783edo
| ← 782edo | 783edo | 784edo → |
783 equal divisions of the octave (783edo), or 783-tone equal temperament (783tet), 783 equal temperament (783et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 783 equal parts of about 1.53 ¢ each.
Theory
783edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is consistent up to the 11-odd-limit, making it a flexible and versatile tuning. The equal temperament tempers out the ennealimma and the counterschisma in the 5-limit; 2401/2400, and 4375/4374 in the 7-limit. It supports counterschismic, dodifo, ennealimmal, raider, vavoom, and francium.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.039 | -0.107 | -0.244 | +0.406 | -0.681 | -0.741 | -0.195 | +0.078 | +0.308 | -0.208 |
| relative (%) | +0 | -3 | -7 | -16 | +27 | -44 | -48 | -13 | +5 | +20 | -14 | |
| Steps (reduced) |
783 (0) |
1241 (458) |
1818 (252) |
2198 (632) |
2709 (360) |
2897 (548) |
3200 (68) |
3326 (194) |
3542 (410) |
3804 (672) |
3879 (747) | |
Subsets and supersets
Since 783 factors into 33 × 29, 783edo has subset edos 3, 9, 27, 29, 87, and 261.
Regular temperament properties
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 73\783 | 111.877 | 16/15 | Vavoom |
| 1 | 224\783 | 343.295 | 8000/6561 | Raider |
| 1 | 233\783 | 357.088 | 768/625 | Dodifo (5-limit) |
| 1 | 325\783 | 498.084 | 4/3 | Counterschismic |
| 9 | 206\783 (32\783) |
315.709 (49.042) |
6/5 (36/35) |
Ennealimmal |
| 29 | 325\783 (1\723) |
498.084 (1.533) |
4/3 (32805/32768) |
Copper |
| 87 | 308\783 (2\783) |
472.031 (3.065) |
[35 1 -6 -3 -4⟩ (?) |
Francium |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct