Xenharmonic Wiki

71edt: Difference between revisions

← Older edit
VisualWikitext
Moremajorthanmajor (talk | contribs)
autopatrolled
3,126 edits
No edit summary
Fredg999 category edits (talk | contribs)
autopatrolled, Bots
4,330 edits
m Removing from Category:Edonoi using Cat-a-lot
 
(10 intermediate revisions by 6 users not shown)
Line 1: Line 1:
{{Infobox ET}}
'''71EDT''' is the [[Edt|equal division of the third harmonic]] into 71 parts of 26.7881 [[cent|cents]] each, corresponding to 44.7960 [[edo]] (45edo with 5.4644 cents octave stretch). It is related to the 13-limit temperament which tempers out 540/539, 1575/1573, 2200/2197, and 4375/4374, which is supported by [[45edo]] (45ef val), [[179edo]] (179ef val), [[224edo]], [[269edo]] (269ce val), and [[403edo]] (403def val).
'''71EDT''' is the [[Edt|equal division of the third harmonic]] into 71 parts of 26.7881 [[cent|cents]] each, corresponding to 44.7960 [[edo]] (45edo with 5.4644 cents octave stretch). It is related to the 13-limit temperament which tempers out 540/539, 1575/1573, 2200/2197, and 4375/4374, which is supported by [[45edo]] (45ef val), [[179edo]] (179ef val), [[224edo]], [[269edo]] (269ce val), and [[403edo]] (403def val).


71EDT is the 13th [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak EDT]].
71EDT is the 13th [[the Riemann zeta function and tuning#Removing primes|no-twos zeta peak EDT]].


