757edo - 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
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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 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]]
	* "developeed" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1RaOpdvBzCxAED154qb5UT Spotify] \| [https://francium223.bandcamp.com/track/developeed Bandcamp] \| [https://www.youtube.com/watch?v=rskZavKFwv4 YouTube] – in Vulture, 757edo tuning		* "developeed" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1RaOpdvBzCxAED154qb5UT Spotify] \| [https://francium223.bandcamp.com/track/developeed Bandcamp] \| [https://www.youtube.com/watch?v=rskZavKFwv4 YouTube] – in Vulture, 757edo tuning

Francium: +music

2025-03-05T12:22:50Z

+music

← Older revision		Revision as of 12:22, 5 March 2025
Line 69:		Line 69:
	\|}		\|}
	<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]]
			* "developeed" from ''wiloliquy'' (2025) – [https://open.spotify.com/track/1RaOpdvBzCxAED154qb5UT Spotify] \| [https://francium223.bandcamp.com/track/developeed Bandcamp] \| [https://www.youtube.com/watch?v=rskZavKFwv4 YouTube] – in Vulture, 757edo tuning

ArrowHead294 at 12:59, 21 February 2025

2025-02-21T12:59:35Z

← Older revision		Revision as of 12:59, 21 February 2025
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	== 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]]		! 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 25:		Line 26:
	\| {{monzo\| 1200 -757 }}		\| {{monzo\| 1200 -757 }}
	\| {{mapping\| 757 1200 }}		\| {{mapping\| 757 1200 }}
	\| -0.0917		\| −0.0917
	\| 0.0917		\| 0.0917
	\| 5.78		\| 5.78
Line 32:		Line 33:
	\| {{monzo\| 24 -21 4 }}, {{monzo\| 78 5 -37 }}		\| {{monzo\| 24 -21 4 }}, {{monzo\| 78 5 -37 }}
	\| {{mapping\| 757 1200 1758 }}		\| {{mapping\| 757 1200 1758 }}
	\| -0.1295		\| −0.1295
	\| 0.0920		\| 0.0920
	\| 5.80		\| 5.80
Line 39:		Line 40:
	\| 4375/4374, 67108864/66976875, 282475249/281250000		\| 4375/4374, 67108864/66976875, 282475249/281250000
	\| {{mapping\| 757 1200 1758 2125 }}		\| {{mapping\| 757 1200 1758 2125 }}
	\| -0.0735		\| −0.0735
	\| 0.1256		\| 0.1256
	\| 7.92		\| 7.92
Line 46:		Line 47:
	\| 4375/4374, 5632/5625, 160083/160000, 5764801/5749920		\| 4375/4374, 5632/5625, 160083/160000, 5764801/5749920
	\| {{mapping\| 757 1200 1758 2125 2619 }}		\| {{mapping\| 757 1200 1758 2125 2619 }}
	\| -0.0780		\| −0.0780
	\| 0.1127		\| 0.1127
	\| 7.11		\| 7.11
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
	\|-		\|-
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	\| [[Vulture]]		\| [[Vulture]]
	\|}		\|}
	<nowiki>*~~</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: changed EDO intro to ED intro

2025-02-21T05:51:05Z

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~~\|757~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Cleanup

2025-01-10T17:09:54Z

Cleanup

← Older revision		Revision as of 17:09, 10 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	757edo is [[consistent]] to the [[7-odd-limit]], [[tempering out]] [[4375/4374]], 67108864/66976875 and 282475249/281250000. Using the [[patent val]], it tempers out [[5632/5625]]~~, 4375/4374~~, [[160083/160000]] and 5764801/5749920 in the [[11-limit]].		757edo is [[consistent]] to the [[7-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[4375/4374]], 67108864/66976875 and 282475249/281250000. Using the [[patent val]], it tempers out [[5632/5625]], [[160083/160000]] and 5764801/5749920 in the [[11-limit]].

	=== Prime harmonics ===		=== Prime harmonics ===
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" \| [[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]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\|1200 -757}}		\| {{monzo\| 1200 -757 }}
	\| {{mapping\|757 1200}}		\| {{mapping\| 757 1200 }}
	\| -0.0917		\| -0.0917
	\| 0.0917		\| 0.0917
Line 30:		Line 30:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{monzo\|24 -21 4}}, {{monzo\|78 5 -37}}		\| {{monzo\| 24 -21 4 }}, {{monzo\| 78 5 -37 }}
	\| {{mapping\|757 1200 1758}}		\| {{mapping\| 757 1200 1758 }}
	\| -0.1295		\| -0.1295
	\| 0.0920		\| 0.0920
Line 38:		Line 38:
	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 67108864/66976875, 282475249/281250000		\| 4375/4374, 67108864/66976875, 282475249/281250000
	\| {{mapping\|757 1200 1758 2125}}		\| {{mapping\| 757 1200 1758 2125 }}
	\| -0.0735		\| -0.0735
	\| 0.1256		\| 0.1256
Line 44:		Line 44:
	\|-		\|-
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 5632/5625~~, 4375/4374~~, 160083/160000, 5764801/5749920		\| 4375/4374, 5632/5625, 160083/160000, 5764801/5749920
	\| {{mapping\|757 1200 1758 2125 2619}}		\| {{mapping\| 757 1200 1758 2125 2619 }}
	\| -0.0780		\| -0.0780
	\| 0.1127		\| 0.1127
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	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>~~Ratio~~*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 66:		Line 66:
	\| [[Vulture]]		\| [[Vulture]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if 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

Francium: Created page with "{{Infobox ET}} {{EDO intro|757}} == Theory == 757edo is consistent to the 7-odd-limit, tempering out 4375/4374, 67108864/66976875 and 282475249/281250000. Usi..."

2025-01-09T14:23:05Z

Created page with "{{Infobox ET}} {{EDO intro|757}} == Theory == 757edo is consistent to the 7-odd-limit, tempering out 4375/4374, 67108864/66976875 and 282475249/281250000. Usi..."

New page

{{Infobox ET}}
{{EDO intro|757}}

== Theory ==
757edo is [[consistent]] to the [[7-odd-limit]], [[tempering out]] [[4375/4374]], 67108864/66976875 and 282475249/281250000. Using the [[patent val]], it tempers out [[5632/5625]], 4375/4374, [[160083/160000]] and 5764801/5749920 in the [[11-limit]].

=== Prime harmonics ===
{{Harmonics in equal|757}}

=== Subsets and supersets ===
757edo is the 134th [[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|1200 -757}}
| {{mapping|757 1200}}
| -0.0917
| 0.0917
| 5.78
|-
| 2.3.5
| {{monzo|24 -21 4}}, {{monzo|78 5 -37}}
| {{mapping|757 1200 1758}}
| -0.1295
| 0.0920
| 5.80
|-
| 2.3.5.7
| 4375/4374, 67108864/66976875, 282475249/281250000
| {{mapping|757 1200 1758 2125}}
| -0.0735
| 0.1256
| 7.92
|-
| 2.3.5.7.11
| 5632/5625, 4375/4374, 160083/160000, 5764801/5749920
| {{mapping|757 1200 1758 2125 2619}}
| -0.0780
| 0.1127
| 7.11
|}

=== 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
| 300\757
| 475.561
| 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