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{{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
! | corresponding <br>JI intervals
! [[Hekt]]s
! | comments
! Corresponding<br />JI intervals
! Comments
|-
|-
| | 0
! colspan="3" | 0
| | 0.0000
| '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
|  
| |  
|-
|-
| | 1
| 1
| | 26.7881
| 26.7881
| | 66/65
| 18.3099
| |  
| 66/65
|  
|-
|-
| | 2
| 2
| | 53.5762
| 53.5762
| | 65/63
| 36.6197
| |  
| 65/63
|  
|-
|-
| | 3
| 3
| | 80.3643
| 80.3643
| | [[22/21]]
| 54.9296
| |  
| [[22/21]]
|  
|-
|-
| | 4
| 4
| | 107.1524
| 107.1524
| | 117/110
| 73.2394
| |  
| 117/110
|  
|-
|-
| | 5
| 5
| | 133.9405
| 133.9405
| | [[27/25]]
| 91.5493
| |  
| [[27/25]]
|  
|-
|-
| | 6
| 6
| | 160.7286
| 160.7286
| | 169/154
| 109.85915
| |  
| 169/154
|  
|-
|-
| | 7
| 7
| | 187.5167
| 187.5167
| | 39/35
| 128.169
| |  
| 39/35
|  
|-
|-
| | 8
| 8
| | 214.3048
| 214.3048
| | 147/130, 198/175
| 146.4789
| |  
| 147/130, 198/175
|  
|-
|-
| | 9
| 9
| | 241.0929
| 241.0929
| | 169/147
| 164.7887
| |  
| 169/147
|  
|-
|-
| | 10
| 10
| | 267.8810
| 267.8810
| | [[7/6]]
| 183.0986
| |  
| [[7/6]]
|  
|-
|-
| | 11
| 11
| | 294.6691
| 294.6691
| | 77/65
| 201.40845
| |  
| 77/65
|  
|-
|-
| | 12
| 12
| | 321.4572
| 321.4572
| | 65/54
| 219.7183
| |  
| 65/54
|  
|-
|-
| | 13
| 13
| | 348.2453
| 348.2453
| | [[11/9]]
| 238.0282
| |  
| [[11/9]]
|  
|-
|-
| | 14
| 14
| | 375.0334
| 375.0334
| | 273/220
| 256.338
| |  
| 273/220
|  
|-
|-
| | 15
| 15
| | 401.8215
| 401.8215
| | 63/50
| 274.6479
| |  
| 63/50
|  
|-
|-
| | 16
| 16
| | 428.6096
| 428.6096
| | 169/132
| 292.95775
| |  
| 169/132
|  
|-
|-
| | 17
| 17
| | 455.3977
| 455.3977
| | [[13/10]]
| 311.2676
| |  
| [[13/10]]
|  
|-
|-
| | 18
| 18
| | 482.1858
| 482.1858
| | 33/25
| 329.5775
| |  
| 33/25
|  
|-
|-
| | 19
| 19
| | 508.9739
| 508.9739
| | 169/126
| 347.8873
| |  
| 169/126
|  
|-
|-
| | 20
| 20
| | 535.7620
| 535.7620
| | [[15/11]]
| 366.1972
| |  
| [[15/11]]
|  
|-
|-
| | 21
| 21
| | 562.5501
| 562.5501
| | [[18/13]]
| 384.507
| |  
| [[18/13]]
|  
|-
|-
| | 22
| 22
| | 589.3382
| 589.3382
| | ([[45/32]])
| 402.8169
| |  
| ([[45/32]])
|  
|-
|-
| | 23
| 23
| | 616.1263
| 616.1263
| | [[10/7]]
| 421.1268
| |  
| [[10/7]]
|  
|-
|-
| | 24
| 24
| | 642.9144
| 642.9144
| | 132/91
| 439.4366
| |  
| 132/91
|  
|-
|-
| | 25
| 25
| | 669.7025
| 669.7025
| |  
| 457.7465
| |  
| 22/15
|  
|-
|-
| | 26
| 26
| | 696.4906
| 696.4906
| | 486/325, 220/147
| 476.0563
| | pseudo-[[3/2]]
| 486/325, 220/147
| pseudo-[[3/2]]
|-
|-
| | 27
| 27
| | 723.2787
| 723.2787
| |  
| 494.3662
| |  
| 50/33
|  
|-
|-
| | 28
| 28
| | 750.0668
| 750.0668
| | 54/35
| 512.6761
| |  
| 54/35
|  
|-
|-
| | 29
| 29
| | 776.8549
| 776.8549
| |  
| 530.9859
| |  
| 264/169
|  
|-
|-
| | 30
| 30
| | 803.6430
| 803.643
| | 35/22
| 549.2958
| |  
| 35/22
|  
|-
|-
| | 31
| 31
| | 830.4311
| 830.4311
| | [[21/13]]
| 567.6056
| |  
| [[21/13]]
|  
|-
|-
| | 32
| 32
| | 857.2192
| 857.2192
| |  
| 585.9155
| |  
| 18/11
|  
|-
|-
| | 33
| 33
| | 884.0073
| 884.0073
| | [[5/3]]
| 604.22535
| |  
| [[5/3]]
|  
|-
|-
| | 34
| 34
| | 910.7954
| 910.7954
| | [[22/13]]
| 622.5352
| |  
| [[22/13]]
|  
|-
|-
| | 35
| 35
| | 937.5835
| 937.5835
| | 189/110
| 640.8451
| |  
| 12/7
|  
|-
|-
| | 36
| 36
| | 964.3715
| 964.3715
| | 110/63
| 659.1549
| |  
