40edf - Revision history

FloraC: Cleanup

2025-01-17T17:13:08Z

Cleanup

← Older revision		Revision as of 17:13, 17 January 2025
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''40EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 40 parts of 17.5489 [[cents]] each, corresponding to 68.3805 [[edo]].~~		{{ED intro}}

	It is related to the [[regular temperament]] which [[tempers out]] 2401/2400, 9801/9800, and 9453125/9437184 in the [[11-limit]], which is supported by [[68edo]], [[274edo]], [[342edo]], [[410edo]], [[616edo]], and [[752edo]] among others.		== Theory ==
			40edf corresponds to 68.3805[[edo]]. It is related to the [[regular temperament]] which [[tempering out\|tempers out]] 2401/2400, 9801/9800, and 9453125/9437184 in the [[11-limit]], which is supported by [[68edo]], [[274edo]], [[342edo]], [[410edo]], [[616edo]], and [[752edo]] among others.

	== Harmonics ==		=== Harmonics ===
	{{Harmonics in equal		{{Harmonics in equal\|40\|3\|2}}
	\| ~~steps =~~ 40		{{Harmonics in equal\|40\|3\|2\|start=12\|collapsed=1}}
	\| ~~num =~~ 3
	\| ~~denom =~~ 2
	}}
	{{Harmonics in equal
	\| ~~steps =~~ 40
	\| ~~num =~~ 3
	\| ~~denom =~~ 2
	\| start = 12
	\| collapsed = 1
	}}

	==Intervals==		== Intervals ==
	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible"
	\|+ Intervals of 40edf		\|+ Intervals of 40edf
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	EDOs: 68, 274, 342, 410, 616i, 752h		EDOs: 68, 274, 342, 410, 616i, 752h

	{{~~todo~~\|expand}}		{{Todo\|cleanup\|expand}}
	~~[[Category:Edf]]~~
	~~[[Category:Edonoi]]~~

BudjarnLambeth: Add links, add todo expand, make table collapsible

2024-12-18T05:05:55Z

Add links, add todo expand, make table collapsible

← Older revision		Revision as of 05:05, 18 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''40EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 40 parts of 17.5489 [[~~cent\|~~cents]] each, corresponding to 68.3805 [[edo]]. It is related to the regular temperament which tempers out 2401/2400, 9801/9800, and 9453125/9437184 in the 11-limit, which is supported by [[68edo]], [[274edo]], [[342edo]], [[410edo]], 616edo, and 752edo among others.		'''40EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 40 parts of 17.5489 [[cents]] each, corresponding to 68.3805 [[edo]].

			It is related to the [[regular temperament]] which [[tempers out]] 2401/2400, 9801/9800, and 9453125/9437184 in the [[11-limit]], which is supported by [[68edo]], [[274edo]], [[342edo]], [[410edo]], [[616edo]], and [[752edo]] among others.

	== Harmonics ==		== Harmonics ==
Line 17:		Line 19:

	==Intervals==		==Intervals==
	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
			\|+ Intervals of 40edf
	\|-		\|-
	! \| degree		! \| degree
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	EDOs: 68, 274, 342, 410, 616i, 752h		EDOs: 68, 274, 342, 410, 616i, 752h

			{{todo\|expand}}
	[[Category:Edf]]		[[Category:Edf]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

BudjarnLambeth: Harmonics

2024-10-03T19:51:53Z

Harmonics

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 '''40EDF''' is the [[EDF|equal division of the just perfect fifth]] into 40 parts of 17.5489 [[cent|cents]] each, corresponding to 68.3805 [[edo]]. It is related to the regular temperament which tempers out 2401/2400, 9801/9800, and 9453125/9437184 in the 11-limit, which is supported by [[68edo]], [[274edo]], [[342edo]], [[410edo]], 616edo, and 752edo among others.
 ==Intervals==

Francium: linking EDOs

2024-02-14T06:13:15Z

linking EDOs

← Older revision		Revision as of 06:13, 14 February 2024
Line 425:		Line 425:
	Mapping: [<2 2 4 5 8\|, <0 40 22 21 -37\|]		Mapping: [<2 2 4 5 8\|, <0 40 22 21 -37\|]

	EDOs: 68, 274, 342, 410, 616, 752		EDOs: {{EDOs\|68, 274, 342, 410, 616, 752}}

	===2.3.5.7.11.17 subgroup 68&342===		===2.3.5.7.11.17 subgroup 68&342===

Plumtree: Infobox ET added

2022-10-05T18:45:04Z

Infobox ET added

← Older revision		Revision as of 18:45, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''40EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 40 parts of 17.5489 [[cent\|cents]] each, corresponding to 68.3805 [[edo]]. It is related to the regular temperament which tempers out 2401/2400, 9801/9800, and 9453125/9437184 in the 11-limit, which is supported by [[68edo]], [[274edo]], [[342edo]], [[410edo]], 616edo, and 752edo among others.		'''40EDF''' is the [[EDF\|equal division of the just perfect fifth]] into 40 parts of 17.5489 [[cent\|cents]] each, corresponding to 68.3805 [[edo]]. It is related to the regular temperament which tempers out 2401/2400, 9801/9800, and 9453125/9437184 in the 11-limit, which is supported by [[68edo]], [[274edo]], [[342edo]], [[410edo]], 616edo, and 752edo among others.

