47edo: Difference between revisions

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== Theory ==

47edo is the first edo that has two [[5L 2s|diatonic]] perfect fifths. The fifth closest to [[3/2]] 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 {{nowrap|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.

47edo is the first edo that has two [[5L 2s|diatonic]] perfect fifths, as both fall between {{nowrap|4\7 {{=}} 686{{c}}}} and {{nowrap|3\5 {{=}} 720{{c}}}}. The fifth closest to [[3/2]] 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 {{nowrap|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]]. The hard diatonic scale generated from its sharp fifth is extremely hard, with {{nowrap|L:s {{=}} 9:1}}. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.

~~47edo is a diatonic edo because its 5th falls between {{nowrap|4\7 {{=}} 686{{c}}}} and {{nowrap|3\5 {{=}} 720{{c}}}}, 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).

47edo is one of the most difficult diatonic edos to notate in [[native fifth notation|native fifths]], because no other diatonic edo's fifth is as extreme.

=== Odd harmonics ===

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 == Theory ==
-edo is the first edo that has two [[5L 2s|diatonic]] perfect fifths. The fifth closest to [[3/2]] 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 {{nowrap|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.
+edo is the first edo that has two [[5L 2s|diatonic]] perfect fifths, as both fall between {{nowrap|4\7 {{=}} 686{{c}}}} and {{nowrap|3\5 {{=}} 720{{c}}}}. The fifth closest to [[3/2]] 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 {{nowrap|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]]. The hard diatonic scale generated from its sharp fifth is extremely hard, with {{nowrap|L:s {{=}} 9:1}}. It has therefore not aroused much interest, but its best approximation to [[9/8]] is actually quite good, one-third-of-a-cent sharp.
-edo is a diatonic edo because its 5th falls between {{nowrap|4\7 {{=}} 686{{c}}}} and {{nowrap|3\5 {{=}} 720{{c}}}}, 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).
+edo is one of the most difficult diatonic edos to notate in [[native fifth notation|native fifths]], because no other diatonic edo's fifth is as extreme.
 === Odd harmonics ===