39ed7/4
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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
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← 38ed7/4 | 39ed7/4 | 40ed7/4 → |
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
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) |
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) |