496edo: Difference between revisions

(3 intermediate revisions by 2 users not shown)

Line 1:

~~==Theory==~~

496edo is strongly related to the [[248edo]], but the patent vals differ on the mapping for 13. As such, in the 11-limit it supports 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.

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 [[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]].

~~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~~.

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===~~

~~{{harmonics in equal|496}}~~

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

=== 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.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|496}}
+{{ED intro}}
-==Theory==
-edo is strongly related to the [[248edo]], but the patent vals differ on the mapping for 13. As such, in the 11-limit it supports 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.
-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 [[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]].
-is the 3rd perfect number, and its divisors are {{EDOs|1, 2, 4, 8, 16, 31, 62, 124, 248}}, the most notable being 31.
+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}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== 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.