10edo: Difference between revisions

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10edo can be thought of as two circles of [[5edo]] separated by 120 cents (or 5 circles of [[2edo]]). It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13/8]] and its inversion [[16/13]]; and the ~~happy~~ 600-cent tritone that appears in every even-numbered edo. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOS scales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap edo, it is a [[The Riemann Zeta Function and Tuning #Zeta edo lists|zeta peak edo]]. One way to interpret it in terms of a temperament of just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.

10edo can be thought of as two circles of [[5edo]] separated by 120 cents (or 5 circles of [[2edo]]). It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13/8]] and its inversion [[16/13]]; and the familiar 600-cent tritone that appears in every even-numbered edo. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOS scales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap edo, it is a [[The Riemann Zeta Function and Tuning #Zeta edo lists|zeta peak edo]]. One way to interpret it in terms of a temperament of just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.

== Intervals ==

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* [https://soundcloud.com/uz1kt3k/fugue-in-10et Fugue in 10ET | SoundCloud] by Aaron Andrew Hunt, 2015

* [http://www.ziaspace.com/ZIA/mp3s/Future.html Future] [http://ziaspace.com/ZIA/mp3s/Future.mp3 play] and [http://www.ziaspace.com/ZIA/mp3s/Sol.html Sol] [http://ziaspace.com/ZIA/mp3s/Sol.mp3 play] by ZIA (synths and voice in 10)

* [~~http~~://web.archive.org/web/20161013092841/http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3 Prelude] by [[Rick McGowan]] (Rhino synthesizer)

* [https://web.archive.org/web/20161013092841/http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3 Prelude] by [[Rick McGowan]] (Rhino synthesizer)

* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Ideas%20on%20the%20Waterfall%20of%20Expression.mp3 Ideas on the Waterfall of Expression]{{dead link}} by [[City of the Asleep]] (synth)

* [http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3 For two violas and gongs] by [[Chris Vaisvil]] [http://chrisvaisvil.com/?p=1039 Details]

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* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/09%20-%209.%2010%20octave.mp3 Comets Over Flatland 9]{{dead link}} by [[Randy Winchester]]

* [http://micro.soonlabel.com/10edo/daily20110923-10edo_dramatic_squirrel_overture.mp3 The Dramatic Squirrel Overture] by Chris Vaisvil [http://chrisvaisvil.com/?p=1368 Details]

* [~~http~~://andrewheathwaite.bandcamp.com/track/shimmerwing Shimmerwing] by [[Andrew Heathwaite]] and Chris Vaisvil

* [https://andrewheathwaite.bandcamp.com/track/shimmerwing Shimmerwing] by [[Andrew Heathwaite]] and Chris Vaisvil

* [~~http~~://soundcloud.com/martinsj013/sirmdbidnud2 Shall I Refuse My Dinner] by [[Steve Martin]] on SoundCloud

* [https://soundcloud.com/martinsj013/sirmdbidnud2 Shall I Refuse My Dinner] by [[Steve Martin]] on SoundCloud

* [https://soundcloud.com/clem-fortuna/10tone 10-tone demo] by [http://clemfortuna.com Clem Fortuna]{{dead link}}

* [https://soundcloud.com/user-544568549/ey-ule-hey-ule Hey, ule!] by [[User:Дмитрий Баженов|Dmitry Bazhenov]] (second part in 10-edo)

@@ Line 17: / Line 17: @@
 {{Harmonics in equal|10}}
-edo can be thought of as two circles of [[5edo]] separated by 120 cents (or 5 circles of [[2edo]]). It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13/8]] and its inversion [[16/13]]; and the happy 600-cent tritone that appears in every even-numbered edo. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOS scales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap edo, it is a [[The Riemann Zeta Function and Tuning #Zeta edo lists|zeta peak edo]]. One way to interpret it in terms of a temperament of just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.
+edo can be thought of as two circles of [[5edo]] separated by 120 cents (or 5 circles of [[2edo]]). It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13/8]] and its inversion [[16/13]]; and the familiar 600-cent tritone that appears in every even-numbered edo. Taking the the 360 cent large neutral third as a generator produces a heptatonic [[MOS scales|moment of symmetry scale]] of the form 1 2 1 2 1 2 1 ([[3L 4s|3L 4s - mosh]]). While not an integral or gap edo, it is a [[The Riemann Zeta Function and Tuning #Zeta edo lists|zeta peak edo]]. One way to interpret it in terms of a temperament of just intonation is as a 2.7.13.15 subgroup, such that 105/104, 225/224, and 16807/16384 are tempered out. It can also be treated as a full 13-limit temperament, but it is a closer match to the aforementioned subgroup.
 == Intervals ==
@@ Line 442: / Line 442: @@
 * [https://soundcloud.com/uz1kt3k/fugue-in-10et Fugue in 10ET &#124; SoundCloud] by Aaron Andrew Hunt, 2015
 * [http://www.ziaspace.com/ZIA/mp3s/Future.html Future] [http://ziaspace.com/ZIA/mp3s/Future.mp3 play] and [http://www.ziaspace.com/ZIA/mp3s/Sol.html Sol] [http://ziaspace.com/ZIA/mp3s/Sol.mp3 play] by ZIA (synths and voice in 10)
-* [http://web.archive.org/web/20161013092841/http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3 Prelude] by [[Rick McGowan]] (Rhino synthesizer)
+* [https://web.archive.org/web/20161013092841/http://azuma-asobi.com/Music/RhinoPrelude-2003-02-22.mp3 Prelude] by [[Rick McGowan]] (Rhino synthesizer)
 * [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Ideas%20on%20the%20Waterfall%20of%20Expression.mp3 Ideas on the Waterfall of Expression]{{dead link}} by [[City of the Asleep]] (synth)
 * [http://micro.soonlabel.com/10edo/daily20110713_q49_10_viola_duet_and_gongs.mp3 For two violas and gongs] by [[Chris Vaisvil]] [http://chrisvaisvil.com/?p=1039 Details]
@@ Line 454: / Line 454: @@
 * [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/09%20-%209.%2010%20octave.mp3 Comets Over Flatland 9]{{dead link}} by [[Randy Winchester]]
 * [http://micro.soonlabel.com/10edo/daily20110923-10edo_dramatic_squirrel_overture.mp3 The Dramatic Squirrel Overture] by Chris Vaisvil [http://chrisvaisvil.com/?p=1368 Details]
-* [http://andrewheathwaite.bandcamp.com/track/shimmerwing Shimmerwing] by [[Andrew Heathwaite]] and Chris Vaisvil
+* [https://andrewheathwaite.bandcamp.com/track/shimmerwing Shimmerwing] by [[Andrew Heathwaite]] and Chris Vaisvil
-* [http://soundcloud.com/martinsj013/sirmdbidnud2 Shall I Refuse My Dinner] by [[Steve Martin]] on SoundCloud
+* [https://soundcloud.com/martinsj013/sirmdbidnud2 Shall I Refuse My Dinner] by [[Steve Martin]] on SoundCloud
 * [https://soundcloud.com/clem-fortuna/10tone 10-tone demo] by [http://clemfortuna.com Clem Fortuna]{{dead link}}
 * [https://soundcloud.com/user-544568549/ey-ule-hey-ule Hey, ule!] by [[User:Дмитрий Баженов|Dmitry Bazhenov]] (second part in 10-edo)