# 27208edt

 ← 27207edt 27208edt 27209edt →
Prime factorization 23 × 19 × 179
Step size 0.0699043¢
Octave 17166\27208edt (1199.98¢) (→8583\13604edt)
Consistency limit 2
Distinct consistency limit 2

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.

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

Approximation of prime harmonics in 27208edt
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)