43ed7/4 - Revision history

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:23:04Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:23, 1 August 2025
Line 394:		Line 394:
	\| 0.923		\| 0.923
	\|}		\|}

	~~[[Category:Edonoi]]~~

BudjarnLambeth: Stub

2024-12-21T22:36:01Z

Stub

← Older revision		Revision as of 22:36, 21 December 2024
Line 1:		Line 1:
			{{stub}}


	{{Infobox ET}}		{{Infobox ET}}
	{{ED intro}} It corresponds to 53.2603edo, which is closely related to [[53edo]] but with 7/4 tuned pure instead of the octave.		{{ED intro}} It corresponds to 53.2603edo, which is closely related to [[53edo]] but with 7/4 tuned pure instead of the octave.

FloraC: Adopt template: ED intro; misc. cleanup

2024-05-24T09:13:53Z

Adopt template: ED intro; misc. cleanup

Show changes

ArrowHead294 at 04:32, 24 May 2024

2024-05-24T04:32:19Z

← Older revision		Revision as of 04:32, 24 May 2024
Line 298:		Line 298:
	\|-		\|-
	\| [[7/4]]		\| [[7/4]]
	\|0.0		\| 0.0
	\|-		\|-
	\| [[2/1]]		\| [[2/1]]
	\|5.866		\| 5.866
	\|-		\|-
	\| [[3/2]]		\| [[3/2]]
	\|3.499		\| 3.499
	\|-		\|-
	\| [[5/4]]		\| [[5/4]]
	\|3.29		\| 3.29
	\|-		\|-
	\| [[9/8]]		\| [[9/8]]
	\|1.132		\| 1.132
	\|-		\|-
	\| [[11/8]]		\| [[11/8]]
	\|10.578		\| 10.578
	\|-		\|-
	\| [[13/8]]		\| [[13/8]]
	\|6.887		\| 6.887
	\|-		\|-
	\| [[15/8]]		\| [[15/8]]
	\|6.789		\| 6.789
	\|-		\|-
	\| [[14/9]]		\| [[14/9]]
	\|1.132		\| 1.132
	\|-		\|-
	\| [[28/15]]		\| [[28/15]]
	\|0.923		\| 0.923
	\|-		\|-
	\| [[10/7]]		\| [[10/7]]
	\|9.155		\| 9.155
	\|-		\|-
	\| [[16/11]]		\| [[16/11]]
	\|4.712		\| 4.712
	\|-		\|-
	\| [[13/10]]		\| [[13/10]]
	\|3.597		\| 3.597
	\|-		\|-
	\| [[9/5]]		\| [[9/5]]
	\|3.709		\| 3.709
	\|-		\|-
	\| [[10/9]]		\| [[10/9]]
	\|2.157		\| 2.157
	\|-		\|-
	\| [[26/15]]		\| [[26/15]]
	\|5.964		\| 5.964
	\|-		\|-
	\| [[13/11]]		\| [[13/11]]
	\|3.691		\| 3.691
	\|-		\|-
	\| [[13/7]]		\| [[13/7]]
	\|9.778		\| 9.778
	\|-		\|-
	\| [[16/13]]		\| [[16/13]]
	\|1.021		\| 1.021
	\|-		\|-
	\| [[7/6]]		\| [[7/6]]
	\|3.499		\| 3.499
	\|-		\|-
	\| [[5/3]]		\| [[5/3]]
	\|5.656		\| 5.656
	\|-		\|-
	\| [[20/13]]		\| [[20/13]]
	\|2.268		\| 2.268
	\|-		\|-
	\| [[11/10]]		\| [[11/10]]
	\|7.288		\| 7.288
	\|-		\|-
	\| [[8/5]]		\| [[8/5]]
	\|2.576		\| 2.576
	\|-		\|-
	\| [[9/7]]		\| [[9/7]]
	\|6.998		\| 6.998
	\|-		\|-
	\| [[11/9]]		\| [[11/9]]
	\|9.445		\| 9.445
	\|-		\|-
	\| [[18/11]]		\| [[18/11]]
	\|3.58		\| 3.58
	\|-		\|-
	\| [[24/13]]		\| [[24/13]]
	\|2.478		\| 2.478
	\|-		\|-
	\| [[22/15]]		\| [[22/15]]
	\|9.655		\| 9.655
	\|-		\|-
	\| [[15/13]]		\| [[15/13]]
	\|0.098		\| 0.098
	\|-		\|-
	\| [[15/11]]		\| [[15/11]]
	\|3.789		\| 3.789
	\|-		\|-
	\| [[16/9]]		\| [[16/9]]
	\|4.733		\| 4.733
	\|-		\|-
	\| [[12/7]]		\| [[12/7]]
	\|9.365		\| 9.365
	\|-		\|-
	\| [[7/5]]		\| [[7/5]]
	\|3.29		\| 3.29
	\|-		\|-
	\| [[12/11]]		\| [[12/11]]
	\|7.079		\| 7.079
	\|-		\|-
	\| [[4/3]]		\| [[4/3]]
	\|2.367		\| 2.367
	\|-		\|-
	\| [[11/6]]		\| [[11/6]]
	\|9.586		\| 9.586
	\|-		\|-
	\| [[13/12]]		\| [[13/12]]
	\|3.388		\| 3.388
	\|-		\|-
	\| [[8/7]]		\| [[8/7]]
	\|5.866		\| 5.866
	\|-		\|-
	\| [[20/11]]		\| [[20/11]]
	\|1.423		\| 1.423
	\|-		\|-
	\| [[14/13]]		\| [[14/13]]
	\|6.887		\| 6.887
	\|-		\|-
	\| [[6/5]]		\| [[6/5]]
	\|0.21		\| 0.21
	\|-		\|-
	\| [[18/13]]		\| [[18/13]]
	\|0.111		\| 0.111
	\|-		\|-
	\| [[15/14]]		\| [[15/14]]
	\|6.789		\| 6.789
	\|-		\|-
	\| [[11/7]]		\| [[11/7]]
	\|6.087		\| 6.087
	\|-		\|-
	\| [[13/9]]		\| [[13/9]]
	\|5.754		\| 5.754
	\|-		\|-
	\| [[14/11]]		\| [[14/11]]
	\|10.578		\| 10.578
	\|-		\|-
	\| [[22/13]]		\| [[22/13]]
	\|9.557		\| 9.557
	\|-		\|-
	\| [[16/15]]		\| [[16/15]]
	\|0.923		\| 0.923
	\|}		\|}


