358edo - Revision history

MisterShafXen: /* Theory */

2025-05-06T20:17:16Z

Theory

← Older revision		Revision as of 20:17, 6 May 2025
Line 5:		Line 5:
	358edo is [[consistent]] to the [[7-odd-limit]], but the [[harmonic]] [[3/1\|3]] is about halfway its steps. It is suitable for use with the 2.9.5.7.13 [[subgroup]] or even better the 2.9.15.7.13 subgroup.		358edo is [[consistent]] to the [[7-odd-limit]], but the [[harmonic]] [[3/1\|3]] is about halfway its steps. It is suitable for use with the 2.9.5.7.13 [[subgroup]] or even better the 2.9.15.7.13 subgroup.

	In the 2.9.5.7.13 subgroup, the equal temperament [[tempering out\|tempers out]] [[4096/4095]], 13720/13689, 59150/59049, 60025/59904, 142884/142805, and [[390625/388962]].		In the 2.9.5.7.13 subgroup, the equal temperament [[tempering out\|tempers out]] [[4096/4095]], [[13720/13689]], 59150/59049, 60025/59904, 142884/142805, and [[390625/388962]].

	The [[patent val]] [[support]]s [[hypnos]] in the 11-limit and [[lee]] in the 2.3.7 subgroup.		The [[patent val]] [[support]]s [[hypnos]] in the 11-limit and [[lee]] in the 2.3.7 subgroup.

ArrowHead294 at 12:34, 21 February 2025

2025-02-21T12:34:12Z

← Older revision		Revision as of 12:34, 21 February 2025
Line 17:		Line 17:
	== 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]] (%)
Line 29:		Line 30:
	\| {{monzo\| 1135 -358 }}		\| {{monzo\| 1135 -358 }}
	\| {{mapping\| 358 1135 }}		\| {{mapping\| 358 1135 }}
	\| -0.0882		\| −0.0882
	\| 0.0882		\| 0.0882
	\| 2.63		\| 2.63

Francium: changed EDO intro to ED intro

2025-02-21T06:10:01Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:10, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|358~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Review

2024-01-11T19:53:56Z

Review

← Older revision		Revision as of 19:53, 11 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~358et~~ is consistent to the [[7-odd-limit]] ~~and~~ the [[harmonic]] 3 is about halfway its steps. It is suitable for use with the 2.9.5.7.11.17.23.~~29.37~~.~~41 [[~~subgroup]]. ~~Using~~ the ~~patent val~~, it tempers out ~~283115520/282475249, 26873856/26796875, 48828125/48771072,~~ [[~~2100875~~/~~2097152~~]] ~~and 200120949/200000000 in the 7-limit; 20155392/20131375~~, ~~234375~~/~~234256~~, ~~29296875~~/~~29218112~~, ~~46656~~/~~46585~~, ~~1953125~~/~~1951488, 226492416/226474325~~, [[~~540~~/~~539~~]]~~, 107495424/107421875, 5788125/5767168, 5767168/5764801, 1375/1372,~~ [[~~3025/3024~~]]~~, 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit. It~~ [[support]]s [[hypnos]] and [[lee]].		358edo is [[consistent]] to the [[7-odd-limit]], but the [[harmonic]] [[3/1\|3]] is about halfway its steps. It is suitable for use with the 2.9.5.7.13 [[subgroup]] or even better the 2.9.15.7.13 subgroup.

			In the 2.9.5.7.13 subgroup, the equal temperament [[tempering out\|tempers out]] [[4096/4095]], 13720/13689, 59150/59049, 60025/59904, 142884/142805, and [[390625/388962]].

