1583edo - 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"

2026-03-13T13:33:09Z

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 13:33, 13 March 2026
Line 61:		Line 61:
	\| [[Lafa]]		\| [[Lafa]]
	\|}		\|}
	<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]]
	* "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] \| [https://francium223.bandcamp.com/track/beefy Bandcamp] \| [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning		* "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] \| [https://francium223.bandcamp.com/track/beefy Bandcamp] \| [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning

Francium: changed EDO intro to ED intro

2025-02-21T05:56:13Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:56, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1583~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:19, 15 January 2025

2025-01-15T16:19:40Z

← Older revision		Revision as of 16:19, 15 January 2025
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	\| {{monzo\|2509 -1583}}		\| {{monzo\|2509 -1583}}
	\| {{mapping\|1583 2509}}		\| {{mapping\|1583 2509}}
	\| ~~−0~~.0010		\| −0.0010
	\| 0.0010		\| 0.0010
	\| 0.13		\| 0.13
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	\| {{monzo\|77 -31 -12}}, {{monzo\|-23 57 -29}}		\| {{monzo\|77 -31 -12}}, {{monzo\|-23 57 -29}}
	\| {{mapping\|1583 2509 3676}}		\| {{mapping\|1583 2509 3676}}
	\| ~~−0~~.0429		\| −0.0429
	\| 0.0592		\| 0.0592
	\| 7.81		\| 7.81
Line 40:		Line 40:
	\| 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875		\| 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875
	\| {{mapping\|1583 2509 3676 4444}}		\| {{mapping\|1583 2509 3676 4444}}
	\| ~~−0~~.0293		\| −0.0293
	\| 0.0564		\| 0.0564
	\| 7.44		\| 7.44
Line 61:		Line 61:
	\| [[Lafa]]		\| [[Lafa]]
	\|}		\|}
	<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]]
	* "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] \| [https://francium223.bandcamp.com/track/beefy Bandcamp] \| [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning		* "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] \| [https://francium223.bandcamp.com/track/beefy Bandcamp] \| [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning

ArrowHead294 at 13:17, 16 November 2024

2024-11-16T13:17:38Z

← Older revision		Revision as of 13:17, 16 November 2024
Line 26:		Line 26:
	\| {{monzo\|2509 -1583}}		\| {{monzo\|2509 -1583}}
	\| {{mapping\|1583 2509}}		\| {{mapping\|1583 2509}}
	\| -0.0010		\| −0.0010
	\| 0.0010		\| 0.0010
	\| 0.13		\| 0.13
Line 33:		Line 33:
	\| {{monzo\|77 -31 -12}}, {{monzo\|-23 57 -29}}		\| {{monzo\|77 -31 -12}}, {{monzo\|-23 57 -29}}
	\| {{mapping\|1583 2509 3676}}		\| {{mapping\|1583 2509 3676}}
	\| -0.0429		\| −0.0429
	\| 0.0592		\| 0.0592
	\| 7.81		\| 7.81
Line 40:		Line 40:
	\| 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875		\| 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875
	\| {{mapping\|1583 2509 3676 4444}}		\| {{mapping\|1583 2509 3676 4444}}
	\| -0.0293		\| −0.0293
	\| 0.0564		\| 0.0564
	\| 7.44		\| 7.44

ArrowHead294: Partial undo

2024-11-16T13:17:18Z

Partial undo

← Older revision		Revision as of 13:17, 16 November 2024
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	== 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
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	\| 0.0564		\| 0.0564
	\| 7.44		\| 7.44
	~~{{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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	\| {{monzo\|-32 13 5}}		\| {{monzo\|-32 13 5}}
	\| [[Lafa]]		\| [[Lafa]]
	~~{{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 ==
	; [[Francium]]		; [[Francium]]
	* "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] \| [https://francium223.bandcamp.com/track/beefy Bandcamp] \| [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning		* "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] \| [https://francium223.bandcamp.com/track/beefy Bandcamp] \| [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning

