773edo - 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"

2026-03-13T13:31:46Z

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 74:		Line 74:
	\| [[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]]
	* "Elvonna Chelf" from ''Don't Give Your Kids These Names'' (2025) − [https://open.spotify.com/track/4xjDobEhkET26uWYP4lgsi Spotify] \| [https://francium223.bandcamp.com/track/elvonna-chelf Bandcamp] \| [https://www.youtube.com/watch?v=YACJumzzMb0 YouTube]		* "Elvonna Chelf" from ''Don't Give Your Kids These Names'' (2025) − [https://open.spotify.com/track/4xjDobEhkET26uWYP4lgsi Spotify] \| [https://francium223.bandcamp.com/track/elvonna-chelf Bandcamp] \| [https://www.youtube.com/watch?v=YACJumzzMb0 YouTube]

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

2025-04-17T02:29:30Z

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

← Older revision		Revision as of 02:29, 17 April 2025
Line 72:		Line 72:
	\| 498.318		\| 498.318
	\| 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

2025-04-16T15:30:43Z

Rank-2 temperaments: Fix helmholtz link

← Older revision		Revision as of 15:30, 16 April 2025
Line 72:		Line 72:
	\| 498.318		\| 498.318
	\| 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

2025-04-03T11:13:33Z

+music

← Older revision		Revision as of 11:13, 3 April 2025
Line 75:		Line 75:
	\|}		\|}
	<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]]
			* "Elvonna Chelf" from ''Don't Give Your Kids These Names'' (2025) − [https://open.spotify.com/track/4xjDobEhkET26uWYP4lgsi Spotify] \| [https://francium223.bandcamp.com/track/elvonna-chelf Bandcamp] \| [https://www.youtube.com/watch?v=YACJumzzMb0 YouTube]

Francium: changed EDO intro to ED intro

2025-02-19T18:21:48Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:21, 19 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|773~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:35, 7 February 2025

2025-02-07T18:35:17Z

← Older revision		Revision as of 18:35, 7 February 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]]
	! 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 simple badness\|Relative]] (%)		! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\|-1225 773}}		\| {{monzo\|-1225 773}}
	\| {{mapping\|773 1225}}		\| {{mapping\|773 1225}}
	\| 0.0862		\| +0.0862
	\| 0.0862		\| 0.0862
	\| 5.55		\| 5.55
Line 32:		Line 33:
	\| 32805/32768, {{monzo\|65 85 -86}}		\| 32805/32768, {{monzo\|65 85 -86}}
	\| {{mapping\|773 1225 1795}}		\| {{mapping\|773 1225 1795}}
	\| 0.0241		\| +0.0241
	\| 0.1125		\| 0.1125
	\| 7.25		\| 7.25
Line 39:		Line 40:
	\| 2401/2400, 32805/32768, {{monzo\|20 22 -20 -3}}		\| 2401/2400, 32805/32768, {{monzo\|20 22 -20 -3}}
	\| {{mapping\|773 1225 1795 2170}}		\| {{mapping\|773 1225 1795 2170}}
	\| 0.0299		\| +0.0299
	\| 0.0979		\| 0.0979
	\| 6.31		\| 6.31
Line 46:		Line 47:
	\| 2401/2400, 32805/32768, 137781/137500, 766656/765625		\| 2401/2400, 32805/32768, 137781/137500, 766656/765625
	\| {{mapping\|773 1225 1795 2170 2674}}		\| {{mapping\|773 1225 1795 2170 2674}}
	\| 0.0365		\| +0.0365
	\| 0.0886		\| 0.0886
	\| 5.71		\| 5.71
Line 53:		Line 54:
	=== 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 72:		Line 74:
	\| [[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 ~~it is~~ distinct

Francium: Created page with "{{Infobox ET}} {{EDO intro|773}} == Theory == 773edo is consistent to the 7-odd-limit. Using the patent val, it tempers out 2401/2400, 328..."

2025-01-24T12:02:08Z

Created page with "{{Infobox ET}} {{EDO intro|773}} == Theory == 773edo is consistent to the 7-odd-limit. Using the patent val, it tempers out 2401/2400, 328..."

New page

{{Infobox ET}}
{{EDO intro|773}}

== Theory ==
773edo is [[consistent]] to the [[7-odd-limit]]. Using the [[patent val]], it [[tempering out|tempers out]] [[2401/2400]], [[32805/32768]], 137781/137500 and 766656/765625 in the [[11-limit]]. It [[support]]s [[counterultrakleismic]].

=== Prime harmonics ===
{{Harmonics in equal|773}}

=== Subsets and supersets ===
773edo is the 137th [[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|-1225 773}}
| {{mapping|773 1225}}
| 0.0862
| 0.0862
| 5.55
|-
| 2.3.5
| 32805/32768, {{monzo|65 85 -86}}
| {{mapping|773 1225 1795}}
| 0.0241
| 0.1125
| 7.25
|-
| 2.3.5.7
| 2401/2400, 32805/32768, {{monzo|20 22 -20 -3}}
| {{mapping|773 1225 1795 2170}}
| 0.0299
| 0.0979
| 6.31
|-
| 2.3.5.7.11
| 2401/2400, 32805/32768, 137781/137500, 766656/765625
| {{mapping|773 1225 1795 2170 2674}}
| 0.0365
| 0.0886
| 5.71
|}

=== 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
| 113\773
| 175.420
| 448/405
| [[Sesquiquartififths]]
|-
| 1
| 321\773
| 498.318
| 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