# 147edo

← 146edo | 147edo | 148edo → |

^{2}(semiconvergent)

**147 equal divisions of the octave** (abbreviated **147edo** or **147ed2**), also called **147-tone equal temperament** (**147tet**) or **147 equal temperament** (**147et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 147 equal parts of about 8.16 ¢ each. Each step represents a frequency ratio of 2^{1/147}, or the 147th root of 2.

## Theory

147edo has a very accurate fifth. Using the patent val, the equal temperament tempers out 32805/32768 in the 5-limit; 225/224 and 3125/3087 in the 7-limit; 243/242 in the 11-limit; 364/363 in the 13-limit; 442/441 and 595/594 in the 17-limit. It is the optimal patent val for 11-limit karadeniz, the 41 & 106 temperament.

### Prime harmonics

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

Error | Absolute (¢) | +0.00 | +0.09 | -2.64 | +2.60 | +3.78 | +0.29 | +1.17 | -3.64 | +0.30 | -1.01 | -2.18 |

Relative (%) | +0.0 | +1.1 | -32.3 | +31.9 | +46.4 | +3.5 | +14.3 | -44.5 | +3.6 | -12.3 | -26.7 | |

Steps (reduced) |
147 (0) |
233 (86) |
341 (47) |
413 (119) |
509 (68) |
544 (103) |
601 (13) |
624 (36) |
665 (77) |
714 (126) |
728 (140) |

### Subsets and supersets

Since 147 = 3 × 7^{2}, 147edo has subset edos 3, 7, 21 and 49.