11edf
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Prime factorization
11 (prime)
Step size
63.8141¢
Octave
19\11edf (1212.47¢)
Twelfth
30\11edf (1914.42¢)
Consistency limit
7
Distinct consistency limit
4
| ← 10edf | 11edf | 12edf → |
11edf is the equal division of the just perfect fifth into 11 parts of 63.8141 cents each, corresponding to 18.8046 edo (similar to every fifth step of 94edo). It is similar to 19edo and nearly identical to Carlos Beta.
While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo, being about four cents flat of that of 7edo.
11edf represents the upper bound of the phoenix tuning range. 11edf benefits from all the desirable properties of phoenix tuning systems.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +12.47 | +12.47 | +24.94 | +21.51 | +24.94 | +13.32 | -26.41 | +24.94 | -29.84 | -3.40 | -26.41 | +26.46 | +25.79 | -29.84 | -13.94 |
| Relative (%) | +19.5 | +19.5 | +39.1 | +33.7 | +39.1 | +20.9 | -41.4 | +39.1 | -46.8 | -5.3 | -41.4 | +41.5 | +40.4 | -46.8 | -21.8 | |
| Steps (reduced) |
19 (8) |
30 (8) |
38 (5) |
44 (0) |
49 (5) |
53 (9) |
56 (1) |
60 (5) |
62 (7) |
65 (10) |
67 (1) |
70 (4) |
72 (6) |
73 (7) |
75 (9) | |
Intervals
| Degree | Cent value | Corresponding JI intervals |
Comments |
|---|---|---|---|
| 0 | exact 1/1 | ||
| 1 | 63.8141 | (28/27), (27/26) | |
| 2 | 127.6282 | 14/13 | |
| 3 | 191.4423 | ||
| 4 | 255.2564 | ||
| 5 | 319.07045 | 6/5 | |
| 6 | 382.8845 | 5/4 | |
| 7 | 446.6986 | ||
| 8 | 510.5127 | ||
| 9 | 574.3268 | 39/28 | |
| 10 | 638.1409 | (13/9) | |
| 11 | 701.955 | exact 3/2 | just perfect fifth |
| 12 | 765.7691 | 14/9, 81/52 | |
| 13 | 828.5732 | 21/13 | |
| 14 | 893.3973 | ||
| 15 | 956.2114 | ||
| 16 | 1020.0255 | 9/5 | |
| 17 | 1084.8395 | 15/8 | |
| 18 | 1148.6536 | ||
| 19 | 1211.4677 | ||
| 20 | 1276.2816 | 117/56 | |
| 21 | 1340.0959 | 13/6 | |
| 22 | 1403.91 | exact 9/4 | |