10ed7/4

 ← 9ed7/4 10ed7/4 11ed7/4 →
Prime factorization 2 × 5
Step size 96.8826¢
Octave 12\10ed7/4 (1162.59¢) (→6\5ed7/4)
Twelfth 20\10ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit 2
Distinct consistency limit 2

10ED7/4 is the equal division of the harmonic seventh into ten parts of 96.8826 cents each, corresponding to 12.3861 EDO.

Intervals

Degree Cents value Ratio
0 0.0000 1/1
1 96.8826 (7/4)1/10
2 193.7652 (7/4)1/5
3 290.6478 (7/4)3/10
4 387.5304 (7/4)2/5
5 484.4130 (7/4)1/2
6 581.2955 (7/4)3/5
7 678.1781 (7/4)7/10
8 775.0607 (7/4)4/5
9 871.9433 (7/4)9/10
10 968.8259 7/4
11 1065.7085 (7/4)11/10
12 1162.5911 (7/4)6/5
13 1259.4737 (7/4)13/10
14 1356.3563 (7/4)7/2
15 1453.2389 (7/4)3/2
16 1550.1215 (7/4)8/5
17 1647.0040 (7/4)17/10
18 1743.8866 (7/4)9/5
19 1840.7692 (7/4)19/10
20 1937.6518 (7/4)2 = 49/16
21 2034.5344 (7/4)21/10
22 2131.4170 (7/4)11/5
23 2228.2996 (7/4)23/10
24 2325.1822 (7/4)12/5
25 2422.0648 (7/4)5/2
26 2518.9474 (7/4)13/5
27 2615.8299 (7/4)27/10
28 2712.7125 (7/4)14/5
29 2809.5951 (7/4)29/10
30 2906.4777 (7/4)3 = 343/64
31 3003.3603 (7/4)31/10
32 3100.2429 (7/4)16/5
33 3197.1255 (7/4)33/10
34 3294.0081 (7/4)17/10
35 3390.8907 (7/4)7/2
36 3487.7733 (7/4)18/5
37 3584.6559 (7/4)37/10
38 3681.5384 (7/4)19/5

Just approximation

Only very few intervals like the just major third and the Huygens' tritone are well approximated by 10ed7/4.

15-odd-limit approximations

The following table shows how 15-odd-limit intervals are represented in 10ed7/4 (can be ordered by absolute error).

Direct approximation (even if inconsistent)
Interval(s) Error (abs, ¢)
7/4 0.0
2/1 37.409
3/2 23.777
5/4 1.217
9/8 10.145
11/8 29.978
13/8 31.416
15/8 22.56
14/9 10.145
28/15 14.849
10/7 36.192
16/11 29.496
13/10 30.199
9/5 48.112
10/9 11.361
26/15 16.567
13/11 1.438
13/7 5.993
16/13 28.058
7/6 23.777
5/3 12.415
20/13 29.275
11/10 28.761
8/5 38.626
9/7 47.554
11/9 40.122
18/11 19.351
24/13 4.281
22/15 15.129
15/13 42.907
15/11 44.345
16/9 27.264
12/7 35.697
7/5 1.217
12/11 43.128
4/3 13.632
11/6 16.346
13/12 41.69
8/7 37.409
20/11 30.713
14/13 31.416
6/5 24.994
18/13 17.913
15/14 22.56
11/7 7.431
13/9 41.56
14/11 29.978
22/13 38.847
16/15 14.849