703edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 702edo703edo704edo →
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.