641edo - Revision history

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:32:28Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:32, 13 March 2026
Line 56:		Line 56:
	\| [[Vulture]]		\| [[Vulture]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

Francium: changed EDO intro to ED intro

2025-02-21T06:09:48Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:09, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|641~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:03, 15 January 2025

2025-01-15T17:03:27Z

← Older revision		Revision as of 17:03, 15 January 2025
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	\| {{monzo\| 1016 -641 }}		\| {{monzo\| 1016 -641 }}
	\| {{mapping\| 641 1016 }}		\| {{mapping\| 641 1016 }}
	\| ~~−0~~.0231		\| −0.0231
	\| 0.0231		\| 0.0231
	\| 1.23		\| 1.23
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	\| [[Vulture]]		\| [[Vulture]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Goofy Individual" from ''Take Advantage'' (2024) ~~–~~ [https://open.spotify.com/track/3wNm7mtNBOuE4utwHFSoRW Spotify] \| [https://francium223.bandcamp.com/track/goofy-individual Bandcamp] \| [https://www.youtube.com/watch?v=c3ZGAeYHmrQ YouTube]		* "Goofy Individual" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/3wNm7mtNBOuE4utwHFSoRW Spotify] \| [https://francium223.bandcamp.com/track/goofy-individual Bandcamp] \| [https://www.youtube.com/watch?v=c3ZGAeYHmrQ YouTube]

	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294: Partial undo

2024-11-16T12:59:00Z

Partial undo

← Older revision		Revision as of 12:59, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 29:		Line 38:
	\| 0.1474		\| 0.1474
	\| 7.87		\| 7.87
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 320/243		\| 320/243
	\| [[Vulture]]		\| [[Vulture]]
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Music ==		== Music ==

ArrowHead294 at 03:01, 16 November 2024

2024-11-16T03:01:06Z

← Older revision		Revision as of 03:01, 16 November 2024
Line 14:		Line 14:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! 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]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| 1016 -641 }}		\| {{monzo\| 1016 -641 }}
	\| {{mapping\| 641 1016 }}		\| {{mapping\| 641 1016 }}
	\| -0.0231		\| −0.0231
	\| 0.0231		\| 0.0231
	\| 1.23		\| 1.23
Line 37:		Line 29:
	\| 0.1474		\| 0.1474
	\| 7.87		\| 7.87
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 53:		Line 39:
	\| 320/243		\| 320/243
	\| [[Vulture]]		\| [[Vulture]]
	\|}		{{rank-2 end}}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Goofy Individual" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/3wNm7mtNBOuE4utwHFSoRW Spotify] \| [https://francium223.bandcamp.com/track/goofy-individual Bandcamp] \| [https://www.youtube.com/watch?v=c3ZGAeYHmrQ YouTube]		* "Goofy Individual" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/3wNm7mtNBOuE4utwHFSoRW Spotify] \| [https://francium223.bandcamp.com/track/goofy-individual Bandcamp] \| [https://www.youtube.com/watch?v=c3ZGAeYHmrQ YouTube]

			[[Category:Listen]]

Francium: +music

2024-09-09T12:21:56Z

+music

← Older revision		Revision as of 12:21, 9 September 2024
Line 55:		Line 55:
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

			== Music ==
			; [[Francium]]
			* "Goofy Individual" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/3wNm7mtNBOuE4utwHFSoRW Spotify] \| [https://francium223.bandcamp.com/track/goofy-individual Bandcamp] \| [https://www.youtube.com/watch?v=c3ZGAeYHmrQ YouTube]

FloraC: /* Theory */ -typo

2024-07-21T07:11:22Z

Theory: -typo

← Older revision		Revision as of 07:11, 21 July 2024
Line 5:		Line 5:
	641edo is only [[consistent]] to the [[5-odd-limit]]. Since both [[harmonic]]s [[7/1\|7]] and [[11/1\|11]] are about halfway between its steps, and since harmonic [[5/1\|5]] is also off by more than a third step, it can be used as a dual-5 dual-7 dual-11 temperament. Alternatively, it can be used as a 2.3.5.13.17.19 [[subgroup]] temperament, as it is consistent in the no-7 no-11 19-odd-limit.		641edo is only [[consistent]] to the [[5-odd-limit]]. Since both [[harmonic]]s [[7/1\|7]] and [[11/1\|11]] are about halfway between its steps, and since harmonic [[5/1\|5]] is also off by more than a third step, it can be used as a dual-5 dual-7 dual-11 temperament. Alternatively, it can be used as a 2.3.5.13.17.19 [[subgroup]] temperament, as it is consistent in the no-7 no-11 19-odd-limit.

