44edt
44 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 44edt or 44ed3), is a nonoctave tuning system that divides the interval of 3/1 into 44 equal parts of about 43.2 ¢ each. Each step represents a frequency ratio of 31/44, or the 44th root of 3.
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 43.2 | 29.5 | |
| 2 | 86.5 | 59.1 | 20/19, 21/20, 22/21 |
| 3 | 129.7 | 88.6 | 14/13, 29/27 |
| 4 | 172.9 | 118.2 | 21/19, 31/28 |
| 5 | 216.1 | 147.7 | 17/15, 26/23 |
| 6 | 259.4 | 177.3 | 22/19 |
| 7 | 302.6 | 206.8 | 31/26 |
| 8 | 345.8 | 236.4 | 11/9, 28/23 |
| 9 | 389 | 265.9 | |
| 10 | 432.3 | 295.5 | 9/7 |
| 11 | 475.5 | 325 | 29/22 |
| 12 | 518.7 | 354.5 | 27/20, 31/23 |
| 13 | 561.9 | 384.1 | 18/13, 29/21 |
| 14 | 605.2 | 413.6 | 27/19 |
| 15 | 648.4 | 443.2 | 29/20 |
| 16 | 691.6 | 472.7 | |
| 17 | 734.8 | 502.3 | 29/19 |
| 18 | 778.1 | 531.8 | 11/7 |
| 19 | 821.3 | 561.4 | 29/18 |
| 20 | 864.5 | 590.9 | 23/14 |
| 21 | 907.8 | 620.5 | 22/13 |
| 22 | 951 | 650 | 19/11 |
| 23 | 994.2 | 679.5 | 23/13 |
| 24 | 1037.4 | 709.1 | 20/11 |
| 25 | 1080.7 | 738.6 | |
| 26 | 1123.9 | 768.2 | 21/11, 23/12 |
| 27 | 1167.1 | 797.7 | |
| 28 | 1210.3 | 827.3 | |
| 29 | 1253.6 | 856.8 | |
| 30 | 1296.8 | 886.4 | 19/9 |
| 31 | 1340 | 915.9 | 13/6 |
| 32 | 1383.2 | 945.5 | 20/9, 29/13 |
| 33 | 1426.5 | 975 | |
| 34 | 1469.7 | 1004.5 | 7/3 |
| 35 | 1512.9 | 1034.1 | |
| 36 | 1556.1 | 1063.6 | 27/11 |
| 37 | 1599.4 | 1093.2 | |
| 38 | 1642.6 | 1122.7 | 31/12 |
| 39 | 1685.8 | 1152.3 | |
| 40 | 1729.1 | 1181.8 | 19/7 |
| 41 | 1772.3 | 1211.4 | |
| 42 | 1815.5 | 1240.9 | 20/7 |
| 43 | 1858.7 | 1270.5 | |
| 44 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.3 | +0.0 | +20.7 | -19.8 | +10.3 | +2.8 | -12.2 | +0.0 | -9.5 | -1.6 | +20.7 |
| Relative (%) | +23.9 | +0.0 | +47.8 | -45.9 | +23.9 | +6.5 | -28.3 | +0.0 | -22.0 | -3.7 | +47.8 | |
| Steps (reduced) |
28 (28) |
44 (0) |
56 (12) |
64 (20) |
72 (28) |
78 (34) |
83 (39) |
88 (0) |
92 (4) |
96 (8) |
100 (12) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +11.8 | +13.2 | -19.8 | -1.9 | -20.4 | +10.3 | +3.2 | +0.8 | +2.8 | +8.7 | +18.2 |
| Relative (%) | +27.2 | +30.4 | -45.9 | -4.4 | -47.2 | +23.9 | +7.4 | +1.9 | +6.5 | +20.2 | +42.2 | |
| Steps (reduced) |
103 (15) |
106 (18) |
108 (20) |
111 (23) |
113 (25) |
116 (28) |
118 (30) |
120 (32) |
122 (34) |
124 (36) |
126 (38) | |
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