128edo: Difference between revisions
m →Theory: (''See regular temperament for more about what all this means and how to use it.'') Tag: Reverted |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ED intro}} It is notable for being the equal division corresponding to a standard [[MIDI]] piano roll of 128 notes. | {{ED intro}} | ||
It is notable for being the equal division corresponding to a standard [[MIDI]] piano roll of 128 notes - hence the largest equal division representable for the span of one whole [[octave]] on a standard MIDI roll. | |||
== Theory == | == Theory == | ||
The equal temperament [[tempering out|tempers out]] 2109375/2097152 ([[semicomma]]) in the [[5-limit]]; [[245/243]], [[1029/1024]] and [[5120/5103]] in the 7-limit; [[385/384]] and [[441/440]] in the 11-limit. It provides the [[optimal patent val]] for [[7-limit]] [[rodan]], the {{nowrap|41 & 87}} temperament, as well as for 7-limit [[fourfives]], the {{nowrap|60 & 68}} temperament. | |||
See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer) | See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer) | ||
=== Prime harmonics === | === Prime harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs| 2, 4, 8, 16, 32, and 64 }}. | Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs| 2, 4, 8, 16, 32, and 64 }}. | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
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| 15\128 | | 15\128 | ||
| 140.625 | | 140.625 | ||
| | | 13/12 | ||
| [[Fifive]] | | [[Fifive]] | ||
|- | |||
| 4 | |||
| 11\128 | |||
| 103.125 | |||
| 625/588 | |||
| [[Undim]] (7-limit) | |||
|- | |- | ||
| 4 | | 4 | ||
| 15\128 | | 15\128 | ||
| 140.625 | | 140.625 | ||
| | | 13/12 | ||
| [[Fourfives]] | | [[Fourfives]] | ||
|} | |} | ||
<nowiki />* [[ | <nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | ||
== Scales == | == Scales == | ||
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[[Category:Rodan]] | [[Category:Rodan]] | ||
[[Category:Fifive]] | |||
[[Category:Fourfives]] | [[Category:Fourfives]] | ||