2113edo

← 2112edo

2113edo

2114edo →

Prime factorization	2113 (prime)
Step size	0.567913 ¢
Fifth	1236\2113 (701.94 ¢)
Semitones (A1:m2)	200:159 (113.6 ¢ : 90.3 ¢)
Consistency limit	21
Distinct consistency limit	21

2113 equal divisions of the octave (abbreviated 2113edo or 2113ed2), also called 2113-tone equal temperament (2113tet) or 2113 equal temperament (2113et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2113 equal parts of about 0.568 ¢ each. Each step represents a frequency ratio of 2^1/2113, or the 2113th root of 2.

2113edo is consistent in the 21-odd-limit and also a strong 2.3.7.13.29 subgroup system. In the 11-limit and the 13-limit, it provides the optimal patent val for the moulin temperament.

Prime harmonics

Approximation of prime harmonics in 2113edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.015	-0.133	+0.034	+0.126	-0.017	+0.108	+0.073	-0.163	+0.049	-0.123
	Relative (%)	+0.0	-2.6	-23.4	+5.9	+22.1	-2.9	+19.1	+12.9	-28.6	+8.6	-21.7
Steps (reduced)		2113 (0)	3349 (1236)	4906 (680)	5932 (1706)	7310 (971)	7819 (1480)	8637 (185)	8976 (524)	9558 (1106)	10265 (1813)	10468 (2016)

Subsets and supersets

2113edo is the 319th prime edo.