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{{Infobox ET}}
'''5ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into five parts of 77.2627 [[cent|cents]] each, corresponding to every second step of [[31edo]]. It is related to [[Carlos Alpha]] and the 7-limit temperaments which temper out 2100875/2097152 (including the [[Breedsmic temperaments|tertiaseptal temperament]] and the [[Starling temperaments|valentine temperament]]).
'''5ED5/4''' is the [[Equal-step tuning|equal division]] of the [[5/4|just major third]] into five parts of 77.2627 [[cent|cents]] each, corresponding to every second step of [[31edo]]. It is related to [[Carlos Alpha]] and the 7-limit temperaments which temper out 2100875/2097152 (including the [[Breedsmic temperaments|tertiaseptal temperament]] and the [[Starling temperaments|valentine temperament]]).


==Intervals==
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 272: Line 274:
|}
|}


==5ED5/4 as tertiaseptal generator==
== Harmonics ==
Aside from 2100875/2097152, tertiaseptal temperament tempers out 2401/2400, 65625/65536, and 703125/702464 in the 7-limit. It can be described as the 31&171 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 68/65) can serve as its generator. In the 17-limit, it tempers out 243/242, 375/374, 441/440, 625/624, and 3584/3575.
{{Harmonics in equal
| steps = 5
| num = 5
| denom = 4
}}
{{Harmonics in equal
| steps = 5
| num = 5
| denom = 4
| start = 12
| collapsed = 1
}}


{| class="wikitable"
==5ED5/4 as a generator==
|-
===Valentine===
! | generator
Aside from 2100875/2097152, [[valentine]] temperament tempers out 126/125, 1029/1024, 6144/6125, and 64827/64000 in the 7-limit. It can be described as the 31&46 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 22/21) can serve as its generator. In the 11-limit, it tempers out 121/120, 176/175, and 441/440.
! | cents value <sup>a</sup>
 
! | ratio<br>(octave-reduced)
===Tertiaseptal===
|-
Aside from 2100875/2097152, [[tertiaseptal]] temperament tempers out 2401/2400, 65625/65536, and 703125/702464 in the 7-limit. It can be described as the 31&amp;171 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 68/65) can serve as its generator. In the 17-limit, it tempers out 243/242, 375/374, 441/440, 625/624, and 3584/3575.
| | 1
 