== Harmonics ==
{{Harmonics in equal
| steps = 71
| num = 3
| denom = 1
| intervals = prime
}}
{{Harmonics in equal
| steps = 71
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = prime
}}
== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! | degree
! Degree
! | cents value
! [[Cent]]s
!hekts
! [[Hekt]]s
! | corresponding <br>JI intervals
! Corresponding<br />JI intervals
! | comments
! Comments
|-
|-
|  colspan="3"| 0
! colspan="3" | 0
| | '''exact [[1/1]]'''
| '''exact [[1/1]]'''
| |  
|  
|-
|-
| | 1
| 1
| | 26.7881
| 26.7881
|18.3099
| 18.3099
| | 66/65
| 66/65
| |  
|  
|-
|-
| | 2
| 2
| | 53.5762
| 53.5762
|36.6197
| 36.6197
| | 65/63
| 65/63
| |  
|  
|-
|-
| | 3
| 3
| | 80.3643
| 80.3643
|54.9296
| 54.9296
| | [[22/21]]
| [[22/21]]
| |  
|  
|-
|-
| | 4
| 4
| | 107.1524
| 107.1524
|73.2394
| 73.2394
| | 117/110
| 117/110
| |  
|  
|-
|-
| | 5
| 5
| | 133.9405
| 133.9405
|91.5493
| 91.5493
| | [[27/25]]
| [[27/25]]
| |  
|  
|-
|-
| | 6
| 6
| | 160.7286
| 160.7286
|109.85915
| 109.85915
| | 169/154
| 169/154
| |  
|  
|-
|-
| | 7
| 7
| | 187.5167
| 187.5167
|128.169
| 128.169
| | 39/35
| 39/35
| |  
|  
|-
|-
| | 8
| 8
| | 214.3048
| 214.3048
|146.4789
| 146.4789
| | 147/130, 198/175
| 147/130, 198/175
| |  
|  
|-
|-
| | 9
| 9
| | 241.0929
| 241.0929
|164.7887
| 164.7887
| | 169/147
| 169/147
| |  
|  
|-
|-
| | 10
| 10
| | 267.8810
| 267.8810
|183.0986
| 183.0986
| | [[7/6]]
| [[7/6]]
| |  
|  
|-
|-
| | 11
| 11
| | 294.6691
| 294.6691
|201.40845
| 201.40845
| | 77/65
| 77/65
| |  
|  
|-
|-
| | 12
| 12
| | 321.4572
| 321.4572
|219.7183
| 219.7183
| | 65/54
| 65/54
| |  
|  
|-
|-
| | 13
| 13
| | 348.2453
| 348.2453
|238.0282
| 238.0282
| | [[11/9]]
| [[11/9]]
| |  
|  
|-
|-
| | 14
| 14
| | 375.0334
| 375.0334
|256.338
| 256.338
| | 273/220
| 273/220
| |  
|  
|-
|-
| | 15
| 15
| | 401.8215
| 401.8215
|274.6479
| 274.6479
| | 63/50
| 63/50
| |  
|  
|-
|-
| | 16
| 16
| | 428.6096
| 428.6096
|292.95775
| 292.95775
| | 169/132
| 169/132
| |  
|  
|-
|-
| | 17
| 17
| | 455.3977
| 455.3977
|311.2676
| 311.2676
| | [[13/10]]
| [[13/10]]
| |  
|  
|-
|-
| | 18
| 18
| | 482.1858
| 482.1858
|329.5775
| 329.5775
| | 33/25
| 33/25
| |  
|  
|-
|-
| | 19
| 19
| | 508.9739
| 508.9739
|347.8873
| 347.8873
| | 169/126
| 169/126
| |  
|  
|-
|-
| | 20
| 20
| | 535.7620
| 535.7620
|366.1972
| 366.1972
| | [[15/11]]
| [[15/11]]
| |  
|  
|-
|-
| | 21
| 21
| | 562.5501
| 562.5501
|384.507
| 384.507
| | [[18/13]]
| [[18/13]]
| |  
|  
|-
|-
| | 22
| 22
| | 589.3382
| 589.3382
|402.8169
| 402.8169
| | ([[45/32]])
| ([[45/32]])
| |  
|  
|-
|-
| | 23
| 23
| | 616.1263
| 616.1263
|421.1268
| 421.1268
| | [[10/7]]
| [[10/7]]
| |  
|  
|-
|-
| | 24
| 24
| | 642.9144
| 642.9144
|439.4366
| 439.4366
| | 132/91
| 132/91
| |  
|  
|-
|-
| | 25
| 25
| | 669.7025
| 669.7025
|457.7465
| 457.7465
| | 22/15
| 22/15
| |  
|  
|-
|-
| | 26
| 26
| | 696.4906
| 696.4906
|476.0563
| 476.0563
| | 486/325, 220/147
| 486/325, 220/147
| | pseudo-[[3/2]]
| pseudo-[[3/2]]
|-
|-
| | 27
| 27
| | 723.2787
| 723.2787
|494.3662
| 494.3662
| |50/33
| 50/33
| |  
|  
|-
|-
| | 28
| 28
| | 750.0668
| 750.0668
|512.6761
| 512.6761
| | 54/35
| 54/35
| |  
|  
|-
|-
| | 29
| 29
| | 776.8549
| 776.8549
|530.9859
| 530.9859
| | 264/169
| 264/169
| |  
|  
|-
|-
| | 30
| 30
| | 803.643
| 803.643
|549.2958
| 549.2958
| | 35/22
| 35/22
| |  
|  
|-
|-
| | 31
| 31
| | 830.4311
| 830.4311
|567.6056
| 567.6056
| | [[21/13]]
| [[21/13]]
| |  
|  
|-
|-
| | 32
| 32
| | 857.2192
| 857.2192
|585.9155
| 585.9155
| | 18/11
| 18/11
| |  
|  
|-
|-
| | 33
| 33
| | 884.0073
| 884.0073
|604.22535
| 604.22535
| | [[5/3]]
| [[5/3]]
| |  
|  
|-
|-
| | 34
| 34
| | 910.7954
| 910.7954
|622.5352
| 622.5352
| | [[22/13]]
| [[22/13]]
| |  
|  
|-
|-
| | 35
| 35
| | 937.5835
| 937.5835
|640.8451
| 640.8451
| |12/7
| 12/7
