6ed4/3

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← 5ed4/36ed4/37ed4/3 →
Prime factorization 2 × 3
Step size 83.0075¢ 
Octave 14\6ed4/3 (1162.1¢) (→7\3ed4/3)
Twelfth 23\6ed4/3 (1909.17¢)
(convergent)
Consistency limit 2
Distinct consistency limit 2
Special properties

6 equal divisions of 4/3 (abbreviated 6ed4/3) is a nonoctave tuning system that divides the interval of 4/3 into 6 equal parts of about 83 ¢ each. Each step represents a frequency ratio of (4/3)1/6, or the 6th root of 4/3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 83.007 18/17, 19/18, 20/19
2 166.015 10/9, 11/10, 13/12, 14/13, 15/14, 17/15, 19/17
3 249.022 13/11, 20/17
4 332.03 11/9, 17/14
5 415.037 9/7, 13/10, 14/11, 21/17
6 498.045 17/13, 19/14

Harmonics

Approximation of harmonics in 6ed4/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -37.9 +7.2 +7.2 +35.9 -30.7 +34.5 -30.7 +14.4 -2.0 -0.9 +14.4
Relative (%) -45.7 +8.7 +8.7 +43.3 -37.0 +41.5 -37.0 +17.4 -2.4 -1.1 +17.4
Steps
(reduced)
14
(2)
23
(5)
29
(5)
34
(4)
37
(1)
41
(5)
43
(1)
46
(4)
48
(0)
50
(2)
52
(4)
Approximation of harmonics in 6ed4/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -41.1 -3.4 -39.8 +14.4 -7.5 -23.5 -34.1 -39.8 -41.3 -38.8 -32.8
Relative (%) -49.5 -4.1 -48.0 +17.4 -9.1 -28.3 -41.0 -48.0 -49.8 -46.8 -39.5
Steps
(reduced)
53
(5)
55
(1)
56
(2)
58
(4)
59
(5)
60
(0)
61
(1)
62
(2)
63
(3)
64
(4)
65
(5)