57ed12 - Revision history

FloraC: +subsets and supersets; +see also

2025-05-27T07:41:51Z

+subsets and supersets; +see also

← Older revision		Revision as of 07:41, 27 May 2025
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	{{Harmonics in equal\|57\|12\|1\|intervals=integer\|columns=11}}		{{Harmonics in equal\|57\|12\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|57\|12\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 57ed12 (continued)}}		{{Harmonics in equal\|57\|12\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 57ed12 (continued)}}

			=== Subsets and supersets ===
			Since 57 factors into primes as {{nowrap\| 3 × 19 }}, 57ed12 contains subset ed12's [[3ed12]] and [[19ed12]].

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== See also ==
			* [[16edo]] – relative edo
			* [[25edt]] – relative edt
			* [[41ed6]] – relative ed6


	[[Category:Mavila]]		[[Category:Mavila]]
	[[Category:Pelog]]		[[Category:Pelog]]

FloraC: Cleanup

2025-05-27T07:39:23Z

Cleanup

← Older revision		Revision as of 07:39, 27 May 2025
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	{{Infobox ET~~}}{{todo\|expand~~}}		{{Infobox ET}}
	{{ED intro}}		{{ED intro}}

	57ed12 is similar to [[16edo]], but has the [[12/1]] ~~tuned just instead of the octave~~, which stretches the octave by 7.6{{c}}. It can be used as a tuning for [[~~Mavila~~]] and has an "antidiatonic" ([[2L 5s]]) scale which approximates [[Pelog]] tunings in Indonesian gamelan music.		== Theory ==
			57ed12 is similar to [[16edo]], but has the 12th harmonic tuned just instead of the [[2/1\|octave]], which stretches the octave by 7.6{{c}}. It can be used as a tuning for [[mavila]] and has an antidiatonic ([[2L 5s]]) scale which approximates [[Pelog]] tunings in Indonesian gamelan music.

			16edo's [[harmonic]]s 3, 11 and 17 are all more than 25 cents away from just, making them unusable for most purposes. 57ed12 improves upon all of their tunings, bringing all those harmonics within 16 cents of just, and bringing 11 and 17 within an impressive 1 cent of just. This dramatically increases the number of [[consonant]] intervals and chords available in the tuning.

			The trade-off is that 57ed12's harmonic 7 is significantly worse than 16edo. It has almost 28 cents of error, compared to 6, making it go from very consonant to completely unusable. So, if one intends to use harmonies involving 7's, 57ed12 is not a good choice. But if one is interested in the [[5-limit]], the 2.3.5.11 [[subgroup]], or the no-7's [[13-limit]] or [[17-limit]], then 57ed12 is by far the superior option, thanks to its dramatically improved 3/1 and 11/1.

	~~== Theory ==~~
	=== Commas ===		=== Commas ===
	As an equal temperament, 57ed12 [[tempering out\|tempers out]] 36/35 and 50/49 in the [[7-limit]]; 33/32 and 45/44 in the 11-limit; 65/64, 66/65, and 78/77 in the 13-limit; 51/50 and 85/84 in the 17-limit; 39/38, 57/56, 77/76, and 96/95 in the 19-limit; 69/68 and 92/91 in the 23-limit; 58/57 and 87/85 in the 29-limit; 63/62, 93/92, and 93/91 in the 31-limit; and 75/74 in the 37-limit.		As an equal temperament, 57ed12 [[tempering out\|tempers out]] 36/35 and 50/49 in the [[7-limit]]; 33/32 and 45/44 in the 11-limit; 65/64, 66/65, and 78/77 in the 13-limit; 51/50 and 85/84 in the 17-limit; 39/38, 57/56, 77/76, and 96/95 in the 19-limit; 69/68 and 92/91 in the 23-limit; 58/57 and 87/85 in the 29-limit; 63/62, 93/92, and 93/91 in the 31-limit; and 75/74 in the 37-limit.

	=== Harmonics ===		=== Harmonics ===
	16edo’s [[harmonic]]s 3/1, 11/1 and 17/1 are all more than 25 cents away from [[just]], making them unusable for most purposes. 57ed12 improves upon all of their tunings, bringing all those harmonics within 16 cents of just, and bringing 11 and 17 within an impressive 1 cent of just. This dramatically increases the number of [[consonant]] intervals and chords available in the tuning.		{{Harmonics in equal\|57\|12\|1\|intervals=integer\|columns=11}}
			{{Harmonics in equal\|57\|12\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 57ed12 (continued)}}
	The trade-off is that 57ed12’s 7/1 is significantly worse than 16edo. It has almost 28 cents of error, compared to 6, making it go from very consonant to completely unusable. So, if one intends to use harmonies involving 7s, 57ed12 is not a good choice. But if one is interested in the [[5-limit]], the 2.3.5.11 [[subgroup]], or the no-7s [[13-limit]] or [[17-limit]]s, then 57ed12 is by far the superior option, thanks to its dramatically improved 3/1 and 11/1.
	{{Harmonics in equal\|57\|12\|1\|intervals=~~prime~~}}


