15th-octave temperaments - Revision history

FloraC: - quindecic, - phosphorus (addressed in proper places)

2026-06-28T10:57:41Z

- quindecic, - phosphorus (addressed in proper places)

@@ Line 2: / Line 2: @@
 [[15edo]] has some close approximations including [[22/21]] to one step and [[77/64]] to four steps.
-Temperaments discussed elsewhere include [[Cloudy clan #Pentadecal|pentadecal]] and [[Landscape microtemperaments#Slendscape|slendscape]].
+Temperaments discussed elsewhere include [[blackwood family #Quindecic|quindecic]], [[keemic temperaments #Pentadecal|pentadecal]], [[Landscape microtemperaments #Slendscape|slendscape]], and [[Landscape microtemperaments #Phosphorus|phosphorus]].
 == Pentadecoid ==
-In pentadecoid, the period (1\15) is given an interpretation of [[22/21]], and four of them represent the keenanismic minor third, [[77/64]] = ([[147/128]])⋅([[22/21]]). The temperament is named for an analog of its relating temperaments, [[decoid]] ({{nowrap| 130 & 140 }}) and [[quintosec family #triacontoid|triacontoid]] ({{nowrap| 120 & 150 }}). Triacontoid is a weak extension of pentadecoid, as well as [[Landscape microtemperaments|slendscape]] ({{nowrap| 255 & 270 }}).
+In pentadecoid, the period (1\15) is given an interpretation of [[22/21]], and four of them represent the keenanismic minor third, [[77/64]] = ([[147/128]])⋅([[22/21]]). The temperament is named for an analog of its relating temperaments, [[decoid]] ({{nowrap| 130 & 140 }}) and [[quintosec family #Triacontoid|triacontoid]] ({{nowrap| 120 & 150 }}). Triacontoid is a weak extension of pentadecoid, as well as [[Landscape microtemperaments #Slendscape|slendscape]] ({{nowrap| 255 & 270 }}).
 [[Subgroup]]: 2.3.7.11
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 [[Badness]] (Sintel): 0.951
 {{Fractional-octave footer}}

FloraC: Consolidate data for pentadecoid

2025-06-11T12:36:24Z

Consolidate data for pentadecoid

← Older revision		Revision as of 12:36, 11 June 2025
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	== Pentadecoid ==		== Pentadecoid ==
			In pentadecoid, the period (1\15) is given an interpretation of [[22/21]], and four of them represent the keenanismic minor third, [[77/64]] = ([[147/128]])⋅([[22/21]]). The temperament is named for an analog of its relating temperaments, [[decoid]] ({{nowrap\| 130 & 140 }}) and [[quintosec family #triacontoid\|triacontoid]] ({{nowrap\| 120 & 150 }}). Triacontoid is a weak extension of pentadecoid, as well as [[Landscape microtemperaments\|slendscape]] ({{nowrap\| 255 & 270 }}).

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

	[[Comma list]]: 1362944/1361367, 1771561/1769472		[[Comma list]]: 1362944/1361367, 1771561/1769472

	~~[[Mapping]]:~~ {{~~mapping~~\| 15 108 0 94 \| 0 -2 1 -1 }}		{{Mapping\|legend=1\| 15 108 0 94 \| 0 -2 1 -1 }}

	: mapping generators: ~22/21, ~7		: mapping generators: ~22/21, ~7

	[[Optimal tuning]] ([[CTE]]): ~22/21 = 80.0000, ~8/7 = 231.0071		[[Optimal tuning]] ([[CTE]]): ~22/21 = 80.0000, ~8/7 = 231.0071 (~1029/1024 = 8.9929)

	{{Optimal ET sequence\|legend=1\| 120, 135, 660, 795, 930, 1065, 1200 }}		{{Optimal ET sequence\|legend=1\| 120, 135, 660, 795, 930, 1065, 1200, 1335, 2535e }}

	[[Badness]]: 0.~~025231~~		[[Badness]] (Sintel): 0.951

	== Phosphorus ==		== Phosphorus ==

Lériendil at 05:04, 14 February 2025

2025-02-14T05:04:38Z

← Older revision		Revision as of 05:04, 14 February 2025
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	[[15edo]] has some close approximations including [[22/21]] to one step and [[77/64]] to four steps.		[[15edo]] has some close approximations including [[22/21]] to one step and [[77/64]] to four steps.

