640edo: Difference between revisions

(3 intermediate revisions by 2 users not shown)

Line 1:

~~The '''640 equal divisions''' divides the octave into 640 equal parts of precisely 1.875 cents each. It~~ is [[~~contorted~~]] in the 5-limit, tempering out the vishnuzma, |23 6 -14~~>~~, with the same tuning as 320edo. In the 7-limit it tempers out 19683/19600 and | 16 2 -1 -6 ~~>~~ and in the 11-limit it tempers out 540/539, 8019/8000 and | 14 -1 -2 -4 1 ~~>~~. It provides the [[~~Optimal_patent_val|~~optimal patent val]] for the rank ~~three~~ [[~~Cataharry_family|~~albus ~~temperament~~]] tempering out 540/539 and 8019/8000, and the ~~125~~&~~130~~ temperament.

640edo is [[enfactoring|enfactored]] in the 5-limit, [[tempering out]] the [[vishnuzma]], {{monzo| 23 6 -14 }}, with the same tuning as [[320edo]]. In the 7-limit it tempers out [[19683/19600]] and {{monzo| 16 2 -1 -6 }} and in the 11-limit it tempers out [[540/539]], [[8019/8000]] and {{monzo| 14 -1 -2 -4 1 }}. It provides the [[optimal patent val]] for the rank-3 [[albus]] temperament tempering out 540/539 and 8019/8000, and [[hemipental]], the 255 & 385 temperament.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 640 factors into {{factorization|640}}, 640edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, and 320 }}.

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

[[Category:Albus]]

[[Category:~~Vishnuzma~~]]

[[Category:Hemipental]]

@@ Line 1: / Line 1: @@
-{{novelty}}{{stub}}{{Infobox ET}}
+{{Infobox ET}}
-The '''640 equal divisions''' divides the octave into 640 equal parts of precisely 1.875 cents each. It is [[contorted]] in the 5-limit, tempering out the vishnuzma, |23 6 -14&gt;, with the same tuning as 320edo. In the 7-limit it tempers out 19683/19600 and | 16 2 -1 -6 &gt; and in the 11-limit it tempers out 540/539, 8019/8000 and | 14 -1 -2 -4 1 &gt;. It provides the [[Optimal_patent_val|optimal patent val]] for the rank three [[Cataharry_family|albus temperament]] tempering out 540/539 and 8019/8000, and the 125&amp;130 temperament.
+{{ED intro}}
+edo is [[enfactoring|enfactored]] in the 5-limit, [[tempering out]] the [[vishnuzma]], {{monzo| 23 6 -14 }}, with the same tuning as [[320edo]]. In the 7-limit it tempers out [[19683/19600]] and {{monzo| 16 2 -1 -6 }} and in the 11-limit it tempers out [[540/539]], [[8019/8000]] and {{monzo| 14 -1 -2 -4 1 }}. It provides the [[optimal patent val]] for the rank-3 [[albus]] temperament tempering out 540/539 and 8019/8000, and [[hemipental]], the 255 &amp; 385 temperament.
+=== Odd harmonics ===
+{{Harmonics in equal|640}}
+=== Subsets and supersets ===
+Since 640 factors into {{factorization|640}}, 640edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, and 320 }}.
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Albus]]
-[[Category:Vishnuzma]]
+[[Category:Hemipental]]