7ed5/4 - Revision history

VectorGraphics at 01:43, 1 December 2025

2025-12-01T01:43:15Z

← Older revision		Revision as of 01:43, 1 December 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''7ED5/4''' is the [[Equal-step tuning\|equal division]] of the [[5/4\|just major third]] into seven parts of 55.1877 [[cent\|cents]] each, corresponding to 21.7440 [[EDO\|edo]] (very nearly [[61ed7]]). It is related to the [[Hemifamity temperaments\|alphaquarter temperament]] and the 5-limit temperament which tempers out \|234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).		'''7ED5/4''' is the [[Equal-step tuning\|equal division]] of the [[5/4\|just major third]] into seven parts of 55.1877 [[cent\|cents]] each, corresponding to 21.7440 [[EDO\|edo]] (very nearly [[61ed7]]). It is related to the [[Hemifamity temperaments\|alphaquarter temperament]] and the 5-limit temperament which tempers out \|234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).

			It can be seen as a sharp version of [[22EDO]].

	== Harmonics ==		== Harmonics ==

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

2025-08-01T19:23:19Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:23, 1 August 2025
Line 411:		Line 411:
	[[Category:Major third]]		[[Category:Major third]]
	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	~~[[Category:Edonoi]]~~

BudjarnLambeth: Harmonics

2024-10-03T10:44:42Z

Harmonics

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 '''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to 21.7440 [[EDO|edo]] (very nearly [[61ed7]]). It is related to the [[Hemifamity temperaments|alphaquarter temperament]] and the 5-limit temperament which tempers out |234 -7 -96&gt; (0.198463 cents, 5-limit 1783&amp;7980 comma).
 ==Intervals==

Plumtree: Infobox ET added

2022-10-05T20:10:49Z

Infobox ET added

← Older revision		Revision as of 20:10, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''7ED5/4''' is the [[Equal-step tuning\|equal division]] of the [[5/4\|just major third]] into seven parts of 55.1877 [[cent\|cents]] each, corresponding to 21.7440 [[EDO\|edo]] (very nearly [[61ed7]]). It is related to the [[Hemifamity temperaments\|alphaquarter temperament]] and the 5-limit temperament which tempers out \|234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).		'''7ED5/4''' is the [[Equal-step tuning\|equal division]] of the [[5/4\|just major third]] into seven parts of 55.1877 [[cent\|cents]] each, corresponding to 21.7440 [[EDO\|edo]] (very nearly [[61ed7]]). It is related to the [[Hemifamity temperaments\|alphaquarter temperament]] and the 5-limit temperament which tempers out \|234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).

Cmloegcmluin: /* 1783&7980 temperament */ map → mapping

2021-11-06T00:04:18Z

1783&7980 temperament: map → mapping

← Older revision		Revision as of 00:04, 6 November 2021
Line 388:		Line 388:
	POTE generator: 55.188		POTE generator: 55.188

	~~Map~~: [<1 6 2\|, <0 -96 7\|]		Mapping: [<1 6 2\|, <0 -96 7\|]

	EDOs: 1783, 4414, 6197, 7980, 9763, 11546, 14177		EDOs: 1783, 4414, 6197, 7980, 9763, 11546, 14177

Xenllium at 04:28, 26 January 2019

2019-01-26T04:28:19Z

← Older revision		Revision as of 04:28, 26 January 2019
Line 394:		Line 394:
	Badness: 0.1157		Badness: 0.1157

	[[Category:~~5/4~~]]		[[Category:Major third]]
	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

Xenllium at 23:49, 25 January 2019

2019-01-25T23:49:54Z

← Older revision		Revision as of 23:49, 25 January 2019
Line 1:		Line 1:
	'''7ED5/4''' is the [[Equal-step tuning\|equal division]] of the [[5/4\|just major third]] into seven parts of 55.1877 [[cent\|cents]] each, corresponding to ~~every fourth step of~~ [[~~87edo~~]]. It is related to the [[Hemifamity temperaments\|alphaquarter temperament]] and the 5-limit temperament which tempers out \|234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).		'''7ED5/4''' is the [[Equal-step tuning\|equal division]] of the [[5/4\|just major third]] into seven parts of 55.1877 [[cent\|cents]] each, corresponding to 21.7440 [[EDO\|edo]] (very nearly [[61ed7]]). It is related to the [[Hemifamity temperaments\|alphaquarter temperament]] and the 5-limit temperament which tempers out \|234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).

