3178edo: Difference between revisions
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3178edo is quite accurate in the [[23-limit]], [[consistent]] to the [[27-odd-limit]], and has an exceptional approximation of [[harmonic]] [[13/1|13]]. However, like most edos of this size, it is rather impractical to use. It [[tempering out|tempers out]] several of the smaller 23-limit [[superparticular ratio|superparticular commas]], including [[9801/9800]] in the 11-limit; [[10648/10647]] and [[123201/123200]] in the 13-limit; [[5832/5831]], [[14400/14399]], and [[28561/28560]] in the 17-limit; [[6175/6174]], 10830/10829, 12636/12635, 14080/14079, 14365/14364, 23409/23408, 28900/28899, and 43681/43680 in the 19-limit; 8625/8624, 11271/11270, 12168/12167 and 43264/43263 in the 23-limit. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|3178}} | {{Harmonics in equal|3178}} | ||
Revision as of 10:44, 12 January 2025
| ← 3177edo | 3178edo | 3179edo → |
3178edo is quite accurate in the 23-limit, consistent to the 27-odd-limit, and has an exceptional approximation of harmonic 13. However, like most edos of this size, it is rather impractical to use. It tempers out several of the smaller 23-limit superparticular commas, including 9801/9800 in the 11-limit; 10648/10647 and 123201/123200 in the 13-limit; 5832/5831, 14400/14399, and 28561/28560 in the 17-limit; 6175/6174, 10830/10829, 12636/12635, 14080/14079, 14365/14364, 23409/23408, 28900/28899, and 43681/43680 in the 19-limit; 8625/8624, 11271/11270, 12168/12167 and 43264/43263 in the 23-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.004 | -0.033 | +0.085 | -0.028 | +0.001 | +0.016 | +0.033 | +0.045 | +0.127 | -0.165 |
| Relative (%) | +0.0 | -1.1 | -8.7 | +22.6 | -7.4 | +0.3 | +4.3 | +8.6 | +12.0 | +33.6 | -43.6 | |
| Steps (reduced) |
3178 (0) |
5037 (1859) |
7379 (1023) |
8922 (2566) |
10994 (1460) |
11760 (2226) |
12990 (278) |
13500 (788) |
14376 (1664) |
15439 (2727) |
15744 (3032) | |