2016edo

← 2015edo

2016edo

2017edo →

Prime factorization	25 × 32 × 7
Step size	0.595238 ¢
Fifth	1179\2016 (701.786 ¢) (→ 131\224)
Semitones (A1:m2)	189:153 (112.5 ¢ : 91.07 ¢)
Consistency limit	5
Distinct consistency limit	5

2016 equal division divides the octave into steps of 595 millicents, or 25/42 cent each.

Theory

Approximation of odd harmonics in 2016edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.169	-0.004	+0.222	+0.257	-0.127	-0.051	-0.173	-0.194	+0.106	+0.052	+0.297
	Relative (%)	-28.4	-0.7	+37.2	+43.1	-21.4	-8.6	-29.1	-32.5	+17.8	+8.8	+49.9
Steps (reduced)		3195 (1179)	4681 (649)	5660 (1628)	6391 (343)	6974 (926)	7460 (1412)	7876 (1828)	8240 (176)	8564 (500)	8855 (791)	9120 (1056)

2016 is a significantly composite number, with its divisors being 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008. It's abundancy index is 2.25.

Prime harmonics (below 61) with less than 22% error in 2016edo are: 2, 5, 11, 13, 19, 41, 47. With next error being 26% on the 37th harmonic, it is reasonable to make cutoff here.

2016 shares the mapping for 3 with 224edo, albeit with a 28 relative cent error. Using the 2016f val gives the same mapping for 13 as 224edo, and unleashes the full power of 224edo's 13 limit chords.

Regular temperament properties

Subgroup	Comma list (zeroes skipped for clarity)	Mapping	Optimal 8ve stretch (¢)	Tuning error
				Absolute (¢)	Relative (%)
2.3.5.7	5250987/5242880, 40353607/40310784, [14, 11, -22, 7⟩	(2016d)	0.060	0.060	10.1
2.5.11.13	[5 -6 9 6⟩, [-38 12 4 -1⟩, [0 -22 3 11⟩		0.013	0.015	2.5