48, 23 March 2026
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	See also [[enneadecal]] and [[superenneadecal]].		See also [[enneadecal]] and [[superenneadecal]].

			For graywood, see [[Syntonic–kleismic equivalence continuum#Graywood]].

	== Meanmag ==		== Meanmag ==

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

2026-03-23T13:27:17Z

Switch to Sintel's badness, WE & CWE tunings

← Older revision		Revision as of 13:27, 23 March 2026
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	{{Infobox fractional-octave\|19}}		{{Infobox fractional-octave\|19}}
	[[19edo]] has excellent 5-limit accuracy, but its quality of higher-limit approximation can be improved. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. Meanmag has the same 5-limit mapping as 19et with ~~harmonics~~ 7, 11, and 13 mapped to an independent generator. Undevigintone has the same 2.3.5.7.13 subgroup mapping as 19et with harmonic 11 mapped to an independent generator.		[[19edo]] has excellent [[5-limit]] accuracy, but its quality of higher-limit approximation can be improved. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. Meanmag has the same 5-limit mapping as 19et with [[harmonic]]s [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]] mapped to an independent generator. Undevigintone has the same [[2.3.5.7.13 subgroup\|2.3.5.7.13-subgroup]] mapping as 19et with harmonic 11 mapped to an independent generator.

	See also [[enneadecal]] and [[superenneadecal]].		See also [[enneadecal]] and [[superenneadecal]].
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	: mapping generators: ~25/24, ~7		: mapping generators: ~25/24, ~7

	[[Optimal tuning]] ([[~~POTE~~]]): ~25/24 = 63.1579{{c}}, ~8/7 = ~~238~~.~~396~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~25/24 = 63.2931{{c}}, ~7/4 = 963.6625{{c}}
			: [[error map]]: {{val\| +2.569 -3.162 -1.417 -0.026 }}
			* [[CWE]]: ~25/24 = 63.1579{{c}}, ~7/4 = 963.4030{{c}}
			: error map: {{val\| 0.000 -7.218 -7.366 -5.423 }}

	{{Optimal ET sequence\|legend=1\| 19~~, 38~~, 57, 76, ~~95bc~~ }}		{{Optimal ET sequence\|legend=1\| 19, 57, 76, 171bbccdd }}

	[[Badness]] (~~Smith~~): 0.~~077023~~		[[Badness]] (Sintel): 1.95

	=== 11-limit ===		=== 11-limit ===
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	Mapping: {{mapping\| 19 30 44 0 119 \| 0 0 0 1 -1 }}		Mapping: {{mapping\| 19 30 44 0 119 \| 0 0 0 1 -1 }}

	Optimal ~~tuning (POTE)~~: ~25/24 = 63.1579{{c}}, ~8/7 = ~~233~~.~~486~~{{c}}		Optimal tunings:
			* WE: ~25/24 = 63.2535{{c}}, ~7/4 = 967.9769{{c}}
			* CWE: ~25/24 = 63.1579{{c}}, ~7/4 = 966.6112{{c}}

	{{Optimal ET sequence\|legend=0\| 19, 38, 57~~, 76~~ }}		{{Optimal ET sequence\|legend=0\| 19, 38, 57 }}

	Badness (~~Smith~~): 0.~~066829~~		Badness (Sintel): 2.21

	==== 13-limit ====		==== 13-limit ====
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	Mapping: {{mapping\| 19 30 44 0 119 17 \| 0 0 0 1 -1 1 }}		Mapping: {{mapping\| 19 30 44 0 119 17 \| 0 0 0 1 -1 1 }}

	Optimal ~~tuning (POTE)~~: ~25/24 = 63.1579{{c}}, ~8/7 = ~~234~~.~~890~~{{c}}		Optimal tunings:
			* WE: ~25/24 = 63.2422{{c}}, ~7/4 = 966.3987{{c}}
			* CWE: ~25/24 = 63.1579{{c}}, ~7/4 = 965.3984{{c}}

	{{Optimal ET sequence\|legend=0\| 19, 38, 57, 76 }}		{{Optimal ET sequence\|legend=0\| 19, 38, 57, 76 }}

	Badness (~~Smith~~): 0.~~045844~~		Badness (Sintel): 1.89

	== Undevigintone ==		== Undevigintone ==
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	: mapping generators: ~28/27, ~11		: mapping generators: ~28/27, ~11