	~~16edo for comparison:~~
	{{Harmonics in equal\|16\|2\|1\|intervals=~~prime~~}}

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

	~~{{todo\|expand}}~~

	~~[[Category:16edo]]~~
	~~[[Category:Edonoi]]~~
	[[Category:Mavila]]		[[Category:Mavila]]
	[[Category:Pelog]]		[[Category:Pelog]]

ArrowHead294 at 19:06, 14 February 2025

2025-02-14T19:06:43Z

← Older revision		Revision as of 19:06, 14 February 2025
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	{{ED intro}}		{{ED intro}}

	57ed12 is similar to [[16edo]], but has the [[12/1]] tuned just instead of the octave, which stretches the octave by 7.6{{c}}. It can be used as a tuning for [[Mavila]] and ~~also~~ approximates [[Pelog]] tunings in Indonesian gamelan music.		57ed12 is similar to [[16edo]], but has the [[12/1]] tuned just instead of the octave, which stretches the octave by 7.6{{c}}. It can be used as a tuning for [[Mavila]] and has an "antidiatonic" ([[2L 5s]]) scale which approximates [[Pelog]] tunings in Indonesian gamelan music.

	== Theory ==		== Theory ==

FloraC: Cleanup

2025-01-17T17:05:46Z

Cleanup

← Older revision		Revision as of 17:05, 17 January 2025
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	== Theory ==		== Theory ==
	=== Commas ===		=== Commas ===
	~~This tuning~~ [[tempers out]] 36/35 and 50/49 in the [[7-limit]]; 33/32 and 45/44 in the 11-limit; 65/64, 66/65, and 78/77 in the 13-limit; 51/50 and 85/84 in the 17-limit; 39/38, 57/56, 77/76, and 96/95 in the 19-limit; 69/68 and 92/91 in the 23-limit; 58/57 and 87/85 in the 29-limit; 63/62, 93/92, and 93/91 in the 31-limit; and 75/74 in the 37-limit.		As an equal temperament, 57ed12 [[tempering out\|tempers out]] 36/35 and 50/49 in the [[7-limit]]; 33/32 and 45/44 in the 11-limit; 65/64, 66/65, and 78/77 in the 13-limit; 51/50 and 85/84 in the 17-limit; 39/38, 57/56, 77/76, and 96/95 in the 19-limit; 69/68 and 92/91 in the 23-limit; 58/57 and 87/85 in the 29-limit; 63/62, 93/92, and 93/91 in the 31-limit; and 75/74 in the 37-limit.

	=== Harmonics ===		=== Harmonics ===

ArrowHead294 at 16:44, 15 January 2025

2025-01-15T16:44:44Z

← Older revision		Revision as of 16:44, 15 January 2025
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	{{Infobox ET}}{{todo\|expand}}		{{Infobox ET}}{{todo\|expand}}
	~~'''57ED12''' is the [[ED12\|equal division of the twelfth harmonic]] into 57 equal parts. It~~ is similar to [[16edo]], but has the [[12/1]] tuned just instead of the octave~~. Octaves are stretched~~ by 7.6~~{{c}} and the step size is 75.47~~{{c}}. It can be used as a tuning for [[Mavila]] and also approximates [[Pelog]] tunings in Indonesian gamelan music.		{{ED intro}}

			57ed12 is similar to [[16edo]], but has the [[12/1]] tuned just instead of the octave, which stretches the octave by 7.6{{c}}. It can be used as a tuning for [[Mavila]] and also approximates [[Pelog]] tunings in Indonesian gamelan music.

