940edo
| ← 939edo | 940edo | 941edo → |
940edo is uniquely consistent through the 11-limit, tempering out 2401/2400 in the 7-limit and 5632/5625 and 9801/9800 in the 11-limit, which means it supports decoid temperament 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 greenland and baffin temperaments, and for the rank five temperament 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-13s 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 940edo's theory in 5-prime-limit where it has good 3/2 and 5/4, but 15/8 is one step off from the "expected" location.
Odd harmonics
| 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
940edo has subset edos 1, 2, 4, 5, 10, 20, 47, 94, 188, 235, 470, of which 94edo is notable.
1880edo, which doubles 940edo, provides good correction for harmonics 13 and 15 and uses a new mapping for 5 which consistently leads to 15.