| 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
|
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.
| 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
|