ArrowHead294 at 01:42, 16 November 2024

2024-11-16T01:42:47Z

← Older revision		Revision as of 01:42, 16 November 2024
Line 12:		Line 12:

	== 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
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	\| 0.0564		\| 0.0564
	\| 7.44		\| 7.44
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ 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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	\| {{monzo\|-32 13 5}}		\| {{monzo\|-32 13 5}}
	\| [[Lafa]]		\| [[Lafa]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:02, 16 November 2024

2024-11-16T01:02:27Z

← Older revision		Revision as of 01:02, 16 November 2024
Line 4:		Line 4:
	== Theory ==		== Theory ==
	1583edo is consistent to the [[9-odd-limit]]. Using the patent val, it [[tempering out\|tempers out]] [[2401/2400]], {{monzo\|36 -16 -7 2}} and {{monzo\|9 21 -17 -1}} in the 7-limit; 2401/2400, 172032/171875, 766656/765625 and 387420489/387200000 in the 11-limit. It [[support]]s [[empress]] and [[vili]].		1583edo is consistent to the [[9-odd-limit]]. Using the patent val, it [[tempering out\|tempers out]] [[2401/2400]], {{monzo\|36 -16 -7 2}} and {{monzo\|9 21 -17 -1}} in the 7-limit; 2401/2400, 172032/171875, 766656/765625 and 387420489/387200000 in the 11-limit. It [[support]]s [[empress]] and [[vili]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1583}}		{{Harmonics in equal\|1583}}
Line 12:		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 simple badness\|Relative]] (%)		! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 45:		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 58:		Line 61:
	\| [[Lafa]]		\| [[Lafa]]
	\|}		\|}
	~~<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]]
	* "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] \| [https://francium223.bandcamp.com/track/beefy Bandcamp] \| [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning		* "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] \| [https://francium223.bandcamp.com/track/beefy Bandcamp] \| [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning

Francium: +music

2024-08-18T14:59:05Z

+music

← Older revision		Revision as of 14:59, 18 August 2024
Line 59:		Line 59:
	\|}		\|}
	<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]]
			* "BEEFY!" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/3XvuplrvNLTKZZ3hQXNb1F Spotify] \| [https://francium223.bandcamp.com/track/beefy Bandcamp] \| [https://www.youtube.com/watch?v=lked66nkh_A YouTube] – vili in 1583edo tuning

Francium: Created page with "{{Infobox ET}} {{EDO intro|1583}} == Theory == 1583edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 2401/2400, {{monzo|36..."

2024-06-26T13:29:10Z

Created page with "{{Infobox ET}} {{EDO intro|1583}} == Theory == 1583edo is consistent to the 9-odd-limit. Using the patent val, it tempers out 2401/2400, {{monzo|36..."

New page

{{Infobox ET}}
{{EDO intro|1583}}

== Theory ==
1583edo is consistent to the [[9-odd-limit]]. Using the patent val, it [[tempering out|tempers out]] [[2401/2400]], {{monzo|36 -16 -7 2}} and {{monzo|9 21 -17 -1}} in the 7-limit; 2401/2400, 172032/171875, 766656/765625 and 387420489/387200000 in the 11-limit. It [[support]]s [[empress]] and [[vili]].
=== Prime harmonics ===
{{Harmonics in equal|1583}}

=== Subsets and supersets ===
1583edo is the 250th [[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|2509 -1583}}
| {{mapping|1583 2509}}
| -0.0010
| 0.0010
| 0.13
|-
| 2.3.5
| {{monzo|77 -31 -12}}, {{monzo|-23 57 -29}}
| {{mapping|1583 2509 3676}}
| -0.0429
| 0.0592
| 7.81
|-
| 2.3.5.7
| 2401/2400, 3367254360064/3363025078125, 5355700839936/5340576171875
| {{mapping|1583 2509 3676 4444}}
| -0.0293
| 0.0564
| 7.44
|}

=== 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
| 341\1583
| 258.497
| {{monzo|-32 13 5}}
| [[Lafa]]
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct