45edt: Difference between revisions

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| | Degrees
| | Degrees
| | Cents
| | Cents
|hekts
| | Approximate Ratios
| | Approximate Ratios
|-
|-
| | 0
| | 0
| | 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
| |
|-
|-
| | 2
| | 2
| | 84.531
| | 84.531
|57.778
| | [[21/20]]
| | [[21/20]]
|-
|-
| | 3
| | 3
| | 126.797
| | 126.797
|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
| | 11/10
| | 11/10
|-
|-
| | 5
| | 5
| | 211.328
| | 211.328
|144.444
| | 9/8
| | 9/8
|-
|-
| | 6
| | 6
| | 253.594
| | 253.594
|173.333
| | [[15/13]]
| | [[15/13]]
|-
|-
| | 7
| | 7
| | 295.860
| | 295.86
|202.222
| | 19/16
| | 19/16
|-
|-
| | 8
| | 8
| | 338.125
| | 338.125
|231.111
| | 17/14
| | 17/14
|-
|-
| | 9
| | 9
| | 380.391
| | 380.391
|260
| | <span style="color: #660000;">[[5/4]]</span>
| | <span style="color: #660000;">[[5/4]]</span>
|-
|-
| | 10
| | 10
| | 422.657
| | 422.657
| |  
|288.889
| |14/11
|-
|-
| | 11
| | 11
| | 464.922
| | 464.922
| | [[17/13]]
|317.778
| | [[21/16]], [[17/13]]
|-
|-
| | 12
| | 12
| | 507.188
| | 507.188
|336.667
| | [[4/3]]
| | [[4/3]]
|-
|-
| | 13
| | 13
| | 549.454
| | 549.454
|375.556
| | 11/8
| | 11/8
|-
|-
| | 14
| | 14
| | 591.719
| | 591.719
|304.444
| | 7/5
| | 7/5
|-
|-
| | 15
| | 15
| | 633.985
| | 633.985
|433.333
| | [[13/9]]
| | [[13/9]]
|-
|-
| | 16
| | 16
| | 676.251
| | 676.251
| |  
|462.222
| |40/27. 189/128
|-
|-
| | 17
| | 17
| | 718.516
| | 718.516
|491.111
| | 50/33
| | 50/33
|-
|-
| | 18
| | 18
| | 760.782
| | 760.782
|520
| | <span style="color: #660000;">[[14/9]]</span>
| | <span style="color: #660000;">[[14/9]]</span>
|-
|-
| | 19
| | 19
| | 803.048
| | 803.048
|548.889
| | 8/5
| | 8/5
|-
|-
| | 20
| | 20
| | 845.313
| | 845.313
| |  
|577.778
| |13/8
|-
|-
| | 21
| | 21
| | 887.579
| | 887.579
| | [[5/3]]
|606.667
| | [[5/3]], 17/11
|-
|-
| | 22
| | 22
| | 929.845
| | 929.845
|635.556
| | 12/7
| | 12/7
|-
|-
| | 23
| | 23
| | 972.110
| | 972.110
|664.444
| | 7/4
| | 7/4
|-
|-
| | 24
| | 24
| | 1014.376
| | 1014.376
| | [[9/5]]
|693.333
| | [[9/5]], 33/17
|-
|-
| | 25
| | 25
| | 1056.642
| | 1056.642
| |  
|722.222
| |24/13
|-
|-
| | 26
| | 26
| | 1098.907
| | 1098.907
|751.111
| | 17/9
| | 17/9
|-
|-
| | 27
| | 27
| | 1141.173
| | 1141.173
|780
| | <span style="color: #660000;">[[27/14]]</span>
| | <span style="color: #660000;">[[27/14]]</span>
|-
|-
| | 28
| | 28
| | 1183.439
| | 1183.439
| |  
|808.889
| |99/50
|-
|-
| | 29
| | 29
| | 1225.704
| | 1225.704
| |  
|837.778
| |81/40, 128/63
|-
|-
| | 30
| | 30
| | 1267.970
| | 1267.97
|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
| | 32/15
| | 32/15
|-
|-
| | 32
| | 32
| | 1352.501
| | 1352.501
|924.444
| | 24/11
| | 24/11
|-
|-
| | 33
| | 33
| | 1394.767
| | 1394.767
|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
| | 16/7
|982.222
| | 16/7, 39/17
|-
|-
| | 35
| | 35
| | 1479.298
| | 1479.298
| |  
|1011.111
| |33/14
|-
|-
| | 36
| | 36
| | 1521.564
| | 1521.564
|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
| | 1563.830
| | 1563.83
| |  
|1068.889
| |42/17
|-
|-
| | 38
| | 38
| | 1606.095
| | 1606.095
| |  
|1097.778
| |48/19
|-
|-
| | 39
| | 39
| | 1648.361
| | 1648.361
|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
| | [[8/3]]
| | [[8/3]]
|-
|-
| | 41
| | 41
| | 1732.892
| | 1732.892
|1184.444
| | 30/11
| | 30/11
|-
|-
| | 42
| | 42
| | 1775.158
| | 1775.158
| | <span style="color: #660000;">[[14/5]]</span> ([[7/5]] plus an octave)
|1213.333
| | <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
| | [[10/7|20/7]]
| | [[10/7|20/7]]
|-
|-
| | 44
| | 44
| | 1859.689
| | 1859.689
|1271.111
| |  
| |  
|-
|-
| | 45
| | 45
| | 1901.955
| | 1901.955
|1300
| | <span style="color: #660000;">[[3/1]]</span>
| | <span style="color: #660000;">[[3/1]]</span>
|}
|}

Revision as of 21:25, 20 April 2019

45EDT is the equal division of the third harmonic into 45 parts of 42.2657 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 no-twos zeta peak edt.

Intervals of 45EDT

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