38ed5/2
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Prime factorization
2 × 19
Step size
41.7451¢
Octave
29\38ed5/2 (1210.61¢)
Twelfth
46\38ed5/2 (1920.27¢) (→23\19ed5/2)
Consistency limit
3
Distinct consistency limit
3
 |
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| ← 37ed5/2 | 38ed5/2 | 39ed5/2 → |
38 equal divisions of 5/2 (abbreviated 38ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 38 equal parts of about 41.7 ¢ each. Each step represents a frequency ratio of (5/2)1/38, or the 38th root of 5/2.
Theory
This tuning tempers out 49/48 in the 7-limit; 33/32, 77/75, and 99/98 in the 11-limit; 65/63 in the 13-limit; 51/50, 119/117, and 121/119 in the 17-limit; 57/56, 76/75, 77/76, and 133/132 in the 19-limit; and 46/45 and 115/114 in the 23-limit.
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 41.7 | |
| 2 | 83.5 | 21/20, 23/22 |
| 3 | 125.2 | 15/14 |
| 4 | 167 | |
| 5 | 208.7 | 9/8, 26/23 |
| 6 | 250.5 | 22/19, 29/25 |
| 7 | 292.2 | 13/11 |
| 8 | 334 | 23/19 |
| 9 | 375.7 | |
| 10 | 417.5 | |
| 11 | 459.2 | 17/13 |
| 12 | 500.9 | 4/3 |
| 13 | 542.7 | 26/19 |
| 14 | 584.4 | 7/5 |
| 15 | 626.2 | |
| 16 | 667.9 | |
| 17 | 709.7 | |
| 18 | 751.4 | 17/11 |
| 19 | 793.2 | |
| 20 | 834.9 | |
| 21 | 876.6 | |
| 22 | 918.4 | 22/13 |
| 23 | 960.1 | |
| 24 | 1001.9 | 16/9, 25/14 |
| 25 | 1043.6 | |
| 26 | 1085.4 | 15/8, 28/15 |
| 27 | 1127.1 | |
| 28 | 1168.9 | |
| 29 | 1210.6 | |
| 30 | 1252.4 | |
| 31 | 1294.1 | |
| 32 | 1335.8 | |
| 33 | 1377.6 | 20/9 |
| 34 | 1419.3 | |
| 35 | 1461.1 | 7/3 |
| 36 | 1502.8 | |
| 37 | 1544.6 | |
| 38 | 1586.3 | 5/2 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.6 | +18.3 | -20.5 | +10.6 | -12.8 | +12.5 | -9.9 | -5.1 | -20.5 | -18.6 | -2.2 |
| Relative (%) | +25.4 | +43.9 | -49.2 | +25.4 | -30.7 | +30.0 | -23.8 | -12.2 | -49.2 | -44.4 | -5.3 | |
| Steps (reduced) |
29 (29) |
46 (8) |
57 (19) |
67 (29) |
74 (36) |
81 (5) |
86 (10) |
91 (15) |
95 (19) |
99 (23) |
103 (27) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -15.5 | -18.6 | -12.8 | +0.7 | -20.8 | +5.5 | -4.6 | -9.9 | -10.9 | -7.9 | -1.4 |
| Relative (%) | -37.2 | -44.6 | -30.7 | +1.6 | -49.8 | +13.2 | -11.0 | -23.8 | -26.1 | -19.0 | -3.4 | |
| Steps (reduced) |
106 (30) |
109 (33) |
112 (36) |
115 (1) |
117 (3) |
120 (6) |
122 (8) |
124 (10) |
126 (12) |
128 (14) |
130 (16) | |