	To start with, consider the 641d val {{val\| 641 1016 1488 '''1799''' 2217 2372 }} in the 13-limit, which [[tempering out\|tempers out]] [[625/624]], [[2200/2197]], [[4459/4455]], 14641/14625, and [[19712/19683]]. The alternative 641df val, {{val\| 641 1016 1488 '''1799''' 2217 '''2371''' }}, tempers out [[676/675]], [[1001/1000]], 19712/19683, [[31213/31104]], and 983125/979776. The 641ce val, {{val\| 641 1016 '''~~1089~~''' 1800 '''2218''' 2372 }}, tempers out 676/675, 1001/1000, [[6144/6125]], [[10985/10976]], and 85294/85184.		To start with, consider the 641d val {{val\| 641 1016 1488 '''1799''' 2217 2372 }} in the 13-limit, which [[tempering out\|tempers out]] [[625/624]], [[2200/2197]], [[4459/4455]], 14641/14625, and [[19712/19683]]. The alternative 641df val, {{val\| 641 1016 1488 '''1799''' 2217 '''2371''' }}, tempers out [[676/675]], [[1001/1000]], 19712/19683, [[31213/31104]], and 983125/979776. The 641ce val, {{val\| 641 1016 '''1489''' 1800 '''2218''' 2372 }}, tempers out 676/675, 1001/1000, [[6144/6125]], [[10985/10976]], and 85294/85184.

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

FloraC: The assesssment of subgroups was too hasty and arbitrary. For edos like this an analysis on the tuning profile is required.

2024-07-21T07:10:24Z

The assesssment of subgroups was too hasty and arbitrary. For edos like this an analysis on the tuning profile is required.

← Older revision		Revision as of 07:10, 21 July 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	641edo is [[consistent]] to the [[5-odd-limit]]. It can be used ~~in the~~ 2.3.5~~.11~~.13.17 [[subgroup]], [[tempering out]] [[625/624]], [[~~2431~~/~~2430~~]], [[1089/~~1088~~]], [[~~4225~~/~~4224~~]] and ~~1384448000~~/~~1382278041~~.		641edo is only [[consistent]] to the [[5-odd-limit]]. Since both [[harmonic]]s [[7/1\|7]] and [[11/1\|11]] are about halfway between its steps, and since harmonic [[5/1\|5]] is also off by more than a third step, it can be used as a dual-5 dual-7 dual-11 temperament. Alternatively, it can be used as a 2.3.5.13.17.19 [[subgroup]] temperament, as it is consistent in the no-7 no-11 19-odd-limit.

			To start with, consider the 641d val {{val\| 641 1016 1488 '''1799''' 2217 2372 }} in the 13-limit, which [[tempering out\|tempers out]] [[625/624]], [[2200/2197]], [[4459/4455]], 14641/14625, and [[19712/19683]]. The alternative 641df val, {{val\| 641 1016 1488 '''1799''' 2217 '''2371''' }}, tempers out [[676/675]], [[1001/1000]], 19712/19683, [[31213/31104]], and 983125/979776. The 641ce val, {{val\| 641 1016 '''1089''' 1800 '''2218''' 2372 }}, tempers out 676/675, 1001/1000, [[6144/6125]], [[10985/10976]], and 85294/85184.

