2000edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|2000}} It is distinctly consistent through the 29 limit and a strong no-31's 41-limit system; the only smaller edo with a smaller [[29-limit]] [[Tenney- | {{EDO intro|2000}} It is distinctly [[consistent]] through the 29-odd-limit and a strong no-31's 41-limit system; the only smaller edo with a smaller [[29-limit]] [[Tenney-Euclidean temperament measures#TE simple badness|relative error]] being [[1578edo]]. The only ones superior to it in the [[23-limit]] are 1578 and [[1889edo]], and in the [[19-limit]], nothing smaller defeats it, the first edo to do so being [[2460edo]]. | ||
2000 = 2 | 2000 = 2<sup>4</sup> × 5<sup>3</sup>; some of its divisors are [[10edo|10]], [[16edo|16]], [[25edo|25]], [[50edo|50]], [[80edo|80]], [[100edo|100]], [[125edo|125]] and [[200edo|200]]. Also there is the 1000 division of [[millioctave]]s, where it might be argued that cutting these in half makes for a better system. | ||
{{ | === Prime harmonic === | ||
{{Harmonics in equal|2000|columns=13}} | |||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | ||
[[Category:29-limit]] | [[Category:29-limit]] | ||
Revision as of 14:01, 22 October 2022
| ← 1999edo | 2000edo | 2001edo → |
Template:EDO intro It is distinctly consistent through the 29-odd-limit and a strong no-31's 41-limit system; the only smaller edo with a smaller 29-limit relative error being 1578edo. The only ones superior to it in the 23-limit are 1578 and 1889edo, and in the 19-limit, nothing smaller defeats it, the first edo to do so being 2460edo.
2000 = 24 × 53; some of its divisors are 10, 16, 25, 50, 80, 100, 125 and 200. Also there is the 1000 division of millioctaves, where it might be argued that cutting these in half makes for a better system.
Prime harmonic
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.045 | +0.086 | +0.174 | +0.082 | +0.072 | +0.045 | +0.087 | -0.074 | +0.023 | -0.236 | +0.056 | -0.062 |
| Relative (%) | +0.0 | +7.5 | +14.4 | +29.0 | +13.7 | +12.1 | +7.4 | +14.5 | -12.4 | +3.8 | -39.3 | +9.3 | -10.4 | |
| Steps (reduced) |
2000 (0) |
3170 (1170) |
4644 (644) |
5615 (1615) |
6919 (919) |
7401 (1401) |
8175 (175) |
8496 (496) |
9047 (1047) |
9716 (1716) |
9908 (1908) |
10419 (419) |
10715 (715) | |