285edo - 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"

2026-03-13T13:32:44Z

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 13:32, 13 March 2026
Line 93:		Line 93:
	\| [[Enneadecal]] (5-limit)		\| [[Enneadecal]] (5-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

Francium: changed EDO intro to ED intro

2025-02-21T06:28:01Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:28, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|285~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 19:28, 15 January 2025

2025-01-15T19:28:08Z

← Older revision		Revision as of 19:28, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 285 factors into ~~3 × 5 × 19~~, 285edo has subset edos {{EDOs\| 3, 5, 15, 19, 57, and 95 }}.		Since 285 factors into {{factorisation\|285}}, 285edo has subset edos {{EDOs\| 3, 5, 15, 19, 57, and 95 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 26:		Line 26:
	\| {{monzo\| 452 -285 }}		\| {{monzo\| 452 -285 }}
	\| {{mapping\| 285 452 }}		\| {{mapping\| 285 452 }}
	\| ~~−0~~.3795		\| −0.3795
	\| 0.3794		\| 0.3794
	\| 9.01		\| 9.01
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	\| 67108864/66430125, {{monzo\| -14 -19 19 }}		\| 67108864/66430125, {{monzo\| -14 -19 19 }}
	\| {{mapping\| 285 452 662 }}		\| {{mapping\| 285 452 662 }}
	\| ~~−0~~.4043		\| −0.4043
	\| 0.3117		\| 0.3117
	\| 7.41		\| 7.41
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	\| 3136/3125, 5120/5103, 40353607/39858075		\| 3136/3125, 5120/5103, 40353607/39858075
	\| {{mapping\| 285 452 662 800 }}		\| {{mapping\| 285 452 662 800 }}
	\| ~~−0~~.2673		\| −0.2673
	\| 0.3596		\| 0.3596
	\| 8.54		\| 8.54
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	\| 3025/3024, 3136/3125, 5120/5103, 12005/11979		\| 3025/3024, 3136/3125, 5120/5103, 12005/11979
	\| {{mapping\| 285 452 662 800 986 }}		\| {{mapping\| 285 452 662 800 986 }}
	\| ~~−0~~.2289		\| −0.2289
	\| 0.3307		\| 0.3307
	\| 7.85		\| 7.85
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	\| 352/351, 676/675, 847/845, 3025/3024, 12005/11979		\| 352/351, 676/675, 847/845, 3025/3024, 12005/11979
	\| {{mapping\| 285 452 662 800 986 1055 }}		\| {{mapping\| 285 452 662 800 986 1055 }}
	\| ~~−0~~.2618		\| −0.2618
	\| 0.3107		\| 0.3107
	\| 7.38		\| 7.38
Line 93:		Line 93:
	\| [[Enneadecal]] (5-limit)		\| [[Enneadecal]] (5-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

ArrowHead294: Partial undo

2024-11-16T13:02:11Z

Partial undo

← Older revision		Revision as of 13:02, 16 November 2024
Line 12:		Line 12:

	== 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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	=== 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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	\| 4/3<br />(15625/15552)		\| 4/3<br />(15625/15552)
	\| [[Enneadecal]] (5-limit)		\| [[Enneadecal]] (5-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

ArrowHead294 at 02:48, 16 November 2024

2024-11-16T02:48:53Z

← Older revision		Revision as of 02:48, 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
	\| {{monzo\| 452 -285 }}		\| {{monzo\| 452 -285 }}
	\| {{mapping\| 285 452 }}		\| {{mapping\| 285 452 }}
	\| -0.3795		\| −0.3795
	\| 0.3794		\| 0.3794
	\| 9.01		\| 9.01
Line 32:		Line 24:
	\| 67108864/66430125, {{monzo\| -14 -19 19 }}		\| 67108864/66430125, {{monzo\| -14 -19 19 }}
	\| {{mapping\| 285 452 662 }}		\| {{mapping\| 285 452 662 }}
	\| -0.4043		\| −0.4043
	\| 0.3117		\| 0.3117
	\| 7.41		\| 7.41
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	\| 3136/3125, 5120/5103, 40353607/39858075		\| 3136/3125, 5120/5103, 40353607/39858075
	\| {{mapping\| 285 452 662 800 }}		\| {{mapping\| 285 452 662 800 }}
	\| -0.2673		\| −0.2673
	\| 0.3596		\| 0.3596
	\| 8.54		\| 8.54
Line 46:		Line 38:
	\| 3025/3024, 3136/3125, 5120/5103, 12005/11979		\| 3025/3024, 3136/3125, 5120/5103, 12005/11979
	\| {{mapping\| 285 452 662 800 986 }}		\| {{mapping\| 285 452 662 800 986 }}
	\| -0.2289		\| −0.2289
	\| 0.3307		\| 0.3307
	\| 7.85		\| 7.85
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	\| 352/351, 676/675, 847/845, 3025/3024, 12005/11979		\| 352/351, 676/675, 847/845, 3025/3024, 12005/11979
	\| {{mapping\| 285 452 662 800 986 1055 }}		\| {{mapping\| 285 452 662 800 986 1055 }}
	\| -0.2618		\| −0.2618
	\| 0.3107		\| 0.3107
	\| 7.38		\| 7.38
Line 59:		Line 51:

