617edo

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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 2^1/617, 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

Music

Francium

• "purple?" from Questions (2024) – Spotify | Bandcamp | YouTube – majvam in 617edo tuning