27208edt
27208edt is a tuning system which divides the tritave, 3/1, into 27208 equal parts of approximately 0.0699¢ each.
27208edt provides an extremely good approximation to the no-twos 7-limit, with the 5th harmonic accurate to 0.045% (approximately 1/2231 of a step), and the 7th harmonic accurate to 0.0073% (approximately 1/13733 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the ditave, 2/1, by approximately a third of a step, making it incomparable with its related edos, 17166edo and 17167edo.
Nevertheless, 27208edt also has good approximations to the 13th and 23rd harmonics, making it an excellent tuning in the 3.5.7.13.23 subgroup.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0235 | +0.0000 | +0.0000 | +0.0000 | +0.0162 | +0.0004 | +0.0165 | -0.0248 | +0.0009 | +0.0183 | -0.0281 |
| Relative (%) | -33.7 | +0.0 | +0.0 | +0.0 | +23.2 | +0.6 | +23.6 | -35.4 | +1.2 | +26.2 | -40.2 | |
| Steps (reduced) |
17166 (17166) |
27208 (0) |
39859 (12651) |
48192 (20984) |
59386 (4970) |
63523 (9107) |
70167 (15751) |
72921 (18505) |
77653 (23237) |
83394 (1770) |
85045 (3421) | |