39ed7/4

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← 38ed7/439ed7/440ed7/4 →
Prime factorization 3 × 13
Step size 24.8417¢ 
Octave 48\39ed7/4 (1192.4¢) (→16\13ed7/4)
Twelfth 77\39ed7/4 (1912.81¢)
Consistency limit 2
Distinct consistency limit 2

39 equal divisions of 7/4 (abbreviated 39ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 39 equal parts of about 24.8 ¢ each. Each step represents a frequency ratio of (7/4)1/39, or the 39th root of 7/4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 24.842
2 49.683
3 74.525 25/24, 26/25
4 99.367
5 124.208 14/13, 15/14
6 149.05 12/11
7 173.892
8 198.734 19/17, 28/25
9 223.575 25/22
10 248.417 15/13, 22/19
11 273.259 7/6
12 298.1
13 322.942 6/5
14 347.784
15 372.625
16 397.467 24/19, 29/23
17 422.309 14/11, 23/18
18 447.15 22/17
19 471.992 25/19
20 496.834
21 521.675 19/14
22 546.517 26/19
23 571.359
24 596.201 17/12, 24/17
25 621.042
26 645.884
27 670.726 25/17, 28/19
28 695.567
29 720.409
30 745.251 23/15
31 770.092
32 794.934 19/12
33 819.776 29/18
34 844.617
35 869.459 28/17
36 894.301
37 919.143 17/10
38 943.984 19/11
39 968.826

Harmonics

Approximation of harmonics in 39ed7/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -7.6 +10.9 +9.6 -4.0 +3.3 +9.6 +2.0 -3.1 -11.6 -2.8 -4.3
Relative (%) -30.6 +43.7 +38.8 -16.3 +13.1 +38.8 +8.2 -12.6 -46.9 -11.1 -17.5
Steps
(reduced)
48
(9)
77
(38)
97
(19)
112
(34)
125
(8)
136
(19)
145
(28)
153
(36)
160
(4)
167
(11)
173
(17)
Approximation of harmonics in 39ed7/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +6.1 +2.0 +6.8 -5.6 -11.1 -10.7 -5.0 +5.6 -4.3 -10.4 +12.1
Relative (%) +24.7 +8.2 +27.4 -22.4 -44.9 -43.2 -20.0 +22.5 -17.5 -41.7 +48.5
Steps
(reduced)
179
(23)
184
(28)
189
(33)
193
(37)
197
(2)
201
(6)
205
(10)
209
(14)
212
(17)
215
(20)
219
(24)