47edo: Difference between revisions

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== Theory ==

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 cents flat of just, unless you use the alternative fifth which is 12.939 cents 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 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 cents flat of just, unless you use the alternative fifth which is 12.939 cents 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. The flat fifth is too flat to support [[meantone]]–in 47edo's [[patent val]], [[81/64]] is mapped to a 357-cent neutral third. Instead 47edo supports the rather counterintuitive [[deeptone]] temperament where [[5/4]] is represented by an augmented third, [[6/5]] by a diminished third, and [[81/80]] actually becomes negative making 81/64 flatter than 5/4.

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.

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[[Category:Listen]]

~~[[Category:Todo:~~add rank 2 temperaments table]]

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 == Theory ==
-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 cents flat of just, unless you use the alternative fifth which is 12.939 cents 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 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 cents flat of just, unless you use the alternative fifth which is 12.939 cents 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. The flat fifth is too flat to support [[meantone]]–in 47edo's [[patent val]], [[81/64]] is mapped to a 357-cent neutral third. Instead 47edo supports the rather counterintuitive [[deeptone]] temperament where [[5/4]] is represented by an augmented third, [[6/5]] by a diminished third, and [[81/80]] actually becomes negative making 81/64 flatter than 5/4.
 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.
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 [[Category:Listen]]
-[[Category:Todo:add rank 2 temperaments table]]
+{{todo|add scales list|add rank 2 temperaments table}}

47edo: Difference between revisions

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