	== Theory ==		== Theory ==
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	[[Category:16edo]]		[[Category:16edo]]
			[[Category:Edonoi]]
	[[Category:Mavila]]		[[Category:Mavila]]
	[[Category:Pelog]]		[[Category:Pelog]]

ArrowHead294 at 19:30, 10 January 2025

2025-01-10T19:30:42Z

← Older revision		Revision as of 19:30, 10 January 2025
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	{{todo\|expand}}		{{todo\|expand}}

	[[Category:16edo]]		[[Category:16edo]]
			[[Category:Mavila]]
			[[Category:Pelog]]

BudjarnLambeth: Expand stub

2025-01-07T08:25:07Z

Expand stub

@@ Line 3: / Line 3: @@
 == Theory ==
-This tuning tempers out 36/35 and 50/49 in the 7-limit; 33/32 and 45/44 in the 11-limit; 65/64, 66/65, and 78/77 in the 13-limit; 51/50 and 85/84 in the 17-limit; 39/38, 57/56, 77/76, and 96/95 in the 19-limit; 69/68 and 92/91 in the 23-limit; 58/57 and 87/85 in the 29-limit; 63/62, 93/92, and 93/91 in the 31-limit; and 75/74 in the 37-limit.
+=== Commas ===
 == Intervals ==
 {{Interval table}}
-== Harmonics ==
+{{todo|expand}}
-{{Harmonics in equal
+[[Category:16edo]]

BudjarnLambeth: Todo

2025-01-02T00:32:56Z

Todo

← Older revision		Revision as of 00:32, 2 January 2025
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	{{Infobox ET}}		{{Infobox ET}}{{todo\|expand}}
	'''57ED12''' is the [[ED12\|equal division of the twelfth harmonic]] into 57 equal parts. It is similar to [[16edo]], but has the [[12/1]] tuned just instead of the octave. Octaves are stretched by 7.6{{c}} and the step size is 75.47{{c}}. It can be used as a tuning for [[Mavila]] and also approximates [[Pelog]] tunings in Indonesian gamelan music.		'''57ED12''' is the [[ED12\|equal division of the twelfth harmonic]] into 57 equal parts. It is similar to [[16edo]], but has the [[12/1]] tuned just instead of the octave. Octaves are stretched by 7.6{{c}} and the step size is 75.47{{c}}. It can be used as a tuning for [[Mavila]] and also approximates [[Pelog]] tunings in Indonesian gamelan music.

MisterShafXen at 18:31, 26 December 2024

2024-12-26T18:31:08Z

← Older revision		Revision as of 18:31, 26 December 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''57ED12''' is the [[ED12\|equal division of the twelfth harmonic]] into 57 equal parts. It is similar to [[16edo]], but has the [[12/1]] tuned just instead of the octave. Octaves are stretched by 7.6{{c}} and the step size is 75.47{{c}}. It can be used as a tuning for [[Mavila]] and also approximates [[Pelog]] tunings in Indonesian gamelan music.		'''57ED12''' is the [[ED12\|equal division of the twelfth harmonic]] into 57 equal parts. It is similar to [[16edo]], but has the [[12/1]] tuned just instead of the octave. Octaves are stretched by 7.6{{c}} and the step size is 75.47{{c}}. It can be used as a tuning for [[Mavila]] and also approximates [[Pelog]] tunings in Indonesian gamelan music.

			== Theory ==
			This tuning tempers out 36/35 and 50/49 in the 7-limit; 33/32 and 45/44 in the 11-limit; 65/64, 66/65, and 78/77 in the 13-limit; 51/50 and 85/84 in the 17-limit; 39/38, 57/56, 77/76, and 96/95 in the 19-limit; 69/68 and 92/91 in the 23-limit; 58/57 and 87/85 in the 29-limit; 63/62, 93/92, and 93/91 in the 31-limit; and 75/74 in the 37-limit.

	== Intervals ==		== Intervals ==

BudjarnLambeth: Intervals harmonics

2024-11-30T02:06:59Z

Intervals harmonics

← Older revision		Revision as of 02:06, 30 November 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''57ED12''' is the [[ED12\|equal division of the twelfth harmonic]] into 57 equal parts. It is similar to [[16edo]], but has the [[12/1]] tuned just instead of the octave. Octaves are stretched by 7.6{{c}} and the step size is 75.47{{c}}. It can be used as a tuning for [[Mavila]] and also approximates [[Pelog]] tunings in Indonesian gamelan music.		'''57ED12''' is the [[ED12\|equal division of the twelfth harmonic]] into 57 equal parts. It is similar to [[16edo]], but has the [[12/1]] tuned just instead of the octave. Octaves are stretched by 7.6{{c}} and the step size is 75.47{{c}}. It can be used as a tuning for [[Mavila]] and also approximates [[Pelog]] tunings in Indonesian gamelan music.

			== Intervals ==
			{{Interval table}}

			== Harmonics ==
			{{Harmonics in equal
			\| steps = 57
			\| num = 12
			\| denom = 1
			}}
			{{Harmonics in equal
			\| steps = 57
			\| num = 12
			\| denom = 1
			\| start = 12
			\| collapsed = 1
			}}