43ed4
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Prime factorization
43 (prime)
Step size
55.814¢
Octave
22\43ed4 (1227.91¢)
Twelfth
34\43ed4 (1897.67¢)
Consistency limit
1
Distinct consistency limit
1
| ← 41ed4 | 43ed4 | 45ed4 → |
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).
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) | |