2053edo - 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"

2026-03-13T13:31:33Z

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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	\| [[Whoosh]]		\| [[Whoosh]]
	\|}		\|}
	<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]]
	* "Willie Dustice" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/6t8HM9dCOjxDuNb5xO9Bma Spotify] \| [https://francium223.bandcamp.com/track/willie-dustice Bandcamp] \| [https://www.youtube.com/watch?v=Osjql2cB9XU YouTube] − in Liebic, 2053edo tuning		* "Willie Dustice" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/6t8HM9dCOjxDuNb5xO9Bma Spotify] \| [https://francium223.bandcamp.com/track/willie-dustice Bandcamp] \| [https://www.youtube.com/watch?v=Osjql2cB9XU YouTube] − in Liebic, 2053edo tuning

Francium: +music

2025-03-30T11:09:53Z

+music

← Older revision		Revision as of 11:09, 30 March 2025
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	\|}		\|}
	<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]]
			* "Willie Dustice" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/6t8HM9dCOjxDuNb5xO9Bma Spotify] \| [https://francium223.bandcamp.com/track/willie-dustice Bandcamp] \| [https://www.youtube.com/watch?v=Osjql2cB9XU YouTube] − in Liebic, 2053edo tuning

Francium: changed EDO intro to ED intro

2025-02-21T05:44:21Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:44, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 14:59, 16 January 2025

2025-01-16T14:59:09Z

← Older revision		Revision as of 14:59, 16 January 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|2053~~}}		{{EDO intro}}

	== Theory ==		== Theory ==
	2053edo is [[consistent]] to the [[5-odd-limit]], its [[harmonic]] [[7/1\|7]] is exactly between its steps. ~~The equal temperament~~ is strong in the 2.3.5.13.19.23.31 [[subgroup]], [[tempering out]] 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969 and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out [[7696/7695]].		2053edo is [[consistent]] to the [[5-odd-limit]], its [[harmonic]] [[7/1\|7]] is exactly between its steps. It is strong in the 2.3.5.13.19.23.31 [[subgroup]], [[tempering out]] 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969, and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out [[7696/7695]].

	=== 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" \|[[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\|3254 -2053}}		\| {{monzo\|3254 -2053}}
	\| {{mapping\|2053 3254}}		\| {{mapping\|2053 3254}}
	\| -0.0133		\| −0.0133
	\| 0.0133		\| 0.0133
	\| 2.28		\| 2.28
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	\| {{monzo\|37 25 -33}}, {{monzo\|93 -66 5}}		\| {{monzo\|37 25 -33}}, {{monzo\|93 -66 5}}
	\| {{mapping\|2053 3254 4767}}		\| {{mapping\|2053 3254 4767}}
	\| -0.0157		\| −0.0157
	\| 0.0114		\| 0.0114
	\| 1.95		\| 1.95
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	=== 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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	\| [[Whoosh]]		\| [[Whoosh]]
	\|}		\|}
			<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|2053}} == Theory == 2053edo is consistent to the 5-odd-limit, its harmonic 7 is exactly between its steps. The equal temperamen..."

2025-01-16T14:37:03Z

Created page with "{{Infobox ET}} {{EDO intro|2053}} == Theory == 2053edo is consistent to the 5-odd-limit, its harmonic 7 is exactly between its steps. The equal temperamen..."

New page

{{Infobox ET}}
{{EDO intro|2053}}

== Theory ==
2053edo is [[consistent]] to the [[5-odd-limit]], its [[harmonic]] [[7/1|7]] is exactly between its steps. The equal temperament is strong in the 2.3.5.13.19.23.31 [[subgroup]], [[tempering out]] 359424/359375, 22816/22815, 96876/96875, 497705/497664, 4784000/4782969 and 369664/369603. Using the 2.3.5.13.19.37 subgroup, it tempers out [[7696/7695]].

=== Prime harmonics ===
{{Harmonics in equal|2053}}

=== Subsets and supersets ===
2053edo is the 310th [[prime edo]]. [[4106edo]], which doubles it, gives a good correction to the harmonic 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|3254 -2053}}
| {{mapping|2053 3254}}
| -0.0133
| 0.0133
| 2.28
|-
| 2.3.5
| {{monzo|37 25 -33}}, {{monzo|93 -66 5}}
| {{mapping|2053 3254 4767}}
| -0.0157
| 0.0114
| 1.95
|}

=== 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
| 959\2053
| 560.546
| 864/625
| [[Whoosh]]
|}

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