6079edo: Difference between revisions
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{{EDO intro|6079}} It is a very strong 11- and 13-limit system, with a lower 11- and 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller division. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]] and distinctly [[consistent]] through the 29-odd-limit. A basis for the 11-limit commas is {3294225/3294172, 14348907/14348180, 35156250/35153041, 100663296/100656875}, and for the 13-limit commas, {123201/123200, 1574640/1574573, 1664000/1663893, 1990656/1990625, 3294225/3294172}. | {{EDO intro|6079}} It is a very strong 11- and 13-limit system, with a lower 11- and 13-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller division. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]] and distinctly [[consistent]] through the 29-odd-limit. A basis for the 11-limit commas is {3294225/3294172, 14348907/14348180, 35156250/35153041, 100663296/100656875}, and for the 13-limit commas, {123201/123200, 1574640/1574573, 1664000/1663893, 1990656/1990625, 3294225/3294172}. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|6079}} | {{Harmonics in equal|6079}} | ||
Revision as of 04:21, 9 July 2023
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Template:EDO intro It is a very strong 11- and 13-limit system, with a lower 11- and 13-limit relative error than any smaller division. It is also a zeta peak edo and distinctly consistent through the 29-odd-limit. A basis for the 11-limit commas is {3294225/3294172, 14348907/14348180, 35156250/35153041, 100663296/100656875}, and for the 13-limit commas, {123201/123200, 1574640/1574573, 1664000/1663893, 1990656/1990625, 3294225/3294172}.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0026 | -0.0002 | +0.0177 | +0.0227 | +0.0053 | +0.0619 | -0.0299 | +0.0527 | +0.0658 | +0.0870 |
| Relative (%) | +0.0 | +1.3 | -0.1 | +8.9 | +11.5 | +2.7 | +31.3 | -15.1 | +26.7 | +33.4 | +44.1 | |
| Steps (reduced) |
6079 (0) |
9635 (3556) |
14115 (1957) |
17066 (4908) |
21030 (2793) |
22495 (4258) |
24848 (532) |
25823 (1507) |
27499 (3183) |
29532 (5216) |
30117 (5801) | |