1794edo
| ← 1793edo | 1794edo | 1795edo → |
1794 equal divisions of the octave (1794edo), or 1794-tone equal temperament (1794tet), 1794 equal temperament (1794et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1794 equal parts of about 0.669 ¢ each.
Theory
The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & 2016 temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).
It's possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the ⟨1794 2834 4160 5037] val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, [-41, 1, 17, 0⟩, [20, 13, 14, -26⟩.
Nonetheless, 1794edo does offer some simpler interpretations.
In the 7-limit in the 1794c val, ⟨1794 2843 4165 5036], it tempers out the horwell comma and the landscape comma, supporting mutt. However, it is not better tuned than 171edo. Using the 1794bd val, ⟨1794 2844 4166 5037], it tempers out [21 -8 -6 2⟩, [-7 -15 6 6⟩, [-2 -3 15 -10⟩. This mapping of harmonic 7 is the same as 26edo's. In the 2.11.17 realm, 1794edo supports the 148 & 83 temperament, defined by tempering out the 2.11.17 [-67 43 -20⟩ comma. 1794edo tempers out the 2.17.19 [277 -21 -45⟩ and the corresponding temperament is 12 & 891.
Remarkably, using the patent val, 1794edo tempers out the schisma.
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.283 | +0.308 | -0.264 | +0.103 | -0.147 | +0.275 | +0.026 | +0.061 | +0.146 | +0.122 | -0.181 |
| relative (%) | -42 | +46 | -39 | +15 | -22 | +41 | +4 | +9 | +22 | +18 | -27 | |
| Steps (reduced) |
2843 (1049) |
4166 (578) |
5036 (1448) |
5687 (305) |
6206 (824) |
6639 (1257) |
7009 (1627) |
7333 (157) |
7621 (445) |
7880 (704) |
8115 (939) | |
Subsets and supersets
1794edo has subset edos 2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal
8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-2843, 1794⟩ | ⟨1794 2843] | 0.0892 | 0.0892 | 5.97 |
| 2.11.17.19.29.31.47 | 9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936 | ⟨1794 6206 7333 7621 8715 8888 9965] | -0.0012 | 0.0259 | 1.74 |
Trivia
The number 1794 is known for being the fatal year of the French Revolution.