1880edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
1880edo is [[consistent]] in the [[7-odd-limit]], and is overall a decent 13-limit system, although its 9/8 is off the stack of two 3/2's by one step, which prevents consistency in the [[9-odd-limit]]. | Since {{nowrap|1880 {{=}} 20 × 94}}, 1880edo shares its [[harmonic]] [[3/1|3]] with [[94edo]]. It is [[consistent]] in the [[7-odd-limit]], and is overall a decent 13-limit system, although its 9/8 is off the stack of two 3/2's by one step, which prevents consistency in the [[9-odd-limit]]. | ||
In the 13-limit, it tempers out [[6656/6655]] and supports the 2.5.7.11.13 subgroup [[eternal revolutionary]] temperament. | In the 13-limit, it tempers out [[6656/6655]] and supports the 2.5.7.11.13 subgroup [[eternal revolutionary]] temperament. | ||
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=== Odd harmonics === | === Odd harmonics === | ||
{{Harmonics in equal|1880}} | {{Harmonics in equal|1880}} | ||
=== Subsets and supersets === | |||
Since 1880 factors into {{factorization|1880}}, 1880edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 20, 40, 47, 94, 188, 235, 376, 470, and 940 }}. | |||
Latest revision as of 23:17, 20 February 2025
| ← 1879edo | 1880edo | 1881edo → |
1880 equal divisions of the octave (abbreviated 1880edo or 1880ed2), also called 1880-tone equal temperament (1880tet) or 1880 equal temperament (1880et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1880 equal parts of about 0.638 ¢ each. Each step represents a frequency ratio of 21/1880, or the 1880th root of 2.
Since 1880 = 20 × 94, 1880edo shares its harmonic 3 with 94edo. It is consistent in the 7-odd-limit, and is overall a decent 13-limit system, although its 9/8 is off the stack of two 3/2's by one step, which prevents consistency in the 9-odd-limit.
In the 13-limit, it tempers out 6656/6655 and supports the 2.5.7.11.13 subgroup eternal revolutionary temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.173 | -0.144 | +0.110 | -0.293 | +0.171 | +0.111 | +0.029 | -0.275 | -0.066 | +0.283 | -0.189 |
| Relative (%) | +27.0 | -22.5 | +17.3 | -45.9 | +26.9 | +17.3 | +4.6 | -43.0 | -10.4 | +44.3 | -29.6 | |
| Steps (reduced) |
2980 (1100) |
4365 (605) |
5278 (1518) |
5959 (319) |
6504 (864) |
6957 (1317) |
7345 (1705) |
7684 (164) |
7986 (466) |
8258 (738) |
8504 (984) | |
Subsets and supersets
Since 1880 factors into 23 × 5 × 47, 1880edo has subset edos 2, 4, 5, 8, 10, 20, 40, 47, 94, 188, 235, 376, 470, and 940.