	Temperaments discussed elsewhere include [[Cloudy clan #Pentadecal\|pentadecal]].		Temperaments discussed elsewhere include [[Cloudy clan #Pentadecal\|pentadecal]] and [[Landscape microtemperaments#Slendscape\|slendscape]].

	== Pentadecoid ==		== Pentadecoid ==

ArrowHead294 at 04:00, 14 February 2025

2025-02-14T04:00:59Z

← Older revision		Revision as of 04:00, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|15}}		{{Infobox fractional-octave\|15}}
	[[15edo]] has some close approximations including [[22/21]] to one step and [[77/64]] to four steps.		[[15edo]] has some close approximations including [[22/21]] to one step and [[77/64]] to four steps.

FloraC: Cleanup

2025-01-01T12:14:22Z

Cleanup

← Older revision		Revision as of 12:14, 1 January 2025
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	[[15edo]] has some close approximations including [[22/21]] to one step and [[77/64]] to four steps.		[[15edo]] has some close approximations including [[22/21]] to one step and [[77/64]] to four steps.

	Temperaments discussed elsewhere include [[Cloudy clan\|pentadecal]].		Temperaments discussed elsewhere include [[Cloudy clan #Pentadecal\|pentadecal]].

	== Pentadecoid ==		== Pentadecoid ==
	Subgroup: 2.3.7.11		[[Subgroup]]: 2.3.7.11

	[[Comma list]]: 1362944/1361367, 1771561/1769472		[[Comma list]]: 1362944/1361367, 1771561/1769472
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	[[Mapping]]: {{mapping\| 15 108 0 94 \| 0 -2 1 -1 }}		[[Mapping]]: {{mapping\| 15 108 0 94 \| 0 -2 1 -1 }}

	: ~~Mapping~~ generators: ~22/21, ~7		: mapping generators: ~22/21, ~7

	[[Optimal tuning]] ([[CTE]]): ~22/21 = ~~1＼15~~, ~8/7 = 231.0071		[[Optimal tuning]] ([[CTE]]): ~22/21 = 80.0000, ~8/7 = 231.0071

	{{Optimal ET sequence\|legend=1\| 120, 135, 660, 795, 930, 1065, 1200 }}		{{Optimal ET sequence\|legend=1\| 120, 135, 660, 795, 930, 1065, 1200 }}
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	== Phosphorus ==		== Phosphorus ==
	Subgroup: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: 250047/250000, {{monzo\|60 -96 1 32}}		[[Comma list]]: 250047/250000, {{monzo\| 60 -96 1 32 }}

	[[Mapping]]: {{mapping\| 15 8 -4 -4 \| 0 13 32 38 }}		[[Mapping]]: {{mapping\| 15 8 -4 -4 \| 0 13 32 38 }}

	: ~~Mapping~~ generators: ~{{monzo\|-21 34 4 -15}}, ~210827008/199290375		: mapping generators: ~{{monzo\| -21 34 4 -15 }}, ~210827008/199290375

	[[Optimal tuning]] ([[CTE]]): ~{{monzo\|-21 34 4 -15}} = ~~1＼15~~, ~28/27 = 62.9267		[[Optimal tuning]] ([[CTE]]): ~{{monzo\|-21 34 4 -15}} = 80.0000, ~28/27 = 62.9267

	{{Optimal ET sequence\|legend=1\| 1125, 1335, 2460 }}		{{Optimal ET sequence\|legend=1\| 1125, 1335, 2460 }}
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	[[Mapping]]: {{mapping\| 15 24 35 42 52 0 \| 0 0 0 0 0 1 }}		[[Mapping]]: {{mapping\| 15 24 35 42 52 0 \| 0 0 0 0 0 1 }}

