# 703edo

 ← 702edo 703edo 704edo →
Prime factorization 19 × 37
Step size 1.70697¢
Fifth 411\703 (701.565¢)
Semitones (A1:m2) 65:54 (111¢ : 92.18¢)
Consistency limit 5
Distinct consistency limit 5

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 21/703, 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

Approximation of odd harmonics in 703edo
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.