47edo: Difference between revisions

CompactStar (talk | contribs)
Not true – 54edo etc. have a flatter fifth
Yourmusic Productions (talk | contribs)
Undo revision 106233 by CompactStar (talk) No, it is correct. Flattest patent val diatonic 5th. (after all, non patent ones can be any size if you're willing to go to high enough edos)
Tag: Undo
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{{EDO intro|47}}
{{EDO intro|47}}
== Theory ==
== Theory ==
47edo has a fifth which is 12.593{{cent}} flat, unless you use the alternative fifth which is 12.939{{cent}} sharp, similar to 35edo. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[k*N_subgroups|2*47 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[Chromatic_pairs#Baldy|baldy]] and [[Chromatic_pairs#Silver|silver]] temperaments and relatives.
47edo has a fifth which is 12.593{{cent}} flat, unless you use the alternative fifth which is 12.939{{cent}} sharp, similar to 35edo. The soft diatonic scale generated from its flat fifth is so soft, with L/s = 7/6, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]]. It has therefore not aroused much interest, but its best approximation to 9/8 is actually quite good, one-third of a cent sharp. It does a good job of approximating the 2.9.5.7.33.13.17.57.69 23-limit [[k*N_subgroups|2*47 subgroup]] of the [[23-limit]], on which it tempers out the same commas as [[94edo]]. It provides a good tuning for [[Chromatic_pairs#Baldy|baldy]] and [[Chromatic_pairs#Silver|silver]] temperaments and relatives.


47edo is a diatonic edo because its 5th falls between 4\7 = 686{{cent}} and 3\5 = 720{{cent}}, as does its alternate 5th as well. 47edo is one of the most difficult diatonic edos to notate, because its fifth is so flat (see [[42edo]] for the opposite extreme). The soft diatonic scale generated from its flat fifth is so soft, with L/s = 7/6, that it stops sounding like [[meantone]] or even a [[flattone]] system like [[26edo]] or [[40edo]], but just sounds like a [[circulating temperament]] of [[7edo]].
47edo is a diatonic edo because its 5th falls between 4\7 = 686{{cent}} and 3\5 = 720{{cent}}, as does its alternate 5th as well. 47edo is one of the most difficult diatonic edos to notate, because no other diatonic edos 5th is as flat (see [[42edo]] for the opposite extreme).


A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a 7edo-like scale:
A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a 7edo-like scale: