59edo: Difference between revisions

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== Theory ==

59edo's best fifth is stretched about 9.91 cents from the just interval, and yet its ~~major third~~ is nearly pure (stretched only 0.127 cents), as the denominator of a convergent to log<sub>2</sub>5. It is a good [[~~Porcupine_family|~~porcupine]] tuning, giving in fact the [[optimal patent val]] for [[11-limit]] porcupine. This patent val tempers out [[250/243]] in the [[5-limit]], [[64/63]] and [[16875/16807]] in the [[7-limit]], and [[55/54]], [[100/99]] and [[176/175]] in the [[11-limit]]. As every other step of [[118edo]], 59edo is an excellent tuning for the 2.9.5.21.11 11-limit [[k*N_subgroups|2*59 subgroup]], on which it takes the same tuning and tempers out the same commas. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&59 temperament with a subminor third generator provides an interesting temperament.

59edo's best [[3/2|fifth]] is stretched about 9.91 cents from the just interval, and yet its [[5/4]] is nearly pure (stretched only 0.127 cents), as the denominator of a convergent to log<sub>2</sub>5. It is a good [[porcupine]] tuning, giving in fact the [[optimal patent val]] for [[11-limit]] porcupine. This patent val tempers out [[250/243]] in the [[5-limit]], [[64/63]] and [[16875/16807]] in the [[7-limit]], and [[55/54]], [[100/99]] and [[176/175]] in the [[11-limit]].

Using the flat fifth instead of the sharp one allows for the 12&35 temperament, which is a kind of bizarre cousin to [[~~Schismatic_family|~~garibaldi ~~temperament~~]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth. The flat fifth also acts as a generator for [[flattertone]] temperament in the 59bcd val, a variant of meantone with very flat fifths.

Using the flat fifth instead of the sharp one allows for the 12 & 35 temperament, which is a kind of bizarre cousin to [[garibaldi]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth. The flat fifth also acts as a generator for [[flattertone]] temperament in the 59bcd val, a variant of meantone with very flat fifths.

59edo is the ~~17th~~ [[~~prime_numbers~~|~~prime~~]] ~~edo~~.

As every other step of [[118edo]], 59edo is an excellent tuning for the 2.9.5.21.11 11-limit [[k*N subgroups|2*59 subgroup]], on which it takes the same tuning and tempers out the same commas. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50 & 59 temperament with a subminor third generator provides an interesting temperament.

=== Odd harmonics ===

=== Subsets and supersets ===

59edo is the 17th [[prime edo]], following [[53edo]] and before [[61edo]].

== Intervals ==

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== Instruments ==

~~'''~~Lumatone~~'''~~

; Lumatone

See [[Lumatone mapping for 59edo]]

See [[Lumatone mapping for 59edo]].

==Music==

== Music ==

; [[Francium]]

* "too powerful if i had social skills" from ''Melancholie'' (2023) [https://open.spotify.com/track/1J8zDrAstQNKgLnXPjKwdm Spotify] | [https://francium223.bandcamp.com/track/too-powerful-if-i-had-social-skills Bandcamp] | [https://www.youtube.com/watch?v=FyzN0P6icf0 YouTube]

* "too powerful if i had social skills" from ''Melancholie'' (2023) – [https://open.spotify.com/track/1J8zDrAstQNKgLnXPjKwdm Spotify] | [https://francium223.bandcamp.com/track/too-powerful-if-i-had-social-skills Bandcamp] | [https://www.youtube.com/watch?v=FyzN0P6icf0 YouTube]

; [[Ray Perlner]]

* [https://www.youtube.com/watch?v=JJ4B47S1TUI Chinchillian Fugue ~~(First~~ mode of Porcupine 7 scale~~, 59EDO)]~~

* [https://www.youtube.com/watch?v=JJ4B47S1TUI ''Chinchillian Fugue''] – first mode of the Porcupine[7] scale in 59edo

[[Category:Porcupine]]

[[Category:Listen]]

