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'''45EDT''' is the [[Edt|equal division of the third harmonic]] into 45 parts of 42.2657 [[cent|cents]] each, corresponding to 28.3918 [[edo]]. It makes for a strong no-twos 17-limit system, particularly with respect to the tuning of 5, 13, and 17. It tempers out 3125/3087 in the 7-limit, 891/875 and 2475/2401 in the 11-limit, 275/273, 351/343, 847/845 and 2197/2187 in the 13-limit, and 121/119, 459/455 and 2025/2023 in the 17-limit (no-twos subgroup). It is the tenth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak edt]].
{{Infobox ET}}
'''45EDT''' is the [[Edt|equal division of the third harmonic]] into 45 parts of 42.2657 [[cent|cents]] each, corresponding to 28.3918 [[edo]]. It makes for a strong no-twos 17-limit system, particularly with respect to the tuning of 5, 13, and 17. It tempers out 3125/3087 in the 7-limit, 891/875 and 2475/2401 in the 11-limit, 275/273, 351/343, 847/845 and 2197/2187 in the 13-limit, and 121/119, 459/455 and 2025/2023 in the 17-limit (no-twos subgroup). It is the tenth [[the Riemann zeta function and tuning#Removing primes|no-twos zeta peak edt]].


=Intervals of 45EDT=
== Harmonics ==
{{Harmonics in equal
| steps = 45
| num = 3
| denom = 1
| intervals = integer
}}
{{Harmonics in equal
| steps = 45
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = integer
}}


== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
| | Degrees
! Degrees
| | Cents
! [[Cent]]s
|hekts
! [[Hekt]]s
| | Approximate Ratios
! Approximate ratios
|-
|-
| | 0
! colspan="3" | 0
|  colspan="2"| 0
| <span style="color: #660000;">[[1/1]]</span>
| | <span style="color: #660000;">[[1/1]]</span>
|-
|-
| | 1
| 1
| | 42.266
| 42.266
|28.889
| 28.889
| |
|  
|-
|-
| | 2
| 2
| | 84.531
| 84.531
|57.778
| 57.778
| | [[21/20]]
| [[21/20]]
|-
|-
| | 3
| 3
| | 126.797
| 126.797
|86.667
| 86.667
| | [[14/13]], [[15/14]], [[16/15]], 29/27
| [[14/13]], [[15/14]], [[16/15]], 29/27
|-
|-
| | 4
| 4
| | 169.063
| 169.063
|115.556
| 115.556
| | 11/10
| 11/10
|-
|-
| | 5
| 5
| | 211.328
| 211.328
|144.444
| 144.444
| | 9/8
| 9/8
|-
|-
| | 6
| 6
| | 253.594
| 253.594
|173.333
| 173.333
| | [[15/13]]
| [[15/13]]
|-
|-
| | 7
| 7
| | 295.86
| 295.86
|202.222
| 202.222
| | 19/16
| 19/16
|-
|-
| | 8
| 8
| | 338.125
| 338.125
|231.111
| 231.111
| | 17/14
| 17/14
|-
|-
| | 9
| 9
| | 380.391
| 380.391
|260
| 260
| | <span style="color: #660000;">[[5/4]]</span>
| <span style="color: #660000;">[[5/4]]</span>
|-
|-
| | 10
| 10
| | 422.657
| 422.657
|288.889
| 288.889
| |14/11
| 14/11
|-
|-
| | 11
| 11
| | 464.922
| 464.922
|317.778
| 317.778
| | [[21/16]], [[17/13]]
| [[21/16]], [[17/13]]
|-
|-
| | 12
| 12
| | 507.188
| 507.188
|336.667
| 336.667
| | [[4/3]]
| [[4/3]]
|-
|-
| | 13
| 13
| | 549.454
| 549.454
|375.556
| 375.556
| | 11/8
| 11/8
|-
|-
| | 14
| 14
| | 591.719
| 591.719
|304.444
| 304.444
| | 7/5
| 7/5
|-
|-
| | 15
| 15
| | 633.985
| 633.985
|433.333
| 433.333
| | [[13/9]]
| [[13/9]]
|-
|-
| | 16
| 16
| | 676.251
| 676.251
|462.222
| 462.222
| |40/27. 189/128
| 40/27. 189/128
|-
|-
| | 17
| 17
| | 718.516
| 718.516
|491.111
| 491.111
| | 50/33
| 50/33
|-
|-
| | 18
| 18
| | 760.782
| 760.782
|520
| 520
| | <span style="color: #660000;">[[14/9]]</span>
| <span style="color: #660000;">[[14/9]]</span>
|-
|-
| | 19
| 19
| | 803.048
| 803.048
|548.889
| 548.889
| | 8/5
| 8/5
|-
|-
| | 20
| 20
| | 845.313
| 845.313
|577.778
| 577.778
| |13/8
| 13/8
|-
|-
| | 21
| 21
| | 887.579
| 887.579
|606.667
| 606.667
| | [[5/3]], 17/11
| [[5/3]], 17/11
|-
|-
| | 22
| 22
| | 929.845
| 929.845
|635.556
| 635.556
| | 12/7
| 12/7
|-
|-
| | 23
| 23
| | 972.110
| 972.110
|664.444
| 664.444
| | 7/4
| 7/4
|-
|-
| | 24
| 24
| | 1014.376
| 1014.376
|693.333
| 693.333
| | [[9/5]], 33/17
| [[9/5]], 33/17
|-
|-
| | 25
| 25
| | 1056.642
| 1056.642
|722.222
| 722.222
| |24/13
| 24/13
|-
|-
| | 26
| 26
| | 1098.907
| 1098.907
|751.111
| 751.111
| | 17/9
| 17/9
|-
|-
| | 27
| 27
| | 1141.173
| 1141.173
|780
| 780
| | <span style="color: #660000;">[[27/14]]</span>
| <span style="color: #660000;">[[27/14]]</span>
|-
|-
| | 28
| 28
| | 1183.439
| 1183.439
|808.889
| 808.889
| |99/50
| 99/50
|-
|-
| | 29
| 29
| | 1225.704
| 1225.704
|837.778
| 837.778
| |81/40, 128/63
| 81/40, 128/63
|-
|-
| | 30
| 30
| | 1267.97
| 1267.97
|866.667
| 866.667
| | <span style="color: #660000;">[[27/26|27/13]]</span>
| <span style="color: #660000;">[[27/26|27/13]]</span>
|-
|-
| | 31
| 31
| | 1310.236
| 1310.236
|895.556
| 895.556
| | 32/15
| 32/15
|-
|-
| | 32
| 32
| | 1352.501
| 1352.501
|924.444
| 924.444
| | 24/11
| 24/11
|-
|-
| | 33
| 33
| | 1394.767
| 1394.767
|953.333
| 953.333
| | <span style="color: #660000;">[[9/4]]</span> ([[9/8]] plus an octave)
| <span style="color: #660000;">[[9/4]]</span> ([[9/8]] plus an octave)
|-
|-
| | 34
| 34
| | 1437.033
| 1437.033
|982.222
| 982.222
| | 16/7, 39/17
| 16/7, 39/17
|-
|-
| | 35
| 35
| | 1479.298
| 1479.298
|1011.111
| 1011.111
| |33/14
| 33/14
|-
|-
| | 36
| 36
| | 1521.564
| 1521.564
|1040
| 1040
| | <span style="color: #660000;">[[12/5]]</span> (<span style="color: #660000;">[[6/5]]</span> plus an octave)
| <span style="color: #660000;">[[12/5]]</span> (<span style="color: #660000;">[[6/5]]</span> plus an octave)
|-
|-
| | 37
| 37
| | 1563.83
| 1563.83
|1068.889
| 1068.889
| |42/17
| 42/17
|-
|-
| | 38
| 38
| | 1606.095
| 1606.095
|1097.778
| 1097.778
| |48/19
| 48/19
|-
|-
| | 39
| 39
| | 1648.361
| 1648.361
|1126.667
| 1126.667
| | <span style="color: #660000;">[[13/5]]</span> ([[13/10]] plus an octave)
| <span style="color: #660000;">[[13/5]]</span> ([[13/10]] plus an octave)
|-
|-
| | 40
| 40
| | 1690.627
| 1690.627
|1155.556
| 1155.556
| | [[8/3]]
| [[8/3]]
|-
|-
| | 41
| 41
| | 1732.892
| 1732.892
|1184.444
| 1184.444
| | 30/11
| 30/11
|-
|-
| | 42
| 42
| | 1775.158
| 1775.158
|1213.333
| 1213.333
| | <span style="color: #660000;">39/14,[[14/5]]</span> ([[7/5]] plus an octave), 45/16, 81/29
| <span style="color: #660000;">39/14, [[14/5]]</span> ([[7/5]] plus an octave), 45/16, 81/29
|-
|-
| | 43
| 43
| | 1817.424
| 1817.424
|1242.222
| 1242.222
| | [[10/7|20/7]]
| [[10/7|20/7]]
|-
|-
| | 44
| 44
| | 1859.689
| 1859.689
|1271.111
| 1271.111
| |  
|  
|-
|-
| | 45
| 45
| | 1901.955
| 1901.955
|1300
| 1300
| | <span style="color: #660000;">[[3/1]]</span>
| <span style="color: #660000;">[[3/1]]</span>
|}
|}


[[Category:Edt]]
{{todo|expand}}
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/45edt"