11edf
11 equal divisions of the perfect fifth (abbreviated 11edf or 11ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 11 equal parts of about 63.8 ¢ each. Each step represents a frequency ratio of (3/2)1/11, or the 11th root of 3/2. It corresponds to 18.8046edo, is is similar to 19edo, and nearly identical to Carlos Beta.
| ← 10edf | 11edf | 12edf → |
While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo. At 510.51 ¢, it is 12.47 ¢ sharper than just and 3.7 ¢ 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 | |