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	641edo is the 116th [[prime ~~EDO~~]]. [[1282edo]], which doubles it, gives a good correction to the ~~[[harmonic]] [[7/1\|~~7]].		641edo is the 116th [[prime edo]]. [[1282edo]], which doubles it, gives a good correction to the 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		\| 2.3
	\| {{monzo\|1016 -641}}		\| {{monzo\| 1016 -641 }}
	\| {{mapping\|641 1016}}		\| {{mapping\| 641 1016 }}
	\| -0.0231		\| -0.0231
	\| 0.0231		\| 0.0231
Line 30:		Line 32:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{monzo\|24 -21 4}}, {{monzo\|-56 -13 33}}		\| {{monzo\| 24 -21 4 }}, {{monzo\| -56 -13 33 }}
	\| {{mapping\|641 1016 1488}}		\| {{mapping\| 641 1016 1488 }}
	\| +0.0803		\| +0.0803
	\| 0.1474		\| 0.1474
	\| 7.87		\| 7.87
	\|-
	~~\| 2.3.5.11~~
	~~\| 166375/165888, 234375/234256, 10485760000/10460353203~~
	~~\| {{mapping\|641 1016 1488 2217}}~~
	~~\| +0.1273~~
	~~\| 0.1514~~
	~~\| 8.09~~
	\|-
	~~\| 2.3.5.11.13~~
	~~\| 625/624, 4225/4224, 17303/17280, 10485760000/10460353203~~
	~~\| {{mapping\|641 1016 1488 2217 2372}}~~
	~~\| +0.1000~~
	~~\| 0.1460~~
	~~\| 7.80~~
	\|-
	~~\| 2.3.5.11.13.17~~
	~~\| 625/624, 2431/2430, 1089/1088, 4225/4224, 1384448000/1382278041~~
	~~\| {{mapping\|641 1016 1488 2217 2372 2620}}~~
	~~\| +0.0882~~
	~~\| 0.1358~~
	~~\| 7.25~~
	\|}		\|}

Francium: Created page with "{{Infobox ET}} {{EDO intro|641}} == Theory == 641edo is consistent to the 5-odd-limit. It can be used in the 2.3.5.11.13.17 subgroup, tempering out [[625/624]..."

2024-07-20T07:34:06Z

Created page with "{{Infobox ET}} {{EDO intro|641}} == Theory == 641edo is consistent to the 5-odd-limit. It can be used in the 2.3.5.11.13.17 subgroup, tempering out [[625/624]..."

New page

{{Infobox ET}}
{{EDO intro|641}}

== Theory ==
641edo is [[consistent]] to the [[5-odd-limit]]. It can be used in the 2.3.5.11.13.17 [[subgroup]], [[tempering out]] [[625/624]], [[2431/2430]], [[1089/1088]], [[4225/4224]] and 1384448000/1382278041.

=== Odd harmonics ===
{{Harmonics in equal|641}}

=== Subsets and supersets ===
641edo is the 116th [[prime EDO]]. [[1282edo]], which doubles it, gives a good correction to the [[harmonic]] [[7/1|7]].

== 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]] (%)
|-
| 2.3
| {{monzo|1016 -641}}
| {{mapping|641 1016}}
| -0.0231
| 0.0231
| 1.23
|-
| 2.3.5
| {{monzo|24 -21 4}}, {{monzo|-56 -13 33}}
| {{mapping|641 1016 1488}}
| +0.0803
| 0.1474
| 7.87
|-
| 2.3.5.11
| 166375/165888, 234375/234256, 10485760000/10460353203
| {{mapping|641 1016 1488 2217}}
| +0.1273
| 0.1514
| 8.09
|-
| 2.3.5.11.13
| 625/624, 4225/4224, 17303/17280, 10485760000/10460353203
| {{mapping|641 1016 1488 2217 2372}}
| +0.1000
| 0.1460
| 7.80
|-
| 2.3.5.11.13.17
| 625/624, 2431/2430, 1089/1088, 4225/4224, 1384448000/1382278041
| {{mapping|641 1016 1488 2217 2372 2620}}
| +0.0882
| 0.1358
| 7.25
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
| 1
| 254\641
| 475.507
| 320/243
| [[Vulture]]
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct