361edo - 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"

2026-03-13T13:33:17Z

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
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	\| [[Enneadecal]]		\| [[Enneadecal]]
	\|}		\|}
	<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

2025-02-21T05:52:23Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:52, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|361~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:01, 15 January 2025

2025-01-15T17:01:06Z

← Older revision		Revision as of 17:01, 15 January 2025
Line 26:		Line 26:
	\| {{monzo\| -572 361 }}		\| {{monzo\| -572 361 }}
	\| {{mapping\| 361 572 }}		\| {{mapping\| 361 572 }}
	\| 0.1798		\| +0.1798
	\| 0.1798		\| 0.1798
	\| 5.41		\| 5.41
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	\| {{monzo\| -36 11 8 }}, {{monzo\| -14 -19 19 }}		\| {{monzo\| -36 11 8 }}, {{monzo\| -14 -19 19 }}
	\| {{mapping\| 361 572 838 }}		\| {{mapping\| 361 572 838 }}
	\| 0.2230		\| +0.2230
	\| 0.1590		\| 0.1590
	\| 4.78		\| 4.78
Line 40:		Line 40:
	\| 4375/4374, 823543/819200, 2460375/2458624		\| 4375/4374, 823543/819200, 2460375/2458624
	\| {{mapping\| 361 572 838 1013 }}		\| {{mapping\| 361 572 838 1013 }}
	\| 0.3020		\| +0.3020
	\| 0.1941		\| 0.1941
	\| 5.84		\| 5.84
Line 67:		Line 67:
	\| [[Enneadecal]]		\| [[Enneadecal]]
	\|}		\|}
	<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

2024-11-16T13:18:16Z

Partial undo

← Older revision		Revision as of 13:18, 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
Line 34:		Line 43:
	\| 0.1941		\| 0.1941
	\| 5.84		\| 5.84
	~~{{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 50:		Line 66:
	\| 4/3<br />(225/224)		\| 4/3<br />(225/224)
	\| [[Enneadecal]]		\| [[Enneadecal]]
	~~{{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 01:40, 16 November 2024

2024-11-16T01:40:47Z

← Older revision		Revision as of 01:40, 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
Line 43:		Line 34:
	\| 0.1941		\| 0.1941
	\| 5.84		\| 5.84
	\|}		{{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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	\| 4/3<br />(225/224)		\| 4/3<br />(225/224)
	\| [[Enneadecal]]		\| [[Enneadecal]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 00:59, 16 November 2024

2024-11-16T00:59:31Z

← Older revision		Revision as of 00:59, 16 November 2024
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\|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
	\|-		\|-
Line 46:		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 60:		Line 62:
	\|-		\|-
	\| 19		\| 19
	\| 150\361<br>(2\361)		\| 150\361<br />(2\361)
	\| 498.61<br>(6.65)		\| 498.61<br />(6.65)
	\| 4/3<br>(225/224)		\| 4/3<br />(225/224)
	\| [[Enneadecal]]		\| [[Enneadecal]]
	\|}		\|}
	~~<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: Review

2024-01-11T19:57:33Z

Review

← Older revision		Revision as of 19:57, 11 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	361et is consistent to the [[9-odd-limit]], tempering out [[~~43046721~~/~~43025920~~]]~~, 2460375/2458624~~, [[703125/702464]], ~~48828125~~/~~48771072 and~~ [[~~4375~~/~~4374~~]] in the 7-limit. It [[support]]s [[submajor]].		361et is [[consistent]] to the [[9-odd-limit]] with flat tunings of [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]]. The equal temperament [[tempering out\|tempers out]] [[4375/4374]], [[703125/702464]], 2460375/2458624, [[43046721/43025920]], and 48828125/48771072 in the 7-limit. It [[support]]s the 5-limit [[submajor]] temperament.

	=== Odd harmonics ===		=== Odd 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\|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\|-572 361}}		\| {{monzo\| -572 361 }}
	\|{{mapping\|361 572}}		\| {{mapping\| 361 572 }}
	\| 0.1798		\| 0.1798
	\| 0.1798		\| 0.1798
	\| 5.41		\| 5.41
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-36 11 8}}, {{monzo\|-14 -19 19}}		\| {{monzo\| -36 11 8 }}, {{monzo\| -14 -19 19 }}
	\|{{mapping\|361 572 838}}		\| {{mapping\| 361 572 838 }}
	\| 0.2230		\| 0.2230
	\| 0.1590		\| 0.1590
	\| 4.78		\| 4.78
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|4375/4374, 2460375/2458624~~, 823543/819200~~		\| 4375/4374, 823543/819200, 2460375/2458624
	\|{{mapping\|361 572 838 1013}}		\| {{mapping\| 361 572 838 1013 }}
	\| 0.3020		\| 0.3020
	\| 0.1941		\| 0.1941
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	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|166\361		\| 166\361
	\|551.80		\| 551.80
	\|48/35		\| 48/35
	\|[[Emka]]		\| [[Emka]]
	\|-		\|-
	\|19		\| 19
	\|150\361<br>(2\361)		\| 150\361<br>(2\361)
	\|498.61<br>(6.65)		\| 498.61<br>(6.65)
	\|4/3<br>(225/224)		\| 4/3<br>(225/224)
	\|[[Enneadecal]]		\| [[Enneadecal]]
	\|}		\|}

	<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

Francium: Created page with "{{Infobox ET}} {{EDO intro|361}} == Theory == 361et is consistent to the 9-odd-limit, tempering out 43046721/43025920, 2460375/2458624, 703125/702464, 48828125/48..."

2023-12-30T12:56:53Z

Created page with "{{Infobox ET}} {{EDO intro|361}} == Theory == 361et is consistent to the 9-odd-limit, tempering out 43046721/43025920, 2460375/2458624, 703125/702464, 48828125/48..."

New page

{{Infobox ET}}
{{EDO intro|361}}

== Theory ==
361et is consistent to the [[9-odd-limit]], tempering out [[43046721/43025920]], 2460375/2458624, [[703125/702464]], 48828125/48771072 and [[4375/4374]] in the 7-limit. It [[support]]s [[submajor]].

=== Odd harmonics ===
{{Harmonics in equal|361}}

=== Subsets and supersets ===
361 factors into 192, with [[19edo]] as its only edo subset.

== 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 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|-572 361}}
|{{mapping|361 572}}
| 0.1798
| 0.1798
| 5.41
|-
|2.3.5
|{{monzo|-36 11 8}}, {{monzo|-14 -19 19}}
|{{mapping|361 572 838}}
| 0.2230
| 0.1590
| 4.78
|-
|2.3.5.7
|4375/4374, 2460375/2458624, 823543/819200
|{{mapping|361 572 838 1013}}
| 0.3020
| 0.1941
| 5.84
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator*
! Cents*
! Associated Ratio*
! Temperaments
|-
|1
|166\361
|551.80
|48/35
|[[Emka]]
|-
|19
|150\361 (2\361)
|498.61 (6.65)
|4/3 (225/224)
|[[Enneadecal]]
|}

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