1793edo
| ← 1792edo | 1793edo | 1794edo → |
Theory
1793edo is naively consistent in the 2.3.5.11.13.17 subgroup, in which it has a comma basis 4225/4224, 6656/6655, 42500/42471, 4787200/4782969, 703125/702559. Higher prime harmonics it supports to <25% error are 23, 31, 41, 53, 61.
If a mapping for 7 is added, this gives two interpretations. First is the patent val, which has a comma basis 2080/2079, 3025/3024, 4225/4224, 5832/5831, 14875/14872, 108086/108085. The 1793d val has a comma basis 1225/1224, 8624/8619, 12376/12375, 14400/14399, 42500/42471, 29755593/29744000.
It tempers out the jacobin comma, which is quite thematic given that 1793 is another notable year of the French Revolution, just as 1789 is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is 6656/6655, [-176 23 -2 35⟩.
1793edo has divisors 1, 11, 163.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.109 | -0.145 | +0.276 | +0.217 | +0.160 | +0.075 | -0.037 | +0.120 | +0.312 | -0.285 | +0.170 |
| Relative (%) | +16.2 | -21.7 | +41.3 | +32.4 | +23.9 | +11.2 | -5.5 | +17.9 | +46.6 | -42.5 | +25.3 | |
| Steps (reduced) |
2842 (1049) |
4163 (577) |
5034 (1448) |
5684 (305) |
6203 (824) |
6635 (1256) |
7005 (1626) |
7329 (157) |
7617 (445) |
7875 (703) |
8111 (939) | |