382edo - Revision history

ArrowHead294 at 12:22, 21 February 2025

2025-02-21T12:22:18Z

← Older revision		Revision as of 12:22, 21 February 2025
Line 15:		Line 15:
	== 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]] (¢)
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	\| {{monzo\| 1211 -382 }}		\| {{monzo\| 1211 -382 }}
	\| {{mapping\| 382 1211 }}		\| {{mapping\| 382 1211 }}
	\| -0.0439		\| −0.0439
	\| 0.0439		\| 0.0439
	\| 1.40		\| 1.40
Line 34:		Line 35:
	\| {{monzo\| 38 -1 -15 }}, {{monzo\| 25 -24 22 }}		\| {{monzo\| 38 -1 -15 }}, {{monzo\| 25 -24 22 }}
	\| {{mapping\| 382 1211 887 }}		\| {{mapping\| 382 1211 887 }}
	\| -0.0399		\| −0.0399
	\| 0.0363		\| 0.0363
	\| 1.16		\| 1.16
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	\| 4375/4374, 52734375/52706752, {{monzo\| 31 0 -2 -6 }}		\| 4375/4374, 52734375/52706752, {{monzo\| 31 0 -2 -6 }}
	\| {{mapping\| 382 1211 887 1678 }}		\| {{mapping\| 382 1211 887 1678 }}
	\| -0.0552		\| −0.0552
	\| 0.0412		\| 0.0412
	\| 1.31		\| 1.31
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T06:18:19Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:18, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|382~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Review

2024-01-16T14:28:15Z

Review

← Older revision		Revision as of 14:28, 16 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~382et~~ is consistent to the [[7-odd-limit]] ~~and the~~ harmonic 3 is about halfway between its steps. ~~Using the patent val~~, ~~it tempers out~~ [[~~65625~~/~~65536~~]] ~~in the 7-limit;~~ [[~~117440512~~/~~117406179~~]], ~~25165824~~/~~25109315~~, ~~2097152~~/~~2096325~~, [[~~4000~~/~~3993~~]], ~~2734375~~/~~2725888~~, ~~2359296~~/~~2358125~~, [[540/539]], ~~1265625~~/~~1261568~~, ~~24057/24010~~ and [[9801/9800]] in the 11-limit. It [[support]]s [[bastille]].		382edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]]s [[3/1\|3]] and [[7/1\|7]] are about halfway between its steps. It is also bad at approximating [[11/1\|11]], [[13/1\|13]], [[15/1\|15]], and [[17/1\|17]], though its [[5/1\|5]], [[9/1\|9]], [[19/1\|19]], [[21/1\|21]], and [[23/1\|23]] are good, making it suitable for a 2.9.5.21.19.23 [[subgroup]] interpretation.

			Using the [[patent val]] nonetheless, the equal temperament [[tempering out\|tempers out]] [[65625/65536]] in the 7-limit; [[540/539]], [[4000/3993]], and [[9801/9800]] in the 11-limit. It [[support]]s [[bastille]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	382 factors into 2 × 191 with [[2edo]] and [[191edo]] as its subset edos. [[764edo]], which doubles it, gives a good correction to the ~~harmonic~~ 3.		382 factors into 2 × 191 with [[2edo]] and [[191edo]] as its subset edos. [[764edo]], which doubles it, gives a good correction to the harmonics 3, 7, 11, 13, and 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\|1211 -382}}		\| {{monzo\| 1211 -382 }}
	\|{{mapping\|382 1211}}		\| {{mapping\| 382 1211 }}
	\| -0.0439		\| -0.0439
	\| 0.0439		\| 0.0439
	\| 1.40		\| 1.40
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|{{monzo\|38 -1 -15}}, {{monzo\|25 -24 22}}		\| {{monzo\| 38 -1 -15 }}, {{monzo\| 25 -24 22 }}
	\|{{mapping\|382 1211 887}}		\| {{mapping\| 382 1211 887 }}
	\| -0.0399		\| -0.0399
	\| 0.0363		\| 0.0363
	\| 1.16		\| 1.16
	\|-		\|-
	\|2.9.5.7		\| 2.9.5.21
	\|~~4802000~~/~~4782969~~, ~~823543~~/~~819200~~, ~~102760448/102515625~~		\| 4375/4374, 52734375/52706752, {{monzo\| 31 0 -2 -6 }}
	\|{{mapping\|382 1211 887 ~~1072~~}}		\| {{mapping\| 382 1211 887 1678 }}
	\| +0.~~0846~~		\| -0.0552
	\| 0.~~2180~~		\| 0.0412
	\| 6.94		\| 1.31
	\|}		\|}

Francium: Created page with "{{Infobox ET}} {{EDO intro|382}} == Theory == 382et is consistent to the 7-odd-limit and the harmonic 3 is about halfway between its steps. Using the patent val, it tempe..."

2024-01-04T22:28:59Z

Created page with "{{Infobox ET}} {{EDO intro|382}} == Theory == 382et is consistent to the 7-odd-limit and the harmonic 3 is about halfway between its steps. Using the patent val, it tempe..."

New page

{{Infobox ET}}
{{EDO intro|382}}

== Theory ==
382et is consistent to the [[7-odd-limit]] and the harmonic 3 is about halfway between its steps. Using the patent val, it tempers out [[65625/65536]] in the 7-limit; [[117440512/117406179]], 25165824/25109315, 2097152/2096325, [[4000/3993]], 2734375/2725888, 2359296/2358125, [[540/539]], 1265625/1261568, 24057/24010 and [[9801/9800]] in the 11-limit. It [[support]]s [[bastille]].

=== Odd harmonics ===
{{Harmonics in equal|382}}

=== Subsets and supersets ===
382 factors into 2 × 191 with [[2edo]] and [[191edo]] as its subset edos. [[764edo]], 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|1211 -382}}
|{{mapping|382 1211}}
| -0.0439
| 0.0439
| 1.40
|-
|2.9.5
|{{monzo|38 -1 -15}}, {{monzo|25 -24 22}}
|{{mapping|382 1211 887}}
| -0.0399
| 0.0363
| 1.16
|-
|2.9.5.7
|4802000/4782969, 823543/819200, 102760448/102515625
|{{mapping|382 1211 887 1072}}
| +0.0846
| 0.2180
| 6.94
|}