246edo: Difference between revisions

Revision as of 11:50, 24 March 2024

246 = 6 × 41, and 246edo shares its fifth with 41edo. It is only consistent to the 5-odd-limit, but the patent val offers excellent approximations (within half a cent) of prime harmonics 11, 19, and 29, and quite good approximations (within one cent) of 5 and 23. It provides the optimal patent val for cata, the 2.3.5.13 subgroup temperament tempering out 325/324 and 625/624.

Approximation of prime harmonics in 246edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.48	-0.95	+1.91	-0.10	-1.50	+2.36	+0.05	+0.99	-0.31	+1.31
Error	Relative (%)	+0.0	+9.9	-19.4	+39.1	-2.0	-30.8	+48.4	+1.0	+20.4	-6.3	+26.8
Steps (reduced)		246 (0)	390 (144)	571 (79)	691 (199)	851 (113)	910 (172)	1006 (22)	1045 (61)	1113 (129)	1195 (211)	1219 (235)

Since 246 factors into 2 × 3 × 41, 246edo has subset edos 2, 3, 6, 41, 82, and 123.

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-edo divides the 2/1 (octave) into 246 equal steps of 4.878 [[cents|cents]].
+{{EDO intro}}
-The patent val offers excellent approximations (within half a cent) of primes 3, 11, 19, and 29, and quite good approximations (within one cent) of primes 5 and 23.
+== Theory ==
+= 6 × 41, and 246edo shares its [[perfect fifth|fifth]] with 41edo. It is only [[consistent]] to the [[5-odd-limit]], but the [[patent val]] offers excellent approximations (within half a cent) of [[prime harmonic]]s [[11/1|11]], [[19/1|19]], and [[29/1|29]], and quite good approximations (within one cent) of [[5/1|5]] and [[23/1|23]]. It provides the [[optimal patent val]] for [[cata]], the 2.3.5.13 [[subgroup]] temperament [[tempering out]] [[325/324]] and [[625/624]].
-== Harmonics ==
+=== Prime harmonics ===
 {{Harmonics in equal|246}}
-==Scales==
+=== Subsets and supersets ===
-* [[cata7]]
+Since 246 factors into {{factorization|246}}, 246edo has subset edos {{EDOs| 2, 3, 6, 41, 82, and 123 }}.
-* [[cata11]]
-* [[cata15]]
-* [[cata19]]
-* [[File:cata_246edo.jpg|alt=cata_246edo.jpg|cata_246edo.jpg]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+== Scales ==
+[[File:cata_246edo.jpg|thumb|alt=cata_246edo.jpg|Cata in 246edo]]
+* [[Cata7]]
+* [[Cata11]]
+* [[Cata15]]
+* [[Cata19]]
+[[Category:Cata]]