53edo: Difference between revisions
Move scales section to its proper place. Rework music section and fix a dead link |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{Wikipedia| 53 equal temperament }} | {{Wikipedia| 53 equal temperament }} | ||
{{EDO intro|53}} | |||
== Theory == | == Theory == | ||
53edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, notably tempering out the [[schisma]] (32805/32768) and the [[kleisma]] (15625/15552). More complex 5-limit commas tempered out include the [[amity comma]] (1600000/1594323), the [[semicomma]] (2109375/2097152), and the [[vulture comma]] ({{monzo| 24 -21 4 }}). In the 7-limit it tempers out [[225/224]], [[1728/1715]] and [[3125/3087]], the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out [[99/98]] and [[121/120]] (in addition to their difference, [[540/539]]), and is the [[optimal patent val]] for [[big brother]] temperament, which tempers out both, as well as 11-limit [[orwell]] temperament, which also tempers out the 11-limit commas [[176/175]] and [[385/384]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[2080/2079]], and [[4096/4095]], and gives the optimal patent val for [[Marvel family #Athene|athene]] temperament. It is the seventh [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta edo]]. It can also be treated as a no-elevens, no-seventeens tuning, on which it is [[consistent]] all the way up to the 23-odd-limit. | 53edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, notably tempering out the [[schisma]] (32805/32768) and the [[kleisma]] (15625/15552). More complex 5-limit commas tempered out include the [[amity comma]] (1600000/1594323), the [[semicomma]] (2109375/2097152), and the [[vulture comma]] ({{monzo| 24 -21 4 }}). In the 7-limit it tempers out [[225/224]], [[1728/1715]] and [[3125/3087]], the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out [[99/98]] and [[121/120]] (in addition to their difference, [[540/539]]), and is the [[optimal patent val]] for [[big brother]] temperament, which tempers out both, as well as 11-limit [[orwell]] temperament, which also tempers out the 11-limit commas [[176/175]] and [[385/384]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], [[2080/2079]], and [[4096/4095]], and gives the optimal patent val for [[Marvel family #Athene|athene]] temperament. It is the seventh [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta edo]]. It can also be treated as a no-elevens, no-seventeens tuning, on which it is [[consistent]] all the way up to the 23-odd-limit. | ||
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Many of its multiples such as [[159edo]], [[212edo]], [[742edo]], [[901edo]] and [[954edo]] have good consistency limit and are each of their own interest. The [[mercator family]] comprises rank-2 temperaments with 1/53-octave periods. | Many of its multiples such as [[159edo]], [[212edo]], [[742edo]], [[901edo]] and [[954edo]] have good consistency limit and are each of their own interest. The [[mercator family]] comprises rank-2 temperaments with 1/53-octave periods. | ||
== Intervals == | == Intervals == | ||
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| [[Untriton]] / [[aufo]] | | [[Untriton]] / [[aufo]] | ||
|} | |} | ||
== Scales == | |||
While there is only one possible generator for the [[5L 2s|diatonic]] [[mos scale]] supported by this edo, there are a greater number of generators for other mosses such as the [[2L 5s|antidiatonic]] scale. | |||
The following pages document various kinds of scales in 53edo: | |||
* [[1953 scale]] | |||
* [[5- to 8-tone scales in 53edo]] | |||
* [[List of MOS scales in 53edo]] | |||
== Music == | == Music == | ||
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=== 21st century === | === 21st century === | ||
; [[Amano Hideya]] | |||
* [https://www.youtube.com/watch?v=QpeCMz9kJ-s ''Like Uminari''] (2021) | |||
; [[Francium]] | ; [[Francium]] | ||
* [https://www.youtube.com/watch?v=GLQ1gD4bshY ''Space Race''] (2022) | * [https://www.youtube.com/watch?v=GLQ1gD4bshY ''Space Race''] (2022) | ||
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* [https://andrewheathwaite.bandcamp.com/track/elf-dine-on-ho-ho ''Elf Dine on Ho Ho''] (2012) [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2005%20Elf%20Dine%20on%20Ho%20Ho.mp3 play]{{dead link}} | * [https://andrewheathwaite.bandcamp.com/track/elf-dine-on-ho-ho ''Elf Dine on Ho Ho''] (2012) [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2005%20Elf%20Dine%20on%20Ho%20Ho.mp3 play]{{dead link}} | ||
* [https://andrewheathwaite.bandcamp.com/track/spun ''Spun''] (2012) [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3 play]{{dead link}} | * [https://andrewheathwaite.bandcamp.com/track/spun ''Spun''] (2012) [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3 play]{{dead link}} | ||
; [[Aaron Krister Johnson]] ([http://www.akjmusic.com site]{{dead link}}) | ; [[Aaron Krister Johnson]] ([http://www.akjmusic.com site]{{dead link}}) | ||
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; [[Prent Rodgers]] | ; [[Prent Rodgers]] | ||
* [https://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html | * ''Whisper Song'' (2007) – [https://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html blog] | [https://web.archive.org/web/20201127013644/http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/sing53-c5-slow.mp3 play] | [https://soundcloud.com/prent-rodgers/whisper-song-in-53-edo SoundCloud] | ||
; [[Gene Ward Smith]] | ; [[Gene Ward Smith]] | ||
* [https://www.archive.org/details/TrioInOrwell | * ''Trio in Orwell'' (2010) – [https://www.archive.org/details/TrioInOrwell detail] | [https://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3 play] – orwell[9] in 53edo | ||
; [[Cam Taylor]] | ; [[Cam Taylor]] | ||
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; [[Chris Vaisvil]] | ; [[Chris Vaisvil]] | ||
* [http://chrisvaisvil.com/the-fallen-of-kleismic15/ | * ''The Fallen of Kleismic15'' (2013) – [http://chrisvaisvil.com/the-fallen-of-kleismic15/ blog] | [http://micro.soonlabel.com/53edo/20130903_Kleismic%5b15%5d.mp3 play] – kleismic[15] in 53edo | ||
; [[Randy Wells]] | ; [[Randy Wells]] | ||
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; [[Xotla]] | ; [[Xotla]] | ||
* "Taking Flight" from ''Nano Particular'' (2019) [https://open.spotify.com/track/2zp6oM57m6BvQgyOZ5kmuZ Spotify] | [https://xotla.bandcamp.com/track/taking-flight-53edo Bandcamp] | [https://www.youtube.com/watch?v=sIsfYQATouc YouTube] | * "Taking Flight" from ''Nano Particular'' (2019) – [https://open.spotify.com/track/2zp6oM57m6BvQgyOZ5kmuZ Spotify] | [https://xotla.bandcamp.com/track/taking-flight-53edo Bandcamp] | [https://www.youtube.com/watch?v=sIsfYQATouc YouTube] | ||
== Instruments == | == Instruments == | ||