43ed7/4

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← 42ed7/443ed7/444ed7/4 →
Prime factorization 43 (prime)
Step size 22.5308¢ 
Octave 53\43ed7/4 (1194.13¢)
Twelfth 84\43ed7/4 (1892.59¢)
Consistency limit 3
Distinct consistency limit 3

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).

Direct approximation (even if inconsistent)
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