324296edo: Difference between revisions
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{{Infobox ET|Consistency=59|Distinct consistency=59}} | {{Infobox ET|Consistency=59|Distinct consistency=59}} | ||
{{ | {{ED intro}} | ||
324296edo is notable for being an exceptionally good representation of the [[47-limit]], being the first EDO with Dirichlet badness in this limit less than 1, and is distinctly consistent in the [[59-limit]]. | 324296edo is notable for being an exceptionally good representation of the [[47-limit]], being the first EDO with Dirichlet badness in this limit less than 1, and is distinctly consistent in the [[59-limit]]. | ||
Revision as of 06:39, 20 February 2025
| ← 324295edo | 324296edo | 324297edo → |
324296 equal divisions of the octave (abbreviated 324296edo or 324296ed2), also called 324296-tone equal temperament (324296tet) or 324296 equal temperament (324296et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 324296 equal parts of about 0.0037 ¢ each. Each step represents a frequency ratio of 21/324296, or the 324296th root of 2.
324296edo is notable for being an exceptionally good representation of the 47-limit, being the first EDO with Dirichlet badness in this limit less than 1, and is distinctly consistent in the 59-limit.
Odd harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00000 | +0.00002 | +0.00010 | +0.00061 | +0.00074 | +0.00056 | +0.00037 | -0.00018 | +0.00072 | -0.00017 | +0.00041 | +0.00117 | +0.00017 | +0.00020 | +0.00114 | +0.00144 |
| Relative (%) | +0.0 | +0.1 | +0.7 | +2.8 | +16.4 | +20.1 | +15.0 | +9.9 | -4.8 | +19.5 | -4.7 | +11.1 | +31.5 | +4.5 | +5.4 | +30.8 | +39.0 | |
| Steps (reduced) |
324296 (0) |
513997 (189701) |
752992 (104400) |
910414 (261822) |
1121880 (148992) |
1200038 (227150) |
1325548 (28364) |
1377586 (80402) |
1466973 (169789) |
1575424 (278240) |
1606626 (309442) |
1689405 (67925) |
1737433 (115953) |
1759716 (138236) |
1801331 (179851) |
1857542 (236062) |
1907718 (286238) | |