761edo - 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"

2026-03-13T13:31:45Z

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 13:31, 13 March 2026
Line 61:		Line 61:
	\| [[Helmholtz (temperament)\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|}		\|}
	<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]]		; [[Francium]]
	* "shortcrust" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/7eX41UXoJhmlzFVe3hWP7d Spotify] \| [https://francium223.bandcamp.com/track/shortcrust Bandcamp] \| [https://www.youtube.com/watch?v=0vPnUo6X9IY YouTube]		* "shortcrust" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/7eX41UXoJhmlzFVe3hWP7d Spotify] \| [https://francium223.bandcamp.com/track/shortcrust Bandcamp] \| [https://www.youtube.com/watch?v=0vPnUo6X9IY YouTube]

Lériendil: Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

2025-04-17T02:30:58Z

Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

← Older revision		Revision as of 02:30, 17 April 2025
Line 59:		Line 59:
	\| 498.292		\| 498.292
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

Sintel: /* Rank-2 temperaments */ Fix helmholtz link

2025-04-16T15:31:05Z

Rank-2 temperaments: Fix helmholtz link

← Older revision		Revision as of 15:31, 16 April 2025
Line 59:		Line 59:
	\| 498.292		\| 498.292
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

Francium: +music

2025-03-06T14:58:26Z

+music

← Older revision		Revision as of 14:58, 6 March 2025
Line 62:		Line 62:
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

			== Music ==
			; [[Francium]]
			* "shortcrust" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/7eX41UXoJhmlzFVe3hWP7d Spotify] \| [https://francium223.bandcamp.com/track/shortcrust Bandcamp] \| [https://www.youtube.com/watch?v=0vPnUo6X9IY YouTube]

ArrowHead294 at 12:58, 21 February 2025

2025-02-21T12:58:43Z

← Older revision		Revision as of 12:58, 21 February 2025
Line 61:		Line 61:
	\| [[Helmholtz]]		\| [[Helmholtz]]
	\|}		\|}

	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

ArrowHead294 at 12:58, 21 February 2025

2025-02-21T12:58:35Z

← Older revision		Revision as of 12:58, 21 February 2025
Line 15:		Line 15:
	\|-		\|-
	! 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 26:		Line 26:
	\| {{monzo\|-1206 761}}		\| {{monzo\|-1206 761}}
	\| {{mapping\|761 1206}}		\| {{mapping\|761 1206}}
	\| 0.0778		\| +0.0778
	\| 0.0778		\| 0.0778
	\| 4.93		\| 4.93
Line 33:		Line 33:
	\| 32805/32768, {{monzo\|69 81 -85}}		\| 32805/32768, {{monzo\|69 81 -85}}
	\| {{mapping\|761 1206 1767}}		\| {{mapping\|761 1206 1767}}
	\| 0.0490		\| +0.0490
	\| 0.0755		\| 0.0755
	\| 4.79		\| 4.79
Line 40:		Line 40:
	\| 32805/32768, 420175/419904, {{monzo\|3 13 -15 4}}		\| 32805/32768, 420175/419904, {{monzo\|3 13 -15 4}}
	\| {{mapping\|761 1206 1767 2136}}		\| {{mapping\|761 1206 1767 2136}}
	\| 0.0925		\| +0.0925
	\| 0.0998		\| 0.0998
	\| 6.33		\| 6.33

Francium: changed EDO intro to ED intro

2025-02-21T05:51:24Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:51, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|761~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:37:27Z

Theory: cleanup

← Older revision		Revision as of 16:37, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	761edo is [[consistent]] to the [[9-odd-limit]]. It [[tempers out]] [[32805/32768]], [[420175/419904]] and {{monzo\|3 13 -15 4}} in the [[7-limit]]. The equal temperament is strong in the 2.3.5.13.29.31 [[subgroup]], tempering out 32805/32768, 21141/21125, 3627/3625, [[140625/140608]] and 45349632/45287125.		761edo is [[consistent]] to the [[9-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[32805/32768]] in the 5-limit; [[420175/419904]] and {{monzo\| 3 13 -15 4 }} in the [[7-limit]]. The equal temperament is strong in the 2.3.5.13.29.31 [[subgroup]], tempering out 32805/32768, 21141/21125, 3627/3625, [[140625/140608]] and 45349632/45287125.

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

ArrowHead294 at 16:16, 15 January 2025

2025-01-15T16:16:40Z

← Older revision		Revision as of 16:16, 15 January 2025
Line 13:		Line 13:
	== 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" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| [[Mapping]]
	! colspan="2" \|Tuning Error		! rowspan="2" \| Optimal<br />8ve Stretch (¢)
			! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 46:		Line 47:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>~~Ratio~~*		! Associated<br />ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 60:		Line 62:
	\|}		\|}

	<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

Francium: Created page with "{{Infobox ET}} {{EDO intro|761}} == Theory == 761edo is consistent to the 9-odd-limit. It tempers out 32805/32768, 420175/419904 and {{monzo|3 13 -15 4}}..."

2025-01-13T12:11:54Z

Created page with "{{Infobox ET}} {{EDO intro|761}} == Theory == 761edo is consistent to the 9-odd-limit. It tempers out 32805/32768, 420175/419904 and {{monzo|3 13 -15 4}}..."

New page

{{Infobox ET}}
{{EDO intro|761}}

== Theory ==
761edo is [[consistent]] to the [[9-odd-limit]]. It [[tempers out]] [[32805/32768]], [[420175/419904]] and {{monzo|3 13 -15 4}} in the [[7-limit]]. The equal temperament is strong in the 2.3.5.13.29.31 [[subgroup]], tempering out 32805/32768, 21141/21125, 3627/3625, [[140625/140608]] and 45349632/45287125.

=== Odd harmonics ===
{{Harmonics in equal|761}}

=== Subsets and supersets ===
761edo is the 135th [[prime edo]].

== 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|-1206 761}}
| {{mapping|761 1206}}
| 0.0778
| 0.0778
| 4.93
|-
| 2.3.5
| 32805/32768, {{monzo|69 81 -85}}
| {{mapping|761 1206 1767}}
| 0.0490
| 0.0755
| 4.79
|-
| 2.3.5.7
| 32805/32768, 420175/419904, {{monzo|3 13 -15 4}}
| {{mapping|761 1206 1767 2136}}
| 0.0925
| 0.0998
| 6.33
|}

=== 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
| 316\761
| 498.292
| 4/3
| [[Helmholtz]]
|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct