275edo - Revision history

FloraC: Update link

2026-04-05T12:20:47Z

Update link

← Older revision		Revision as of 12:20, 5 April 2026
Line 21:		Line 21:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[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
	\|-		\|-
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	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 436 -275 }}		\| {{Monzo\| 436 -275 }}
	\| {{~~mapping~~\| 275 436 }}		\| {{Mapping\| 275 436 }}
	\| −0.1863		\| −0.1863
	\| 0.1862		\| 0.1862
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 24 -21 4 }}, {{monzo\| 19 10 -15 }}		\| {{Monzo\| 24 -21 4 }}, {{monzo\| 19 10 -15 }}
	\| {{~~mapping~~\| 275 436 639 }}		\| {{Mapping\| 275 436 639 }}
	\| −0.4184		\| −0.4184
	\| 0.3618		\| 0.3618
Line 43:		Line 43:
	\| 2.3.5.7		\| 2.3.5.7
	\| 6144/6125, 10976/10935, 9882516/9765625		\| 6144/6125, 10976/10935, 9882516/9765625
	\| {{~~mapping~~\| 275 436 639 772 }}		\| {{Mapping\| 275 436 639 772 }}
	\| −0.3051		\| −0.3051
	\| 0.3698		\| 0.3698
Line 50:		Line 50:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 441/440, 4000/3993, 6144/6125, 10976/10935		\| 441/440, 4000/3993, 6144/6125, 10976/10935
	\| {{~~mapping~~\| 275 436 639 772 952 }} (275e)		\| {{Mapping\| 275 436 639 772 952 }} (275e)
	\| −0.4096		\| −0.4096
	\| 0.3912		\| 0.3912
Line 57:		Line 57:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 364/363, 441/440, 676/675, 6144/6125, 10976/10935		\| 364/363, 441/440, 676/675, 6144/6125, 10976/10935
	\| {{~~mapping~~\| 275 436 639 772 952 1018 }} (275e)		\| {{Mapping\| 275 436 639 772 952 1018 }} (275e)
	\| −0.4158		\| −0.4158
	\| 0.3574		\| 0.3574
Line 67:		Line 67:
	\|+ style="font-size: 105%;" \| 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 98:		Line 98:
	\|-		\|-
	\| 11		\| 11
	\| 114\275<br />(11\275)		\| 114\275<br>(11\275)
	\| 497.45<br />(48.00)		\| 497.45<br>(48.00)
	\| 4/3<br />(36/35)		\| 4/3<br>(36/35)
	\| [[Hendecatonic]]		\| [[Hendecatonic (temperament)\|Hendecatonic]]
	\|}		\|}
	<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		<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

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"

2026-03-13T13:32:40Z

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 103:		Line 103:
	\| [[Hendecatonic]]		\| [[Hendecatonic]]
	\|}		\|}
	<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

ArrowHead294 at 23:09, 20 February 2025

2025-02-20T23:09:47Z

← Older revision		Revision as of 23:09, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|275~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:50, 15 January 2025

2025-01-15T17:50:26Z

← Older revision		Revision as of 17:50, 15 January 2025
Line 13:		Line 13:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 275 factors into ~~5<sup>2</sup> × 11~~, 275edo has subset edos {{EDOs\| 5, 11, 25 and 55 }}.		Since 275 factors into {{factorisation\|275}}, 275edo has subset edos {{EDOs\| 5, 11, 25 and 55 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 30:		Line 30:
	\| {{monzo\| 436 -275 }}		\| {{monzo\| 436 -275 }}
	\| {{mapping\| 275 436 }}		\| {{mapping\| 275 436 }}
	\| ~~−0~~.1863		\| −0.1863
	\| 0.1862		\| 0.1862
	\| 4.27		\| 4.27
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	\| {{monzo\| 24 -21 4 }}, {{monzo\| 19 10 -15 }}		\| {{monzo\| 24 -21 4 }}, {{monzo\| 19 10 -15 }}
	\| {{mapping\| 275 436 639 }}		\| {{mapping\| 275 436 639 }}
	\| ~~−0~~.4184		\| −0.4184
	\| 0.3618		\| 0.3618
	\| 8.29		\| 8.29
Line 44:		Line 44:
	\| 6144/6125, 10976/10935, 9882516/9765625		\| 6144/6125, 10976/10935, 9882516/9765625
	\| {{mapping\| 275 436 639 772 }}		\| {{mapping\| 275 436 639 772 }}
	\| ~~−0~~.3051		\| −0.3051
	\| 0.3698		\| 0.3698
	\| 8.48		\| 8.48
Line 51:		Line 51:
	\| 441/440, 4000/3993, 6144/6125, 10976/10935		\| 441/440, 4000/3993, 6144/6125, 10976/10935
	\| {{mapping\| 275 436 639 772 952 }} (275e)		\| {{mapping\| 275 436 639 772 952 }} (275e)
	\| ~~−0~~.4096		\| −0.4096
	\| 0.3912		\| 0.3912
	\| 8.97		\| 8.97
Line 58:		Line 58:
	\| 364/363, 441/440, 676/675, 6144/6125, 10976/10935		\| 364/363, 441/440, 676/675, 6144/6125, 10976/10935
	\| {{mapping\| 275 436 639 772 952 1018 }} (275e)		\| {{mapping\| 275 436 639 772 952 1018 }} (275e)
	\| ~~−0~~.4158		\| −0.4158
	\| 0.3574		\| 0.3574
	\| 8.19		\| 8.19
Line 103:		Line 103:
	\| [[Hendecatonic]]		\| [[Hendecatonic]]
	\|}		\|}
	<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

