236edo - Revision history

Overthink: /* Theory */ added section about 236dghin val

2025-10-31T22:08:08Z

Theory: added section about 236dghin val

← Older revision		Revision as of 22:08, 31 October 2025
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	The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden [[diaschismic]] sequence.		The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden [[diaschismic]] sequence.

			The 236dghin val makes for a reasonable flat-tending system as far as the [[43-limit]], and is in fact [[diamond monotone]] in the [[43-odd-limit]]. This works best with a stretched octave.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|236}}		{{Harmonics in equal\|236}}
			{{Harmonics in equal\|236\|start=12}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

ArrowHead294 at 12:29, 21 February 2025

2025-02-21T12:29:20Z

← Older revision		Revision as of 12:29, 21 February 2025
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	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list~~\|Comma List~~]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve ~~Stretch~~ (¢)		! rowspan="2" \| Optimal<br />8ve stretch (¢)
	! colspan="2" \| Tuning ~~Error~~		! colspan="2" \| Tuning error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
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	\| 6144/6125, 19683/19600, 390625/388962		\| 6144/6125, 19683/19600, 390625/388962
	\| {{mapping\| 236 374 548 663 }}		\| {{mapping\| 236 374 548 663 }}
	\| -0.1830		\| −0.1830
	\| 0.03883		\| 0.03883
	\| 7.64		\| 7.64
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T06:15:22Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:15, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|236~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: RTT table should start with the 7-limit as the 5-limit is enfactored; misc. cleanup

2024-03-25T13:05:14Z

RTT table should start with the 7-limit as the 5-limit is enfactored; misc. cleanup

← Older revision		Revision as of 13:05, 25 March 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|236}}		{{EDO intro\|236}}
	==Theory==
	236edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. The 7-limit mapping is worse over that of 118edo, as it leans on the very sharp side. It tempers out [[6144/6125]] and [[19683/19600]], supporting [[hemischis]]. Using the 236e [[val]] {{val\| 236 374 548 663 '''817''' }}, it tempers out [[243/242]], 1375/1372, [[6250/6237]], 14700/14641 and [[16384/16335]].		== Theory ==
			236edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by [[tempering out]] the [[schisma]] and the [[parakleisma]]. The 7-limit mapping is worse over that of 118edo in terms of relative error, as it leans on the very sharp side. It tempers out [[6144/6125]] and [[19683/19600]], supporting [[hemischis]]. Using the 236e [[val]] {{val\| 236 374 548 663 '''817''' }}, it tempers out [[243/242]], 1375/1372, [[6250/6237]], 14700/14641 and [[16384/16335]].

	The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden [[diaschismic]] sequence.		The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden [[diaschismic]] sequence.
Line 12:		Line 13:
	Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs\| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.		Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs\| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.

	==Regular temperament properties==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-
	~~\|2.3~~
	~~\|{{monzo\|-187 118}}~~
	~~\|{{val\|236 374}}~~
	~~\| 0.0820~~
	~~\| 0.0821~~
	~~\| 1.61~~
	\|-		\|-
	\|2.3.5		\| 2.3.5.7
	\|~~32805~~/~~32768~~, ~~{{monzo\|8 14 -13}}~~		\| 6144/6125, 19683/19600, 390625/388962
	\|{{~~val~~\|236 374 548}}		\| {{mapping\| 236 374 548 663 }}
	\| 0.~~0365~~		\| -0.1830
	\| 0.~~0930~~		\| 0.03883
	\| 1.83		\| 7.64
	\|}		\|}

Yourmusic Productions: /* Subsets and supersets */ Fix math error

2023-10-31T07:59:18Z

Subsets and supersets: Fix math error

← Older revision		Revision as of 07:59, 31 October 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs\| 2, 4, 53 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.		Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs\| 2, 4, 59 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.

	==Regular temperament properties==		==Regular temperament properties==

Francium at 19:10, 30 October 2023

2023-10-30T19:10:52Z

← Older revision		Revision as of 19:10, 30 October 2023
Line 10:		Line 10:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs\| 2, 4, 53 and 118 }}.		Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs\| 2, 4, 53 and 118 }}. [[472edo]], which doubles it, provides good correction to harmonics 7 and 11.

