# 647edo

 ← 646edo 647edo 648edo →
Prime factorization 647 (prime)
Step size 1.85471¢
Fifth 378\647 (701.082¢)
Semitones (A1:m2) 58:51 (107.6¢ : 94.59¢)
Dual sharp fifth 379\647 (702.937¢)
Dual flat fifth 378\647 (701.082¢)
Dual major 2nd 110\647 (204.019¢)
Consistency limit 7
Distinct consistency limit 7

647 equal divisions of the octave (abbreviated 647edo or 647ed2), also called 647-tone equal temperament (647tet) or 647 equal temperament (647et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 647 equal parts of about 1.85 ¢ each. Each step represents a frequency ratio of 21/647, or the 647th root of 2.

## Theory

647edo is consistent to the 7-odd-limit and its harmonic 3 is about halfway its steps. It tends heavily flat in the first few harmonics. Using the patent val it tempers out 2401/2400, 7381125/7340032 and 1224440064/1220703125 in the 7-limit; 8019/8000, 2401/2400, 46656/46585 and 1265625/1261568 in the 11-limit. Alternatively, the 2.9.5.7.11.13 subgroup might be worth considering.

### Odd harmonics

Approximation of odd harmonics in 647edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.873 -0.533 -0.665 +0.109 -0.468 -0.342 +0.448 +0.763 -0.759 +0.316 +0.474
Relative (%) -47.1 -28.7 -35.9 +5.9 -25.2 -18.4 +24.2 +41.2 -40.9 +17.1 +25.5
Steps
(reduced)
1025
(378)
1502
(208)
1816
(522)
2051
(110)
2238
(297)
2394
(453)
2528
(587)
2645
(57)
2748
(160)
2842
(254)
2927
(339)

### Subsets and supersets

647edo is the 118th prime EDO. 1294edo, which doubles it, gives a good correction to the harmonic 3.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [2051 -647 [647 2051]] -0.0171 0.0171 0.92
2.9.5 [-50 -4 27, [63 -25 7 [647 2051 1502]] +0.0651 0.1172 6.32
2.9.5.7 703125/702464, 3500000000/3486784401, 4202539929/4194304000 [647 2051 1502 1816]] +0.1081 0.1258 6.78
2.9.5.7.11 496125/495616, 1684375/1679616, 151263/151250, 40960000/40920957 [647 2051 1502 1816 2238]] +0.1135 0.1131 6.10
2.9.5.7.11.13 4459/4455, 35750/35721, 47432/47385, 60025/59904, 1146880/1146717 [647 2051 1502 1816 2238 2394]] +0.1100 0.1035 5.58