2024-11-16T12:45:37Z

Partial undo

← Older revision		Revision as of 12:45, 16 November 2024
Line 16:		Line 16:

	== 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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	\| 0.3574		\| 0.3574
	\| 8.19		\| 8.19
	~~{{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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	\| 4/3<br />(36/35)		\| 4/3<br />(36/35)
	\| [[Hendecatonic]]		\| [[Hendecatonic]]
	~~{{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 04:00, 16 November 2024

2024-11-16T04:00:17Z

← Older revision		Revision as of 04:00, 16 November 2024
Line 16:		Line 16:

	== 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\| 436 -275 }}		\| {{monzo\| 436 -275 }}
	\| {{mapping\| 275 436 }}		\| {{mapping\| 275 436 }}
	\| -0.1863		\| −0.1863
	\| 0.1862		\| 0.1862
	\| 4.27		\| 4.27
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	\| {{monzo\| 24 -21 4 }}, {{monzo\| 19 10 -15 }}		\| {{monzo\| 24 -21 4 }}, {{monzo\| 19 10 -15 }}
	\| {{mapping\| 275 436 639 }}		\| {{mapping\| 275 436 639 }}
	\| -0.4184		\| −0.4184
	\| 0.3618		\| 0.3618
	\| 8.29		\| 8.29
Line 43:		Line 35:
	\| 6144/6125, 10976/10935, 9882516/9765625		\| 6144/6125, 10976/10935, 9882516/9765625
	\| {{mapping\| 275 436 639 772 }}		\| {{mapping\| 275 436 639 772 }}
	\| -0.3051		\| −0.3051
	\| 0.3698		\| 0.3698
	\| 8.48		\| 8.48
Line 50:		Line 42:
	\| 441/440, 4000/3993, 6144/6125, 10976/10935		\| 441/440, 4000/3993, 6144/6125, 10976/10935
	\| {{mapping\| 275 436 639 772 952 }} (275e)		\| {{mapping\| 275 436 639 772 952 }} (275e)
	\| -0.4096		\| −0.4096
	\| 0.3912		\| 0.3912
	\| 8.97		\| 8.97
Line 57:		Line 49:
	\| 364/363, 441/440, 676/675, 6144/6125, 10976/10935		\| 364/363, 441/440, 676/675, 6144/6125, 10976/10935
	\| {{mapping\| 275 436 639 772 952 1018 }} (275e)		\| {{mapping\| 275 436 639 772 952 1018 }} (275e)
	\| -0.4158		\| −0.4158
	\| 0.3574		\| 0.3574
	\| 8.19		\| 8.19
	\|}		{{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
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	\|-		\|-
	\| 11		\| 11
	\| 114\275<br>(11\275)		\| 114\275<br />(11\275)
	\| 497.45<br>(48.00)		\| 497.45<br />(48.00)
	\| 4/3<br>(36/35)		\| 4/3<br />(36/35)
	\| [[Hendecatonic]]		\| [[Hendecatonic]]
	\|}		{{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

2024-03-08T06:41:24Z

Cleanup

← Older revision		Revision as of 06:41, 8 March 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	If harmonic 5 is used, 275et tends very sharp. It tempers out {{monzo\| 24 -21 4 }} ([[vulture comma]]) and {{monzo\| 19 10 -15 }} ([[trisedodge comma]]) in the 5-limit; [[6144/6125]] and [[10976/10935]] in the 7-limit.		If [[harmonic]] [[5/1\|5]] is used, 275et tends very sharp. It [[tempering out\|tempers out]] {{monzo\| 24 -21 4 }} ([[vulture comma]]) and {{monzo\| 19 10 -15 }} (trisedodge comma) in the 5-limit; [[6144/6125]] and [[10976/10935]] in the 7-limit.

	The 275e val {{val\| 275 436 639 772 '''952''' }} being the best, tempers out [[441/440]], [[4000/3993]], [[14700/14641]], and [[19712/19683]]. This can be extended to the 13-limit through [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]].		The 275e val {{val\| 275 436 639 772 '''952''' }} being the best, tempers out [[441/440]], [[4000/3993]], [[14700/14641]], and [[19712/19683]]. This can be extended to the 13-limit through [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]].

