11edf: Difference between revisions
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{{ED intro}} It corresponds to 18.8046[[edo]], is is similar to [[19edo]], and nearly identical to [[Carlos Beta]]. | {{ED intro}} It corresponds to 18.8046[[edo]], is 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, | While the fifth is just, the fourth is very sharp and significantly less accurate than in 19edo. At 510.51{{c}}, it is 12.47{{c}} sharper than just and 3.7{{c}} 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. | 11edf represents the upper bound of the [[phoenix]] tuning range. 11edf benefits from all the desirable properties of phoenix tuning systems. | ||
Revision as of 20:02, 6 March 2025
| ← 10edf | 11edf | 12edf → |
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.
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 | |