6664edo

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← 6663edo6664edo6665edo →
Prime factorization 23 × 72 × 17
Step size 0.180072¢
Fifth 3898\6664 (701.921¢) (→1949\3332)
Semitones (A1:m2) 630:502 (113.4¢ : 90.4¢)
Consistency limit 9
Distinct consistency limit 9

6664 equal divisions of the octave (abbreviated 6664edo), or 6664-tone equal temperament (6664tet), 6664 equal temperament (6664et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 6664 equal parts of about 0.18 ¢ each. Each step of 6664edo represents a frequency ratio of 21/6664, or the 6664th root of 2.

6664edo is the unique system tempering out both the barium comma, which maps 81/80 into 1\56, and the septendecima, which maps 25/24 into 1\17. Therefore in 6664edo steps of 56edo and 17edo can be used as chromas in this particular fashion.

Odd harmonics

Approximation of odd harmonics in 6664edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) -0.0342 -0.0592 -0.0384 -0.0685 +0.0626 +0.0486 +0.0866 +0.0266 -0.0340 -0.0726 -0.0030
relative (%) -19 -33 -21 -38 +35 +27 +48 +15 -19 -40 -2
Steps
(reduced)
10562
(3898)
15473
(2145)
18708
(5380)
21124
(1132)
23054
(3062)
24660
(4668)
26036
(6044)
27239
(583)
28308
(1652)
29270
(2614)
30145
(3489)

Subsest and supersets

6664edo has subset edos 1, 2, 4, 7, 8, 14, 17, 28, 34, 49, 56, 68, 98, 119, 136, 196, 238, 392, 476, 833, 952, 1666, 3332.