	==Intervals==		==Intervals==

Xenllium at 11:18, 25 January 2019

2019-01-25T11:18:02Z

← Older revision		Revision as of 11:18, 25 January 2019
Line 379:		Line 379:
	==7ED5/4 as a generator==		==7ED5/4 as a generator==
	===Alphaquarter===		===Alphaquarter===
	7ED5/4 leads the alphaquarter temperament using its three steps for [[11/10]], its nine steps for [[4/3]], and its 61 steps for [[7/1]]. Alphaquarter tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit, supported by [[87edo]], [[152edo]], [[239edo]], and [[391edo]].		7ED5/4 leads the alphaquarter temperament using its three steps for [[11/10]], its nine steps for [[4/3]], and its 61 steps for [[7/1]]. Alphaquarter tempers out 3025/3024, 4000/3993, and 5120/5103 in the 11-limit, supported by [[87edo]], [[152edo]], [[239edo]], and [[391edo]] among others.

	===1783&7980 temperament===		===1783&7980 temperament===
Line 390:		Line 390:
	Map: [<1 6 2\|, <0 -96 7\|]		Map: [<1 6 2\|, <0 -96 7\|]

	EDOs: ~~[[1783edo\|~~1783]], 4414, 6197, ~~[[7980edo\|~~7980]], 9763, 11546, 14177		EDOs: 1783, 4414, 6197, 7980, 9763, 11546, 14177

	Badness: 0.1157		Badness: 0.1157

Xenllium at 10:31, 25 January 2019

2019-01-25T10:31:25Z

@@ Line 1: / Line 1: @@
-'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to every fourth step of [[87edo]]. It is related to the 5-limit temperament which tempers out |234 -7 -96&gt; (0.198463 cents, 5-limit 1783&amp;7980 comma).
+'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to every fourth step of [[87edo]]. It is related to the [[Hemifamity temperaments|alphaquarter temperament]] and the 5-limit temperament which tempers out |234 -7 -96&gt; (0.198463 cents, 5-limit 1783&amp;7980 comma).
 ==Intervals==
@@ Line 376: / Line 376: @@
 | | (5/4)<font style="vertical-align:super;font-size:0.8em;">13</font> = 1220703125/67108864
 |}
 [[Category:5/4]]
 [[Category:Equal-step tuning]]
 [[Category:Edonoi]]

Xenllium: Created page with "'''7ED5/4''' is the equal division of the just major third into seven parts of 55.1877 cents each, corresponding to every fourth step of..."

2019-01-25T08:49:48Z

Created page with "'''7ED5/4''' is the equal division of the just major third into seven parts of 55.1877 cents each, corresponding to every fourth step of..."

New page

'''7ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into seven parts of 55.1877 [[cent|cents]] each, corresponding to every fourth step of [[87edo]]. It is related to the 5-limit temperament which tempers out |234 -7 -96> (0.198463 cents, 5-limit 1783&7980 comma).

