1448edo: Difference between revisions

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-The 1448 division divides the octave into 1448 equal parts of 0.8287 cents each. It is a strong 13-limit system, and if you don't care about 17, a terrific 2.3.5.7.11.13.19.23 system. It is a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak]] edo. A basis for the 13-limit commas is 3025/3024, 4225/4224, 4375/4374, 140625/140608 and 823680/823543.
+{{Infobox ET}}
+{{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 [[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}}
+{{Harmonics in equal|1448|columns=12|start=13|collapsed=1|title=Approximation of prime harmonics in 1448edo (continued)}}
+=== Subsets and supersets ===
+Since 1448 factors into {{factorization|1448}}, it has subset edos 2, 4, 8, 181, 362, and 724.
+[[Category:Thor]]
+[[Category:Donar]]