# 840edo

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Prime factorization
2
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

← 839edo | 840edo | 841edo → |

^{3}× 3 × 5 × 7**840 equal divisions of the octave** (abbreviated **840edo**), or **840-tone equal temperament** (**840tet**), **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 of 840edo represents a frequency ratio of 2^{1/840}, or the 840th root of 2.

## Theory

840edo is the 15th highly melodic 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

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 (%) | -37 | -42 | -18 | +26 | +8 | -37 | +21 | -47 | -26 | +45 | +21 | |

Steps (reduced) |
1331 (491) |
1950 (270) |
2358 (678) |
2663 (143) |
2906 (386) |
3108 (588) |
3282 (762) |
3433 (73) |
3568 (208) |
3690 (330) |
3800 (440) |