619edo

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619edo

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Prime factorization	619 (prime)
Step size	1.93861¢
Fifth	362\619 (701.777¢)
Semitones (A1:m2)	58:47 (112.4¢ : 91.11¢)
Consistency limit	5
Distinct consistency limit	5

619 equal divisions of the octave (abbreviated 619edo or 619ed2), also called 619-tone equal temperament (619tet) or 619 equal temperament (619et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 619 equal parts of about 1.94 ¢ each. Each step represents a frequency ratio of 2^1/619, or the 619th root of 2.

Theory

619edo is consistent to the 5-odd-limit. It can be used in the 2.3.5.11.17.19.23.29.41 subgroup, tempering out 2025/2024, 1089/1088, 3520/3519, 1045/1044, 2755/2754, 71875/71808, 374000/373977 and 1025/1024.

Prime harmonics

Approximation of prime harmonics in 619edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.178	-0.530	+0.479	-0.753	+0.829	-0.270	-0.906	-0.164	-0.175	+0.683
	Relative (%)	+0.0	-9.2	-27.3	+24.7	-38.8	+42.8	-13.9	-46.7	-8.5	-9.0	+35.2
Steps (reduced)		619 (0)	981 (362)	1437 (199)	1738 (500)	2141 (284)	2291 (434)	2530 (54)	2629 (153)	2800 (324)	3007 (531)	3067 (591)

Subsets and supersets

619edo is the 114th prime EDO.

Regular temperament properties

Subgroup	Comma list	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3	[-981 619⟩	[⟨619 981]]	0.0561	0.0561	2.89
2.3.5	32805/32768, [-54 -67 69⟩	[⟨619 981 1437]]	0.1135	0.0932	4.81
2.3.5.11	32805/32768, 234375/234256, 314552734375/313456656384	[⟨619 981 1437 2141]]	0.1395	0.0925	4.77

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	257\619	498.223	4/3	Helmholtz

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

Music

Francium

• "Would You Like An Egg?" from Questions (2024) – Spotify | Bandcamp | YouTube – helmholtz in 619edo tuning