User:Overthink/The 7-limit in 53edo: Difference between revisions
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added more to table |
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| Line 12: | Line 12: | ||
| 1 | | 1 | ||
| 22.642 | | 22.642 | ||
| 81/80, 64/63, 50/49 | | 531441/524288, 81/80, 64/63, 50/49 | ||
|- | |- | ||
| 2 | | 2 | ||
| 45.283 | | 45.283 | ||
| 49/48, 128/125 | | 36/35, 49/48, 128/125 | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 24: | Line 24: | ||
| 4 | | 4 | ||
| 90.566 | | 90.566 | ||
| 256/243, 21/20 | | 256/243, 135/128, 21/20 | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 32: | Line 32: | ||
| 6 | | 6 | ||
| 135.849 | | 135.849 | ||
| 27/25 | | 27/25 | ||
|- | |- | ||
| 7 | | 7 | ||
| 158.491 | | 158.491 | ||
| | | 35/32, | ||
|- | |- | ||
| 8 | | 8 | ||
| Line 52: | Line 52: | ||
| 11 | | 11 | ||
| 249.057 | | 249.057 | ||
| | | 81/70 | ||
|- | |- | ||
| 12 | | 12 | ||
| Line 68: | Line 68: | ||
| 15 | | 15 | ||
| 339.623 | | 339.623 | ||
| | | 105/64, 243/200 | ||
|- | |- | ||
| 16 | | 16 | ||
| 362.264 | | 362.264 | ||
| | | 100/81, 315/256 | ||
|- | |- | ||
| 17 | | 17 | ||
| Line 80: | Line 80: | ||
| 18 | | 18 | ||
| 407.547 | | 407.547 | ||
| 81/64 | | 81/64, | ||
|- | |- | ||
| 19 | | 19 | ||
| Line 88: | Line 88: | ||
| 20 | | 20 | ||
| 452.830 | | 452.830 | ||
| | | 64/49, 35/27 | ||
|- | |- | ||
| 21 | | 21 | ||
| 475.472 | | 475.472 | ||
| | | 21/16 | ||
|- | |- | ||
| 22 | | 22 | ||
| Line 100: | Line 100: | ||
| 23 | | 23 | ||
| 520.755 | | 520.755 | ||
| | | 27/20 | ||
|- | |- | ||
| 24 | | 24 | ||
| 543.396 | | 543.396 | ||
| | | 2187/1600, 48/35 | ||
|- | |- | ||
| 25 | | 25 | ||
| Line 112: | Line 112: | ||
| 26 | | 26 | ||
| 588.679 | | 588.679 | ||
| | | 729/512, 7/5, 45/32 | ||
|- | |- | ||
| 27 | | 27 | ||
| 611.321 | | 611.321 | ||
| | | 1024/729, 10/7, 64/45 | ||
|- | |- | ||
| 28 | | 28 | ||
| Line 221: | Line 221: | ||
| 1200.000 | | 1200.000 | ||
| 2/1 | | 2/1 | ||
|} | |||
Revision as of 04:06, 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.
| 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 |
| 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 |
| 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 | 2187/1600, 48/35 |
| 25 | 566.038 | 1/1 |
| 26 | 588.679 | 729/512, 7/5, 45/32 |
| 27 | 611.321 | 1024/729, 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 |