1001edo: Difference between revisions

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~~'''1001edo''' divides the octave into parts of 1.(19880) cents each.~~

~~== Theory ==~~

~~1001 factorizes as 7 x 11 x 13, and therefore by extension it contains all these smaller EDOs. It's composite divisors are 77, 91, and 143.~~

The best prime subgroup for 1001edo is 2.7.11.13.19.23. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832. Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775.

~~Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520.~~

The best prime subgroup for 1001edo is 2.7.11.13.19.23. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832. Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775. Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520, as well as the [[parakleisma]].

=== Odd harmonics ===

=== Subsets and supersets ===

1001 factorizes as 7 x 11 x 13, and has subset EDOs {{EDOs|7, 11, 13, 77, 91, and 143}}.

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

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''1001edo''' divides the octave into parts of 1.(19880) cents each.
+{{EDO intro|1001}}
-== Theory ==
-{{primes in edo|1001|columns=15}}
-factorizes as 7 x 11 x 13, and therefore by extension it contains all these smaller EDOs. It's composite divisors are 77, 91, and 143.
-The best prime subgroup for 1001edo is 2.7.11.13.19.23. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832. Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775.
-Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520.
+The best prime subgroup for 1001edo is 2.7.11.13.19.23. In such a subgroup, it tempers out 14651/14641, 157757/157696, and 184877/184832. Taking the full 23-limit enables to determine that 1001edo tempers out 1288/1287, 2300/2299, 2737/2736, 2926/2925, and 5776/5775. Using the 1001b val, that is putting the 3/2 fifth on the 585th step instead of the 586th, 1001edo tempers out 936/935, 1197/1196, and 1521/1520, as well as the [[parakleisma]].
+=== Odd harmonics ===
+{{harmonics in equal|1001}}
+=== Subsets and supersets ===
+factorizes as 7 x 11 x 13, and has subset EDOs {{EDOs|7, 11, 13, 77, 91, and 143}}.
 [[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->