| |  
|  
|-
|-
| | 36
| 36
| | 964.3715
| 964.3715
|659.1549
| 659.1549
| |7/4
| 7/4
| |  
|  
|-
|-
| | 37
| 37
| | 991.1596
| 991.1596
|677.4648
| 677.4648
| | 39/22
| 39/22
| |  
|  
|-
|-
| | 38
| 38
| | 1017.9477
| 1017.9477
|695.77465
| 695.77465
| | [[9/5]]
| [[9/5]]
| |  
|  
|-
|-
| | 39
| 39
| | 1044.7358
| 1044.7358
|714.0845
| 714.0845
| | 11/6
| 11/6
| |  
|  
|-
|-
| | 40
| 40
| | 1071.5239
| 1071.5239
|732.3944
| 732.3944
| | [[13/7]]
| [[13/7]]
| |  
|  
|-
|-
| | 41
| 41
| | 1098.312
| 1098.312
|750.7042
| 750.7042
| | 66/35
| 66/35
| |  
|  
|-
|-
| | 42
| 42
| | 1125.1001
| 1125.1001
|769.0141
| 769.0141
| | 21/11
| 21/11
| |  
|  
|-
|-
| | 43
| 43
| | 1151.8882
| 1151.8882
|787.3239
| 787.3239
| | 35/18
| 35/18
| |  
|  
|-
|-
| | 44
| 44
| | 1178.6763
| 1178.6763
|805.6338
| 805.6338
| | 22/13
| 22/13
| |  
|  
|-
|-
| | 45
| 45
| | 1205.4644
| 1205.4644
|823.9437
| 823.9437
| | 441/220, 325/162
| 441/220, 325/162
| | pseudo-[[octave]]
| pseudo-[[octave]]
|-
|-
| | 46
| 46
| | 1232.2525
| 1232.2525
|842.2535
| 842.2535
| | 45/22
| 45/22
| |  
|  
|-
|-
| | 47
| 47
| | 1259.0406
| 1259.0406
|860.5634
| 860.5634
| | 91/44
| 91/44
| |  
|  
|-
|-
| | 48
| 48
| | 1285.8287
| 1285.8287
|878.8732
| 878.8732
| | [[21/20|21/10]]
| [[21/20|21/10]]
| |  
|  
|-
|-
| | 49
| 49
| | 1312.6168
| 1312.6168
|897.1831
| 897.1831
| | ([[16/15|32/15]])
| ([[16/15|32/15]])
| |  
|  
|-
|-
| | 50
| 50
| | 1339.4049
| 1339.4049
|915.493
| 915.493
| | [[13/6]]
| [[13/6]]
| |  
|  
|-
|-
| | 51
| 51
| | 1366.193
| 1366.193
|933.8028
| 933.8028
| | [[11/5]]
| [[11/5]]
| |  
|  
|-
|-
| | 52
| 52
| | 1392.9811
| 1392.9811
|952.1127
| 952.1127
| | 378/169
| 378/169
| |  
|  
|-
|-
| | 53
| 53
| | 1419.7692
| 1419.7692
|970.4225
| 970.4225
| | [[25/22|25/11]]
| [[25/11]]
| |  
|  
|-
|-
| | 54
| 54
| | 1446.5573
| 1446.5573
|988.7324
| 988.7324
| | [[15/13|30/13]]
| [[15/13|30/13]]
| |  
|  
|-
|-
| | 55
| 55
| | 1473.3454
| 1473.3454
|1007.04225
| 1007.04225
| | 396/169
| 396/169
| |  
|  
|-
|-
| | 56
| 56
| | 1500.1335
| 1500.1335
|1025.3521
| 1025.3521
| | 50/21
| 50/21
| |  
|  
|-
|-
| | 57
| 57
| | 1526.9216
| 1526.9216
|1043.662
| 1043.662
| | 220/91
| 220/91
| |  
|  
|-
|-
| | 58
| 58
| | 1553.7097
| 1553.7097
|1061.9718
| 1061.9718
| | [[27/22|27/11]]
| [[27/22|27/11]]
| |  
|  
|-
|-
| | 59
| 59
| | 1580.4978
| 1580.4978
|1080.2817
| 1080.2817
| | 162/65
| 162/65
| |  
|  
|-
|-
| | 60
| 60
| | 1607.2859
| 1607.2859
|1098.59155
| 1098.59155
| | 195/77
| 195/77
| |  
|  
|-
|-
| | 61
| 61
| | 1634.0740
| 1634.0740
|1161.9014
| 1161.9014
| | [[9/7|18/7]]
| [[9/7|18/7]]
| |  
|  
|-
|-
| | 62
| 62
| | 1660.8621
| 1660.8621
|1135.2113
| 1135.2113
| | 441/169
| 441/169
| |  
|  
|-
|-
| | 63
| 63
| | 1687.6502
| 1687.6502
|1153.5211
| 1153.5211
| | 175/66, 130/49
| 175/66, 130/49
| |  
|  
|-
|-
| | 64
| 64
| | 1714.4383
| 1714.4383
|1171.831
| 1171.831
| | 35/13, 132/49
| 35/13, 132/49
| |  
|  
|-
|-
| | 65
| 65
| | 1741.2264
| 1741.2264
|1190.14085
| 1190.14085
| | 462/169
| 462/169
| |  
|  
|-
|-
| | 66
| 66
| | 1768.0145
| 1768.0145
|1208.4507
| 1208.4507
| | [[25/18|25/9]]
| [[25/18|25/9]]
| |  
|  
|-
|-
| | 67
| 67
| | 1794.8026
| 1794.8026
|1226.7606
| 1226.7606
| | 110/39
| 110/39
| |  
|  
|-
|-
| | 68
| 68
| | 1821.5907
| 1821.5907
|1245.0704
| 1245.0704
| | 63/22
| 63/22
| |  
|  
|-
|-
| | 69
| 69
| | 1848.3788
| 1848.3788
|1263.3803
| 1263.3803
| | 189/65
| 189/65
| |  
|  
|-
|-
| | 70
| 70
| | 1875.1669
| 1875.1669
|1281.6901
| 1281.6901
| | 65/22
| 65/22
| |  
|  
|-
|-
| | 71
| 71
| | 1901.9550
| 1901.9550
|1300
| 1300
| | '''exact [[3/1]]'''
| '''exact [[3/1]]'''
| | [[3/2|just perfect fifth]] plus an octave
| [[3/2|just perfect fifth]] plus an octave
|}
|}
[[Category:Edt]]
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/71edt"