# 306edo

← 305edo | 306edo | 307edo → |

^{2}× 17(convergent)

**306 equal divisions of the octave** (abbreviated **306edo** or **306ed2**), also called **306-tone equal temperament** (**306tet**) or **306 equal temperament** (**306et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 306 equal parts of about 3.92 ¢ each. Each step represents a frequency ratio of 2^{1/306}, or the 306th root of 2.

306edo provides a very accurate fifth, only 0.0058 cents stretched. In the 5-limit, the patent val tempers out 78732/78125 (sensipent comma), whereas the alternative 306c val tempers out 32805/32768 (schisma). In the 7-limit the patent val tempers out 6144/6125, whereas 306c tempers out 16875/16807. 306 is the denominator of 179\306, the continued fraction convergent after 31\53 and before 389\665 in the sequence of continued fraction approximations to to log_{2}(3/2). On the 2*306 subgroup 2.3.25.7.55 it takes the same values as 612edo.

### Prime harmonics

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | +0.000 | +0.006 | +1.922 | -0.198 | +1.623 | -1.312 | +0.927 | +0.526 | -0.823 | +1.795 | +0.062 |

Relative (%) | +0.0 | +0.1 | +49.0 | -5.1 | +41.4 | -33.5 | +23.6 | +13.4 | -21.0 | +45.8 | +1.6 | |

Steps (reduced) |
306 (0) |
485 (179) |
711 (99) |
859 (247) |
1059 (141) |
1132 (214) |
1251 (27) |
1300 (76) |
1384 (160) |
1487 (263) |
1516 (292) |

### Subsets and supersets

Since 306 factors into 2 × 3^{2} × 17, 306edo has subset edos 2, 3, 6, 9, 17, 18, 34, 51, 102, and 153.