4ed4/3

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← 3ed4/3 4ed4/3 5ed4/3 →
Prime factorization 22
Step size 124.511¢ 
Octave 10\4ed4/3 (1245.11¢) (→5\2ed4/3)
Twelfth 15\4ed4/3 (1867.67¢)
(semiconvergent)
Consistency limit 2
Distinct consistency limit 1
Special properties

4 equal divisions of 4/3 (abbreviated 4ed4/3) is a nonoctave tuning system that divides the interval of 4/3 into 4 equal parts of about 125⁠ ⁠¢ each. Each step represents a frequency ratio of (4/3)1/4, or the 4th root of 4/3.

Intervals

Steps Cents Approximate ratios
0 0 1/1, 21/20
1 124.5 11/10, 13/12, 14/13, 18/17, 19/18, 20/19, 21/19
2 249 7/6, 10/9, 17/14, 17/15, 19/17
3 373.5 6/5, 9/7, 11/9, 13/11, 17/13, 20/17, 21/17
4 498 13/10, 14/11, 15/11, 18/13, 19/14, 19/15

Harmonics

Approximation of harmonics in 4ed4/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +45.1 -34.3 -34.3 -47.1 +10.8 -7.0 +10.8 +55.9 -2.0 -42.4 +55.9
Relative (%) +36.2 -27.5 -27.5 -37.8 +8.7 -5.6 +8.7 +44.9 -1.6 -34.1 +44.9
Steps
(reduced)
10
(2)
15
(3)
19
(3)
22
(2)
25
(1)
27
(3)
29
(1)
31
(3)
32
(0)
33
(1)
35
(3)
Approximation of harmonics in 4ed4/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +41.9 +38.1 +43.2 +55.9 -49.0 -23.5 +7.4 +43.2 -41.3 +2.7 +50.2
Relative (%) +33.6 +30.6 +34.7 +44.9 -39.4 -18.8 +6.0 +34.7 -33.2 +2.1 +40.3
Steps
(reduced)
36
(0)
37
(1)
38
(2)
39
(3)
39
(3)
40
(0)
41
(1)
42
(2)
42
(2)
43
(3)
44
(0)