4320edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|4320}} ==Theory== 4320edo is consistent in the 23-limit. It is also a Highly composite equal division#Largely composite numbers|largely compo..." |
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{{EDO intro|4320}} | {{EDO intro|4320}} | ||
==Theory== | ==Theory== | ||
4320edo is consistent in the [[23-limit]]. | 4320edo is distinctly consistent in the [[23-odd-limit]]. While this fact is not remarkable on its own right ([[282edo]] is the first such EDO), what's remarkable is the relationship that 4320edo offers to fractions of the octave, given that it is also a [[Highly composite equal division#Largely composite numbers|largely composite EDO]]. It is the first largely composite EDO with a greater consistency limit since [[72edo]]. | ||
===Harmonics=== | |||
{{harmonics in equal|4320}} | {{harmonics in equal|4320}} | ||
[[Category:Equal divisions of the octave|####]] | |||
Revision as of 14:39, 25 November 2022
| ← 4319edo | 4320edo | 4321edo → |
Theory
4320edo is distinctly consistent in the 23-odd-limit. While this fact is not remarkable on its own right (282edo is the first such EDO), what's remarkable is the relationship that 4320edo offers to fractions of the octave, given that it is also a largely composite EDO. It is the first largely composite EDO with a greater consistency limit since 72edo.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.011 | +0.075 | +0.063 | +0.071 | +0.028 | +0.045 | -0.013 | +0.059 | -0.133 | -0.036 |
| Relative (%) | +0.0 | -3.8 | +27.1 | +22.7 | +25.5 | +10.0 | +16.1 | -4.7 | +21.2 | -47.8 | -12.8 | |
| Steps (reduced) |
4320 (0) |
6847 (2527) |
10031 (1391) |
12128 (3488) |
14945 (1985) |
15986 (3026) |
17658 (378) |
18351 (1071) |
19542 (2262) |
20986 (3706) |
21402 (4122) | |