935edo: Difference between revisions

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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]].
{{EDO intro|935}}
 
935edo 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]].
935 = 5 × 11 × 17, with subset edos 5, 11, 17, 55, 85, and 187.  


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|935}}
{{Harmonics in equal|935}}
=== Divisors ===
935 = 5 × 11 × 17, with subset edos 5, 11, 17, 55, 85, and 187.


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->

Revision as of 15:30, 29 December 2022

← 934edo 935edo 936edo →
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

Template:EDO intro 935edo 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

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)

Divisors

935 = 5 × 11 × 17, with subset edos 5, 11, 17, 55, 85, and 187.

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