| 7/4
|  
|-
|-
| | 37
| 37
| | 991.1596
| 991.1596
| | 39/22
| 677.4648
| |  
| 39/22
|  
|-
|-
| | 38
| 38
| | 1017.9477
| 1017.9477
| | [[9/5]]
| 695.77465
| |  
| [[9/5]]
|  
|-
|-
| | 39
| 39
| | 1044.7358
| 1044.7358
| |  
| 714.0845
| |  
| 11/6
|  
|-
|-
| | 40
| 40
| | 1071.5239
| 1071.5239
| | [[13/7]]
| 732.3944
| |  
| [[13/7]]
|  
|-
|-
| | 41
| 41
| | 1098.3120
| 1098.312
| | 66/35
| 750.7042
| |  
| 66/35
|  
|-
|-
| | 42
| 42
| | 1125.1001
| 1125.1001
| |  
| 769.0141
| |  
| 21/11
|  
|-
|-
| | 43
| 43
| | 1151.8882
| 1151.8882
| | 35/18
| 787.3239
| |  
| 35/18
|  
|-
|-
| | 44
| 44
| | 1178.6763
| 1178.6763
| |  
| 805.6338
| |  
| 22/13
|  
|-
|-
| | 45
| 45
| | 1205.4644
| 1205.4644
| | 441/220, 325/162
| 823.9437
| | pseudo-[[octave]]
| 441/220, 325/162
| pseudo-[[octave]]
|-
|-
| | 46
| 46
| | 1232.2525
| 1232.2525
| |  
| 842.2535
| |  
| 45/22
|  
|-
|-
| | 47
| 47
| | 1259.0406
| 1259.0406
| | 91/44
| 860.5634
| |  
| 91/44
|  
|-
|-
| | 48
| 48
| | 1285.8287
| 1285.8287
| | [[21/20|21/10]]
| 878.8732
| |  
| [[21/20|21/10]]
|  
|-
|-
| | 49
| 49
| | 1312.6168
| 1312.6168
| | ([[16/15|32/15]])
| 897.1831
| |  
| ([[16/15|32/15]])
|  
|-
|-
| | 50
| 50
| | 1339.4049
| 1339.4049
| | [[13/6]]
| 915.493
| |  
| [[13/6]]
|  
|-
|-
| | 51
| 51
| | 1366.1930
| 1366.193
| | [[11/5]]
| 933.8028
| |  
| [[11/5]]
|  
|-
|-
| | 52
| 52
| | 1392.9811
| 1392.9811
| | 378/169
| 952.1127
| |  
| 378/169
|  
|-
|-
| | 53
| 53
| | 1419.7692
| 1419.7692
| | [[25/22|25/11]]
| 970.4225
| |  
| [[25/11]]
|  
|-
|-
| | 54
| 54
| | 1446.5573
| 1446.5573
| | [[15/13|30/13]]
| 988.7324
| |  
| [[15/13|30/13]]
|  
|-
|-
| | 55
| 55
| | 1473.3454
| 1473.3454
| | 396/169
| 1007.04225
| |  
| 396/169
|  
|-
|-
| | 56
| 56
| | 1500.1335
| 1500.1335
| | 50/21
| 1025.3521
| |  
| 50/21
|  
|-
|-
| | 57
| 57
| | 1526.9216
| 1526.9216
| | 220/91
| 1043.662
| |  
| 220/91
|  
|-
|-
| | 58
| 58
| | 1553.7097
| 1553.7097
| | [[27/22|27/11]]
| 1061.9718
| |  
| [[27/22|27/11]]
|  
|-
|-
| | 59
| 59
| | 1580.4978
| 1580.4978
| | 162/65
| 1080.2817
| |  
| 162/65
|  
|-
|-
| | 60
| 60
| | 1607.2859
| 1607.2859
| | 195/77
| 1098.59155
| |  
| 195/77
|  
|-
|-
| | 61
| 61
| | 1634.0740
| 1634.0740
| | [[9/7|18/7]]
| 1161.9014
| |  
| [[9/7|18/7]]
|  
|-
|-
| | 62
| 62
| | 1660.8621
| 1660.8621
| | 441/169
| 1135.2113
| |  
| 441/169
|  
|-
|-
| | 63
| 63
| | 1687.6502
| 1687.6502
| | 175/66, 130/49
| 1153.5211
| |  
| 175/66, 130/49
|  
|-
|-
| | 64
| 64
| | 1714.4383
| 1714.4383
| | 35/13, 132/49
| 1171.831
| |  
| 35/13, 132/49
|  
|-
|-
| | 65
| 65
| | 1741.2264
| 1741.2264
| | 462/169
| 1190.14085
| |  
| 462/169
|  
|-
|-
| | 66
| 66
| | 1768.0145
| 1768.0145
| | [[25/18|25/9]]
| 1208.4507
| |  
| [[25/18|25/9]]
|  
|-
|-
| | 67
| 67
| | 1794.8026
| 1794.8026
| | 110/39
| 1226.7606
| |  
| 110/39
|  
|-
|-
| | 68
| 68
| | 1821.5907
| 1821.5907
| | 63/22
| 1245.0704
| |  
| 63/22
|  
|-
|-
| | 69
| 69
| | 1848.3788
| 1848.3788
| | 189/65
| 1263.3803
| |  
| 189/65
|  
|-
|-
| | 70
| 70
| | 1875.1669
| 1875.1669
| | 65/22
| 1281.6901
| |  
| 65/22
|  
|-
|-
| | 71
| 71
| | 1901.9550
| 1901.9550
| | '''exact [[3/1]]'''
| 1300
| | [[3/2|just perfect fifth]] plus an octave
| '''exact [[3/1]]'''
| [[3/2|just perfect fifth]] plus an octave
|}
|}
[[Category:Edt]]
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/71edt"