	==Regular temperament properties==		==Regular temperament properties==
Line 37:		Line 37:
	\| 1.83		\| 1.83
	\|}		\|}

	~~472edo, which doubles it, provides good correction to harmonics 7 and 11.~~

Francium at 19:10, 30 October 2023

2023-10-30T19:10:05Z

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|236}}
+==Theory==
 edo is [[enfactoring|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. The 7-limit mapping is worse over that of 118edo, as it leans on the very sharp side. It tempers out [[6144/6125]] and [[19683/19600]], supporting [[hemischis]]. Using the 236e [[val]] {{val| 236 374 548 663 '''817''' }}, it tempers out [[243/242]], 1375/1372, [[6250/6237]], 14700/14641 and [[16384/16335]].
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
 Since 236 factors into 2<sup>2</sup> × 53, 236edo has subset edos {{EDOs| 2, 4, 53 and 118 }}.
 edo, which doubles it, provides good correction to harmonics 7 and 11.

Yourmusic Productions: More temperament notes

2023-08-28T11:53:06Z

More temperament notes

← Older revision		Revision as of 11:53, 28 August 2023
Line 4:		Line 4:
	236edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. The 7-limit mapping is worse over that of 118edo, as it leans on the very sharp side. It tempers out [[6144/6125]] and [[19683/19600]], supporting [[hemischis]]. Using the 236e [[val]] {{val\| 236 374 548 663 '''817''' }}, it tempers out [[243/242]], 1375/1372, [[6250/6237]], 14700/14641 and [[16384/16335]].		236edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. The 7-limit mapping is worse over that of 118edo, as it leans on the very sharp side. It tempers out [[6144/6125]] and [[19683/19600]], supporting [[hemischis]]. Using the 236e [[val]] {{val\| 236 374 548 663 '''817''' }}, it tempers out [[243/242]], 1375/1372, [[6250/6237]], 14700/14641 and [[16384/16335]].

	The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer.		The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden [[diaschismic]] sequence.

	=== Prime harmonics ===		=== Prime harmonics ===

Eliora: 118edo has just ~20% error on 7/4, this has over 40%

2023-07-02T17:09:16Z

118edo has just ~20% error on 7/4, this has over 40%

← Older revision		Revision as of 17:09, 2 July 2023
Line 2:		Line 2:
	{{EDO intro\|236}}		{{EDO intro\|236}}

	236edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. The 7-limit mapping is ~~of little improvement~~ over that of 118edo, as it leans on the very sharp side. It tempers out [[6144/6125]] and [[19683/19600]], supporting [[hemischis]]. Using the 236e [[val]] {{val\| 236 374 548 663 '''817''' }}, it tempers out [[243/242]], 1375/1372, [[6250/6237]], 14700/14641 and [[16384/16335]].		236edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. The 7-limit mapping is worse over that of 118edo, as it leans on the very sharp side. It tempers out [[6144/6125]] and [[19683/19600]], supporting [[hemischis]]. Using the 236e [[val]] {{val\| 236 374 548 663 '''817''' }}, it tempers out [[243/242]], 1375/1372, [[6250/6237]], 14700/14641 and [[16384/16335]].

	The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer.		The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to [[quarter-comma meantone]], although [[205edo]] is even closer.

FloraC: Expansion

2023-07-02T14:29:10Z

Expansion

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|236}}
-==Theory==
-{{Primes in edo|236}}
+edo is [[enfactoring|enfactored]] in the 5-limit, with the same tuning as [[118edo]], defined by tempering out the [[schisma]] and the [[parakleisma]]. The 7-limit mapping is of little improvement over that of 118edo, as it leans on the very sharp side. It tempers out [[6144/6125]] and [[19683/19600]], supporting [[hemischis]]. Using the 236e [[val]] {{val| 236 374 548 663 '''817''' }}, it tempers out [[243/242]], 1375/1372, [[6250/6237]], 14700/14641 and [[16384/16335]].