496edo: Difference between revisions

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

==~~Theory~~==

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. As such, in the 11-limit it [[support]]s a compound of two chains of 11-limit [[bischismic]] temperaments. In the 13-limit patent val, it tempers out [[4225/4224]].

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.

=== Odd harmonics ===

=== 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.

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-EDO divides the octave into steps of 2.42 cents each.
+{{Infobox ET}}
+{{ED intro}}
-==Theory==
+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. As such, in the 11-limit it [[support]]s a compound of two chains of 11-limit [[bischismic]] temperaments. In the 13-limit patent val, it tempers out [[4225/4224]].
-{{primes in edo|496|columns=15}}
+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.
+=== Odd harmonics ===
+{{Harmonics in equal|496}}
+=== 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.