482edo - Revision history

ArrowHead294 at 23:04, 20 February 2025

2025-02-20T23:04:34Z

← Older revision		Revision as of 23:04, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|482~~}}		{{ED intro}}

	== Theory ==		== Theory ==
Line 15:		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]]
Line 44:		Line 45:
	\| 0.1389		\| 0.1389
	\| 5.58		\| 5.58
	\|-		\|- style="border-top: double;"
	\| style="border-top: double;" \| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	~~\| style="border-top: double;"~~ \| 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536		\| 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536
	~~\| style="border-top: double;"~~ \| {{mapping\| 482 764 1119 1353 1667 1783 }} (482f)		\| {{mapping\| 482 764 1119 1353 1667 1783 }} (482f)
	~~\| style="border-top: double;"~~ \| +0.1612		\| +0.1612
	~~\| style="border-top: double;"~~ \| 0.1692		\| 0.1692
	~~\| style="border-top: double;"~~ \| 6.80		\| 6.80
	\|-		\|- style="border-top: double;"
	\| style="border-top: double;" \| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	~~\| style="border-top: double;"~~ \| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721		\| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721
	~~\| style="border-top: double;"~~ \| {{mapping\| 482 764 1119 1353 1667 1784 }} (482)		\| {{mapping\| 482 764 1119 1353 1667 1784 }} (482)
	~~\| style="border-top: double;"~~ \| +0.0491		\| +0.0491
	~~\| style="border-top: double;"~~ \| 0.1880		\| 0.1880
	~~\| style="border-top: double;"~~ \| 7.55		\| 7.55
	\|}		\|}

FloraC: Cleanup; +subsets and supersets

2023-11-03T06:20:56Z

Cleanup; +subsets and supersets

← Older revision		Revision as of 06:20, 3 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~Prime harmonics with less than 17% (~~1 ~~standard deviation error) in 482edo are~~ 3, 5, 7, 17, 31, 37. 11 and 13 have rather large errors, but they are reasonable to work with.		482edo has good approximations of [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], [[17/1\|17]], [[31/1\|31]], and [[37/1\|37]]. [[11/1\|11]] and [[13/1\|13]] have rather large errors, but they are reasonable to work with.

	In the 7-limit, 482edo provides excellent tuning for the [[tertiaseptal]] temperament.		In the 7-limit, 482edo provides excellent tuning for the [[tertiaseptal]] temperament.
Line 9:		Line 9:
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|482}}		{{Harmonics in equal\|482}}

			=== Subsets and supersets ===
			Since 482 factors into {{factorization\|482}}, 482edo contains [[2edo]] and [[241edo]] as subsets.

	== 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 (¢)
	! colspan="2" \| Tuning ~~error~~		! colspan="2" \| Tuning Error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
Line 23:		Line 26:
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| 24 -21 4 }}, {{monzo\| -59 5 22 }}		\| {{monzo\| 24 -21 4 }}, {{monzo\| -59 5 22 }}
	\| [{{~~val~~\| 482 764 1119 }}]		\| {{mapping\| 482 764 1119 }}
	\| +0.0353		\| +0.0353
	\| 0.0587		\| 0.0587
Line 30:		Line 33:
	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 65625/65536, {{monzo\| 8 -20 9 1 }}		\| 2401/2400, 65625/65536, {{monzo\| 8 -20 9 1 }}
	\| [{{~~val~~\| 482 764 1119 1353 }}]		\| {{mapping\| 482 764 1119 1353 }}
	\| +0.0587		\| +0.0587
	\| 0.1018		\| 0.1018
Line 37:		Line 40:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 9801/9800, 19712/19683, 65625/65536		\| 2401/2400, 9801/9800, 19712/19683, 65625/65536
	\| [{{~~val~~\| 482 764 1119 1353 1667 }}]		\| {{mapping\| 482 764 1119 1353 1667 }}
	\| +0.1111		\| +0.1111
	\| 0.1389		\| 0.1389
	\| 5.58		\| 5.58
	\|-		\|-
	\| 2.3.5.7.11.13		\| style="border-top: double;" \| 2.3.5.7.11.13
	\| 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536		\| style="border-top: double;" \| 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536
	\| [{{~~val~~\| 482 764 1119 1353 1667 1783 }}] (482f)		\| style="border-top: double;" \| {{mapping\| 482 764 1119 1353 1667 1783 }} (482f)
	\| +0.1612		\| style="border-top: double;" \| +0.1612
	\| 0.1692		\| style="border-top: double;" \| 0.1692
	\| 6.80		\| style="border-top: double;" \| 6.80
	\|-		\|-
	\| 2.3.5.7.11.13		\| style="border-top: double;" \| 2.3.5.7.11.13
	\| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721		\| style="border-top: double;" \| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721
	\| [{{~~val~~\| 482 764 1119 1353 1667 1784 }}] (482)		\| style="border-top: double;" \| {{mapping\| 482 764 1119 1353 1667 1784 }} (482)
	\| +0.0491		\| style="border-top: double;" \| +0.0491
	\| 0.1880		\| style="border-top: double;" \| 0.1880
	\| 7.55		\| style="border-top: double;" \| 7.55
	\|}		\|}

