39ed5
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Prime factorization
3 × 13
Step size
71.4439¢
Octave
17\39ed5 (1214.55¢)
Twelfth
27\39ed5 (1928.99¢) (→9\13ed5)
Consistency limit
4
Distinct consistency limit
4
| ← 38ed5 | 39ed5 | 40ed5 → |
Division of the 5th harmonic into 39 equal parts (39ED5) is a good hyperpyth tuning. The step size about 71.4439 cents. It is compared to every fifth step of 84EDO, but with the 5/1 rather than the 2/1 being just.
Intervals
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 71.4439 | 25/24, 24/23 | |
| 2 | 142.8879 | 38/35, 25/23 | |
| 3 | 214.3318 | 26/23, 43/38, 60/53, 17/15 | |
| 4 | 285.7758 | 33/28, 46/39, 13/11 | |
| 5 | 357.2197 | 16/13 | |
| 6 | 428.6636 | 32/25, 41/32, 50/39 | |
| 7 | 500.1076 | 4/3 | |
| 8 | 571.5515 | 25/18 | -11.0 cents from 7/5 |
| 9 | 642.9955 | 45/31 | |
| 10 | 714.4394 | 80/53, 77/51, 68/45, 65/43 | |
| 11 | 785.8834 | 11/7 | |
| 12 | 857.3273 | 41/25, 23/14 | |
| 13 | 928.7712 | 70/41, 65/38 | |
| 14 | 1000.2152 | 57/32, 98/55, 41/23 | -17.4 cents from 9/5 |
| 15 | 1071.6591 | 13/7 | |
| 16 | 1143.1031 | 29/15, 31/16 | |
| 17 | 1214.5470 | 125/62, 115/57, 105/52 | |
| 18 | 1285.9909 | 21/10 | |
| 19 | 1357.4349 | 35/16, 46/21, 125/57 | -7.6 cents from 11/5 |
| 20 | 1428.8788 | 57/25, 105/46, 16/7 | |
| 21 | 1500.3228 | 50/21 | |
| 22 | 1571.7667 | 52/21, 57/23, 62/25 | |
| 23 | 1643.2107 | 80/31, 75/29 | -11.0 cents from 13/5 |
| 24 | 1714.6546 | 35/13 | |
| 25 | 1786.0985 | 115/41, 160/57 | |
| 26 | 1857.5425 | 38/13, 41/14 | |
| 27 | 1928.9864 | 70/23 | +27.0 cents from 3/1 |
| 28 | 2000.4304 | 35/11 | |
| 29 | 2071.8743 | 43/13, 53/16 | |
| 30 | 2143.3182 | 31/9 | +24.7 cents from 17/5 |
| 31 | 2214.7622 | 18/5 | |
| 32 | 2286.2061 | 15/4 | -25.0 cents from 19/5 |
| 33 | 2357.6501 | 39/10 | |
| 34 | 2429.0940 | 65/16 | |
| 35 | 2500.5379 | 55/13 | +16.1 cents from 21/5 |
| 36 | 2571.9819 | 75/17, 53/12, 190/43, 115/26 | |
| 37 | 2643.4258 | 23/5 | +1.5 cents from 23/5 |
| 38 | 2714.8698 | 24/5 | |
| 39 | 2786.3137 | exact 5/1 | just major third plus two octaves |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +14.5 | +27.0 | +29.1 | +0.0 | -29.9 | -11.0 | -27.8 | -17.4 | +14.5 | -7.6 | -15.3 |
| Relative (%) | +20.4 | +37.8 | +40.7 | +0.0 | -41.8 | -15.3 | -38.9 | -24.3 | +20.4 | -10.6 | -21.4 | |
| Steps (reduced) |
17 (17) |
27 (27) |
34 (34) |
39 (0) |
43 (4) |
47 (8) |
50 (11) |
53 (14) |
56 (17) |
58 (19) |
60 (21) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.0 | +3.6 | +27.0 | -13.3 | +24.7 | -2.8 | -25.0 | +29.1 | +16.1 | +7.0 | +1.5 |
| Relative (%) | -15.4 | +5.0 | +37.8 | -18.6 | +34.5 | -4.0 | -35.0 | +40.7 | +22.5 | +9.8 | +2.1 | |
| Steps (reduced) |
62 (23) |
64 (25) |
66 (27) |
67 (28) |
69 (30) |
70 (31) |
71 (32) |
73 (34) |
74 (35) |
75 (36) |
76 (37) | |