# 840edo

 ← 839edo 840edo 841edo →
Prime factorization 23 × 3 × 5 × 7
Step size 1.42857¢
Fifth 491\840 (701.429¢)
Semitones (A1:m2) 77:65 (110¢ : 92.86¢)
Dual sharp fifth 492\840 (702.857¢) (→41\70)
Dual flat fifth 491\840 (701.429¢)
Dual major 2nd 143\840 (204.286¢)
Consistency limit 7
Distinct consistency limit 7
Special properties

840 equal divisions of the octave (abbreviated 840edo or 840ed2), also called 840-tone equal temperament (840tet) or 840 equal temperament (840et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 840 equal parts of about 1.43 ¢ each. Each step represents a frequency ratio of 21/840, or the 840th root of 2.

## Theory

840edo is the 15th highly composite EDO, and it is the first one divisible by 7. It does not tune the 9-odd-limit consistently, though a reasonable 13-limit interpretation exists through the patent val. A comma basis for the 13-limit is 729/728, 1575/1573, 67392/67375, 804375/802816, 250047/250000.

### Odd harmonics

Approximation of odd harmonics in 840edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.526 -0.599 -0.254 +0.376 +0.111 -0.528 +0.303 -0.670 -0.370 +0.648 +0.297
Relative (%) -36.9 -42.0 -17.8 +26.3 +7.7 -36.9 +21.2 -46.9 -25.9 +45.3 +20.8
Steps
(reduced)
1331
(491)
1950
(270)
2358
(678)
2663
(143)
2906
(386)
3108
(588)
3282
(762)
3433
(73)
3568
(208)
3690
(330)
3800
(440)