1793edo: Difference between revisions

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~~{{novelty}}{{stub}}~~{{Infobox ET}}

~~== Theory ==~~

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.

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.

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 }}}.

~~1793edo has divisors {{EDOs| 1, 11, 163~~ }}.

=== Odd harmonics ===

[[~~Category:Equal divisions of the octave|####~~]] ~~~~

=== Subsets and supersets ===

Since 1793 factors into {{factorization|1793}}, 1793edo contains [[11edo]] and [[163edo]] as subsets.

@@ Line 1: / Line 1: @@
-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-{{EDO intro|1793}}
+{{ED intro}}
-== Theory ==
+edo 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.
-edo 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.
-edo 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 }}.
+edo [[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 }}}.
-edo has divisors {{EDOs| 1, 11, 163 }}.
 === Odd harmonics ===
 {{Harmonics in equal|1793|columns=11}}
-[[Category:Equal divisions of the octave|####]] <!-- four-digit number -->
+=== Subsets and supersets ===
+Since 1793 factors into {{factorization|1793}}, 1793edo contains [[11edo]] and [[163edo]] as subsets.