	The 275 val {{val\| 275 436 639 772 '''951''' }} tempers out [[3025/3024]], [[3773/3750]], [[8019/8000]]. This can be extended to the 13-limit through [[352/351]], 676/675, [[1716/1715]], [[2200/2197]], and [[3584/3575]].		The 275 val {{val\| 275 436 639 772 '''951''' }} tempers out [[3025/3024]], 3773/3750, [[8019/8000]]. This can be extended to the 13-limit through [[352/351]], 676/675, [[1716/1715]], [[2200/2197]], and 3584/3575.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|275\|intervals=prime~~\|columns=11~~}}		{{Harmonics in equal\|275\|intervals=prime}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
Line 28:		Line 28:
	\| 2.3		\| 2.3
	\| {{monzo\| 436 -275 }}		\| {{monzo\| 436 -275 }}
	\| [{{~~val~~\| 275 436 }}]		\| {{mapping\| 275 436 }}
	\| -0.1863		\| -0.1863
	\| 0.1862		\| 0.1862
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	\| 2.3.5		\| 2.3.5
	\| {{monzo\| 24 -21 4 }}, {{monzo\| 19 10 -15 }}		\| {{monzo\| 24 -21 4 }}, {{monzo\| 19 10 -15 }}
	\| [{{~~val~~\| 275 436 639 }}]		\| {{mapping\| 275 436 639 }}
	\| -0.4184		\| -0.4184
	\| 0.3618		\| 0.3618
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	\| 2.3.5.7		\| 2.3.5.7
	\| 6144/6125, 10976/10935, 9882516/9765625		\| 6144/6125, 10976/10935, 9882516/9765625
	\| [{{~~val~~\| 275 436 639 772 }}]		\| {{mapping\| 275 436 639 772 }}
	\| -0.3051		\| -0.3051
	\| 0.3698		\| 0.3698
Line 49:		Line 49:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 441/440, 4000/3993, 6144/6125, 10976/10935		\| 441/440, 4000/3993, 6144/6125, 10976/10935
	\| [{{~~val~~\| 275 436 639 772 952 }}] (275e)		\| {{mapping\| 275 436 639 772 952 }} (275e)
	\| -0.4096		\| -0.4096
	\| 0.3912		\| 0.3912
Line 56:		Line 56:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 364/363, 441/440, 676/675, 6144/6125, 10976/10935		\| 364/363, 441/440, 676/675, 6144/6125, 10976/10935
	\| [{{~~val~~\| 275 436 639 772 952 1018 }}] (275e)		\| {{mapping\| 275 436 639 772 952 1018 }} (275e)
	\| -0.4158		\| -0.4158
	\| 0.3574		\| 0.3574
Line 66:		Line 66:
	\|+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
	\|-		\|-
Line 101:		Line 101:
	\| [[Hendecatonic]]		\| [[Hendecatonic]]
	\|}		\|}
			<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: +subsets and supersets; style; -redundant category

2023-06-09T05:32:09Z

+subsets and supersets; style; -redundant category

← Older revision		Revision as of 05:32, 9 June 2023
Line 11:		Line 11:
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|275\|intervals=prime\|columns=11}}		{{Harmonics in equal\|275\|intervals=prime\|columns=11}}

			=== Subsets and supersets ===
			Since 275 factors into 5<sup>2</sup> × 11, 275edo has subset edos {{EDOs\| 5, 11, 25 and 55 }}.

	== 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]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
Line 98:		Line 101:
	\| [[Hendecatonic]]		\| [[Hendecatonic]]
	\|}		\|}

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

Aura at 18:21, 22 December 2022

2022-12-22T18:21:44Z

← Older revision		Revision as of 18:21, 22 December 2022
Line 99:		Line 99:
	\|}		\|}

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

FloraC: +RTT table and rank-2 temperaments

2022-11-04T18:25:16Z

+RTT table and rank-2 temperaments

@@ Line 5: / Line 5: @@
 If harmonic 5 is used, 275et tends very sharp. It tempers out {{monzo| 24 -21 4 }} ([[vulture comma]]) and {{monzo| 19 10 -15 }} ([[trisedodge comma]]) in the 5-limit; [[6144/6125]] and [[10976/10935]] in the 7-limit.
-The 275e val {{val| 275 436 639 772 '''952''' }} being the best, tempers out [[441/440]], [[4000/3993]], [[14700/14641]], and [[19712/19683]]. This can be extended to the 13-limit through [[364/363]], [[676/675]], [[1001/1000]], and [[2080/2079]].
+The 275e val {{val| 275 436 639 772 '''952''' }} being the best, tempers out [[441/440]], [[4000/3993]], [[14700/14641]], and [[19712/19683]]. This can be extended to the 13-limit through [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]].
 The 275 val {{val| 275 436 639 772 '''951''' }} tempers out [[3025/3024]], [[3773/3750]], [[8019/8000]]. This can be extended to the 13-limit through [[352/351]], 676/675, [[1716/1715]], [[2200/2197]], and [[3584/3575]].
@@ Line 11: / Line 11: @@
 === Prime harmonics ===
 {{Harmonics in equal|275|intervals=prime|columns=11}}
 [[Category:Equal divisions of the octave]]