	[[Optimal tuning]] ([[~~POTE~~]]): ~28/27 = 63.1579{{c}}, ~11/8 = ~~538~~.~~047~~{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~28/27 = 63.3591{{c}}, ~11/8 = 539.7611{{c}}
			* [[CWE]]: ~28/27 = 63.1579{{c}}, ~11/8 = 540.6837{{c}}

	{{Optimal ET sequence\|legend=1\| 19, 38d }}		{{Optimal ET sequence\|legend=1\| 19, 38d }}

	[[Badness]] (~~Smith~~): 0.~~036387~~		[[Badness]] (Sintel): 1.20

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 19 30 44 53 0 70 \| 0 0 0 0 1 0 }}		Mapping: {{mapping\| 19 30 44 53 0 70 \| 0 0 0 0 1 0 }}

	Optimal ~~tuning (POTE)~~: ~28/27 = 63.1579{{c}}, ~11/8 = ~~537~~.~~061~~{{c}}		Optimal tunings:
			* WE: ~28/27 = 63.3741{{c}}, ~11/8 = 538.8996{{c}}
			* CWE: ~28/27 = 63.1579{{c}}, ~11/8 = 539.4216{{c}}

	{{Optimal ET sequence\|legend=0\| 19, 38df }}		{{Optimal ET sequence\|legend=0\| 19, 38df }}

	Badness (~~Smith~~): 0.~~022933~~		Badness (Sintel): 0.948

	{{Navbox fractional-octave}}		{{Navbox fractional-octave}}

FloraC: Units & misc. cleanup

2026-03-23T13:09:56Z

Units & misc. cleanup

← Older revision		Revision as of 13:09, 23 March 2026
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	{{Mapping\|legend=1\| 19 30 44 0 \| 0 0 0 1 }}		{{Mapping\|legend=1\| 19 30 44 0 \| 0 0 0 1 }}

	: mapping generators: ~25/24, ~7		: mapping generators: ~25/24, ~7

	[[Optimal tuning]] ([[POTE]]): ~25/24 = ~~1\19~~, ~8/7 = 238.396		[[Optimal tuning]] ([[POTE]]): ~25/24 = 63.1579{{c}}, ~8/7 = 238.396{{c}}

	{{Optimal ET sequence\|legend=1\| 19, 38, 57, 76, 95bc }}		{{Optimal ET sequence\|legend=1\| 19, 38, 57, 76, 95bc }}

	[[Badness]]: 0.077023		[[Badness]] (Smith): 0.077023

	=== 11-limit ===		=== 11-limit ===
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	Mapping: {{mapping\| 19 30 44 0 119 \| 0 0 0 1 -1 }}		Mapping: {{mapping\| 19 30 44 0 119 \| 0 0 0 1 -1 }}

	Optimal tuning (POTE): ~25/24 = ~~1\19~~, ~8/7 = 233.486		Optimal tuning (POTE): ~25/24 = 63.1579{{c}}, ~8/7 = 233.486{{c}}

	{{Optimal ET sequence\|legend=1\| 19, 38, 57, 76 }}		{{Optimal ET sequence\|legend=0\| 19, 38, 57, 76 }}

	Badness: 0.066829		Badness (Smith): 0.066829

	==== 13-limit ====		==== 13-limit ====
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	Mapping: {{mapping\| 19 30 44 0 119 17 \| 0 0 0 1 -1 1 }}		Mapping: {{mapping\| 19 30 44 0 119 17 \| 0 0 0 1 -1 1 }}

	Optimal tuning (POTE): ~25/24 = ~~1\19~~, ~8/7 = 234.890		Optimal tuning (POTE): ~25/24 = 63.1579{{c}}, ~8/7 = 234.890{{c}}

	{{Optimal ET sequence\|legend=1\| 19, 38, 57, 76 }}		{{Optimal ET sequence\|legend=0\| 19, 38, 57, 76 }}

	Badness: 0.045844		Badness (Smith): 0.045844

	== Undevigintone ==		== Undevigintone ==
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	{{Mapping\|legend=1\| 19 30 44 53 0 \| 0 0 0 0 1 }}		{{Mapping\|legend=1\| 19 30 44 53 0 \| 0 0 0 0 1 }}

	: mapping generators: ~28/27, ~11		: mapping generators: ~28/27, ~11

	[[Optimal tuning]] ([[POTE]]): ~28/27 = ~~1\19~~, ~11/8 = 538.047		[[Optimal tuning]] ([[POTE]]): ~28/27 = 63.1579{{c}}, ~11/8 = 538.047{{c}}

	{{Optimal ET sequence\|legend=1\| 19, 38d }}		{{Optimal ET sequence\|legend=1\| 19, 38d }}

	[[Badness]]: 0.036387		[[Badness]] (Smith): 0.036387

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 19 30 44 53 0 70 \| 0 0 0 0 1 0 }}		Mapping: {{mapping\| 19 30 44 53 0 70 \| 0 0 0 0 1 0 }}

	Optimal tuning (POTE): ~28/27 = ~~1\19~~, ~11/8 = 537.061		Optimal tuning (POTE): ~28/27 = 63.1579{{c}}, ~11/8 = 537.061{{c}}

	{{Optimal ET sequence\|legend=1\| 19, 38df }}		{{Optimal ET sequence\|legend=0\| 19, 38df }}

	Badness: 0.022933		Badness (Smith): 0.022933

	{{Navbox fractional-octave}}		{{Navbox fractional-octave}}

FloraC: Move graywood and 5-limit enneadecal to the equivalence continuum

2026-03-23T12:56:32Z

Move graywood and 5-limit enneadecal to the equivalence continuum

@@ Line 3: / Line 3: @@
 See also [[enneadecal]] and [[superenneadecal]].
 == Meanmag ==
@@ Line 55: / Line 44: @@
 Badness: 0.045844
 == Undevigintone ==

VectorGraphics at 05:09, 12 June 2025

2025-06-12T05:09:54Z

← Older revision		Revision as of 05:09, 12 June 2025
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	: mapping generators: ~25/24, ~7		: mapping generators: ~25/24, ~7

	~~{{Multival\|legend=1\| 0 0 19 0 30 44 }}~~

	[[Optimal tuning]] ([[POTE]]): ~25/24 = 1\19, ~8/7 = 238.396		[[Optimal tuning]] ([[POTE]]): ~25/24 = 1\19, ~8/7 = 238.396

ArrowHead294 at 03:58, 14 February 2025

2025-02-14T03:58:11Z

← Older revision		Revision as of 03:58, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|19}}		{{Infobox fractional-octave\|19}}
	[[19edo]] has excellent 5-limit accuracy, but its quality of higher-limit approximation can be improved. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. Meanmag has the same 5-limit mapping as 19et with harmonics 7, 11, and 13 mapped to an independent generator. Undevigintone has the same 2.3.5.7.13 subgroup mapping as 19et with harmonic 11 mapped to an independent generator.		[[19edo]] has excellent 5-limit accuracy, but its quality of higher-limit approximation can be improved. This page accommodates a number of temperaments that are otherwise difficult to catalog because they belong to multiple families. Meanmag has the same 5-limit mapping as 19et with harmonics 7, 11, and 13 mapped to an independent generator. Undevigintone has the same 2.3.5.7.13 subgroup mapping as 19et with harmonic 11 mapped to an independent generator.

Roeesi: /* Meanmag */If Undevigintone gets its own top level paragraph then Meanmag should too.

2025-02-13T10:45:31Z

Meanmag: If Undevigintone gets its own top level paragraph then Meanmag should too.

← Older revision		Revision as of 10:45, 13 February 2025
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	[[Support]]ing [[ET]]s: {{EDOs\|19, 38c, 57c, 76c, 95bcc }}		[[Support]]ing [[ET]]s: {{EDOs\|19, 38c, 57c, 76c, 95bcc }}

	=== Meanmag ===		== Meanmag ==
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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	[[Badness]]: 0.077023		[[Badness]]: 0.077023

	==== 11-limit ====		=== 11-limit ===
	Subgroup: 2.3.5.7.11		Subgroup: 2.3.5.7.11

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	Badness: 0.066829		Badness: 0.066829

	===== 13-limit =====		==== 13-limit ====
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

BudjarnLambeth: navbox

2024-12-05T07:19:22Z

navbox

← Older revision		Revision as of 07:19, 5 December 2024
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	Badness: 0.022933		Badness: 0.022933

			{{Navbox fractional-octave}}

Lériendil at 10:34, 25 August 2024

2024-08-25T10:34:39Z

@@ Line 14: / Line 14: @@
 [[Support]]ing [[ET]]s: {{EDOs|19, 38c, 57c, 76c, 95bcc }}
 === Meanmag ===
 [[Subgroup]]: 2.3.5.7
@@ Line 56: / Line 57: @@
 Badness: 0.045844
 == Undevigintone ==

CompactStar at 09:06, 2 February 2024

2024-02-02T09:06:23Z

← Older revision		Revision as of 09:06, 2 February 2024
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	Badness: 0.066829		Badness: 0.066829

	==== 13-limit ====		===== 13-limit =====
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13