47edo: Difference between revisions
Temporary until full version is made |
CompactStar (talk | contribs) |
||
| (5 intermediate revisions by 3 users not shown) | |||
| Line 3: | Line 3: | ||
== Theory == | == 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 | 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. | 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. | ||
| Line 387: | Line 387: | ||
* Quasi-equal [[equiheptatonic]] (Mixolydian): 7 7 6 7 7 6 7 | * Quasi-equal [[equiheptatonic]] (Mixolydian): 7 7 6 7 7 6 7 | ||
* Quasi-equal [[equipentatonic]]: 9 10 9 10 9 | * Quasi-equal [[equipentatonic]]: 9 10 9 10 9 | ||
* Sabertooth hexatonic: 3 9 3 13 12 7 (this is the original/default tuning; [[scalesmith|designed]] for the "gold" and "platinum" timbres in [[Scale Workshop]]) | * Sabertooth hexatonic{{idio}}: 3 9 3 13 12 7 (this is the original/default tuning; [[scalesmith|designed]] for the "gold" and "platinum" timbres in [[Scale Workshop]]) | ||
** Sabertooth pentatonic: 3 9 3 13 19 (this is the original/default tuning) | ** Sabertooth pentatonic{{idio}}: 3 9 3 13 19 (this is the original/default tuning) | ||
** Sabertooth neutral: 3 11 14 11 8 (this is the original/default tuning) | ** Sabertooth neutral{{idio}}: 3 11 14 11 8 (this is the original/default tuning) | ||
== Instruments == | == Instruments == | ||
| Line 402: | Line 402: | ||
== Music == | == Music == | ||
* [https://youtu.be/_TqaWw7tv_E Improvisation in 47edo (octave-compressed tuning, 7-note subset of Negri[9 | ; [[Budjarn Lambeth]] | ||
* [https://youtu.be/_TqaWw7tv_E ''Improvisation in 47edo''] (2024-01-28) (octave-compressed tuning, 7-note subset of <nowiki>Negri[9]</nowiki>) | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/fg-MzRBctxc ''47edo improv''] (2026) | |||
[[Category:Listen]] | [[Category:Listen]] | ||
{{todo|add scales list|add rank 2 temperaments table}} | |||