1448edo: Difference between revisions

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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}.

Notably, it is the first edo to be [[diamond monotone]] to the [[95-odd-limit]], completing the first five octaves and a fifth of the [[harmonic series]], in fact by the [[patent val]]. It is thus usable in the full [[89-limit]], where prime 89 is the start of a record {{W|prime gap}} from 89 to 97.

=== Prime harmonics ===

{{Harmonics in equal|1448|columns=12|start=13|collapsed=1|title=Approximation of prime harmonics in 1448edo (continued)}}

=== ~~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]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1448}}
+{{ED intro}}
-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}.
+Notably, it is the first edo to be [[diamond monotone]] to the [[95-odd-limit]], completing the first five octaves and a fifth of the [[harmonic series]], in fact by the [[patent val]]. It is thus usable in the full [[89-limit]], where prime 89 is the start of a record {{W|prime gap}} from 89 to 97.
 === Prime harmonics ===
-{{Harmonics in equal|1448}}
+{{Harmonics in equal|1448|columns=12}}
+{{Harmonics in equal|1448|columns=12|start=13|collapsed=1|title=Approximation of prime harmonics in 1448edo (continued)}}
-=== 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]]