# 617edo

 ← 616edo 617edo 618edo →
Prime factorization 617 (prime)
Step size 1.94489¢
Fifth 361\617 (702.107¢)
Semitones (A1:m2) 59:46 (114.7¢ : 89.47¢)
Consistency limit 5
Distinct consistency limit 5

617 equal divisions of the octave (abbreviated 617edo or 617ed2), also called 617-tone equal temperament (617tet) or 617 equal temperament (617et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 617 equal parts of about 1.94 ¢ each. Each step represents a frequency ratio of 21/617, or the 617th root of 2.

## Theory

617edo is consistent to the 5-odd-limit. The equal temperament can be used in the 2.3.5.7.13.17.19.23.31 subgroup, tempering out 1701/1700, 1216/1215, 1729/1728, 676/675, 1127/1125, 260253/260000, 3969/3968 and 137241/137200. It supports majvam.

Using the 617c val (617 978 1432 1732]), it tempers out 15625/15552, 2460375/2458624 and 3276800000/3268642167 in the 7-limit, supporting kleismic and marthirds.

Using the 617de val (617 978 1433 1733 2135]), it tempers out 540/539, 5632/5631, 43923/43904 and 40960000/40920957 in the 11-limit, supporting jupiter.

### Prime harmonics

Approximation of prime harmonics in 617edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.152 +0.720 -0.268 -0.913 -0.333 +0.069 +0.056 -0.073 -0.728 +0.507
Relative (%) +0.0 +7.8 +37.0 -13.8 -46.9 -17.1 +3.5 +2.9 -3.8 -37.4 +26.1
Steps
(reduced)
617
(0)
978
(361)
1433
(199)
1732
(498)
2134
(283)
2283
(432)
2522
(54)
2621
(153)
2791
(323)
2997
(529)
3057
(589)

### Subsets and supersets

617edo is the 113th prime EDO.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [978 -617 [617 978]] -0.0479 0.0479 2.46
2.3.5 [39 -29 3, [40 7 -22 [617 978 1433]] -0.1354 0.1297 6.67
2.3.5.7 420175/419904, 1959552/1953125, 67108864/66976875 [617 978 1433 1732]] -0.0776 0.1504 7.73

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 236\617 458.995 125/96 Majvam
1 291\617 565.964 81920/59049 Tricot

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct