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~~-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 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.

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default [[File:47b_Evo-SZ_Sagittal.svg]]

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== 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 ==

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* Quasi-equal [[equiheptatonic]] (Mixolydian): 7 7 6 7 7 6 7

* 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 ==

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== Music ==

* [https://youtu.be/_TqaWw7tv_E Improvisation in 47edo (octave-compressed tuning, 7-note subset of Negri[9~~<nowiki>~~]</nowiki>)~~] by~~ [[~~Budjarn Lambeth~~]]~~, Jan 2024~~

; [[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:Todo:add rank 2 temperaments table]]

@@ Line 3: / Line 3: @@
 == 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-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 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 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 377: / Line 377: @@
 default [[File:47b_Evo-SZ_Sagittal.svg]]
 </imagemap>
+== Octave stretch or compression ==
+edo'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 ==
@@ Line 384: / Line 387: @@
 * Quasi-equal [[equiheptatonic]] (Mixolydian): 7 7 6 7 7 6 7
 * 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 ==
@@ Line 399: / Line 402: @@
 == Music ==
-* [https://youtu.be/_TqaWw7tv_E Improvisation in 47edo (octave-compressed tuning, 7-note subset of Negri[9<nowiki>]</nowiki>)] by [[Budjarn Lambeth]], Jan 2024
+; [[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:Todo:add rank 2 temperaments table]]