# 616edo

← 615edo | 616edo | 617edo → |

^{3}× 7 × 11**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 cents.

### Odd harmonics

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 2^{3} × 7 × 11, 616edo has subset edos 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308.