Cmloegcmluin: /* Related regular temperaments */ map → mapping

2021-11-05T20:00:42Z

Related regular temperaments: map → mapping

← Older revision		Revision as of 20:00, 5 November 2021
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	POTE generator: ~99/98 = 17.545		POTE generator: ~99/98 = 17.545

	~~Map~~: [<2 2 4 5 8\|, <0 40 22 21 -37\|]		Mapping: [<2 2 4 5 8\|, <0 40 22 21 -37\|]

	EDOs: 68, 274, 342, 410, 616, 752		EDOs: 68, 274, 342, 410, 616, 752
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	POTE generator: ~99/98 = 17.546		POTE generator: ~99/98 = 17.546

	~~Map~~: [<2 2 4 5 8 8\|, <0 40 22 21 -37 6\|]		Mapping: [<2 2 4 5 8 8\|, <0 40 22 21 -37 6\|]

	EDOs: 68, 274, 342, 410, 616, 752		EDOs: 68, 274, 342, 410, 616, 752
Line 440:		Line 440:
	POTE generator: ~96/95 = 17.547		POTE generator: ~96/95 = 17.547

	~~Map~~: [<2 2 4 5 8 8 8\|, <0 40 22 21 -37 6 17\|]		Mapping: [<2 2 4 5 8 8 8\|, <0 40 22 21 -37 6 17\|]

	EDOs: 68, 274, 342, 410, 616, 752h		EDOs: 68, 274, 342, 410, 616, 752h
Line 449:		Line 449:
	POTE generator: ~96/95 = 17.546		POTE generator: ~96/95 = 17.546

	~~Map~~: [<2 2 4 5 8 8 8 7\|, <0 40 22 21 -37 6 17 70\|]		Mapping: [<2 2 4 5 8 8 8 7\|, <0 40 22 21 -37 6 17 70\|]

	EDOs: 68, 274, 342, 410, 616i, 752h		EDOs: 68, 274, 342, 410, 616i, 752h

Moremajorthanmajor at 22:42, 19 August 2019

2019-08-19T22:42:44Z

← Older revision		Revision as of 22:42, 19 August 2019
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	! \| comments		! \| comments
	\|-		\|-
	\| \| 0		\| colspan="2"\| 0
	~~\| \| 0.~~0000
	\| \| '''exact [[1/1]]'''		\| \| '''exact [[1/1]]'''
	\| \|		\| \|

Moremajorthanmajor at 18:49, 10 March 2019

2019-03-10T18:49:41Z

Show changes

Xenllium: /* Related regular temperaments */

2019-02-11T02:32:29Z

Related regular temperaments

← Older revision		Revision as of 02:32, 11 February 2019
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	EDOs: 68, 274, 342, 410, 616, 752		EDOs: 68, 274, 342, 410, 616, 752

	===2.3.5.7.11.17 68&342===		===2.3.5.7.11.17 subgroup 68&342===
	Commas: 1089/1088, 1225/1224, 2401/2400, 24576/24565		Commas: 1089/1088, 1225/1224, 2401/2400, 24576/24565

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	EDOs: 68, 274, 342, 410, 616, 752		EDOs: 68, 274, 342, 410, 616, 752

	===2.3.5.7.11.17.19 68&342===		===2.3.5.7.11.17.19 subgroup 68&342===
	Commas: 1089/1088, 1225/1224, 1445/1444, 1617/1615, 2401/2400		Commas: 1089/1088, 1225/1224, 1445/1444, 1617/1615, 2401/2400

Line 245:		Line 245:
	EDOs: 68, 274, 342, 410, 616, 752h		EDOs: 68, 274, 342, 410, 616, 752h

	===2.3.5.7.11.17.19.23 68&342===		===2.3.5.7.11.17.19.23 subgroup 68&342===
	Commas: 875/874, 1089/1088, 1225/1224, 1445/1444, 1617/1615, 2024/2023		Commas: 875/874, 1089/1088, 1225/1224, 1445/1444, 1617/1615, 2024/2023

Xenllium: Created page with "'''40EDF''' is the equal division of the just perfect fifth into 40 parts of 17.5489 cents each, corresponding to 68.3805 edo. It is related to the regula..."

2019-02-11T02:30:08Z

Created page with "'''40EDF''' is the equal division of the just perfect fifth into 40 parts of 17.5489 cents each, corresponding to 68.3805 edo. It is related to the regula..."

