# 236edo

← 235edo | 236edo | 237edo → |

^{2}× 59**236 equal divisions of the octave** (abbreviated **236edo** or **236ed2**), also called **236-tone equal temperament** (**236tet**) or **236 equal temperament** (**236et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 236 equal parts of about 5.08 ¢ each. Each step represents a frequency ratio of 2^{1/236}, or the 236th root of 2.

## Theory

236edo is enfactored in the 5-limit, with the same tuning as 118edo, defined by tempering out the schisma and the parakleisma. The 7-limit mapping is worse over that of 118edo in terms of relative error, as it leans on the very sharp side. It tempers out 6144/6125 and 19683/19600, supporting hemischis. Using the 236e val ⟨236 374 548 663 **817**], it tempers out 243/242, 1375/1372, 6250/6237, 14700/14641 and 16384/16335.

The 236bb val (where fifth is flattened by single step, approximately 1/4 comma) gives a tuning very close to quarter-comma meantone, although 205edo is even closer. Alternately, sharpening it to 236b gives a fifth that is in the golden diaschismic sequence.

### Prime harmonics

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

Error | Absolute (¢) | +0.00 | -0.26 | +0.13 | +2.36 | -2.17 | -1.54 | +1.82 | +2.49 | +2.23 | -2.46 | -0.97 |

Relative (%) | +0.0 | -5.1 | +2.5 | +46.4 | -42.6 | -30.4 | +35.9 | +48.9 | +43.9 | -48.4 | -19.0 | |

Steps (reduced) |
236 (0) |
374 (138) |
548 (76) |
663 (191) |
816 (108) |
873 (165) |
965 (21) |
1003 (59) |
1068 (124) |
1146 (202) |
1169 (225) |

### Subsets and supersets

Since 236 factors into 2^{2} × 53, 236edo has subset edos 2, 4, 59 and 118. 472edo, which doubles it, provides good correction to harmonics 7 and 11.

## Regular temperament properties

Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
---|---|---|---|---|---|

Absolute (¢) | Relative (%) | ||||

2.3.5.7 | 6144/6125, 19683/19600, 390625/388962 | [⟨236 374 548 663]] | -0.1830 | 0.03883 | 7.64 |