| | 77.2
===Tertia===
| |
Aside from 2100875/2097152, [[tertiaseptal|tertia]] temperament tempers out 385/384, 1331/1323, and 1375/1372 in the 11-limit. It can be described as the 31&amp;140 temperament, and the step interval of 5ED5/4 (tuned between 256/245 and 68/65) can serve as its generator. In the 17-limit, it tempers out 352/351, 385/384, 561/560, 625/624, and 715/714.
|-
| | 2
| | 154.4
| |
|-
| | 3
| | 231.6
| | [[8/7]]
|-
| | 4
| | 308.8
| |
|-
| | 5
| | 386.0
| | [[5/4]]
|-
| | 6
| | 463.2
| | [[17/13]]
|-
| | 7
| | 540.4
| |
|-
| | 8
| | 617.6
| | [[10/7]]
|-
| | 9
| | 694.8
| |
|-
| | 10
| | 772.0
| | [[25/16]]
|-
| | 11
| | 849.2
| | [[18/11]]
|-
| | 12
| | 926.4
| |
|-
| | 13
| | 1003.6
| | [[25/14]]
|-
| | 14
| | 1080.8
| | [[28/15]]
|-
| | 15
| | 1158.0
| |
|-
| | 16
| | 35.2
| |
|-
| | 17
| | 112.4
| | [[16/15]]
|-
| | 18
| | 189.6
| |
|-
| | 19
| | 266.8
| | [[7/6]]
|-
| | 20
| | 344.0
| |
|-
| | 21
| | 421.2
| |
|-
| | 22
| | 498.4
| | [[4/3]]
|-
| | 23
| | 575.6
| |
|-
| | 24
| | 652.8
| |
|-
| | 25
| | 730.0
| | [[32/21]]
|-
| | 26
| | 807.2
| |
|-
| | 27
| | 884.4
| | [[5/3]]
|-
| | 28
| | 961.6
| |
|-
| | 29
| | 1038.8
| |
|-
| | 30
| | 1116.0
| | [[40/21]], [[21/11]]
|-
| | 31
| | 1193.2
| |
|-
| | 32
| | 70.4
| | [[26/25]], [[25/24]]
|-
| | 33
| | 147.6
| | [[12/11]]
|-
| | 34
| | 224.8
| |
|-
| | 35
| | 302.0
| | [[25/21]]
|-
| | 36
| | 379.3
| |
|-
| | 37
| | 456.5
| | [[13/10]]
|-
| | 38
| | 533.7
| | 34/25, [[15/11]]
|-
| | 39
| | 610.9
| |
|-
| | 40
| | 688.1
| |
|-
| | 41
| | 765.3
| | [[14/9]]
|-
| | 42
| | 842.5
| | [[13/8]]
|-
| | 43
| | 919.7
| | [[17/10]]
|-
| | 44
| | 996.9
| | [[16/9]]
|-
| | 45
| | 1074.1
| | [[13/7]]
|-
| | 46
| | 1151.3
| |
|-
| | 47
| | 28.5
| |
|-
| | 48
| | 105.7
| | [[17/16]]
|-
| | 49
| | 182.9
| | [[10/9]]
|-
| | 50
| | 260.1
| |
|-
| | 51
| | 337.3
| | [[17/14]]
|-
| | 52
| | 414.5
| | [[14/11]]
|-
| | 53
| | 491.7
| |
|-
| | 54
| | 568.9
| | [[25/18]]
|-
| | 55
| | 646.1
| | [[16/11]]
|-
| | 56
| | 723.3
| |
|-
| | 57
| | 800.5
| |
|-
| | 58
| | 877.7
| |
|-
| | 59
| | 954.9
| | [[26/15]]
|-
| | 60
| | 1032.1
| | [[20/11]]
|-
| | 61
| | 1109.3
| |
|-
| | 62
| | 1186.5
| |
|-
| | 63
| | 63.7
| |
|-
| | 64
| | 140.9
| | [[13/12]]
|-
| | 65
| | 218.1
| | [[17/15]], [[25/22]]
|-
| | 66
| | 295.3
| |
|-
| | 67
| | 372.5
| | [[26/21]]
|-
| | 68
| | 449.7
| |
|-
| | 69
| | 526.9
| |
|-
| | 70
| | 604.1
| | [[17/12]]
|-
| | 71
| | 681.3
| |
|-
| | 72
| | 758.5
| |
|-
| | 73
| | 835.7
| | [[34/21]]
|-
| | 74
| | 912.9
| |
|-
| | 75
| | 990.1
| |
|-
| | 76
| | 1067.3
| |
|-
| | 77
| | 1144.5
| |
|-
| | 78
| | 21.7
| |
|-
| | 79
| | 98.9
| |
|-
| | 80
| | 176.1
| |
|-
| | 81
| | 253.3
| |
|-
| | 82
| | 330.5
| |
|-
| | 83
| | 407.7
| |
|-
| | 84
| | 484.9
| |
|-
| | 85
| | 562.1
| |
|-
| | 86
| | 639.3
| | [[13/9]]
|-
| | 87
| | 716.5
| |
|-
| | 88
| | 793.7
| |
|-
| | 89
| | 870.9
| |
|-
| | 90
| | 948.1
| |
|-
| | 91
| | 1025.3
| |
|-
| | 92
| | 1102.5
| | [[17/9]]
|-
| | 93
| | 1179.7
| |
|-
| | 94
| | 56.9
| |
|-
| | 95
| | 134.1
| |
|-
| | 96
| | 211.3
| |
|-
| | 97
| | 288.5
| | [[13/11]]
|-
| | 98
| | 365.7
| |
|-
| | 99
| | 442.9
| |
|-
| | 100
| | 520.1
| |
|-
| | 101
| | 597.3
| |
|-
| | 102
| | 674.5
| |
|-
| | 103
| | 751.7
| | [[17/11]]
|}
<sup>a</sup> in 17-limit POTE tuning


[[Category:5/4]]
[[Category:Major third]]
[[Category:Equal-step tuning]]
[[Category:Equal-step tuning]]
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/5ed5/4"