	[[Category:Subminor seventh]]		[[Category:Subminor seventh]]
	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

Plumtree: Infobox ET added

2022-10-05T20:14:56Z

Infobox ET added

← Older revision		Revision as of 20:14, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''43ED7/4''' is the [[Equal-step tuning\|equal division]] of the [[7/4\|harmonic seventh]] into 43 parts of 22.5308 [[cent\|cents]] each, corresponding to 53.2603 [[EDO]].		'''43ED7/4''' is the [[Equal-step tuning\|equal division]] of the [[7/4\|harmonic seventh]] into 43 parts of 22.5308 [[cent\|cents]] each, corresponding to 53.2603 [[EDO]].

Lupus: Created page with "'''43ED7/4''' is the equal division of the harmonic seventh into 43 parts of 22.5308 cents each, corresponding to 53.2603 EDO. ==..."

2021-12-10T15:33:57Z

Created page with "'''43ED7/4''' is the equal division of the harmonic seventh into 43 parts of 22.5308 cents each, corresponding to 53.2603 EDO. ==..."

New page

'''43ED7/4''' is the [[Equal-step tuning|equal division]] of the [[7/4|harmonic seventh]] into 43 parts of 22.5308 [[cent|cents]] each, corresponding to 53.2603 [[EDO]].

== Intervals ==
{| class="wikitable"
|-
! | degree
! | cents value
! | ratio
|-
| | 0
| | 0.0000
| | '''[[1/1]]'''

