1793edo: Difference between revisions

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~~== 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.

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

=== Odd harmonics ===

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

=== Subsets and supersets ===

1793edo has [[11edo]] and [[163edo]] as its subsets.

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 {{EDO intro|1793}}
-== Theory ==
+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.
-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 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 ===
+edo has [[11edo]] and [[163edo]] as its subsets.