1448edo: Difference between revisions

The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 subgroup system. It is a zeta peak edo, and provides the optimal patent val for donar. A basis for the 13-limit commas is {3025/3024, 4225/4224, 4375/4374, 140625/140608, 823680/823543}.

Approximation of prime harmonics in 1448edo
Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	-0.021	-0.126	-0.041	-0.213	-0.196	+0.293	+0.001	-0.098	-0.295	+0.268
Error	Relative (%)	+0.0	-2.6	-15.2	-5.0	-25.7	-23.7	+35.4	+0.1	-11.8	-35.6	+32.4
Steps (reduced)		1448 (0)	2295 (847)	3362 (466)	4065 (1169)	5009 (665)	5358 (1014)	5919 (127)	6151 (359)	6550 (758)	7034 (1242)	7174 (1382)

Since 1448 factors into 2³ × 181, it has subset edos 2, 4, 8, 181, 362, and 724.

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 {{EDO intro|1448}}
-The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak]] edo, and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit commas is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.
+The 1448edo is a strong 13-limit system, and it is an excellent 2.3.5.7.11.13.19.23 [[subgroup]] system. It is a [[zeta peak edo]], and provides the [[optimal patent val]] for [[donar]]. A basis for the 13-limit [[comma]]s is {[[3025/3024]], [[4225/4224]], [[4375/4374]], 140625/140608, 823680/823543}.
 === Prime harmonics ===
 {{Harmonics in equal|1448}}
-=== Divisors ===
+=== Subsets and supersets ===
-Since 1448 factors into 2<sup>3</sup> × 181, it has subset edos 2, 4, 8, 181, 362, and 724.
+Since 1448 factors into {{factorization|1448}}, it has subset edos 2, 4, 8, 181, 362, and 724.
 [[Category:Thor]]
 [[Category:Donar]]

Revision as of 09:07, 31 October 2023