38edt
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Prime factorization
2 × 19
Step size
50.0514¢
Octave
24\38edt (1201.23¢) (→12\19edt)
Consistency limit
5
Distinct consistency limit
5
| ← 37edt | 38edt | 39edt → |
38 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 38edt or 38ed3), is a nonoctave tuning system that divides the interval of 3/1 into 38 equal parts of about 50.1 ¢ each. Each step represents a frequency ratio of 31/38, or the 38th root of 3.
38EDT is related to 24edo (quarter-tone tuning), but with the 3/1 rather than the 2/1 being just, which stretches the octave by about 1.2347 cents. It is consistent to the 6-integer-limit.
Lookalikes: 14edf, 24edo, 56ed5, 62ed6
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.2 | +0.0 | +2.5 | +16.6 | +1.2 | -15.4 | +3.7 | +0.0 | +17.8 | +3.0 | +2.5 |
| Relative (%) | +2.5 | +0.0 | +4.9 | +33.1 | +2.5 | -30.7 | +7.4 | +0.0 | +35.6 | +5.9 | +4.9 | |
| Steps (reduced) |
24 (24) |
38 (0) |
48 (10) |
56 (18) |
62 (24) |
67 (29) |
72 (34) |
76 (0) |
80 (4) |
83 (7) |
86 (10) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +14.1 | -14.1 | +16.6 | +4.9 | +0.1 | +1.2 | +7.7 | +19.0 | -15.4 | +4.2 | -22.7 |
| Relative (%) | +28.1 | -28.3 | +33.1 | +9.9 | +0.2 | +2.5 | +15.5 | +38.0 | -30.7 | +8.4 | -45.4 | |
| Steps (reduced) |
89 (13) |
91 (15) |
94 (18) |
96 (20) |
98 (22) |
100 (24) |
102 (26) |
104 (28) |
105 (29) |
107 (31) |
108 (32) | |
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 50.1 | 34.2 | |
| 2 | 100.1 | 68.4 | 17/16, 18/17, 19/18 |
| 3 | 150.2 | 102.6 | 12/11, 23/21 |
| 4 | 200.2 | 136.8 | 9/8, 19/17 |
| 5 | 250.3 | 171.1 | 15/13, 22/19 |
| 6 | 300.3 | 205.3 | 19/16 |
| 7 | 350.4 | 239.5 | 11/9, 27/22 |
| 8 | 400.4 | 273.7 | 24/19, 29/23 |
| 9 | 450.5 | 307.9 | 13/10, 22/17 |
| 10 | 500.5 | 342.1 | 4/3 |
| 11 | 550.6 | 376.3 | 11/8, 26/19 |
| 12 | 600.6 | 410.5 | 17/12, 24/17 |
| 13 | 650.7 | 444.7 | 16/11, 19/13 |
| 14 | 700.7 | 478.9 | 3/2 |
| 15 | 750.8 | 513.2 | 17/11, 20/13 |
| 16 | 800.8 | 547.4 | 19/12, 27/17 |
| 17 | 850.9 | 581.6 | 18/11 |
| 18 | 900.9 | 615.8 | 27/16 |
| 19 | 951 | 650 | 19/11, 26/15 |
| 20 | 1001 | 684.2 | 16/9 |
| 21 | 1051.1 | 718.4 | 11/6 |
| 22 | 1101.1 | 752.6 | 17/9 |
| 23 | 1151.2 | 786.8 | |
| 24 | 1201.2 | 821.1 | 2/1 |
| 25 | 1251.3 | 855.3 | |
| 26 | 1301.3 | 889.5 | 17/8 |
| 27 | 1351.4 | 923.7 | 24/11 |
| 28 | 1401.4 | 957.9 | 9/4 |
| 29 | 1451.5 | 992.1 | |
| 30 | 1501.5 | 1026.3 | 19/8 |
| 31 | 1551.6 | 1060.5 | 22/9, 27/11 |
| 32 | 1601.6 | 1094.7 | |
| 33 | 1651.7 | 1128.9 | 13/5 |
| 34 | 1701.7 | 1163.2 | 8/3 |
| 35 | 1751.8 | 1197.4 | 11/4 |
| 36 | 1801.9 | 1231.6 | 17/6 |
| 37 | 1851.9 | 1265.8 | |
| 38 | 1902 | 1300 | 3/1 |
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