	=== 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
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	\|-		\|-
	\| 3		\| 3
	\| 59\285<br>(36\285)		\| 59\285<br />(36\285)
	\| 248.42<br>(151.58)		\| 248.42<br />(151.58)
	\| 15/13<br>(12/11)		\| 15/13<br />(12/11)
	\| [[Hemimist]]		\| [[Hemimist]]
	\|-		\|-
	\| 3		\| 3
	\| 59\285<br>(23\285)		\| 59\285<br />(23\285)
	\| 496.84<br>(96.84)		\| 496.84<br />(96.84)
	\| 4/3<br>(256/243)		\| 4/3<br />(256/243)
	\| [[Misty]]		\| [[Misty]]
	\|-		\|-
	\| 19		\| 19
	\| 118\285<br>(2\285)		\| 118\285<br />(2\285)
	\| 496.84<br>(8.42)		\| 496.84<br />(8.42)
	\| 4/3<br>(15625/15552)		\| 4/3<br />(15625/15552)
	\| [[Enneadecal]] (5-limit)		\| [[Enneadecal]] (5-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}}

FloraC: Cleanup

2024-03-08T05:20:42Z

Cleanup

← Older revision		Revision as of 05:20, 8 March 2024
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	== Theory ==		== Theory ==
	285edo has a sharp tendency. It tempers out the [[misty comma]] and the [[enneadeca]] in the 5-limit; [[3136/3125]] and [[5120/5103]] in the 7-limit; [[3025/3024]] and [[3388/3375]] in the 11-limit; [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], and [[2080/2079]] in the 13-limit. It supports the 13-limit [[hemimist]] temperament.		285edo has a sharp tendency. The equal temperament [[tempering out\|tempers out]] the [[misty comma]] and the [[enneadeca]] in the 5-limit; [[3136/3125]] and [[5120/5103]] in the 7-limit; [[3025/3024]] and [[3388/3375]] in the 11-limit; [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], and [[2080/2079]] in the 13-limit. It supports the 13-limit [[hemimist]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|285}}		{{Harmonics in equal\|285\|intervals=prime}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
Line 24:		Line 24:
	\| 2.3		\| 2.3
	\| {{monzo\| 452 -285 }}		\| {{monzo\| 452 -285 }}
	\| [{{~~val~~\| 285 452 }}]		\| {{mapping\| 285 452 }}
	\| -0.3795		\| -0.3795
	\| 0.3794		\| 0.3794
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	\| 2.3.5		\| 2.3.5
	\| 67108864/66430125, {{monzo\| -14 -19 19 }}		\| 67108864/66430125, {{monzo\| -14 -19 19 }}
	\| [{{~~val~~\| 285 452 662 }}]		\| {{mapping\| 285 452 662 }}
	\| -0.4043		\| -0.4043
	\| 0.3117		\| 0.3117
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	\| 2.3.5.7		\| 2.3.5.7
	\| 3136/3125, 5120/5103, 40353607/39858075		\| 3136/3125, 5120/5103, 40353607/39858075
	\| [{{~~val~~\| 285 452 662 800 }}]		\| {{mapping\| 285 452 662 800 }}
	\| -0.2673		\| -0.2673
	\| 0.3596		\| 0.3596
Line 45:		Line 45:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 3136/3125, 5120/5103, 12005/11979		\| 3025/3024, 3136/3125, 5120/5103, 12005/11979
	\| [{{~~val~~\| 285 452 662 800 986 }}]		\| {{mapping\| 285 452 662 800 986 }}
	\| -0.2289		\| -0.2289
	\| 0.3307		\| 0.3307
Line 52:		Line 52:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 352/351, 676/675, 847/845, 3025/3024, 12005/11979		\| 352/351, 676/675, 847/845, 3025/3024, 12005/11979
	\| [{{~~val~~\| 285 452 662 800 986 1055 }}]		\| {{mapping\| 285 452 662 800 986 1055 }}
	\| -0.2618		\| -0.2618
	\| 0.3107		\| 0.3107
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	\|+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
	\|-		\|-
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	\| [[Enneadecal]] (5-limit)		\| [[Enneadecal]] (5-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

FloraC: Expansion

2023-06-11T07:31:44Z

Expansion

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|285}}
 ==Theory==
-{{Primes in edo|285}}
+== Theory ==

CompactStar: Created page with "{{Infobox ET}} {{EDO intro|285}} ==Theory== {{Primes in edo|285}}"

2023-05-23T22:18:35Z

Created page with "{{Infobox ET}} {{EDO intro|285}} ==Theory== {{Primes in edo|285}}"

New page

{{Infobox ET}}
{{EDO intro|285}}
==Theory==
{{Primes in edo|285}}