45edt: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Wikispaces>FREEZE
No edit summary
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,012 edits
No edit summary
Line 1: Line 1:
The 45 equal division of 3, the tritave, divides it into 45 equal parts of 42.266 cents each, corresponding to 28.392 edo. It makes for a strong 17-limit no-twos 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. It is the tenth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak edt]].
'''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]].


=<span style="font-size: 1.4em;">Intervals of 45edt</span>=
=Intervals of 45EDT=


{| class="wikitable"
{| class="wikitable"
Line 11: Line 11:
| | 0
| | 0
| | 0
| | 0
| | <span style="color: #660000;"><span style="color: #660000;">[[1/1|1/1]]</span></span>
| | <span style="color: #660000;">[[1/1]]</span>
|-
|-
| | 1
| | 1
Line 19: Line 19:
| | 2
| | 2
| | 84.531
| | 84.531
| |  
| | [[21/20]]
|-
|-
| | 3
| | 3
| | 126.797
| | 126.797
| | [[14/13|14/13]], [[15/14|15/14]], [[16/15|16/15]], 29/27
| | [[14/13]], [[15/14]], [[16/15]], 29/27
|-
|-
| | 4
| | 4
| | 169.063
| | 169.063
| |  
| | 11/10
|-
|-
| | 5
| | 5
Line 35: Line 35:
| | 6
| | 6
| | 253.594
| | 253.594
| | [[15/13|15/13]]
| | [[15/13]]
|-
|-
| | 7
| | 7
| | 295.860
| | 295.860
| |  
| | 19/16
|-
|-
| | 8
| | 8
| | 338.125
| | 338.125
| |  
| | 17/14
|-
|-
| | 9
| | 9
| | 380.391
| | 380.391
| | <span style="color: #660000;">[[5/4|5/4]]</span>
| | <span style="color: #660000;">[[5/4]]</span>
|-
|-
| | 10
| | 10
Line 55: Line 55:
| | 11
| | 11
| | 464.922
| | 464.922
| | 13/10
| | [[17/13]]
|-
|-
| | 12
| | 12
| | 507.188
| | 507.188
| | [[4/3|4/3]]
| | [[4/3]]
|-
|-
| | 13
| | 13
| | 549.454
| | 549.454
| |  
| | 11/8
|-
|-
| | 14
| | 14
Line 71: Line 71:
| | 15
| | 15
| | 633.985
| | 633.985
| | [[13/9|13/9]]
| | [[13/9]]
|-
|-
| | 16
| | 16
Line 79: Line 79:
| | 17
| | 17
| | 718.516
| | 718.516
| |  
| | 50/33
|-
|-
| | 18
| | 18
| | 760.782
| | 760.782
| | <span style="color: #660000;"><span style="color: #660000;">[[14/9|14/9]]</span></span>
| | <span style="color: #660000;">[[14/9]]</span>
|-
|-
| | 19
| | 19
Line 95: Line 95:
| | 21
| | 21
| | 887.579
| | 887.579
| | [[5/3|5/3]]
| | [[5/3]]
|-
|-
| | 22
| | 22
Line 107: Line 107:
| | 24
| | 24
| | 1014.376
| | 1014.376
| | [[9/5|9/5]]
| | [[9/5]]
|-
|-
| | 25
| | 25
Line 119: Line 119:
| | 27
| | 27
| | 1141.173
| | 1141.173
| | <span style="color: #660000;"><span style="color: #660000;">[[27/14|27/14]]</span></span>
| | <span style="color: #660000;">[[27/14]]</span>
|-
|-
| | 28
| | 28
Line 131: Line 131:
| | 30
| | 30
| | 1267.970
| | 1267.970
| | <span style="color: #660000;">[[27/13|27/13]]</span>
| | <span style="color: #660000;">[[27/26|27/13]]</span>
|-
|-
| | 31
| | 31
| | 1310.236
| | 1310.236
| |  
| | 32/15
|-
|-
| | 32
| | 32
| | 1352.501
| | 1352.501
| |  
| | 24/11
|-
|-
| | 33
| | 33
| | 1394.767
| | 1394.767
| | <span style="color: #660000;">[[9/4|9/4]]</span> ([[9/8|9/8]] plus an octave)
| | <span style="color: #660000;">[[9/4]]</span> ([[9/8]] plus an octave)
|-
|-
| | 34
| | 34
Line 155: Line 155:
| | 36
| | 36
| | 1521.564
| | 1521.564
| | <span style="color: #660000;">[[12/5|12/5]]</span> (<span style="color: #660000;">[[6/5|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
Line 167: Line 167:
| | 39
| | 39
| | 1648.361
| | 1648.361
| | <span style="color: #660000;">[[13/5|13/5]]</span> ([[13/10|13/10]] plus an octave)
| | <span style="color: #660000;">[[13/5]]</span> ([[13/10]] plus an octave)
|-
|-
| | 40
| | 40
| | 1690.627
| | 1690.627
| | 8/3
| | [[8/3]]
|-
|-
| | 41
| | 41
| | 1732.892
| | 1732.892
| |  
| | 30/11
|-
|-
| | 42
| | 42
| | 1775.158
| | 1775.158
| | <span style="color: #660000;">[[14/5|14/5]]</span> ([[7/5|7/5]] plus an octave)
| | <span style="color: #660000;">[[14/5]]</span> ([[7/5]] plus an octave)
|-
|-
| | 43
| | 43
| | 1817.424
| | 1817.424
| | 20/7
| | [[10/7|20/7]]
|-
|-
| | 44
| | 44
Line 191: Line 191:
| | 45
| | 45
| | 1901.955
| | 1901.955
| | <span style="color: #660000;">[[3/1|3/1]]</span>
| | <span style="color: #660000;">[[3/1]]</span>
|}
|}
[[Category:Edt]]
[[Category:Edonoi]]

Revision as of 10:15, 3 March 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 Approximate Ratios
0 0 1/1
1 42.266
2 84.531 21/20
3 126.797 14/13, 15/14, 16/15, 29/27
4 169.063 11/10
5 211.328 9/8
6 253.594 15/13
7 295.860 19/16
8 338.125 17/14
9 380.391 5/4
10 422.657
11 464.922 17/13
12 507.188 4/3
13 549.454 11/8
14 591.719 7/5
15 633.985 13/9
16 676.251
17 718.516 50/33
18 760.782 14/9
19 803.048 8/5
20 845.313
21 887.579 5/3
22 929.845 12/7
23 972.110 7/4
24 1014.376 9/5
25 1056.642
26 1098.907 17/9
27 1141.173 27/14
28 1183.439
29 1225.704
30 1267.970 27/13
31 1310.236 32/15
32 1352.501 24/11
33 1394.767 9/4 (9/8 plus an octave)
34 1437.033 16/7
35 1479.298
36 1521.564 12/5 (6/5 plus an octave)
37 1563.830
38 1606.095
39 1648.361 13/5 (13/10 plus an octave)
40 1690.627 8/3
41 1732.892 30/11
42 1775.158 14/5 (7/5 plus an octave)
43 1817.424 20/7
44 1859.689
45 1901.955 3/1
Retrieved from "https://en.xen.wiki/index.php?title=45edt&oldid=40611"