17th-octave temperaments - Revision history

Xenllium at 02:14, 23 February 2026

2026-02-23T02:14:50Z

← Older revision		Revision as of 02:14, 23 February 2026
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	=== 7-limit ===		=== 7-limit ===
			Gothic is identical to 17et in the no-5 subgroups, but has an independent generator for prime 5.

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

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	Mapping: {{mapping\| 17 0 26 -87 207 \| 0 2 1 10 -11 }}		Mapping: {{mapping\| 17 0 26 -87 207 \| 0 2 1 10 -11 }}

	[[Optimal ~~tuning]]s~~:		Optimal tunings:
	* [[CTE]]: ~25/24 = 70.588{{c}} (1\17), ~693/400 = 950.978{{c}}		* CTE: ~25/24 = 70.588{{c}} (1\17), ~693/400 = 950.978{{c}}
	* [[CWE]]: ~25/24 = 70.588{{c}} (1\17), ~693/400 = 950.975{{c}}		* CWE: ~25/24 = 70.588{{c}} (1\17), ~693/400 = 950.975{{c}}

	{{Optimal ET sequence\|legend=0\| 289, 323, 612 }}		{{Optimal ET sequence\|legend=0\| 289, 323, 612 }}
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	== Leaves ==		== Leaves ==
	Defined as the 323 & 2023 temperament. 2 generators reach [[17/13]], 7 generators reach [[5/4]], 10 generators produce [[13/11]].		Defined as the {{nowrap\|323 & 2023}} temperament. 2 generators reach [[17/13]], 7 generators reach [[5/4]], 10 generators produce [[13/11]].

			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: 1729951171875/1727094849536, {{monzo\|10 39 -14 -14}}

			[[Mapping]]: [{{val\|17 10 31 9}}, {{val\|0 14 7 32}}]

			: mapping generators: ~25/24, ~6125/5832

			[[Optimal tuning]]s:
			* [[CTE]]: ~25/24 = 70.588{{c}} (1\17), ~6125/5832 = 85.427{{c}}
			* [[CWE]]: ~25/24 = 70.588{{c}} (1\17), ~6125/5832 = 85.426{{c}}

			{{Optimal ET sequence\|legend=1\| 323, 1700d, 2023, 2346}}

			[[Badness]] (Sintel): 32.032

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

			Comma list: 160083/160000, 198359290368/198165034375, 1729951171875/1727094849536

			Mapping: [{{val\|17 10 31 9 106}}, {{val\|0 14 7 32 -39}}]

			Optimal tunings:
			* CTE: ~25/24 = 70.588{{c}} (1\17), ~6125/5832 = 85.421{{c}}
			* CWE: ~25/24 = 70.588{{c}} (1\17), ~6125/5832 = 85.420{{c}}

			{{Optimal ET sequence\|legend=0\| 323, 1700d, 2023, 2346e}}

			Badness (Sintel): 20.456

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

	Comma list: 160083/160000, 928125/927472, 1990656/1990625, ~~20726199~~/~~20706224~~		Comma list: 160083/160000, 928125/927472, 1990656/1990625, 4831530/4826809

	Mapping: [{{val\|17 10 31 9 106 98}}, {{val\|0 14 7 32 -39 -29}}]		Mapping: [{{val\|17 10 31 9 106 98}}, {{val\|0 14 7 32 -39 -29}}]

	~~Mapping generators~~: ~25/24, ~1024/975		Optimal tunings:
			* CTE: ~25/24 = 70.588{{c}} (1\17), ~1024/975 = 85.421{{c}}
			* CWE: ~25/24 = 70.588{{c}} (1\17), ~1024/975 = 85.420{{c}}

	Optimal ~~tuning (CTE): ~1024/975~~ = ~~85.421~~		{{Optimal ET sequence\|legend=0\| 323, 1700d, 2023, 2346e}}

	~~{{Optimal ET sequence\|legend=1\| 323, 1700, 2023}}~~		Badness (Sintel): 10.096

	=== 17-limit ===		=== 17-limit ===
	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

	Comma list: 57375/57344, 111537/111475, 140800/140777~~, 111537/111475, 1026675/1026256~~		Comma list: 39325/39304, 57375/57344, 71874/71825, 111537/111475, 140800/140777

	Mapping: [{{val\|17 10 31 9 106 98 107}}, {{val\|0 14 7 32 -39 -29 -31}}]		Mapping: [{{val\|17 10 31 9 106 98 107}}, {{val\|0 14 7 32 -39 -29 -31}}]

	~~Mapping generators~~: ~25/24, ~765/728		Optimal tunings:
			* CTE: ~25/24 = 70.588{{c}} (1\17), ~765/728 = 85.421{{c}}
			* CWE: ~25/24 = 70.588{{c}} (1\17), ~765/728 = 85.421{{c}}

