347edo - 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"

2026-03-13T13:33:18Z

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 87:		Line 87:
	\| [[Countermeantone]]		\| [[Countermeantone]]
	\|}		\|}
	<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

	[[Category:Hemimean]]		[[Category:Hemimean]]
	[[Category:Sengagen]]		[[Category:Sengagen]]

ArrowHead294 at 14:44, 20 February 2025

2025-02-20T14:44:34Z

← Older revision		Revision as of 14:44, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|347~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	The equal temperament [[tempering out\|tempers out]] {{monzo\| 32 -7 -9 }} ([[escapade comma]]) and {{monzo\| 54 -37 2 }} ([[monzisma]]), [[3136/3125]], 420175/419904, and 5250987/5242880 in the 7-limit. It provides an excellent tuning for [[sengagen]], the 99 & 248 temperament tempering out both 3136/3125 and 420175/419904, and the rank-3 [[hemimean]] temperament tempering out 3136/3125.		The equal temperament [[tempering out\|tempers out]] {{monzo\| 32 -7 -9 }} ([[escapade comma]]) and {{monzo\| 54 -37 2 }} ([[monzisma]]), [[3136/3125]], 420175/419904, and 5250987/5242880 in the 7-limit. It provides an excellent tuning for [[sengagen]], the {{nowrap\|99 & 248}} temperament tempering out both 3136/3125 and 420175/419904, and the rank-3 [[hemimean]] temperament tempering out 3136/3125.

	Extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far off the mark. It makes more sense as a 2.3.5.7.13 [[subgroup]] temperament, where it tempers out [[676/675]] and [[4096/4095]], or as a 2.3.5.7.13.19 subgroup temperament, where it tempers out [[1521/1520]] and [[1729/1728]].		Extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far off the mark. It makes more sense as a 2.3.5.7.13 [[subgroup]] temperament, where it tempers out [[676/675]] and [[4096/4095]], or as a 2.3.5.7.13.19 subgroup temperament, where it tempers out [[1521/1520]] and [[1729/1728]].

ArrowHead294 at 17:01, 15 January 2025

2025-01-15T17:01:20Z

← Older revision		Revision as of 17:01, 15 January 2025
Line 87:		Line 87:
	\| [[Countermeantone]]		\| [[Countermeantone]]
	\|}		\|}
	<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

	[[Category:Hemimean]]		[[Category:Hemimean]]
	[[Category:Sengagen]]		[[Category:Sengagen]]

ArrowHead294: Partial undo

2024-11-16T13:05:25Z

Partial undo

← Older revision		Revision as of 13:05, 16 November 2024
Line 14:		Line 14:

	== 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 36:		Line 45:
	\| 0.2259		\| 0.2259
	\| 6.53		\| 6.53
	~~{{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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	\| 104976/78125		\| 104976/78125
	\| [[Countermeantone]]		\| [[Countermeantone]]
	~~{{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

	[[Category:Hemimean]]		[[Category:Hemimean]]
	[[Category:Sengagen]]		[[Category:Sengagen]]

ArrowHead294 at 02:39, 16 November 2024

2024-11-16T02:39:34Z

← Older revision		Revision as of 02:39, 16 November 2024
Line 14:		Line 14:

	== 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 44:		Line 36:
	\| 0.2259		\| 0.2259
	\| 6.53		\| 6.53
	\|}		{{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 84:		Line 70:
	\| 104976/78125		\| 104976/78125
	\| [[Countermeantone]]		\| [[Countermeantone]]
	\|}		{{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}}

	[[Category:Hemimean]]		[[Category:Hemimean]]
	[[Category:Sengagen]]		[[Category:Sengagen]]

FloraC: Review

2023-12-10T12:37:18Z

Review

← Older revision		Revision as of 12:37, 10 December 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	The equal temperament [[tempering out\|tempers out]] [[3136/3125]] ~~and~~ 420175/419904 in the 7-limit~~, and~~ provides an excellent tuning for [[sengagen]], the 99 & 248 temperament tempering out both, and the ~~planar~~ [[hemimean]] temperament tempering out 3136/3125.		The equal temperament [[tempering out\|tempers out]] {{monzo\| 32 -7 -9 }} ([[escapade comma]]) and {{monzo\| 54 -37 2 }} ([[monzisma]]), [[3136/3125]], 420175/419904, and 5250987/5242880 in the 7-limit. It provides an excellent tuning for [[sengagen]], the 99 & 248 temperament tempering out both 3136/3125 and 420175/419904, and the rank-3 [[hemimean]] temperament tempering out 3136/3125.

			Extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far off the mark. It makes more sense as a 2.3.5.7.13 [[subgroup]] temperament, where it tempers out [[676/675]] and [[4096/4095]], or as a 2.3.5.7.13.19 subgroup temperament, where it tempers out [[1521/1520]] and [[1729/1728]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 13:		Line 15:
	== 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\|550 -347}}		\| {{monzo\| 550 -347 }}
	\|{{mapping\|347 550}}		\| {{mapping\| 347 550 }}
	\| -0.0197		\| -0.0197
	\| 0.0197		\| 0.0197
	\| 0.57		\| 0.57
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|32 -7 -9}}, {{monzo\|-22 30 -11}}		\| {{monzo\| 32 -7 -9 }}, {{monzo\| -22 30 -11 }}
	\|{{mapping\|347 550 806}}		\| {{mapping\| 347 550 806 }}
	\| -0.1576		\| -0.1576
	\| 0.1956		\| 0.1956
	\| 5.66		\| 5.66
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|3136/3125, 420175/419904, 5250987/5242880		\| 3136/3125, 420175/419904, 5250987/5242880
	\|{{mapping\|347 550 806 974}}		\| {{mapping\| 347 550 806 974 }}
	\| -0.0713		\| -0.0713
	\| 0.2259		\| 0.2259
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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
	\|-		\|-
	\|1		\| 1
	\|7\347		\| 7\347
	\|24.21		\| 24.21
	\|686/675		\| 686/675
	\|[[Sengagen]]		\| [[Sengagen]]
	\|-		\|-
	\|1		\| 1
	\|16\347		\| 16\347
	\|55.33		\| 55.33
	\|16875/16384		\| 16875/16384
	\|[[Escapade]]		\| [[Escapade]]
	\|-		\|-
	\|1		\| 1
	\|69\347		\| 69\347
	\|238.62		\| 238.62
	\|147/128		\| 147/128
	\|[[Tokko]]		\| [[Tokko]]
	\|-		\|-
	\|1		\| 1
	\|72\347		\| 72\347
	\|248.99		\| 248.99
	\|{{monzo\|-26 18 -1}}		\| {{monzo\| -26 18 -1 }}
	\|[[Monzismic]]		\| [[Monzismic]]
	\|-		\|-
	\|1		\| 1
	\|146\347		\| 146\347
	\|504.90		\| 504.90
	\|104976/78125		\| 104976/78125
	\|[[Countermeantone]]		\| [[Countermeantone]]
	\|}		\|}

	<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

	[[Category:Hemimean]]		[[Category:Hemimean]]
	[[Category:Sengagen]]		[[Category:Sengagen]]

Francium: /* Rank-2 temperaments */

2023-12-08T11:26:55Z

Rank-2 temperaments

← Older revision		Revision as of 11:26, 8 December 2023
Line 83:		Line 83:
	\|[[Countermeantone]]		\|[[Countermeantone]]
	\|}		\|}

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

	[[Category:Hemimean]]		[[Category:Hemimean]]
	[[Category:Sengagen]]		[[Category:Sengagen]]

Francium: +regular temperament properties

2023-12-08T11:26:02Z

+regular temperament properties

@@ Line 2: / Line 2: @@
 {{EDO intro|347}}
 The equal temperament [[tempering out|tempers out]] [[3136/3125]] and 420175/419904 in the 7-limit, and provides an excellent tuning for [[sengagen]], the 99 &amp; 248 temperament tempering out both, and the planar [[hemimean]] temperament tempering out 3136/3125.
@@ Line 9: / Line 10: @@
 === Subsets and supersets ===
 edo is the 69th [[prime edo]].
 [[Category:Hemimean]]
 [[Category:Sengagen]]

FloraC: Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories

2023-11-15T07:01:32Z

Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories

← Older revision		Revision as of 07:01, 15 November 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''347EDO''' is the [[~~EDO\|~~equal division of the octave]] into~~ 347 parts of 3.45821 [[cent]]s each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides an excellent tuning for the temperament tempering out both, the 49&50 temperament, and the planar hemimean temperament tempering out 3136/3125.		{{EDO intro\|347}}

	~~347EDO~~ is the 69th [[prime ~~EDO~~]].		The equal temperament [[tempering out\|tempers out]] [[3136/3125]] and 420175/419904 in the 7-limit, and provides an excellent tuning for [[sengagen]], the 99 & 248 temperament tempering out both, and the planar [[hemimean]] temperament tempering out 3136/3125.

			=== Prime harmonics ===
			{{Harmonics in equal\|347}}

			=== Subsets and supersets ===
			347edo is the 69th [[prime edo]].

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	~~[[Category:Prime EDO]]~~
	[[Category:Hemimean]]		[[Category:Hemimean]]
			[[Category:Sengagen]]

Plumtree: Infobox ET added

2022-10-04T21:51:42Z

Infobox ET added

← Older revision		Revision as of 21:51, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''347EDO''' is the [[EDO\|equal division of the octave]] into 347 parts of 3.45821 [[cent]]s each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides an excellent tuning for the temperament tempering out both, the 49&50 temperament, and the planar hemimean temperament tempering out 3136/3125.		'''347EDO''' is the [[EDO\|equal division of the octave]] into 347 parts of 3.45821 [[cent]]s each. It tempers out 3136/3125 and 420175/419904 in the 7-limit, and provides an excellent tuning for the temperament tempering out both, the 49&50 temperament, and the planar hemimean temperament tempering out 3136/3125.