43ed4
43 equal divisions of the 4th harmonic (abbreviated 43ed4) is a nonoctave tuning system that divides the interval of 4/1 into 43 equal parts of about 55.8 ¢ each. Each step represents a frequency ratio of 41/43, or the 43rd root of 4. (Every second step of 43edo).
| ← 41ed4 | 43ed4 | 45ed4 → |
It is closely related to 34edt, but the patent vals differ on the mapping for 13. Using the patent val, it tempers out 49/48, 81/80, and 16128/15625 in the 3.4.5.7 subgroup; 77/75, 176/175, 891/875, and 1331/1280 in the 3.4.5.7.11 subgroup; 121/117, 144/143, 147/143, 175/169, and 729/715 in the 3.4.5.7.11.13 subgroup.
Lookalikes: 34edt
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 55.8 | |
| 2 | 111.6 | |
| 3 | 167.4 | 21/19 |
| 4 | 223.3 | 17/15, 25/22 |
| 5 | 279.1 | 27/23 |
| 6 | 334.9 | 17/14, 23/19 |
| 7 | 390.7 | |
| 8 | 446.5 | 22/17 |
| 9 | 502.3 | |
| 10 | 558.1 | 18/13, 29/21 |
| 11 | 614 | 27/19 |
| 12 | 669.8 | 25/17 |
| 13 | 725.6 | 29/19 |
| 14 | 781.4 | 11/7 |
| 15 | 837.2 | |
| 16 | 893 | |
| 17 | 948.8 | 19/11 |
| 18 | 1004.7 | 25/14 |
| 19 | 1060.5 | |
| 20 | 1116.3 | 21/11 |
| 21 | 1172.1 | |
| 22 | 1227.9 | |
| 23 | 1283.7 | |
| 24 | 1339.5 | 13/6 |
| 25 | 1395.3 | |
| 26 | 1451.2 | 30/13 |
| 27 | 1507 | |
| 28 | 1562.8 | |
| 29 | 1618.6 | 23/9 |
| 30 | 1674.4 | 29/11 |
| 31 | 1730.2 | 19/7 |
| 32 | 1786 | 14/5 |
| 33 | 1841.9 | |
| 34 | 1897.7 | 3/1 |
| 35 | 1953.5 | |
| 36 | 2009.3 | |
| 37 | 2065.1 | 23/7 |
| 38 | 2120.9 | 17/5 |
| 39 | 2176.7 | |
| 40 | 2232.6 | |
| 41 | 2288.4 | |
| 42 | 2344.2 | |
| 43 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +27.9 | -4.3 | +0.0 | +4.4 | +23.6 | -20.0 | +27.9 | -8.6 | -23.5 | -21.1 | -4.3 |
| Relative (%) | +50.0 | -7.7 | +0.0 | +7.9 | +42.3 | -35.8 | +50.0 | -15.3 | -42.1 | -37.8 | -7.7 | |
| Steps (reduced) |
22 (22) |
34 (34) |
43 (0) |
50 (7) |
56 (13) |
60 (17) |
65 (22) |
68 (25) |
71 (28) |
74 (31) |
77 (34) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +24.6 | +7.9 | +0.1 | +0.0 | +6.7 | +19.3 | -18.4 | +4.4 | -24.3 | +6.8 | -14.3 |
| Relative (%) | +44.1 | +14.2 | +0.2 | +0.0 | +12.0 | +34.7 | -33.0 | +7.9 | -43.5 | +12.2 | -25.7 | |
| Steps (reduced) |
80 (37) |
82 (39) |
84 (41) |
86 (0) |
88 (2) |
90 (4) |
91 (5) |
93 (7) |
94 (8) |
96 (10) |
97 (11) | |