# 940edo

 ← 939edo 940edo 941edo →
Prime factorization 22 × 5 × 47
Step size 1.2766¢
Fifth 550\940 (702.128¢) (→55\94)
Semitones (A1:m2) 90:70 (114.9¢ : 89.36¢)
Consistency limit 11
Distinct consistency limit 11

940 equal divisions of the octave (abbreviated 940edo or 940ed2), also called 940-tone equal temperament (940tet) or 940 equal temperament (940et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 940 equal parts of about 1.28 ¢ each. Each step represents a frequency ratio of 21/940, or the 940th root of 2.

940edo is distinctly consistent through the 11-odd-limit. The equal temperament tempers out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it supports decoid and in fact gives an excellent tuning for it. In the 13-limit, it tempers out 676/675, 1001/1000, 1716/1715, 2080/2079, 4096/4095 and 4225/4224, so that it supports and gives the optimal patent val for 13-limit decoid. It also gives the optimal patent val for the greenland and baffin temperaments, and for the rank-5 temperament tempering out 676/675.

The non-patent val 940 1491 2184 2638 3254 3481] gives a tuning almost identical to the POTE tuning for the 13-limit pele temperament, tempering out 196/195, 352/351 and 364/363.

In higher limits, it is a satisfactory no-13's 23-limit tuning. Another thing to note is that its 15th harmonic is just barely off of the sum of mappings for 3rd and 5th harmonics, which adds a peculiarity to it where it has good 3/2 and 5/4, but 15/8 is one step off from the closest location.

### Odd harmonics

Approximation of odd harmonics in 940edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.173 +0.495 +0.110 +0.345 +0.171 -0.528 -0.609 -0.275 -0.066 +0.283 -0.189
Relative (%) +13.5 +38.8 +8.6 +27.0 +13.4 -41.3 -47.7 -21.5 -5.2 +22.2 -14.8
Steps
(reduced)
1490
(550)
2183
(303)
2639
(759)
2980
(160)
3252
(432)
3478
(658)
3672
(852)
3842
(82)
3993
(233)
4129
(369)
4252
(492)

### Subsets and supersets

Since 940 factors into 22 × 5 × 47, 940edo has subset edos 2, 4, 5, 10, 20, 47, 94, 188, 235, 470, of which 94edo is notable.

1880edo, which doubles 940edo, provides good correction for harmonics 5 and 13, though the error of 3 has accumulated to the point of inconsistency in the 9-odd-limit.