	Optimal ~~tuning (CTE): ~765/728~~ = ~~85.421~~		{{Optimal ET sequence\|legend=0\| 323, 1700d, 2023, 2346e}}

	~~{{Optimal ET sequence\|legend=1\| 323, 1700, 2023}}~~		Badness (Sintel): 6.678

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

	[[Category:17edo]]		[[Category:17edo]]

Xenllium at 00:24, 21 February 2026

2026-02-21T00:24:02Z

@@ Line 21: / Line 21: @@
 [[Badness]] (Sintel): 12.7
 == Chlorine ==
@@ Line 50: / Line 95: @@
 {{Mapping|legend=1| 17 0 26 -87 | 0 2 1 10 }}
-[[Optimal tuning]] ([[POTE]]): ~{{monzo| 24 -5 -9 2 }} = 950.9995
+[[Optimal tuning]]s:
 {{Optimal ET sequence|legend=1| 289, 323, 612, 935, 1547 }}
@@ Line 61: / Line 108: @@
 Comma list: 4375/4374, 41503/41472, 1879453125/1879048192
-Mapping: {{mapping|  17 0 26 -87 207 | 0 2 1 10 -11  }}
+Mapping: {{mapping| 17 0 26 -87 207 | 0 2 1 10 -11 }}
-Optimal tuning (POTE): ~{{monzo| 24 -5 -9 2 }} = 950.9749
+[[Optimal tuning]]s:
 {{Optimal ET sequence|legend=0| 289, 323, 612 }}

Xenllium at 23:57, 20 February 2026

2026-02-20T23:57:32Z

@@ Line 15: / Line 15: @@
 [[Optimal tuning]]s:
-* [[CTE]]: ~256/243 = 1\17, ~5/4 = 386.3137 (~20480/19683 = 33.3725)
+* [[CTE]]: ~256/243 = 70.5882{{c}} (1\17), ~5/4 = 386.3137{{c}} (~20480/19683 = 33.3725{{c}})
-* [[CWE]]: ~256/243 = 1\17, ~5/4 = 388.2316 (~20480/19683 = 35.2904)
+* [[CWE]]: ~256/243 = 70.5882{{c}} (1\17), ~5/4 = 388.2316{{c}} (~20480/19683 = 35.2904{{c}})
 {{Optimal ET sequence|legend=1| 17c, 34, 323bbcc, 357bbcc, 391bbcc }}
-[[Badness]]: 0.541
+[[Badness]] (Sintel): 12.7
 == Chlorine ==
@@ Line 61: / Line 35: @@
 : mapping generators: ~25/24, ~{{monzo| 26 9 -17 }}
-[[Optimal tuning]] ([[POTE]]): ~{{monzo| 26 9 -17 }} = 950.9746
+[[Optimal tuning]]s:
 {{Optimal ET sequence|legend=1| 34, 153, 187, 221, 255, 289, 323, 612, 3349, 3961, 4573, 5185, 5797 }}
-[[Badness]]: 0.077072
+[[Badness]] (Sintel): 1.81
 === 7-limit ===
@@ Line 78: / Line 54: @@
 {{Optimal ET sequence|legend=1| 289, 323, 612, 935, 1547 }}
-[[Badness]]: 0.041658
+[[Badness]] (Sintel): 1.05
 === 11-limit ===
@@ Line 89: / Line 65: @@
 Optimal tuning (POTE): ~{{monzo| 24 -5 -9 2 }} = 950.9749
-{{Optimal ET sequence|legend=1| 289, 323, 612 }}
+{{Optimal ET sequence|legend=0| 289, 323, 612 }}
-Badness: 0.063706
+{{Optimal ET sequence|legend=1| 323, 1700, 2023}}
 {{Navbox fractional-octave}}
 [[Category:17edo]]

Jerdle: /* Chlorine */ Mentioned the lack of connection with the chlorisma.

2025-06-15T01:50:31Z

Chlorine: Mentioned the lack of connection with the chlorisma.

← Older revision		Revision as of 01:50, 15 June 2025
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	== Chlorine ==		== Chlorine ==
	The name of chlorine temperament comes from ~~Chlorine~~, the 17th element.		The name of chlorine temperament comes from chlorine, the 17th element, and has no relation to the [[chlorisma]].

	Chlorine temperament has a period of 1/17 octave. It tempers out the [[septendecima]], {{monzo\| -52 -17 34 }}, by which 17 chromatic semitones (25/24) exceed an octave. This temperament can be described as 289 & 323 temperament, which tempers out {{monzo\| -49 4 22 -3 }} as well as the ragisma. Not only the semitwelfth, but also the ~5/4 can be used as a generator.		Chlorine temperament has a period of 1/17 octave. It tempers out the [[septendecima]], {{monzo\| -52 -17 34 }}, by which 17 chromatic semitones (25/24) exceed an octave. This temperament can be described as 289 & 323 temperament, which tempers out {{monzo\| -49 4 22 -3 }} as well as the ragisma. Not only the semitwelfth, but also the ~5/4 can be used as a generator.

