48edt
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Prime factorization
24 × 3
Step size
39.6241¢
Octave
30\48edt (1188.72¢) (→5\8edt)
Consistency limit
2
Distinct consistency limit
2
Special properties
 |
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| ← 47edt | 48edt | 49edt → |
48 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 48edt or 48ed3), is a nonoctave tuning system that divides the interval of 3/1 into 48 equal parts of about 39.6 ¢ each. Each step represents a frequency ratio of 31/48, or the 48th root of 3.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 39.624 | |
| 2 | 79.248 | 22/21, 23/22 |
| 3 | 118.872 | 15/14, 29/27, 31/29 |
| 4 | 158.496 | 23/21 |
| 5 | 198.12 | 19/17, 28/25 |
| 6 | 237.744 | 31/27 |
| 7 | 277.368 | 27/23 |
| 8 | 316.993 | 6/5 |
| 9 | 356.617 | 27/22 |
| 10 | 396.241 | 29/23 |
| 11 | 435.865 | 9/7 |
| 12 | 475.489 | 29/22 |
| 13 | 515.113 | 31/23 |
| 14 | 554.737 | 29/21 |
| 15 | 594.361 | 31/22 |
| 16 | 633.985 | 13/9 |
| 17 | 673.609 | 31/21 |
| 18 | 713.233 | |
| 19 | 752.857 | 17/11 |
| 20 | 792.481 | |
| 21 | 832.105 | 21/13 |
| 22 | 871.729 | |
| 23 | 911.353 | 22/13 |
| 24 | 950.978 | 19/11, 26/15 |
| 25 | 990.602 | 23/13 |
| 26 | 1030.226 | |
| 27 | 1069.85 | 13/7 |
| 28 | 1109.474 | |
| 29 | 1149.098 | |
| 30 | 1188.722 | |
| 31 | 1228.346 | |
| 32 | 1267.97 | 25/12, 27/13 |
| 33 | 1307.594 | |
| 34 | 1347.218 | |
| 35 | 1386.842 | 29/13 |
| 36 | 1426.466 | |
| 37 | 1466.09 | 7/3 |
| 38 | 1505.714 | 31/13 |
| 39 | 1545.338 | 22/9 |
| 40 | 1584.963 | 5/2 |
| 41 | 1624.587 | 23/9 |
| 42 | 1664.211 | |
| 43 | 1703.835 | |
| 44 | 1743.459 | |
| 45 | 1783.083 | 14/5 |
| 46 | 1822.707 | |
| 47 | 1862.331 | |
| 48 | 1901.955 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.3 | +0.0 | +17.1 | -12.6 | -11.3 | -0.8 | +5.8 | +0.0 | +15.7 | +9.2 | +17.1 |
| Relative (%) | -28.5 | +0.0 | +43.1 | -31.9 | -28.5 | -2.0 | +14.6 | +0.0 | +39.7 | +23.2 | +43.1 | |
| Steps (reduced) |
30 (30) |
48 (0) |
61 (13) |
70 (22) |
78 (30) |
85 (37) |
91 (43) |
96 (0) |
101 (5) |
105 (9) |
109 (13) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | -12.1 | -12.6 | -5.5 | +8.4 | -11.3 | +14.0 | +4.4 | -0.8 | -2.1 | +0.2 |
| Relative (%) | -6.6 | -30.4 | -31.9 | -13.9 | +21.3 | -28.5 | +35.3 | +11.2 | -2.0 | -5.2 | +0.6 | |
| Steps (reduced) |
112 (16) |
115 (19) |
118 (22) |
121 (25) |
124 (28) |
126 (30) |
129 (33) |
131 (35) |
133 (37) |
135 (39) |
137 (41) | |