# 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 21/616, 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 cents.

### 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.