1920edo

← 1919edo

1920edo

1921edo →

Prime factorization	27 × 3 × 5
Step size	0.625 ¢
Fifth	1123\1920 (701.875 ¢)
Semitones (A1:m2)	181:145 (113.1 ¢ : 90.63 ¢)
Consistency limit	25
Distinct consistency limit	25

Theory

1920edo is distinctly consistent through the 25-odd-limit, and in terms of 23-limit relative error, only 1578 and 1889 are both smaller and with a lower relative error. In the 29-limit, only 1578 beats it, and in the 31-, 37-, 41-, 43- and 47-limit, nothing beats it. Because of this and because it is a very composite number divisible by 12, it is another candidate for interval size measure.

Prime harmonics

Approximation of prime harmonics in 1920edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31	37	41	43	47
Error	Absolute (¢)	+0.000	-0.080	-0.064	-0.076	-0.068	+0.097	+0.045	-0.013	-0.149	-0.202	-0.036	-0.094	-0.312	-0.268	+0.118
	Relative (%)	+0.0	-12.8	-10.2	-12.1	-10.9	+15.6	+7.1	-2.1	-23.9	-32.4	-5.7	-15.0	-50.0	-42.8	+18.9
Steps (reduced)		1920 (0)	3043 (1123)	4458 (618)	5390 (1550)	6642 (882)	7105 (1345)	7848 (168)	8156 (476)	8685 (1005)	9327 (1647)	9512 (1832)	10002 (402)	10286 (686)	10418 (818)	10665 (1065)

Subsets and supersets

Since 1920 factors into 2⁷ × 3 × 5, 1920edo has subset edos 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960.

Regular temperament properties

1920edo has the lowest relative error in the 31-, 37-, 41-, and 47-limit.

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated ratio*	Temperaments
1	179\1920	111.875	16/15	Vavoom
30	583\1920 (7\1920)	364.375 (4.375)	216/175 (385/384)	Zinc
60	583\1920 (7\1920)	364.375 (4.375)	216/175 (385/384)	Neodymium / neodymium magnet

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

Music

Eliora

• Jazz Improvisation (2023)