	: ~~Mapping~~ generators: ~22/21, ~13		: mapping generators: ~22/21, ~13

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[CTE]]: ~22/21 = ~~1＼15~~, ~13/8 = 840.528 (~40/39 = 39.472)		* [[CTE]]: ~22/21 = 80.000, ~13/8 = 840.528 (~40/39 = 39.472)
	* [[POTE]]: ~22/21 = ~~1＼15~~, ~13/8 = 852.924 (~40/39 = 27.076)		* [[POTE]]: ~22/21 = 80.000, ~13/8 = 852.924 (~40/39 = 27.076)

	{{Optimal ET sequence\|legend=1\| 15, 30 }}		{{Optimal ET sequence\|legend=1\| 15, 30 }}

Xenllium at 05:35, 1 January 2025

2025-01-01T05:35:03Z

← Older revision		Revision as of 05:35, 1 January 2025
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	Temperaments discussed elsewhere include [[Cloudy clan\|pentadecal]].		Temperaments discussed elsewhere include [[Cloudy clan\|pentadecal]].

	== ~~Unnamed 2.3.7.11 temperament (135 & 255)~~ ==		== Pentadecoid ==
	Subgroup: 2.3.7.11		Subgroup: 2.3.7.11

Xenllium at 02:15, 31 December 2024

2024-12-31T02:15:32Z

@@ Line 1: / Line 1: @@
 {{Fractional-octave navigation|15}}
 == Quindecic ==
@@ Line 10: / Line 43: @@
 [[Mapping]]: {{mapping| 15 24 35 42 52 0 | 0 0 0 0 0 1 }}
-: mapping generators: ~22/21, ~13
+: Mapping generators: ~22/21, ~13
 [[Optimal tuning]]s:
-* [[CTE]]: ~22/21 = 80.000, ~13/8 = 840.528 (~40/39 = 39.472)
+* [[CTE]]: ~22/21 = 1＼15, ~13/8 = 840.528 (~40/39 = 39.472)
-* [[POTE]]: ~22/21 = 80.000, ~13/8 = 852.924 (~40/39 = 27.076)
+* [[POTE]]: ~22/21 = 1＼15, ~13/8 = 852.924 (~40/39 = 27.076)
 {{Optimal ET sequence|legend=1| 15, 30 }}
-[[Badness]] (Smith): 0.028944
+[[Badness]]: 0.028944
 {{Fractional-octave footer}}

FloraC: Undo moving pentadecal here

2024-12-22T09:34:03Z

Undo moving pentadecal here

@@ Line 1: / Line 1: @@
 {{Fractional-octave navigation|15}}
-== Pentadecal ==
+== Quindecic ==
 Quindecic preserves the [[11-limit]] structure of [[15edo]], with an independent generator for [[13/1|harmonic 13]].

Lériendil at 15:50, 21 December 2024

2024-12-21T15:50:06Z

@@ Line 1: / Line 1: @@
 {{Fractional-octave navigation|15}}
 == Pentadecal ==
@@ Line 110: / Line 91: @@
 Badness: 0.055361
 {{Fractional-octave footer}}

Lériendil at 15:30, 21 December 2024

2024-12-21T15:30:00Z

← Older revision		Revision as of 15:30, 21 December 2024
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	== Pentadecal ==		== Pentadecal ==
			The ''pentadecal'' temperament tempers out the 15-5/3-comma (Quintriyo, pentadecatonic minor thirds comma), {{monzo\|-11 -15 15}}. This temperament can be described as 15&60 temperament; in the 7-limit, it tempers out the [[cloudy comma]], 16807/16384, and the [[875/864\|keema]], 875/864.

	Subgroup: 2.3.5		Subgroup: 2.3.5

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	=== 7-limit ===		=== 7-limit ===
	The ''pentadecal'' temperament tempers out the 15-5/3-comma (Quintriyo, pentadecatonic minor thirds comma), {{monzo\|-11 -15 15}}. This temperament can be described as 15&60 temperament, tempering out the [[cloudy comma]], 16807/16384 and the [[875/864\|keema]], 875/864 in the 7-limit.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7