User:Overthink/The 7-limit in 53edo: Difference between revisions

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In 53edo, the [[7-limit]] is well-approximated, and especially the 5- and 3-limits. On this page, we will analyze the approximations and structures of 53edo in the 7-limit.
In 53edo, the [[7-limit]] is well-approximated, and especially the 5- and 3-limits. On this page, we will analyze the approximations and structures of 53edo in the 7-limit.
{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable mw-collapsible"
|+ Intervals of 53edo
|+ Intervals of 53edo
! Steps
! Steps
Line 12: Line 12:
| 1
| 1
| 22.642
| 22.642
| 1/1
| 81/80, 64/63, 50/49, 531441/524288
|-
|-
| 2
| 2
| 45.283
| 45.283
| 1/1
| 49/48, 128/125, ...
|-
|-
| 3
| 3
| 67.925
| 67.925
| 1/1
| 28/27, 25/24
|-
|-
| 4
| 4
| 90.566
| 90.566
| 1/1
| 256/243, 21/20
|-
|-
| 5
| 5
| 113.208
| 113.208
| 1/1
| 16/15, 15/14, 2187/2048
|-
|-
| 6
| 6
| 135.849
| 135.849
| 1/1
| 27/25,
|-
|-
| 7
| 7
| 158.491
| 158.491
| 1/1
|  
|-
|-
| 8
| 8
| 181.132
| 181.132
| 1/1
| 10/9
|-
|-
| 9
| 9
| 203.774
| 203.774
| 1/1
| 9/8
|-
|-
| 10
| 10
| 226.415
| 226.415
| 1/1
| 8/7
|-
|-
| 11
| 11
| 249.057
| 249.057
| 1/1
|  
|-
|-
| 12
| 12
| 271.698
| 271.698
| 1/1
| 7/6, 75/64
|-
|-
| 13
| 13
| 294.340
| 294.340
| 1/1
| 32/27
|-
|-
| 14
| 14
| 316.981
| 316.981
| 1/1
| 6/5
|-
|-
| 15
| 15
| 339.623
| 339.623
| 1/1
|  
|-
|-
| 16
| 16
| 362.264
| 362.264
| 1/1
|  
|-
|-
| 17
| 17
| 384.906
| 384.906
| 1/1
| 5/4
|-
|-
| 18
| 18
| 407.547
| 407.547
| 1/1
| 81/64
|-
|-
| 19
| 19
| 430.189
| 430.189
| 1/1
| 9/7, 32/25
|-
|-
| 20
| 20

Revision as of 01:51, 29 October 2025

In 53edo, the 7-limit is well-approximated, and especially the 5- and 3-limits. On this page, we will analyze the approximations and structures of 53edo in the 7-limit.

Intervals of 53edo
Steps Cents Approximate ratios
0 0.000 1/1
1 22.642 81/80, 64/63, 50/49, 531441/524288
2 45.283 49/48, 128/125, ...
3 67.925 28/27, 25/24
4 90.566 256/243, 21/20
5 113.208 16/15, 15/14, 2187/2048
6 135.849 27/25,
7 158.491
8 181.132 10/9
9 203.774 9/8
10 226.415 8/7
11 249.057
12 271.698 7/6, 75/64
13 294.340 32/27
14 316.981 6/5
15 339.623
16 362.264
17 384.906 5/4
18 407.547 81/64
19 430.189 9/7, 32/25
20 452.830 1/1
21 475.472 1/1
22 498.113 4/3
23 520.755 1/1
24 543.396 1/1
25 566.038 1/1
26 588.679 1/1
27 611.321 1/1
28 633.962 1/1
29 656.604 1/1
30 679.245 1/1
31 701.887 3/2
32 724.528 1/1
33 747.170 1/1
34 769.811 1/1
35 792.453 1/1
36 815.094 1/1
37 837.736 1/1
38 860.377 1/1
39 883.019 1/1
40 905.660 1/1
41 928.302 1/1
42 950.943 1/1
43 973.585 1/1
44 996.226 1/1
45 1018.868 1/1
46 1041.509 1/1
47 1064.151 1/1
48 1086.792 1/1
49 1109.434 1/1
50 1132.075 1/1
51 1154.717 1/1
52 1177.358 1/1
53 1200.000 2/1
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