47edo: Difference between revisions
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== 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]]. 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 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. | ||
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{{Harmonics in equal|47}} | {{Harmonics in equal|47}} | ||
47edo 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 [[baldy]] and [[silver]] and their relatives. It also provides a good tuning for the [[baseball]] temperament. | 47edo 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 [[baldy]] and [[silver]] and their relatives. It also provides a good tuning for the [[baseball]] temperament. | ||
47edo can be treated as a [[dual-fifth system]] in the 2.3+.3-.5.7.13 subgroup, or the 3+.3-.5.7.11+.11-.13 subgroup for those who aren’t intimidated by lots of [[basis element]]s. As a dual-fifth system, it really shines, as both of its fifths have low enough [[harmonic entropy]] to sound [[consonant]] to many listeners, giving two consonant intervals for the price of one. | 47edo can be treated as a [[dual-fifth system]] in the 2.3+.3-.5.7.13 subgroup, or the 3+.3-.5.7.11+.11-.13 subgroup for those who aren’t intimidated by lots of [[basis element]]s. As a dual-fifth system, it really shines, as both of its fifths have low enough [[harmonic entropy]] to sound [[consonant]] to many listeners, giving two consonant intervals for the price of one. | ||
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default [[File:47b_Evo-SZ_Sagittal.svg]] | default [[File:47b_Evo-SZ_Sagittal.svg]] | ||
</imagemap> | </imagemap> | ||
== Octave stretch or compression == | |||
47edo's [[prime]] 11 is very sharp, and its sharp and flat mapping of 3 are about equally bad, it can benefit from slight [[octave shrinking]]. [[APS|25.5cET]] or [[ed9/8|8ed9/8]] make good compressed-octave versions of 47edo. | |||
== Scales == | == Scales == | ||
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* 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 == | ||
=== Lumatone === | |||
* [[Lumatone mapping for 47edo]] | * [[Lumatone mapping for 47edo]] | ||
=== Skip fretting === | |||
'''Skip fretting system 47 3 11''' is a [[skip-fretting]] system for [[47edo]] where strings are 11\47 and frets are 3\47. This is effectively 15.6666...-edo. All examples of this system on this page are for 5-string bass. | |||
; Chords | |||
Neutral-dominant 7th: 1 0 1 2 2 | |||
== 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]] | ||
[[Category:Todo:add rank 2 temperaments table]] | [[Category:Todo:add rank 2 temperaments table]] | ||