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
|
531441/524288, 81/80, 64/63, 50/49
|
| 2
|
45.283
|
36/35, 49/48, 128/125, 250/243
|
| 3
|
67.925
|
28/27, 25/24
|
| 4
|
90.566
|
256/243, 135/128, 21/20
|
| 5
|
113.208
|
16/15, 15/14, 2187/2048
|
| 6
|
135.849
|
27/25
|
| 7
|
158.491
|
35/32
|
| 8
|
181.132
|
10/9
|
| 9
|
203.774
|
9/8
|
| 10
|
226.415
|
8/7
|
| 11
|
249.057
|
81/70, 125/108, 144/125, 147/128
|
| 12
|
271.698
|
7/6, 75/64
|
| 13
|
294.340
|
32/27
|
| 14
|
316.981
|
6/5
|
| 15
|
339.623
|
105/64, 243/200
|
| 16
|
362.264
|
100/81, 315/256
|
| 17
|
384.906
|
5/4
|
| 18
|
407.547
|
81/64
|
| 19
|
430.189
|
9/7, 32/25
|
| 20
|
452.830
|
64/49, 35/27
|
| 21
|
475.472
|
21/16
|
| 22
|
498.113
|
4/3
|
| 23
|
520.755
|
27/20
|
| 24
|
543.396
|
48/35
|
| 25
|
566.038
|
1/1
|
| 26
|
588.679
|
1024/729, 7/5, 45/32
|
| 27
|
611.321
|
729/512, 10/7, 64/45
|
| 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
|
The 81/80 and 64/63 commas translate pythagorean intervals into nearby pental and septimal intervals respectively. Considering them seperately is too complex, so we conflate them into one comma step, tempering out 5120/5103. Here's a table of intervals organized using tempering of 5120/5103. Each interval is a fifth above the interval to the left of it, and a comma above the interval below it. Not all ratios are shown, or else the table will be too complex.
Interval table (far fourthward)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Interval table (middle)
|
|
|
|
|
|
|
|
256/245, 729/700
|
384/245
|
|
|
|
|
|
|
| 48/25
|
36/25
|
27/25
|
81/50
|
128/105, 243/200
|
64/35
|
48/35
|
36/35
|
54/35
|
81/70
|
243/140, 256/147
|
64/49
|
96/49
|
72/49
|
54/49
|
| 135/128
|
64/45
|
16/15
|
8/5
|
6/5
|
9/5
|
27/20
|
64/63, 81/80
|
32/21
|
8/7
|
12/7
|
9/7
|
27/14
|
81/56
|
243/224
|
| 28/15
|
7/5
|
21/20
|
63/40, 128/81
|
32/27
|
16/9
|
4/3
|
1/1
|
3/2
|
9/8
|
27/16
|
81/64, 80/63
|
40/21
|
10/7
|
15/14
|
| 448/243
|
112/81
|
28/27
|
14/9
|
7/6
|
7/4
|
21/16
|
63/32, 160/81
|
40/27
|
10/9
|
5/3
|
5/4
|
15/8
|
45/32
|
135/128
|
| 49/27
|
49/36
|
49/48
|
49/32
|
147/128, 280/243
|
140/81
|
35/27
|
35/18
|
35/24
|
35/32
|
105/64, 400/243
|
315/256, 100/81
|
50/27
|
25/18
|
25/24
|
|
|
|
|
|
|
|
|
245/128, 1400/729
|
|
|
|
|
|
|
|
Interval table (far fifthward)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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