496edo: Difference between revisions

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~~496 EDO divides the octave into steps of 2.42 cents each.~~

==Theory==

== Theory ==

~~{{primes in edo|496|columns=15}}~~

496edo is [[enfactoring|enfactored]] in the 11-limit, with the same tuning as [[248edo]], but the [[patent val]]s differ on the mapping for 13. In the 13-limit patent val, it tempers out [[4225/4224]].

496edo is ~~good~~ with the ~~2.3.11.19 subgroup~~, for ~~low~~-~~complexity just intonation. Higher limits that~~ it ~~appreciates are 31, 37, and 47~~.

In the 2.3.11.19 subgroup, ~~496edo~~ tempers out 131072/131043.

496edo is good with the 2.3.11.19 [[subgroup]]. For higher limits, it has good approximations of [[31/1|31]], [[37/1|37]], and [[47/1|47]]. In the 2.3.11.19 subgroup, it tempers out 131072/131043.

~~496 is the 3rd perfect number, and its divisors are~~ {{~~EDOs~~|~~1, 2, 4, 8, 16, 31, 62, 124, 248~~}}~~, the most notable being 31.~~

=== Odd harmonics ===

~~496edo~~ is ~~contorted order~~ 2 ~~up to the 11-limit~~, ~~meaning it shares~~ the ~~mapping with~~ 248edo~~. As such~~, in the 11-limit it is a compound of two chains of 11-limit bischismic temperaments~~. In the 13-limit patent val~~, ~~first step where 496edo is not contorted, it tempers out 4225/4224~~.

=== Subsets and supersets ===

496 is the 3rd {{w|perfect number}}, factoring into {{factorization|496}}. Its nontrivial divisors are {{EDOs| 2, 4, 8, 16, 31, 62, 124, 248 }}, the most notable being 31.

== Scales ==

Since 496edo is enfactored 248edo, in the 11-limit it can represent a [[compound scale|compound]] of two chains of 11-limit [[bischismic]] temperaments, interlaced.

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-EDO divides the octave into steps of 2.42 cents each.
+{{Infobox ET}}
+{{ED intro}}
-==Theory==
+== Theory ==
-{{primes in edo|496|columns=15}}
+edo is [[enfactoring|enfactored]] in the 11-limit, with the same tuning as [[248edo]], but the [[patent val]]s differ on the mapping for 13. In the 13-limit patent val, it tempers out [[4225/4224]].
-edo is good with the 2.3.11.19 subgroup, for low-complexity just intonation. Higher limits that it appreciates are 31, 37, and 47.
-In the 2.3.11.19 subgroup, 496edo tempers out 131072/131043.
+edo is good with the 2.3.11.19 [[subgroup]]. For higher limits, it has good approximations of [[31/1|31]], [[37/1|37]], and [[47/1|47]]. In the 2.3.11.19 subgroup, it tempers out 131072/131043.
-is the 3rd perfect number, and its divisors are {{EDOs|1, 2, 4, 8, 16, 31, 62, 124, 248}}, the most notable being 31.
+=== Odd harmonics ===
+{{Harmonics in equal|496}}
-edo is contorted order 2 up to the 11-limit, meaning it shares the mapping with 248edo. As such, in the 11-limit it is a compound of two chains of 11-limit bischismic temperaments.  In the 13-limit patent val, first step where 496edo is not contorted, it tempers out 4225/4224.
+=== Subsets and supersets ===
+is the 3rd {{w|perfect number}}, factoring into {{factorization|496}}. Its nontrivial divisors are {{EDOs| 2, 4, 8, 16, 31, 62, 124, 248 }}, the most notable being 31.
+== Scales ==
+Since 496edo is enfactored 248edo, in the 11-limit it can represent a [[compound scale|compound]] of two chains of 11-limit [[bischismic]] temperaments, interlaced.