# 27208edt

← 27207edt | 27208edt | 27209edt → |

^{3}× 19 × 179**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 3^{1/27208}, 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

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) |