# 6664edo

 ← 6663edo 6664edo 6665edo →
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 6664ed2), also called 6664-tone equal temperament (6664tet) or 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 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 (%) -19.0 -32.9 -21.3 -38.0 +34.8 +27.0 +48.1 +14.8 -18.9 -40.3 -1.7
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.