==Intervals==
{| class="wikitable"
|-
! | degree
! | cents value
! | ratio
|-
| | 0
| | 0.0000
| | '''[[1/1]]'''
|-
| | 1
| | 55.1877
| | (5/4)1/7
|-
| | 2
| | 110.3753
| | (5/4)2/7
|-
| | 3
| | 165.5630
| | (5/4)3/7
|-
| | 4
| | 220.7507
| | (5/4)4/7
|-
| | 5
| | 275.9384
| | (5/4)5/7
|-
| | 6
| | 331.1260
| | (5/4)6/7
|-
| | 7
| | 386.3137
| | '''[[5/4]]'''
|-
| | 8
| | 441.5014
| | (5/4)8/7
|-
| | 9
| | 496.6891
| | (5/4)9/7
|-
| | 10
| | 551.8767
| | (5/4)10/7
|-
| | 11
| | 607.0644
| | (5/4)11/7
|-
| | 12
| | 662.2521
| | (5/4)12/7
|-
| | 13
| | 717.4398
| | (5/4)13/7
|-
| | 14
| | 772.6274
| | (5/4)2 = [[25/16]]
|-
| | 15
| | 827.8151
| | (5/4)15/7
|-
| | 16
| | 883.0028
| | (5/4)16/7
|-
| | 17
| | 938.1904
| | (5/4)17/7
|-
| | 18
| | 993.3781
| | (5/4)18/7
|-
| | 19
| | 1048.5658
| | (5/4)19/7
|-
| | 20
| | 1103.7535
| | (5/4)20/7
|-
| | 21
| | 1158.9411
| | (5/4)3 = 125/64
|-
| | 22
| | 1214.1288
| | (5/4)22/7
|-
| | 23
| | 1269.3165
| | (5/4)23/7
|-
| | 24
| | 1324.5042
| | (5/4)24/7
|-
| | 25
| | 1379.6918
| | (5/4)25/7
|-
| | 26
| | 1434.8795
| | (5/4)26/7
|-
| | 27
| | 1490.0672
| | (5/4)27/7
|-
| | 28
| | 1545.2549
| | (5/4)4 = 625/256
|-
| | 29
| | 1600.4425
| | (5/4)29/7
|-
| | 30
| | 1655.6302
| | (5/4)30/7
|-
| | 31
| | 1710.8179
| | (5/4)31/7
|-
| | 32
| | 1766.0055
| | (5/4)32/7
|-
| | 33
| | 1821.1932
| | (5/4)33/7
|-
| | 34
| | 1876.3809
| | (5/4)34/7
|-
| | 35
| | 1931.5686
| | (5/4)5 = 3125/1024
|-
| | 36
| | 1986.7562
| | (5/4)36/7
|-
| | 37
| | 2041.9439
| | (5/4)37/7
|-
| | 38
| | 2097.1316
| | (5/4)38/7
|-
| | 39
| | 2152.3193
| | (5/4)39/7
|-
| | 40
| | 2207.5069
| | (5/4)40/7
|-
| | 41
| | 2262.6946
| | (5/4)41/7
|-
| | 42
| | 2317.8823
| | (5/4)6 = 15625/4096
|-
| | 43
| | 2373.0700
| | (5/4)43/7
|-
| | 44
| | 2428.2576
| | (5/4)44/7
|-
| | 45
| | 2483.4453
| | (5/4)45/7
|-
| | 46
| | 2538.6330
| | (5/4)46/7
|-
| | 47
| | 2593.8207
| | (5/4)47/7
|-
| | 48
| | 2649.0083
| | (5/4)48/7
|-
| | 49
| | 2704.1960
| | (5/4)7 = 78125/16384
|-
| | 50
| | 2759.3837
| | (5/4)50/7
|-
| | 51
| | 2814.5713
| | (5/4)51/7
|-
| | 52
| | 2869.7590
| | (5/4)52/7
|-
| | 53
| | 2924.9467
| | (5/4)53/7
|-
| | 54
| | 2980.1344
| | (5/4)54/7
|-
| | 55
| | 3035.3220
| | (5/4)55/7
|-
| | 56
| | 3090.5097
| | (5/4)8 = 390625/65536
|-
| | 57
| | 3145.6974
| | (5/4)57/7
|-
| | 58
| | 3200.8851
| | (5/4)58/7
|-
| | 59
| | 3256.0727
| | (5/4)59/7
|-
| | 60
| | 3311.2604
| | (5/4)60/7
|-
| | 61
| | 3366.4481
| | (5/4)61/7
|-
| | 62
| | 3421.6358
| | (5/4)62/7
|-
| | 63
| | 3476.8234
| | (5/4)9 = 1953125/262144
|-
| | 64
| | 3532.0111
| | (5/4)64/7
|-
| | 65
| | 3587.1988
| | (5/4)65/7
|-
| | 66
| | 3642.3864
| | (5/4)66/7
|-
| | 67
| | 3697.5741
| | (5/4)67/7
|-
| | 68
| | 3752.7618
| | (5/4)68/7
|-
| | 69
| | 3807.9495
| | (5/4)69/7
|-
| | 70
| | 3863.1371
| | (5/4)10 = 9765625/1048576
|-
| | 71
| | 3918.3248
| | (5/4)71/7
|-
| | 72
| | 3973.5125
| | (5/4)72/7
|-
| | 73
| | 4028.7002
| | (5/4)73/7
|-
| | 74
| | 4083.8878
| | (5/4)74/7
|-
| | 75
| | 4139.0755
| | (5/4)75/7
|-
| | 76
| | 4194.2632
| | (5/4)76/7
|-
| | 77
| | 4249.4509
| | (5/4)11 = 48828125/4194304
|-
| | 78
| | 4304.6385
| | (5/4)78/7
|-
| | 79
| | 4359.8262
| | (5/4)79/7
|-
| | 80
| | 4415.0139
| | (5/4)80/7
|-
| | 81
| | 4470.2015
| | (5/4)81/7
|-
| | 82
| | 4525.3892
| | (5/4)82/7
|-
| | 83
| | 4580.5769
| | (5/4)83/7
|-
| | 84
| | 4635.7646
| | (5/4)12 = 244140625/16777216
|-
| | 85
| | 4690.9522
| | (5/4)85/7
|-
| | 86
| | 4746.1399
| | (5/4)86/7
|-
| | 87
| | 4801.3276
| | (5/4)87/7
|-
| | 88
| | 4856.5153
| | (5/4)88/7
|-
| | 89
| | 4911.7029
| | (5/4)89/7
|-
| | 90
| | 4966.8906
| | (5/4)90/7
|-
| | 91
| | 5022.0783
| | (5/4)13 = 1220703125/67108864
|}

[[Category:5/4]]
[[Category:Equal-step tuning]]
[[Category:Edonoi]]