935edo

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Prime factorization 5 × 11 × 17
Step size 1.28342¢ 
Fifth 547\935 (702.032¢)
Semitones (A1:m2) 89:70 (114.2¢ : 89.84¢)
Consistency limit 27
Distinct consistency limit 27
Special properties

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. The equal temperament tempers out the [39 -29 3 (tricot 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

Approximation of prime harmonics in 935edo
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.