1793edo
| ← 1792edo | 1793edo | 1794edo → |
1793 equal divisions of the octave (1793edo), or 1793-tone equal temperament (1793tet), 1793 equal temperament (1793et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1793 equal parts of about 0.669 ¢ each.
Theory
1793edo is a good 2.3.5.11.13.17 subgroup system, 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 provides the optimal patent val for the luminal temperament.
1793edo 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 | -22 | +41 | +32 | +24 | +11 | -5 | +18 | +47 | -43 | +25 | |
| Steps (reduced) |
2842 (1049) |
4163 (577) |
5034 (1448) |
5684 (305) |
6203 (824) |
6635 (1256) |
7005 (1626) |
7329 (157) |
7617 (445) |
7875 (703) |
8111 (939) | |