6691edo

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← 6690edo6691edo6692edo →
Prime factorization 6691 (prime)
Step size 0.179345¢ 
Fifth 3914\6691 (701.958¢)
Semitones (A1:m2) 634:503 (113.7¢ : 90.21¢)
Consistency limit 15
Distinct consistency limit 15

The 6691 division divides the octave into 6691 equal parts of 0.17935 cents each. It is a very strong 11-limit division, with a lower 11-limit relative error than any division until 40006. It is also strong in the 7-limit, where only 3125 is both smaller and with a lesser relative error.

A basis for the 11-limit commas is {1771561/1771470, 3294225/3294172, 67110351/67108864, 78125000/78121827} and for the 7-limit commas, {78125000/78121827, 281484423828125/281474976710656, 8936733825332544112/8936247052719140625}.

Approximation of prime harmonics in 6691edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.0000 +0.0029 -0.0037 -0.0021 -0.0102 +0.0642 -0.0384 +0.0210 -0.0274 +0.0447 +0.0847
Relative (%) +0.0 +1.6 -2.1 -1.2 -5.7 +35.8 -21.4 +11.7 -15.3 +24.9 +47.2
Steps
(reduced)
6691
(0)
10605
(3914)
15536
(2154)
18784
(5402)
23147
(3074)
24760
(4687)
27349
(585)
28423
(1659)
30267
(3503)
32505
(5741)
33149
(6385)
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