			The [[patent val]] [[support]]s [[hypnos]] in the 11-limit and [[lee]] in the 2.3.7 subgroup.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 13:		Line 17:
	== 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]] (%)
	\|-		\|-
	\|2.9		\| 2.9
	\|{{monzo\|1135 -358}}		\| {{monzo\| 1135 -358 }}
	\|{{mapping\|358 1135}}		\| {{mapping\| 358 1135 }}
	\| -0.0882		\| -0.0882
	\| 0.0882		\| 0.0882
	\| 2.63		\| 2.63
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|{{monzo\|3 -9 11}}, {{monzo\|-98 17 19}}		\| {{monzo\| 3 -9 11 }}, {{monzo\| -98 17 19 }}
	\|{{mapping\|358 1135 831}}		\| {{mapping\| 358 1135 831 }}
	\| +0.0616		\| +0.0616
	\| 0.2238		\| 0.2238
	\| 6.68		\| 6.68
	\|-		\|-
	\|2.9.5.7		\| 2.9.5.7
	\|390625/388962, 4802000/4782969~~, 2100875/2097152~~		\| 390625/388962, 2100875/2097152, 4802000/4782969
	\|{{mapping\|358 1135 831 1005}}		\| {{mapping\| 358 1135 831 1005 }}
	\| +0.0561		\| +0.0561
	\| 0.1941		\| 0.1941
	\| 5.79		\| 5.79
	\|}		\|}

Francium: /* Theory */

2023-12-30T12:36:57Z

Theory

← Older revision		Revision as of 12:36, 30 December 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	358et is consistent to the [[7-odd-limit]] and the [[harmonic]] 3 is about halfway its steps. It is suitable for use with the 2.9.5.7.11.17.23.29.37.41 [[subgroup]]. Using the patent val, it tempers out 283115520/282475249, 26873856/26796875, 48828125/48771072, [[2100875/2097152]] and 200120949/200000000 in the 7-limit; 20155392/20131375, 234375/234256, 29296875/29218112, 46656/46585, 1953125/1951488, 226492416/226474325, [[540/539]], 107495424/107421875, 5788125/5767168, 5767168/5764801, 1375/1372, [[3025/3024]], 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit. It ~~supports~~ [[hypnos]] and [[lee]].		358et is consistent to the [[7-odd-limit]] and the [[harmonic]] 3 is about halfway its steps. It is suitable for use with the 2.9.5.7.11.17.23.29.37.41 [[subgroup]]. Using the patent val, it tempers out 283115520/282475249, 26873856/26796875, 48828125/48771072, [[2100875/2097152]] and 200120949/200000000 in the 7-limit; 20155392/20131375, 234375/234256, 29296875/29218112, 46656/46585, 1953125/1951488, 226492416/226474325, [[540/539]], 107495424/107421875, 5788125/5767168, 5767168/5764801, 1375/1372, [[3025/3024]], 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit. It [[support]]s [[hypnos]] and [[lee]].

	=== Odd harmonics ===		=== Odd harmonics ===

Francium: Created page with "{{Infobox ET}} {{EDO intro|358}} == Theory == 358et is consistent to the 7-odd-limit and the harmonic 3 is about halfway its steps. It is suitable for use with the 2...."

2023-12-30T12:34:38Z

Created page with "{{Infobox ET}} {{EDO intro|358}} == Theory == 358et is consistent to the 7-odd-limit and the harmonic 3 is about halfway its steps. It is suitable for use with the 2...."

New page

{{Infobox ET}}
{{EDO intro|358}}

== Theory ==
358et is consistent to the [[7-odd-limit]] and the [[harmonic]] 3 is about halfway its steps. It is suitable for use with the 2.9.5.7.11.17.23.29.37.41 [[subgroup]]. Using the patent val, it tempers out 283115520/282475249, 26873856/26796875, 48828125/48771072, [[2100875/2097152]] and 200120949/200000000 in the 7-limit; 20155392/20131375, 234375/234256, 29296875/29218112, 46656/46585, 1953125/1951488, 226492416/226474325, [[540/539]], 107495424/107421875, 5788125/5767168, 5767168/5764801, 1375/1372, [[3025/3024]], 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit. It supports [[hypnos]] and [[lee]].

=== Odd harmonics ===
{{Harmonics in equal|358}}

=== Subset and supersets ===
358 factors into 2 × 179, with [[2edo]] and [[179edo]] as its subset edos. [[716edo]], which doubles it, gives a good correction to the harmonic 3.

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.9
|{{monzo|1135 -358}}
|{{mapping|358 1135}}
| -0.0882
| 0.0882
| 2.63
|-
|2.9.5
|{{monzo|3 -9 11}}, {{monzo|-98 17 19}}
|{{mapping|358 1135 831}}
| +0.0616
| 0.2238
| 6.68
|-
|2.9.5.7
|390625/388962, 4802000/4782969, 2100875/2097152
|{{mapping|358 1135 831 1005}}
| +0.0561
| 0.1941
| 5.79
|}