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 {{Infobox ET}}
 {{EDO intro|59}}
 == Theory ==
-edo's best fifth is stretched about 9.91 cents from the just interval, and yet its major third is nearly pure (stretched only 0.127 cents), as the denominator of a convergent to log<sub>2</sub>5. It is a good [[Porcupine_family|porcupine]] tuning, giving in fact the [[optimal patent val]] for [[11-limit]] porcupine. This patent val tempers out [[250/243]] in the [[5-limit]], [[64/63]] and [[16875/16807]] in the [[7-limit]], and [[55/54]], [[100/99]] and [[176/175]] in the [[11-limit]]. As every other step of [[118edo]], 59edo is an excellent tuning for the 2.9.5.21.11 11-limit [[k*N_subgroups|2*59 subgroup]], on which it takes the same tuning and tempers out the same commas. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50&amp;59 temperament with a subminor third generator provides an interesting temperament.
+edo's best [[3/2|fifth]] is stretched about 9.91 cents from the just interval, and yet its [[5/4]] is nearly pure (stretched only 0.127 cents), as the denominator of a convergent to log<sub>2</sub>5. It is a good [[porcupine]] tuning, giving in fact the [[optimal patent val]] for [[11-limit]] porcupine. This patent val tempers out [[250/243]] in the [[5-limit]], [[64/63]] and [[16875/16807]] in the [[7-limit]], and [[55/54]], [[100/99]] and [[176/175]] in the [[11-limit]].
-Using the flat fifth instead of the sharp one allows for the 12&amp;35 temperament, which is a kind of bizarre cousin to [[Schismatic_family|garibaldi temperament]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth. The flat fifth also acts as a generator for [[flattertone]] temperament in the 59bcd val, a variant of meantone with very flat fifths.
+Using the flat fifth instead of the sharp one allows for the 12 &amp; 35 temperament, which is a kind of bizarre cousin to [[garibaldi]] with a generator of an approximate 15/14, tuned to the size of a whole tone, rather than a fifth. The flat fifth also acts as a generator for [[flattertone]] temperament in the 59bcd val, a variant of meantone with very flat fifths.
-edo is the 17th [[prime_numbers|prime]] edo.
+As every other step of [[118edo]], 59edo is an excellent tuning for the 2.9.5.21.11 11-limit [[k*N subgroups|2*59 subgroup]], on which it takes the same tuning and tempers out the same commas. This can be extended to the 19-limit 2*59 subgroup 2.9.5.21.11.39.17.57, for which the 50 &amp; 59 temperament with a subminor third generator provides an interesting temperament.
+=== Odd harmonics ===
 {{Harmonics in equal|59|columns=13}}
+=== Subsets and supersets ===
+edo is the 17th [[prime edo]], following [[53edo]] and before [[61edo]].
 == Intervals ==
@@ Line 14: / Line 19: @@
 == Instruments ==
-'''Lumatone'''
+; Lumatone
-See [[Lumatone mapping for 59edo]]
+See [[Lumatone mapping for 59edo]].
-==Music==
+== Music ==
 ; [[Francium]]
-* "too powerful if i had social skills" from ''Melancholie'' (2023) [https://open.spotify.com/track/1J8zDrAstQNKgLnXPjKwdm Spotify] | [https://francium223.bandcamp.com/track/too-powerful-if-i-had-social-skills Bandcamp] | [https://www.youtube.com/watch?v=FyzN0P6icf0 YouTube]
+* "too powerful if i had social skills" from ''Melancholie'' (2023) – [https://open.spotify.com/track/1J8zDrAstQNKgLnXPjKwdm Spotify] | [https://francium223.bandcamp.com/track/too-powerful-if-i-had-social-skills Bandcamp] | [https://www.youtube.com/watch?v=FyzN0P6icf0 YouTube]
 ; [[Ray Perlner]]
-* [https://www.youtube.com/watch?v=JJ4B47S1TUI Chinchillian Fugue (First mode of Porcupine 7 scale, 59EDO)]
+* [https://www.youtube.com/watch?v=JJ4B47S1TUI ''Chinchillian Fugue''] – first mode of the Porcupine[7] scale in 59edo
 [[Category:Porcupine]]
 [[Category:Listen]]