New page

'''40EDF''' is the [[EDF|equal division of the just perfect fifth]] into 40 parts of 17.5489 [[cent|cents]] each, corresponding to 68.3805 [[edo]]. It is related to the regular temperament which tempers out 2401/2400, 9801/9800, and 9453125/9437184 in the 11-limit, which is supported by [[68edo]], [[274edo]], [[342edo]], [[410edo]], 616edo, and 752edo among others.

==Intervals==
{| class="wikitable"
|-
! | degree
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
| | 0
| | 0.0000
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 17.5489
| | [[100/99]], [[99/98]]
| |
|-
| | 2
| | 35.0978
| | [[50/49]], [[49/48]]
| |
|-
| | 3
| | 52.6466
| | [[33/32]]
| |
|-
| | 4
| | 70.1955
| | [[25/24]]
| |
|-
| | 5
| | 87.7444
| | [[20/19]]
| |
|-
| | 6
| | 105.2933
| | [[17/16]]
| |
|-
| | 7
| | 122.8421
| |
| |
|-
| | 8
| | 140.3910
| |
| |
|-
| | 9
| | 157.9399
| | 23/21
| |
|-
| | 10
| | 175.4888
| |
| |
|-
| | 11
| | 193.0376
| | [[19/17]]
| |
|-
| | 12
| | 210.5865
| |
| |
|-
| | 13
| | 228.1354
| |
| |
|-
| | 14
| | 245.6843
| |
| |
|-
| | 15
| | 263.2331
| |
| |
|-
| | 16
| | 280.7820
| | [[20/17]]
| |
|-
| | 17
| | 298.3309
| | [[19/16]]
| |
|-
| | 18
| | 315.8798
| | [[6/5]]
| |
|-
| | 19
| | 333.4286
| |
| |
|-
| | 20
| | 350.9775
| | [[60/49]], [[49/40]]
| |
|-
| | 21
| | 368.5264
| |
| |
|-
| | 22
| | 386.0753
| | [[5/4]]
| |
|-
| | 23
| | 403.6241
| | [[24/19]]
| |
|-
| | 24
| | 421.1730
| | [[51/40]]
| |
|-
| | 25
| | 438.7219
| |
| |
|-
| | 26
| | 456.2708
| |
| |
|-
| | 27
| | 473.8196
| |
| |
|-
| | 28
| | 491.3685
| |
| |
|-
| | 29
| | 508.9174
| |
| |
|-
| | 30
| | 526.4663
| |
| |
|-
| | 31
| | 544.0151
| |
| |
|-
| | 32
| | 561.5640
| |
| |
|-
| | 33
| | 579.1129
| |
| |
|-
| | 34
| | 596.6618
| | [[24/17]]
| |
|-
| | 35
| | 614.2106
| |
| |
|-
| | 36
| | 631.7595
| | [[36/25]]
| |
|-
| | 37
| | 649.3084
| | [[16/11]]
| |
|-
| | 38
| | 666.8573
| |
| |
|-
| | 39
| | 694.4061
| | 49/33
| |
|-
| | 40
| | 701.9550
| | '''exact [[3/2]]'''
| | just perfect fifth
|}

==Related regular temperaments==
Adding [[2edo|one half of the octave]] as a generator, 40EDF leads the regular temperament which tempers out 2401/2400, 9801/9800, and 9453125/9437184 in the 11-limit.

===11-limit 68&342===
Commas: 2401/2400, 9801/9800, 9453125/9437184

POTE generator: ~99/98 = 17.545

Map: [<2 2 4 5 8|, <0 40 22 21 -37|]

EDOs: 68, 274, 342, 410, 616, 752

===2.3.5.7.11.17 68&342===
Commas: 1089/1088, 1225/1224, 2401/2400, 24576/24565

POTE generator: ~99/98 = 17.546

Map: [<2 2 4 5 8 8|, <0 40 22 21 -37 6|]

EDOs: 68, 274, 342, 410, 616, 752

===2.3.5.7.11.17.19 68&342===
Commas: 1089/1088, 1225/1224, 1445/1444, 1617/1615, 2401/2400

POTE generator: ~96/95 = 17.547

Map: [<2 2 4 5 8 8 8|, <0 40 22 21 -37 6 17|]

EDOs: 68, 274, 342, 410, 616, 752h

===2.3.5.7.11.17.19.23 68&342===
Commas: 875/874, 1089/1088, 1225/1224, 1445/1444, 1617/1615, 2024/2023

POTE generator: ~96/95 = 17.546

Map: [<2 2 4 5 8 8 8 7|, <0 40 22 21 -37 6 17 70|]

EDOs: 68, 274, 342, 410, 616i, 752h

[[Category:Edf]]
[[Category:Edonoi]]