# 703edo

← 702edo | 703edo | 704edo → |

**703 equal divisions of the octave** (abbreviated **703edo** or **703ed2**), also called **703-tone equal temperament** (**703tet**) or **703 equal temperament** (**703et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 703 equal parts of about 1.71 ¢ each. Each step represents a frequency ratio of 2^{1/703}, or the 703rd root of 2.

703edo is only consistent to the 5-odd-limit since harmonic 7 is about halfway between its steps. The equal temperament tempers out the enneadeca, [-14 -19 19⟩ in the 5-limit.

In the 7-limit, the patent val ⟨703 1114 1632 **1974**] and the 703d val ⟨703 1114 1632 **1973**] may be worth considering.

Using the patent val, it tempers out 16875/16807 and 65625/65536 and in the 11-limit 1375/1372, 540/539 and 3025/3024, so that it supports and gives the optimal patent val for indra and eris. In the 13-limit, it tempers out 729/728, 2080/2079 and 6656/6655, and provides the optimal patent val for shibi.

The alternative 703d val tempers out 4375/4374 and 703125/702464, supporting 7-limit enneadecal.

### Odd harmonics

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | Absolute (¢) | -0.390 | -0.538 | +0.733 | -0.781 | +0.033 | -0.698 | +0.778 | -0.830 | -0.500 | +0.343 | -0.109 |

Relative (%) | -22.9 | -31.5 | +42.9 | -45.7 | +2.0 | -40.9 | +45.6 | -48.6 | -29.3 | +20.1 | -6.4 | |

Steps (reduced) |
1114 (411) |
1632 (226) |
1974 (568) |
2228 (119) |
2432 (323) |
2601 (492) |
2747 (638) |
2873 (61) |
2986 (174) |
3088 (276) |
3180 (368) |

### Subsets and supersets

Since 703 factors into 19 × 37, 703edo contains 19edo and 37edo as subsets.