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

BudjarnLambeth at 06:36, 9 July 2023

2023-07-09T06:36:35Z

← Older revision		Revision as of 06:36, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|482}}		{{EDO intro\|482}}

BudjarnLambeth at 05:46, 9 July 2023

2023-07-09T05:46:07Z

← Older revision		Revision as of 05:46, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|482}}		{{EDO intro\|482}}

Plumtree: Infobox ET added

2022-10-04T21:57:21Z

Infobox ET added

← Older revision		Revision as of 21:57, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	{{EDO intro\|482}}		{{EDO intro\|482}}

Fredg999 category edits: Sort key

2022-07-04T00:59:40Z

Sort key

← Older revision		Revision as of 00:59, 4 July 2022
Line 56:		Line 56:
	\|}		\|}

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

FloraC: +data for an alternative 13-limit mapping that's actually better

2022-04-22T17:38:50Z

+data for an alternative 13-limit mapping that's actually better

← Older revision		Revision as of 17:38, 22 April 2022
Line 17:		Line 17:
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3.5		\| 2.3.5
Line 40:		Line 40:
	\| 0.1389		\| 0.1389
	\| 5.58		\| 5.58
			\|-
			\| 2.3.5.7.11.13
			\| 676/675, 1001/1000, 1716/1715, 10648/10647, 65625/65536
			\| [{{val\| 482 764 1119 1353 1667 1783 }}] (482f)
			\| +0.1612
			\| 0.1692
			\| 6.80
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721		\| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721
	\| [{{val\| 482 764 1119 1353 1667 1784 }}]		\| [{{val\| 482 764 1119 1353 1667 1784 }}] (482)
	\| +0.0491		\| +0.0491
	\| 0.1880		\| 0.1880

FloraC: Rework RTT table

2022-04-22T17:14:17Z

Rework RTT table

← Older revision		Revision as of 17:14, 22 April 2022
Line 22:		Line 22:
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| 24 -21 4 }}, {{monzo\| -59 5 22 }}		\| {{monzo\| 24 -21 4 }}, {{monzo\| -59 5 22 }}
	\| [{{val\| 482 764 1119}}]		\| [{{val\| 482 764 1119 }}]
	\| 0.0353		\| +0.0353
	\| 0.0587		\| 0.0587
	\|		\| 4.33
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| ~~{{monzo\| -6 3 9 -7}}~~, ~~{{monzo\| -26 -1 1 9 }}~~, {{monzo\| 8 -20 9 1 }}		\| 2401/2400, 65625/65536, {{monzo\| 8 -20 9 1 }}
	\| [{{val\| 482 764 1119 1353 }}]		\| [{{val\| 482 764 1119 1353 }}]
	\| 0.0587		\| +0.0587
	\| 0.1018		\| 0.1018
	\| 4.09		\| 4.09
Line 37:		Line 37:
	\| 2401/2400, 9801/9800, 19712/19683, 65625/65536		\| 2401/2400, 9801/9800, 19712/19683, 65625/65536
	\| [{{val\| 482 764 1119 1353 1667 }}]		\| [{{val\| 482 764 1119 1353 1667 }}]
	\| 0.1111		\| +0.1111
	\| 0.1389		\| 0.1389
	\|		\| 5.58
	\|-		\|-
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721		\| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721
	\| [{{val\| 482 764 1119 1353 1667 1784 }}]		\| [{{val\| 482 764 1119 1353 1667 1784 }}]
	\| 0.0491		\| +0.0491
	\| 0.1880		\| 0.1880
	\|		\| 7.55
	\|}		\|}

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]

FloraC: Cleanup, +categories

2022-04-22T17:11:01Z

Cleanup, +categories

← Older revision		Revision as of 17:11, 22 April 2022
Line 2:		Line 2:

	== Theory ==		== Theory ==
	~~{{Harmonics in equal\|482}}~~
	Prime harmonics with less than 17% (1 standard deviation error) in 482edo are 3, 5, 7, 17, 31, 37. 11 and 13 have rather large errors, but they are reasonable to work with.		Prime harmonics with less than 17% (1 standard deviation error) in 482edo are 3, 5, 7, 17, 31, 37. 11 and 13 have rather large errors, but they are reasonable to work with.