|-
| | 1
| | 22.5308
| | (7/4)1/43

|-
| | 2
| | 45.0617
| | (7/4)2/43

|-
| | 3
| | 67.5925
| | (7/4)3/43

|-
| | 4
| | 90.1233
| | (7/4)4/43

|-
| | 5
| | 112.6542
| | (7/4)5/43

|-
| | 6
| | 135.1850
| | (7/4)6/43

|-
| | 7
| | 157.7158
| | (7/4)7/43

|-
| | 8
| | 180.2467
| | (7/4)8/43

|-
| | 9
| | 202.7775
| | (7/4)9/43

|-
| | 10
| | 225.3084
| | (7/4)10/43

|-
| | 11
| | 247.8392
| | (7/4)11/43

|-
| | 12
| | 270.3700
| | (7/4)12/43

|-
| | 13
| | 292.9009
| | (7/4)13/43

|-
| | 14
| | 315.4317
| | (7/4)14/43

|-
| | 15
| | 337.9625
| | (7/4)15/43

|-
| | 16
| | 360.4934
| | (7/4)16/43

|-
| | 17
| | 383.0242
| | (7/4)17/43

|-
| | 18
| | 405.5550
| | (7/4)18/43

|-
| | 19
| | 428.0859
| | (7/4)19/43

|-
| | 20
| | 450.6167
| | (7/4)20/43

|-
| | 21
| | 473.1475
| | (7/4)21/43

|-
| | 22
| | 495.6784
| | (7/4)22/43

|-
| | 23
| | 518.2092
| | (7/4)23/43

|-
| | 24
| | 540.7400
| | (7/4)24/43

|-
| | 25
| | 563.2709
| | (7/4)25/43

|-
| | 26
| | 585.8017
| | (7/4)26/43

|-
| | 27
| | 608.3325
| | (7/4)27/43

|-
| | 28
| | 630.8634
| | (7/4)28/43

|-
| | 29
| | 653.3942
| | (7/4)29/43

|-
| | 30
| | 675.9251
| | (7/4)30/43

|-
| | 31
| | 698.4559
| | (7/4)31/43

|-
| | 32
| | 720.9867
| | (7/4)32/43

|-
| | 33
| | 743.5176
| | (7/4)33/43

|-
| | 34
| | 766.0484
| | (7/4)34/43

|-
| | 35
| | 788.5792
| | (7/4)35/43

|-
| | 36
| | 811.1101
| | (7/4)36/43

|-
| | 37
| | 833.6409
| | (7/4)37/43

|-
| | 38
| | 856.1717
| | (7/4)38/43

|-
| | 39
| | 878.7026
| | (7/4)39/43

|-
| | 40
| | 901.2334
| | (7/4)40/43

|-
| | 41
| | 923.7642
| | (7/4)41/43

|-
| | 42
| | 946.2951
| | (7/4)42/43

|-
| | 43
| | 968.8259
| | '''[[7/4]]'''

|-
| | 44
| | 991.3567
| | (7/4)44/43

|-
| | 45
| | 1013.8876
| | (7/4)45/43

|-
| | 46
| | 1036.4184
| | (7/4)46/43

|-
| | 47
| | 1058.9492
| | (7/4)47/43

|-
| | 48
| | 1081.4801
| | (7/4)48/43

|-
| | 49
| | 1104.0109
| | (7/4)49/43

|-
| | 50
| | 1126.5418
| | (7/4)50/43

|-
| | 51
| | 1149.0726
| | (7/4)51/43

|-
| | 52
| | 1171.6034
| | (7/4)52/43

|-
| | 53
| | 1194.1343
| | (7/4)53/43

|-
| | 54
| | 1216.6651
| | (7/4)54/43
|}

== Just approximation ==
Several intervals like the [[6/5|just minor third]] and the [[9/8|whole tone]] are well approximated by 43ed7/4.
=== 15-odd-limit mappings ===
The following table shows how [[15-odd-limit intervals]] are represented in 43ed7/4 (can be ordered by absolute error).

{| class="wikitable sortable"
|-
|+ Direct mapping (even if inconsistent)
|-
! Interval(s)
! Error (abs, [[cent|¢]])
|-
|-
| [[7/4]]
|0.0
|-
| [[2/1]]
|5.866
|-
| [[3/2]]
|3.499
|-
| [[5/4]]
|3.29
|-
| [[9/8]]
|1.132
|-
| [[11/8]]
|10.578
|-
| [[13/8]]
|6.887
|-
| [[15/8]]
|6.789
|-
| [[14/9]]
|1.132
|-
| [[28/15]]
|0.923
|-
| [[10/7]]
|9.155
|-
| [[16/11]]
|4.712
|-
| [[13/10]]
|3.597
|-
| [[9/5]]
|3.709
|-
| [[10/9]]
|2.157
|-
| [[26/15]]
|5.964
|-
| [[13/11]]
|3.691
|-
| [[13/7]]
|9.778
|-
| [[16/13]]
|1.021
|-
| [[7/6]]
|3.499
|-
| [[5/3]]
|5.656
|-
| [[20/13]]
|2.268
|-
| [[11/10]]
|7.288
|-
| [[8/5]]
|2.576
|-
| [[9/7]]
|6.998
|-
| [[11/9]]
|9.445
|-
| [[18/11]]
|3.58
|-
| [[24/13]]
|2.478
|-
| [[22/15]]
|9.655
|-
| [[15/13]]
|0.098
|-
| [[15/11]]
|3.789
|-
| [[16/9]]
|4.733
|-
| [[12/7]]
|9.365
|-
| [[7/5]]
|3.29
|-
| [[12/11]]
|7.079
|-
| [[4/3]]
|2.367
|-
| [[11/6]]
|9.586
|-
| [[13/12]]
|3.388
|-
| [[8/7]]
|5.866
|-
| [[20/11]]
|1.423
|-
| [[14/13]]
|6.887
|-
| [[6/5]]
|0.21
|-
| [[18/13]]
|0.111
|-
| [[15/14]]
|6.789
|-
| [[11/7]]
|6.087
|-
| [[13/9]]
|5.754
|-
| [[14/11]]
|10.578
|-
| [[22/13]]
|9.557
|-
| [[16/15]]
|0.923
|}

[[Category:Subminor seventh]]
[[Category:Equal-step tuning]]
[[Category:Edonoi]]