935edo: Difference between revisions
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[[ | == Theory == | ||
[[ | 935edo is a very strong 23-limit system, and is [[consistency|distinctly consistent]] through to the [[27-odd-limit]]. It is also a [[zeta peak edo]]. It [[tempering out|tempers out]] the {{monzo| 39 -29 3 }} ([[alphatricot comma]]), {{monzo| -52 -17 34 }} ([[septendecima]]), and {{monzo| 91 -12 -31 }} (astro) in the 5-limit; [[4375/4374]] and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and [[2080/2079]], [[4096/4095]] and [[4225/4224]] in the 13-limit. | ||
=== Prime harmonics === | |||
{{Harmonics in equal|935}} | |||
=== Subsets and supersets === | |||
Since 935 factors into {{factorization|935}}, 935edo has subset edos {{EDOs| 5, 11, 17, 55, 85, and 187 }}. | |||
== Regular temperament properties == | |||
935et has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19- and 23-limit. It is the first to beat [[764edo|764]] in the 13-limit, [[814edo|814]] in the 17- and 23-limit, and [[742edo|742]] in the 19-limit, only to be bettered by [[954edo|954h]] in all of those subgroups. | |||
Latest revision as of 17:38, 12 June 2025
| ← 934edo | 935edo | 936edo → |
935 equal divisions of the octave (abbreviated 935edo or 935ed2), also called 935-tone equal temperament (935tet) or 935 equal temperament (935et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 935 equal parts of about 1.28 ¢ each. Each step represents a frequency ratio of 21/935, or the 935th root of 2.
Theory
935edo is a very strong 23-limit system, and is distinctly consistent through to the 27-odd-limit. It is also a zeta peak edo. It tempers out the [39 -29 3⟩ (alphatricot comma), [-52 -17 34⟩ (septendecima), and [91 -12 -31⟩ (astro) in the 5-limit; 4375/4374 and 52734375/52706752 in the 7-limit; 161280/161051 and 117649/117612 in the 11-limit; and 2080/2079, 4096/4095 and 4225/4224 in the 13-limit.
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) | |
Subsets and supersets
Since 935 factors into 5 × 11 × 17, 935edo has subset edos 5, 11, 17, 55, 85, and 187.
Regular temperament properties
935et has lower absolute errors than any previous equal temperaments in the 13-, 17-, 19- and 23-limit. It is the first to beat 764 in the 13-limit, 814 in the 17- and 23-limit, and 742 in the 19-limit, only to be bettered by 954h in all of those subgroups.