59edo: Difference between revisions

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Using the flat fifth instead of the sharp one allows for the {{nowrap|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.

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.

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 [[50edo|50]] & 59 temperament with a subminor third generator provides an interesting temperament.

=== Odd harmonics ===

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== Intervals ==

== Notation ==

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Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is also a Stein–Zimmerman notation.

== Octave stretch or compression ==

59edo’s approximations of 3/1, 7/1 and 11/1 are improved by [[93edt]], a [[Octave stretch|stretched-octave]] version of 59edo. The trade-off is a slightly worse 2/1 and 5/1.

[[ed12|211ed12]] is also a solid stretched-octave option, which improves 59edo's 3/1, doing a little, but not much, damage to most other primes.

If one prefers ''[[Octave shrinking|compressed octaves]]'', then [[ed6|153ed6]] is a viable option. It improves upon 59edo’s 3/1, 7/1 and 13/1 at the cost of a slightly worse 2/1 and 5/1, but substantially worse 11/1.

== Scales ==

; [[Porcupine]] scales

* Porcupine[7]: 8 8 8 11 8 8 8

* Porcupine[15]: 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3

* Porcupine[22]: 3 2 3 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 3 2 3

* [[User:BudjarnLambeth/Antechinus|Antechinus]] (''nonoctave period'')

== Instruments ==

; Lumatone

See [[Lumatone mapping for 59edo]].

== Music ==

; [[Bryan Deister]]

* [https://www.youtube.com/watch?v=-UsnINWSvzo ''Microtonal improvisation in 59edo''] (2025)

* [https://www.youtube.com/shorts/unVwXrAWnzI ''icosa - Oliver Buckland (microtonal cover in 59edo)''] (2025)

* [https://www.youtube.com/shorts/XYr4j6Abwlw ''Le Ciel - Malice Mizer (microtonal cover in 59edo)''] (2026)

; [[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]

* "Stay Away From The Fog" from ''Void'' (2025) – [https://open.spotify.com/track/6swFGV70cPYwruPrnu3iHX Spotify] | [https://francium223.bandcamp.com/track/stay-away-from-the-fog Bandcamp] | [https://www.youtube.com/watch?v=zVsjM-LRjNo YouTube]

; [[Budjarn Lambeth]]

* [https://youtu.be/YDbqf3g88BE ''The Odd Effects of Breathing the Fairy Dust''] (2026)

; [[Ray Perlner]]

@@ Line 7: / Line 7: @@
 Using the flat fifth instead of the sharp one allows for the {{nowrap|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.
-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.
+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 [[50edo|50]] &amp; 59 temperament with a subminor third generator provides an interesting temperament.
 === Odd harmonics ===
@@ Line 16: / Line 16: @@
 == Intervals ==
-{{Interval table}}
+{{Interval table}}{{Todo|text=ADD 3|inline=1}}
 == Notation ==
@@ Line 86: / Line 86: @@
 Because it contains no Sagittal symbols, this Evo-SZ Sagittal notation is also a Stein–Zimmerman notation.
+== Octave stretch or compression ==
+edo’s approximations of 3/1, 7/1 and 11/1 are improved by [[93edt]], a [[Octave stretch|stretched-octave]] version of 59edo. The trade-off is a slightly worse 2/1 and 5/1.
+[[ed12|211ed12]] is also a solid stretched-octave option, which improves 59edo's 3/1, doing a little, but not much, damage to most other primes.
+If one prefers ''[[Octave shrinking|compressed octaves]]'', then [[ed6|153ed6]] is a viable option. It improves upon 59edo’s 3/1, 7/1 and 13/1 at the cost of a slightly worse 2/1 and 5/1, but substantially worse 11/1.
+== Scales ==
+; [[Porcupine]] scales
+* Porcupine[7]: 8 8 8 11 8 8 8
+* Porcupine[15]: 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3
+* Porcupine[22]: 3 2 3 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 3 2 3
+* [[User:BudjarnLambeth/Antechinus|Antechinus]] (''nonoctave period'')
 == Instruments ==
 ; Lumatone
 See [[Lumatone mapping for 59edo]].
 == Music ==
 ; [[Bryan Deister]]
 * [https://www.youtube.com/watch?v=-UsnINWSvzo ''Microtonal improvisation in 59edo''] (2025)
+* [https://www.youtube.com/shorts/unVwXrAWnzI ''icosa - Oliver Buckland (microtonal cover in 59edo)''] (2025)
+* [https://www.youtube.com/shorts/XYr4j6Abwlw ''Le Ciel - Malice Mizer (microtonal cover in 59edo)''] (2026)
 ; [[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]
 * "Stay Away From The Fog" from ''Void'' (2025) – [https://open.spotify.com/track/6swFGV70cPYwruPrnu3iHX Spotify] | [https://francium223.bandcamp.com/track/stay-away-from-the-fog Bandcamp] | [https://www.youtube.com/watch?v=zVsjM-LRjNo YouTube]
+; [[Budjarn Lambeth]]
+* [https://youtu.be/YDbqf3g88BE ''The Odd Effects of Breathing the Fairy Dust''] (2026)
 ; [[Ray Perlner]]