45/38 is a 19-limit interval, 292.7 cents in size. In the Functional Just System and Helmholtz-Ellis notation, it is an augmented second, obtained by subtracting 81/80 and 513/512 to the Pythagorean augmented second, but it may be called the Eratosthenes' minor third as it is flatter than the Pythagorean minor third by the password aka Eratosthenes' comma (1216/1215), an unnoticeable comma of about 1.4243 cents.
Approximation
Edo approximations for 45/38 (292.71 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 4 |
1\4 |
300.00 |
+7.29 |
+2.43
|
| 8 |
2\8 |
300.00 |
+7.29 |
+4.86
|
| 12 |
3\12 |
300.00 |
+7.29 |
+7.29
|
| 16 |
4\16 |
300.00 |
+7.29 |
+9.72
|
| 25 |
6\25 |
288.00 |
-4.71 |
-9.81
|
| 29 |
7\29 |
289.66 |
-3.06 |
-7.38
|
| 33 |
8\33 |
290.91 |
-1.80 |
-4.95
|
| 37 |
9\37 |
291.89 |
-0.82 |
-2.52
|
| 41 |
10\41 |
292.68 |
-0.03 |
-0.09
|
| 45 |
11\45 |
293.33 |
+0.62 |
+2.33
|
| 49 |
12\49 |
293.88 |
+1.17 |
+4.76
|
| 53 |
13\53 |
294.34 |
+1.63 |
+7.19
|
| 57 |
14\57 |
294.74 |
+2.03 |
+9.62
|
| 66 |
16\66 |
290.91 |
-1.80 |
-9.91
|
| 70 |
17\70 |
291.43 |
-1.28 |
-7.48
|
| 74 |
18\74 |
291.89 |
-0.82 |
-5.05
|
| 78 |
19\78 |
292.31 |
-0.40 |
-2.62
|
See also