1001edo: Difference between revisions

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1001edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], [[19/1|19]], and [[23/1|23]], making it suitable for a 2.9.7.11.13.19.23 [[subgroup]] interpretation, with an optional addition of either [[5/1|5]], or [[15/1|15]]. 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]].

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}}.

Since 1001 factorizes as {{factorization|1001}}, 1001edo has subset edos {{EDOs| 7, 11, 13, 77, 91, and 143 }}.

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

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 {{Infobox ET}}
-{{EDO intro|1001}}
+{{ED intro}}
+edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it has good approximations to harmonics [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], [[19/1|19]], and [[23/1|23]], making it suitable for a 2.9.7.11.13.19.23 [[subgroup]] interpretation, with an optional addition of either [[5/1|5]], or [[15/1|15]]. 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]].
-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}}
+{{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}}.
+Since 1001 factorizes as {{factorization|1001}}, 1001edo has subset edos {{EDOs| 7, 11, 13, 77, 91, and 143 }}.
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->