584edo - 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"

2026-03-13T13:33:02Z

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 74:		Line 74:
	\| [[Hemiluna]] (584, 7-limit)		\| [[Hemiluna]] (584, 7-limit)
	\|}		\|}
	<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

	== Scales ==		== Scales ==

Francium: changed EDO intro to ED intro

2025-02-21T06:26:36Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:26, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|584~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:52, 15 January 2025

2025-01-15T16:52:44Z

← Older revision		Revision as of 16:52, 15 January 2025
Line 25:		Line 25:
	\| {{monzo\| 463 -292 }}		\| {{monzo\| 463 -292 }}
	\| {{mapping\| 584 926 }}		\| {{mapping\| 584 926 }}
	\| ~~−0~~.2476		\| −0.2476
	\| 0.2475		\| 0.2475
	\| 12.05		\| 12.05
Line 32:		Line 32:
	\| {{monzo\| 3 -18 11 }}, {{monzo\| 21 -20 4 }}		\| {{monzo\| 3 -18 11 }}, {{monzo\| 21 -20 4 }}
	\| {{mapping\| 584 926 1356 }}		\| {{mapping\| 584 926 1356 }}
	\| ~~−0~~.1633		\| −0.1633
	\| 0.2346		\| 0.2346
	\| 11.42		\| 11.42
Line 39:		Line 39:
	\| 1500625/1492992, 1605632/1594323, 235298/234375		\| 1500625/1492992, 1605632/1594323, 235298/234375
	\| {{mapping\| 584 926 1356 1639 }}		\| {{mapping\| 584 926 1356 1639 }}
	\| ~~−0~~.0319		\| −0.0319
	\| 0.3052		\| 0.3052
	\| 14.85		\| 14.85
Line 74:		Line 74:
	\| [[Hemiluna]] (584, 7-limit)		\| [[Hemiluna]] (584, 7-limit)
	\|}		\|}
	<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

	== Scales ==		== Scales ==

ArrowHead294: Partial undo

2024-11-16T13:03:06Z

Partial undo

← Older revision		Revision as of 13:03, 16 November 2024
Line 11:		Line 11:

	== 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
Line 47:		Line 56:
	\| 0.2613		\| 0.2613
	\| 12.72		\| 12.72
	~~{{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
Line 57:		Line 73:
	\| 200/189		\| 200/189
	\| [[Hemiluna]] (584, 7-limit)		\| [[Hemiluna]] (584, 7-limit)
	~~{{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

	== Scales ==		== Scales ==

ArrowHead294 at 02:45, 16 November 2024

2024-11-16T02:45:08Z

← Older revision		Revision as of 02:45, 16 November 2024
Line 47:		Line 47:
	\| 0.2613		\| 0.2613
	\| 12.72		\| 12.72
	\|{{comma basis end}}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===

ArrowHead294 at 02:44, 16 November 2024

2024-11-16T02:44:39Z

← Older revision		Revision as of 02:44, 16 November 2024
Line 11:		Line 11:

	== 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
	\| {{monzo\| 463 -292 }}		\| {{monzo\| 463 -292 }}
	\| {{mapping\| 584 926 }}		\| {{mapping\| 584 926 }}
	\| -0.2476		\| −0.2476
	\| 0.2475		\| 0.2475
	\| 12.05		\| 12.05
Line 31:		Line 23:
	\| {{monzo\| 3 -18 11 }}, {{monzo\| 21 -20 4 }}		\| {{monzo\| 3 -18 11 }}, {{monzo\| 21 -20 4 }}
	\| {{mapping\| 584 926 1356 }}		\| {{mapping\| 584 926 1356 }}
	\| -0.1633		\| −0.1633
	\| 0.2346		\| 0.2346
	\| 11.42		\| 11.42
Line 38:		Line 30:
	\| 1500625/1492992, 1605632/1594323, 235298/234375		\| 1500625/1492992, 1605632/1594323, 235298/234375
	\| {{mapping\| 584 926 1356 1639 }}		\| {{mapping\| 584 926 1356 1639 }}
	\| -0.0319		\| −0.0319
	\| 0.3052		\| 0.3052
	\| 14.85		\| 14.85
Line 55:		Line 47:
	\| 0.2613		\| 0.2613
	\| 12.72		\| 12.72
	\|}		\|{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 71:		Line 57:
	\| 200/189		\| 200/189
	\| [[Hemiluna]] (584, 7-limit)		\| [[Hemiluna]] (584, 7-limit)
	\|}		{{rank-2 end}}
	~~<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}}

	== Scales ==		== Scales ==
Line 79:		Line 65:
	== Music ==		== Music ==
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* [https://www.youtube.com/watch?v=7qF6IwKB8Iw ''Are You From The Moon?''] (2023) – hemiluna in 584edo tuning		* [https://www.youtube.com/watch?v=7qF6IwKB8Iw ''Are You From The Moon?''] (2023) – hemiluna in 584edo tuning

