10ed7/4
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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
| ← 9ed7/4 | 10ed7/4 | 11ed7/4 → |
10ED7/4 is the equal division of the harmonic seventh into ten parts of 96.8826 cents each, corresponding to 12.3861 EDO.
Theory
This tuning tempers out 36/35 and 50/49 in the 7-limit; 55/54 in the 11-limit; 34/33 and 56/51 in the 17-limit; 31/30 in the 31-limit; and 38/37 in the 37-limit.
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).
| 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 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -37.4 | +35.7 | +22.1 | +23.3 | -1.7 | +22.1 | -15.3 | -25.5 | -14.1 | +14.6 | -39.1 |
| Relative (%) | -38.6 | +36.8 | +22.8 | +24.0 | -1.8 | +22.8 | -15.8 | -26.3 | -14.6 | +15.1 | -40.4 | |
| Steps (reduced) |
12 (2) |
20 (0) |
25 (5) |
29 (9) |
32 (2) |
35 (5) |
37 (7) |
39 (9) |
41 (1) |
43 (3) |
44 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +16.1 | -15.3 | -37.9 | +44.1 | +36.1 | +34.0 | +37.3 | +45.3 | -39.1 | -22.8 | -2.8 |
| Relative (%) | +16.6 | -15.8 | -39.1 | +45.5 | +37.2 | +35.1 | +38.5 | +46.8 | -40.4 | -23.5 | -2.9 | |
| Steps (reduced) |
46 (6) |
47 (7) |
48 (8) |
50 (0) |
51 (1) |
52 (2) |
53 (3) |
54 (4) |
54 (4) |
55 (5) |
56 (6) | |