616edo

← 615edo

616edo

617edo →

Prime factorization	23 × 7 × 11
Step size	1.94805¢
Fifth	360\616 (701.299¢) (→45\77)
Semitones (A1:m2)	56:48 (109.1¢ : 93.51¢)
Dual sharp fifth	361\616 (703.247¢)
Dual flat fifth	360\616 (701.299¢) (→45\77)
Dual major 2nd	105\616 (204.545¢) (→15\88)
Consistency limit	7
Distinct consistency limit	7

616 equal divisions of the octave (abbreviated 616edo or 616ed2), also called 616-tone equal temperament (616tet) or 616 equal temperament (616et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 616 equal parts of about 1.95 ¢ each. Each step represents a frequency ratio of 2^1/616, or the 616th root of 2.

616edo is consistent to the 7-odd-limit, but it tends heavily flat in the first few harmonics. The equal temperament tempers out 2401/2400, 48828125/48771072, and 129140163/128450560 in the 7-limit; 9801/9800, 46656/46585, 117649/117612, and 1265625/1261568 in the 11-limit. Alternatively, the 2.9.15.21.11 subgroup may be worth considering. Finally, as every third step of 1848edo, it provides an excellent tuning for the 3*616 2.5/3.7/3.11 subgroup, approximating 6/5, 7/6, 7/5, and 11/8 within 0.057 ¢.

Odd harmonics

Approximation of odd harmonics in 616edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.656	-0.599	-0.644	+0.635	-0.019	-0.917	+0.692	+0.239	+0.539	+0.648	+0.946
	Relative (%)	-33.7	-30.8	-33.1	+32.6	-1.0	-47.1	+35.5	+12.3	+27.7	+33.2	+48.6
Steps (reduced)		976 (360)	1430 (198)	1729 (497)	1953 (105)	2131 (283)	2279 (431)	2407 (559)	2518 (54)	2617 (153)	2706 (242)	2787 (323)

Subsets and supersets

Since 616 factors into 2³ × 7 × 11, 616edo has subset edos 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308.