			[[Category:Listen]]

FloraC: Rework; cleanup; clarify the title row of the rank-2 temp table

2023-10-25T10:07:41Z

Rework; cleanup; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 10:07, 25 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|584}}		{{EDO intro\|584}}
	==Theory==
	~~584et tempers out 48828125/48771072 and 67108864/66976875 in~~ the 7-limit ~~(hemiluna temperament),~~ and ~~12005~~/~~11979~~, [[~~131072~~/~~130977~~]], [[~~5632~~/~~5625~~]], ~~537109375~~/~~536870912~~, ~~9453125~~/~~9437184~~, ~~160083/160000~~ and ~~391314~~/~~390625 in~~ the 11-~~limit~~.		== Theory ==
			584edo is only [[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[3/1\|3]] is quite large. With reasonable approximations to harmonics [[5/1\|5]], [[7/1\|7]], [[9/1\|9]], [[11/1\|11]], [[13/1\|13]], and [[17/1\|17]], it commends itself as a 2.9.5.7.11.13.17 [[subgroup]] tuning.

			If we use the harmonic 3 instead, we notice the better-tuned 584d [[val]] is [[enfactoring\|enfactored]], with the same tuning as [[292edo]]. Therefore, we are left with the [[patent val]], which tempers out 48828125/48771072 and 67108864/66976875, [[support]]ing [[hemiluna]].

			=== Odd harmonics ===
	{{Harmonics in equal\|584}}		{{Harmonics in equal\|584}}
	==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\|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\| 463 -292}}		\| {{monzo\| 463 -292 }}
	\|{{~~val~~\| 584 926}}		\| {{mapping\| 584 926 }}
	\| -0.2476		\| -0.2476
	\| 0.2475		\| 0.2475
	\| 12.05		\| 12.05
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\| 3 -18 11}}, {{monzo\| 21 -20 4}}		\| {{monzo\| 3 -18 11 }}, {{monzo\| 21 -20 4 }}
	\|{{~~val~~\| 584 926 1356}}		\| {{mapping\| 584 926 1356 }}
	\| -0.1633		\| -0.1633
	\| 0.2346		\| 0.2346
	\| 11.42		\| 11.42
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|1500625/1492992, 1605632/1594323, 235298/234375		\| 1500625/1492992, 1605632/1594323, 235298/234375
	\|{{~~val~~\| 584 926 1356 1639}}		\| {{mapping\| 584 926 1356 1639 }}
	\| -0.0319		\| -0.0319
	\| 0.3052		\| 0.3052
	\| 14.85		\| 14.85
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|5632/5625, 160083/160000, 26411/26244, 968000/964467		\| 5632/5625, 160083/160000, 26411/26244, 968000/964467
	\|{{~~val~~\| 584 926 1356 1639 2020}}		\| {{mapping\| 584 926 1356 1639 2020 }}
	\| +0.0111		\| +0.0111
	\| 0.2862		\| 0.2862
	\| 13.93		\| 13.93
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|2080/2079, 1001/1000, 4096/4095, 85750/85293, 983125/979776		\| 2080/2079, 1001/1000, 4096/4095, 85750/85293, 983125/979776
	\|{{~~val~~\| 584 926 1356 1639 2020 2161}}		\| {{mapping\| 584 926 1356 1639 2020 2161 }}
	\| +0.0145		\| +0.0145
	\| 0.2613		\| 0.2613
Line 55:		Line 61:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~		! Generator*
	! Cents~~<br>(reduced)~~		! Cents*
	! Associated<br>~~ratio~~		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|47\584		\| 47\584
	\|96.58		\| 96.58
	\|200/189		\| 200/189
	\|Hemiluna		\| [[Hemiluna]] (584, 7-limit)
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	==Scales==		== Scales ==
	* [[Hemiluna14]]		* [[Hemiluna14]]
	==Music==
	* [https://www.youtube.com/watch?v=7qF6IwKB8Iw Are You From The Moon?] ~~by Francium~~		== Music ==
			; [[User:Francium\|Francium]]
			* [https://www.youtube.com/watch?v=7qF6IwKB8Iw ''Are You From The Moon?''] (2023) – hemiluna in 584edo tuning

BudjarnLambeth at 06:40, 9 July 2023

2023-07-09T06:40:38Z

← Older revision		Revision as of 06:40, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|584}}		{{EDO intro\|584}}
	==Theory==		==Theory==

BudjarnLambeth at 05:39, 9 July 2023

2023-07-09T05:39:27Z

← Older revision		Revision as of 05:39, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|584}}		{{EDO intro\|584}}
	==Theory==		==Theory==

Francium: /* Regular temperament properties */

2023-03-28T14:27:48Z

Regular temperament properties

@@ Line 50: / Line 50: @@
 | 12.72
 |}
 ==Scales==
 * [[Hemiluna14]]
 ==Music==
 * [https://www.youtube.com/watch?v=7qF6IwKB8Iw Are You From The Moon?] by Francium