1793edo: Difference between revisions
Cleanup; -redundant categories |
Rework theory; adopt template: Factorization |
||
| Line 2: | Line 2: | ||
{{EDO intro|1793}} | {{EDO intro|1793}} | ||
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. | 1793edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1|7]] is about halfway between its steps. Nonetheless, it 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. | 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 [[1789edo|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is 6656/6655, {{monzo| -176 23 -2 35 }}. | 1793edo [[tempering out|tempers out]] the [[jacobin comma]], which is quite thematic given that 1793 is another notable year of the French Revolution, just as [[1789edo|1789]] is. The comma basis for the 1789 & 1793 temperament in the 2.5.11.13 subgroup is {6656/6655, {{monzo| -176 23 -2 35 }}}. | ||
=== Odd harmonics === | === Odd harmonics === | ||
| Line 12: | Line 12: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
1793edo | Since 1793 factors into {{factorization|1793}}, 1793edo contains [[11edo]] and [[163edo]] as subsets. | ||
Revision as of 12:54, 30 October 2023
| ← 1792edo | 1793edo | 1794edo → |
1793edo is only consistent to the 5-odd-limit since harmonic 7 is about halfway between its steps. Nonetheless, it 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⟩}.
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) | |
Subsets and supersets
Since 1793 factors into 11 × 163, 1793edo contains 11edo and 163edo as subsets.