43ed7/4
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43 equal divisions of 7/4 (abbreviated 43ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 43 equal parts of about 22.5 ¢ each. Each step represents a frequency ratio of (7/4)1/43, or the 43rd root of 7/4. It corresponds to 53.2603edo, which is closely related to 53edo but with 7/4 tuned pure instead of the octave.
Intervals
| # | Cents Value | Ratio |
|---|---|---|
| 0 | 0.0000 | 1/1 |
| 1 | 22.5308 | (7/4)1/43 |
| 2 | 45.0617 | (7/4)2/43 |
| 3 | 67.5925 | (7/4)3/43 |
| 4 | 90.1233 | (7/4)4/43 |
| 5 | 112.6542 | (7/4)5/43 |
| 6 | 135.1850 | (7/4)6/43 |
| 7 | 157.7158 | (7/4)7/43 |
| 8 | 180.2467 | (7/4)8/43 |
| 9 | 202.7775 | (7/4)9/43 |
| 10 | 225.3084 | (7/4)10/43 |
| 11 | 247.8392 | (7/4)11/43 |
| 12 | 270.3700 | (7/4)12/43 |
| 13 | 292.9009 | (7/4)13/43 |
| 14 | 315.4317 | (7/4)14/43 |
| 15 | 337.9625 | (7/4)15/43 |
| 16 | 360.4934 | (7/4)16/43 |
| 17 | 383.0242 | (7/4)17/43 |
| 18 | 405.5550 | (7/4)18/43 |
| 19 | 428.0859 | (7/4)19/43 |
| 20 | 450.6167 | (7/4)20/43 |
| 21 | 473.1475 | (7/4)21/43 |
| 22 | 495.6784 | (7/4)22/43 |
| 23 | 518.2092 | (7/4)23/43 |
| 24 | 540.7400 | (7/4)24/43 |
| 25 | 563.2709 | (7/4)25/43 |
| 26 | 585.8017 | (7/4)26/43 |
| 27 | 608.3325 | (7/4)27/43 |
| 28 | 630.8634 | (7/4)28/43 |
| 29 | 653.3942 | (7/4)29/43 |
| 30 | 675.9251 | (7/4)30/43 |
| 31 | 698.4559 | (7/4)31/43 |
| 32 | 720.9867 | (7/4)32/43 |
| 33 | 743.5176 | (7/4)33/43 |
| 34 | 766.0484 | (7/4)34/43 |
| 35 | 788.5792 | (7/4)35/43 |
| 36 | 811.1101 | (7/4)36/43 |
| 37 | 833.6409 | (7/4)37/43 |
| 38 | 856.1717 | (7/4)38/43 |
| 39 | 878.7026 | (7/4)39/43 |
| 40 | 901.2334 | (7/4)40/43 |
| 41 | 923.7642 | (7/4)41/43 |
| 42 | 946.2951 | (7/4)42/43 |
| 43 | 968.8259 | 7/4 |
| 44 | 991.3567 | (7/4)44/43 |
| 45 | 1013.8876 | (7/4)45/43 |
| 46 | 1036.4184 | (7/4)46/43 |
| 47 | 1058.9492 | (7/4)47/43 |
| 48 | 1081.4801 | (7/4)48/43 |
| 49 | 1104.0109 | (7/4)49/43 |
| 50 | 1126.5418 | (7/4)50/43 |
| 51 | 1149.0726 | (7/4)51/43 |
| 52 | 1171.6034 | (7/4)52/43 |
| 53 | 1194.1343 | (7/4)53/43 |
| 54 | 1216.6651 | (7/4)54/43 |
Approximation to JI
Several intervals like the just minor third and the whole tone are well approximated by 43ed7/4.
15-odd-limit mappings
The following table shows how 15-odd-limit intervals are represented in 43ed7/4 (can be ordered by absolute error).
| Interval(s) | Error (abs, ¢) |
|---|---|
| 7/4 | 0.0 |
| 2/1 | 5.866 |
| 3/2 | 3.499 |
| 5/4 | 3.29 |
| 9/8 | 1.132 |
| 11/8 | 10.578 |
| 13/8 | 6.887 |
| 15/8 | 6.789 |
| 14/9 | 1.132 |
| 28/15 | 0.923 |
| 10/7 | 9.155 |
| 16/11 | 4.712 |
| 13/10 | 3.597 |
| 9/5 | 3.709 |
| 10/9 | 2.157 |
| 26/15 | 5.964 |
| 13/11 | 3.691 |
| 13/7 | 9.778 |
| 16/13 | 1.021 |
| 7/6 | 3.499 |
| 5/3 | 5.656 |
| 20/13 | 2.268 |
| 11/10 | 7.288 |
| 8/5 | 2.576 |
| 9/7 | 6.998 |
| 11/9 | 9.445 |
| 18/11 | 3.58 |
| 24/13 | 2.478 |
| 22/15 | 9.655 |
| 15/13 | 0.098 |
| 15/11 | 3.789 |
| 16/9 | 4.733 |
| 12/7 | 9.365 |
| 7/5 | 3.29 |
| 12/11 | 7.079 |
| 4/3 | 2.367 |
| 11/6 | 9.586 |
| 13/12 | 3.388 |
| 8/7 | 5.866 |
| 20/11 | 1.423 |
| 14/13 | 6.887 |
| 6/5 | 0.21 |
| 18/13 | 0.111 |
| 15/14 | 6.789 |
| 11/7 | 6.087 |
| 13/9 | 5.754 |
| 14/11 | 10.578 |
| 22/13 | 9.557 |
| 16/15 | 0.923 |