27208edt
| ← 27207edt | 27208edt | 27209edt → |
27208 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 27208edt or 27208ed3), is a nonoctave tuning system that divides the interval of 3/1 into 27208 equal parts of about 0.0699 ¢ each. Each step represents a frequency ratio of 31/27208, or the 27208th root of 3.
27208edt provides an extremely good approximation to the no-twos 7-limit, with the 5th harmonic tuned 0.045% sharp (approximately 1/2231 of a step), and the 7th harmonic tuned 0.0073% sharp (approximately 1/13733 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the octave, 2/1, by approximately a third of a step, making it incomparable with its related edos, 17166edo and 17167edo. Though the 8th harmonic is tuned only 1% flat, tripling the tuning to 51499edo increases the error several hundredfold on the 3rd, 5th, and 7th harmonics; even so, this makes 51499edo a relatively good EDO for 7-limit, with errors comparable to those of 18355edo.
27208edt also has good approximations to the 8th, 13th and 23rd harmonics, making it an excellent tuning in the 3.5.7.8.13.23 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) | |