	In the 7-limit, 482edo provides excellent tuning for the [[tertiaseptal]] temperament.		In the 7-limit, 482edo provides excellent tuning for the [[tertiaseptal]] temperament.

			=== Prime harmonics ===
			{{Harmonics in equal\|482}}

	== 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]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	8ve stretch (¢)		! colspan="2" \| Tuning error
	! colspan="2" \|Tuning error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		![[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		![[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|[24, -21, ~~4⟩, [~~-59, 5~~, 22⟩~~		\| {{monzo\| 24 -21 4 }}, {{monzo\| -59 5 22 }}
	\|[{{val\| 482 764 1119}}]		\| [{{val\| 482 764 1119}}]
	\|0.~~035344~~		\| 0.0353
	\|0.~~058672~~		\| 0.0587
	\|		\|
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|[-6, 3, 9, -7⟩, [-26, -1, 1, ~~9⟩, [~~8, -20, 9~~, 1⟩~~		\| {{monzo\| -6 3 9 -7}}, {{monzo\| -26 -1 1 9 }}, {{monzo\| 8 -20 9 1 }}
	\|[{{val\| 482 764 1119 1353}}]		\| [{{val\| 482 764 1119 1353 }}]
	\|0.~~058672~~		\| 0.0587
	\|0.~~101802~~		\| 0.1018
	\|4.~~089~~		\| 4.09
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|2401/2400, 9801/9800, 19712/19683, 65625/65536		\| 2401/2400, 9801/9800, 19712/19683, 65625/65536
	\|[{{val\| 482 764 1119 1353 1667}}]		\| [{{val\| 482 764 1119 1353 1667 }}]
	\|0.~~111136~~		\| 0.1111
	\|0.~~138937~~		\| 0.1389
	\|		\|
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|625/624, 847/845, 2401/2400, 9801/9800, 35750/35721		\| 625/624, 847/845, 2401/2400, 9801/9800, 35750/35721
	\|[{{val\| 482 764 1119 1353 1667 1784}}]		\| [{{val\| 482 764 1119 1353 1667 1784 }}]
	\|0.~~049077~~		\| 0.0491
	\|0.~~187961~~		\| 0.1880
	\|		\|
	\|}		\|}

			[[Category:Equal divisions of the octave]]

Eliora: Created page with "{{EDO intro|482}} == Theory == {{Harmonics in equal|482}} Prime harmonics with less than 17% (1 standard deviation error) in 482edo are 3, 5, 7, 17, 31, 37. 11 and 13 have ra..."

2022-04-22T12:14:03Z

Created page with "{{EDO intro|482}} == Theory == {{Harmonics in equal|482}} Prime harmonics with less than 17% (1 standard deviation error) in 482edo are 3, 5, 7, 17, 31, 37. 11 and 13 have ra..."

New page

{{EDO intro|482}}

== Theory ==
{{Harmonics in equal|482}}
Prime harmonics with less than 17% (1 standard deviation error) in 482edo are 3, 5, 7, 17, 31, 37. 11 and 13 have rather large errors, but they are reasonable to work with.

In the 7-limit, 482edo provides excellent tuning for the [[tertiaseptal]] temperament.

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |Subgroup
! rowspan="2" |[[Comma list]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal
8ve stretch (¢)
! colspan="2" |Tuning error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3.5
|[24, -21, 4⟩, [-59, 5, 22⟩
|[{{val| 482 764 1119}}]
|0.035344
|0.058672
|
|-
|2.3.5.7
|[-6, 3, 9, -7⟩, [-26, -1, 1, 9⟩, [8, -20, 9, 1⟩
|[{{val| 482 764 1119 1353}}]
|0.058672
|0.101802
|4.089
|-
|2.3.5.7.11
|2401/2400, 9801/9800, 19712/19683, 65625/65536
|[{{val| 482 764 1119 1353 1667}}]
|0.111136
|0.138937
|
|-
|2.3.5.7.11.13
|625/624, 847/845, 2401/2400, 9801/9800, 35750/35721
|[{{val| 482 764 1119 1353 1667 1784}}]
|0.049077
|0.187961
|
|}