128edo: Difference between revisions
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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. | ||
== 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) | |||
=== Prime harmonics === | |||
{{Harmonics in equal|128}} | {{Harmonics in equal|128}} | ||
=== Subsets and supersets === | |||
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 == | ||
{| class="wikitable center- | {| class="wikitable center-all left-5" | ||
|+ | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
|1 | | 1 | ||
| | | 25\128 | ||
| | | 234.375 | ||
| | | 8/7 | ||
|[[ | | [[Rodan]] | ||
|- | |- | ||
|1 | | 1 | ||
| | | 29\128 | ||
| | | 271.875 | ||
| | | 75/64 | ||
|[[ | | [[Orson]] | ||
|- | |- | ||
|1 | | 1 | ||
| | | 33\128 | ||
| | | 309.375 | ||
| | | 448/375 | ||
|[[ | | [[Triwell]] | ||
|- | |- | ||
| | | 1 | ||
| | | 53\128 | ||
| | | 496.875 | ||
| | | 4/3 | ||
|[[ | | [[Undecental]] | ||
|- | |- | ||
|2 | | 2 | ||
| | | 13\128 | ||
| | | 121.875 | ||
| | | 15/14 | ||
|[[ | | [[Lagaca]] | ||
|- | |- | ||
| | | 2 | ||
|15\128 | | 15\128 | ||
|140.625 | | 140.625 | ||
|27/25 | | 27/25 | ||
|[[Fifive | | [[Fifive]] | ||
|- | |- | ||
|4 | | 4 | ||
|53\128 | | 15\128 | ||
(11\128) | | 140.625 | ||
|496.875 | | 27/25 | ||
| [[Fourfives]] | |||
(103.125) | |- | ||
|4/3 | | 4 | ||
|[[Undim]] (7-limit) | | 53\128<br />(11\128) | ||
| 496.875<br />(103.125) | |||
| 4/3 | |||
| [[Undim]] (7-limit) | |||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Scales == | == Scales == | ||
* [[Radon5]] | |||
* [[Radon11]] | |||
* [[Radon16]] | |||
[[Category:Rodan]] | [[Category:Rodan]] | ||
[[Category:Fourfives]] | |||