581edo: Difference between revisions
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{{EDO intro|581}} | |||
581edo is a very strong 19- and 23-limit system, distinctly [[consistent]] to the [[25-odd-limit]]. It tempers out [[2401/2400]] in the 7-limit, [[3025/3024]], [[19712/19683]], 151263/151250 in the 11-limit, and [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]] in the 13-limit. It [[support]]s and gives a good tuning for [[newt]], the 41 & 229 microtemperament, which has a neutral thirds generator. It is the first division after 270 with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and the first past 311 with a lower 23-limit relative error, and not until [[1578edo|1578]] do we reach a lower 23-limit relative error. | |||
{{Harmonics in equal|581|columns=11}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Newt]] | |||
Revision as of 18:10, 17 August 2022
581edo is a very strong 19- and 23-limit system, distinctly consistent to the 25-odd-limit. It tempers out 2401/2400 in the 7-limit, 3025/3024, 19712/19683, 151263/151250 in the 11-limit, and 2080/2079, 4096/4095, 4225/4224, 6656/6655 and 10648/10647 in the 13-limit. It supports and gives a good tuning for newt, the 41 & 229 microtemperament, which has a neutral thirds generator. It is the first division after 270 with a lower 19-limit relative error, and the first past 311 with a lower 23-limit relative error, and not until 1578 do we reach a lower 23-limit relative error.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.283 | -0.083 | -0.151 | +0.145 | +0.092 | +0.380 | -0.095 | -0.391 | -1.006 | -0.801 |
| Relative (%) | +0.0 | +13.7 | -4.0 | -7.3 | +7.0 | +4.5 | +18.4 | -4.6 | -18.9 | -48.7 | -38.8 | |
| Steps (reduced) |
581 (0) |
921 (340) |
1349 (187) |
1631 (469) |
2010 (267) |
2150 (407) |
2375 (51) |
2468 (144) |
2628 (304) |
2822 (498) |
2878 (554) | |