VectorGraphics at 05:13, 12 June 2025

2025-06-12T05:13:47Z

← Older revision		Revision as of 05:13, 12 June 2025
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	{{Mapping\|legend=1\| 17 0 26 -87 \| 0 2 1 10 }}		{{Mapping\|legend=1\| 17 0 26 -87 \| 0 2 1 10 }}

	~~{{Multival\|legend=1\| 34 17 170 -52 174 347 }}~~

	[[Optimal tuning]] ([[POTE]]): ~{{monzo\| 24 -5 -9 2 }} = 950.9995		[[Optimal tuning]] ([[POTE]]): ~{{monzo\| 24 -5 -9 2 }} = 950.9995

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

" to "{{Technical data page}}"

2025-04-13T13:42:21Z

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

← Older revision		Revision as of 13:42, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	{{Infobox fractional-octave\|17}}		{{Infobox fractional-octave\|17}}
	[[17edo]] is a "wheel" for some [[fractional-octave temperaments]]. The most notable relationship is the tempering out of the [[septendecima]], the amount by which seventeen [[25/24]] chromatic semitones exceed an octave.		[[17edo]] is a "wheel" for some [[fractional-octave temperaments]]. The most notable relationship is the tempering out of the [[septendecima]], the amount by which seventeen [[25/24]] chromatic semitones exceed an octave.

BudjarnLambeth: {{Technical data page}}

+ add links

2025-04-13T11:06:41Z

{{Technical data page}}<br><br> + add links

← Older revision		Revision as of 11:06, 13 April 2025
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			{{Technical data page}}<br><br>
	{{Infobox fractional-octave\|17}}		{{Infobox fractional-octave\|17}}
	17edo is a "wheel" for some fractional-octave temperaments. The most notable relationship is the tempering out of the [[septendecima]], the amount by which seventeen [[25/24]] chromatic semitones exceed an octave.		[[17edo]] is a "wheel" for some [[fractional-octave temperaments]]. The most notable relationship is the tempering out of the [[septendecima]], the amount by which seventeen [[25/24]] chromatic semitones exceed an octave.

	== Gothic ==		== Gothic ==

ArrowHead294 at 03:40, 14 February 2025

2025-02-14T03:40:40Z

← Older revision		Revision as of 03:40, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|17}}		{{Infobox fractional-octave\|17}}
	17edo is a "wheel" for some fractional-octave temperaments. The most notable relationship is the tempering out of the [[septendecima]], the amount by which seventeen [[25/24]] chromatic semitones exceed an octave.		17edo is a "wheel" for some fractional-octave temperaments. The most notable relationship is the tempering out of the [[septendecima]], the amount by which seventeen [[25/24]] chromatic semitones exceed an octave.

FloraC: +old name. Fix a copying error

2024-12-22T11:17:56Z

+old name. Fix a copying error

← Older revision		Revision as of 11:17, 22 December 2024
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	== Gothic ==		== Gothic ==
	The gothic temperament is associated with the [[17-comma]].		The gothic temperament is associated with the [[17-comma]]. It used to be known as '''septendecic'''.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
Line 21:		Line 21:
	[[Badness]]: 0.541		[[Badness]]: 0.541

	==Leaves==		== Leaves ==
	Defined as the 323 & 2023 temperament. 2 generators reach [[17/13]], 7 generators reach [[5/4]], 10 generators produce [[13/11]].		Defined as the 323 & 2023 temperament. 2 generators reach [[17/13]], 7 generators reach [[5/4]], 10 generators produce [[13/11]].

Line 33:		Line 33:

	Optimal tuning (CTE): ~1024/975 = 85.421		Optimal tuning (CTE): ~1024/975 = 85.421

	=== 17-limit ===		=== 17-limit ===

	Subgroup: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

Line 44:		Line 44:

	Optimal tuning (CTE): ~765/728 = 85.421		Optimal tuning (CTE): ~765/728 = 85.421

			{{Optimal ET sequence\|legend=1\|323, 1700, 2023}}

	== Chlorine ==		== Chlorine ==
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	Badness: 0.063706		Badness: 0.063706

	~~{{Optimal ET sequence\|legend=1\|323, 1700, 2023}}~~

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

	[[Category:17edo]]		[[Category:17edo]]

BudjarnLambeth: navbox

2024-12-05T07:19:06Z

navbox

← Older revision		Revision as of 07:19, 5 December 2024
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	{{Optimal ET sequence\|legend=1\|323, 1700, 2023}}		{{Optimal ET sequence\|legend=1\|323, 1700, 2023}}

			{{Navbox fractional-octave}}

	[[Category:17edo]]		[[Category:17edo]]
	~~[[Category:Temperament collections]]~~