935edo: Difference between revisions
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The 935 equal | The '''935 equal divisions of the octave''' ('''935edo''') divides the [[octave]] into 935 parts of 1.283 [[cent]]s each. It is a very strong 23-limit system, and distinctly [[consistent]] through to the [[27-odd-limit]]. It is also a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak tuning]]. In the 5-limit it tempers out the {{monzo| 39 -29 3 }} ([[tricot comma]]), {{monzo| -52 -17 34 }} ([[septendecima]]), and {{monzo| 91 -12 -31 }} (astro). In the 7-limit it tempers out [[4375/4374]] and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612, and in the 13-limit [[2080/2079]], [[4096/4095]] and [[4225/4224]]. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|935}} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
Revision as of 15:07, 4 April 2022
The 935 equal divisions of the octave (935edo) divides the octave into 935 parts of 1.283 cents each. It is a very strong 23-limit system, and distinctly consistent through to the 27-odd-limit. It is also a zeta peak tuning. In the 5-limit it tempers out the [39 -29 3⟩ (tricot comma), [-52 -17 34⟩ (septendecima), and [91 -12 -31⟩ (astro). In the 7-limit it tempers out 4375/4374 and 52734375/52706752, in the 11-limit 161280/161051 and 117649/117612, and in the 13-limit 2080/2079, 4096/4095 and 4225/4224.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.077 | -0.004 | +0.158 | +0.554 | +0.114 | +0.285 | +0.241 | +0.603 | -0.272 | -0.223 |
| Relative (%) | +0.0 | +6.0 | -0.3 | +12.3 | +43.1 | +8.9 | +22.2 | +18.8 | +47.0 | -21.2 | -17.4 | |
| Steps (reduced) |
935 (0) |
1482 (547) |
2171 (301) |
2625 (755) |
3235 (430) |
3460 (655) |
3822 (82) |
3972 (232) |
4230 (490) |
4542 (802) |
4632 (892) | |