2320edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|2320}} 2320edo is consistent in the 21-odd-limit. In the 5-limit, it supports the 29th-octave temperament copper. In higher limits, it supports..." |
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{{EDO intro|2320}} | {{EDO intro|2320}} | ||
2320edo is consistent in the 21-odd-limit. | 2320edo is consistent in the 21-odd-limit and is overall a strong 19-limit system with errors less than 19%, although it doesn't support any "famous temperaments". Nonetheless, in the 5-limit, it supports the 29th-octave temperament [[copper]]. In higher limits, it supports 80th-octave temperaments [[tetraicosic]] and [[mercury]], as well as an unnamed 400 & 1920 temperament which also divides the octave in 80 and can also be consistently described to the 19-limit. | ||
=== Prime harmonics === | |||
{{harmonics in equal|2320}} | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
2320edo has subset edos {{EDOs|1, 2, 4, 5, 8, 10, 16, 20, 29, 40, 58, 80, 116, 145, 232, 290, 464, 580, 1160}}. | 2320edo has subset edos {{EDOs|1, 2, 4, 5, 8, 10, 16, 20, 29, 40, 58, 80, 116, 145, 232, 290, 464, 580, 1160}}. | ||
Revision as of 23:10, 11 July 2023
| ← 2319edo | 2320edo | 2321edo → |
2320edo is consistent in the 21-odd-limit and is overall a strong 19-limit system with errors less than 19%, although it doesn't support any "famous temperaments". Nonetheless, in the 5-limit, it supports the 29th-octave temperament copper. In higher limits, it supports 80th-octave temperaments tetraicosic and mercury, as well as an unnamed 400 & 1920 temperament which also divides the octave in 80 and can also be consistently described to the 19-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.058 | +0.066 | -0.033 | +0.061 | -0.010 | +0.045 | -0.099 | +0.174 | +0.250 | +0.137 |
| Relative (%) | +0.0 | -11.3 | +12.7 | -6.3 | +11.9 | -2.0 | +8.6 | -19.2 | +33.6 | +48.4 | +26.5 | |
| Steps (reduced) |
2320 (0) |
3677 (1357) |
5387 (747) |
6513 (1873) |
8026 (1066) |
8585 (1625) |
9483 (203) |
9855 (575) |
10495 (1215) |
11271 (1991) |
11494 (2214) | |
Subsets and supersets
2320edo has subset edos 1, 2, 4, 5, 8, 10, 16, 20, 29, 40, 58, 80, 116, 145, 232, 290, 464, 580, 1160.