128edo: Difference between revisions

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{{EDO intro|128}}It is notable ~~because it is~~ the equal division corresponding to a standard MIDI piano roll of 128 notes.

{{EDO intro|128}} It is notable for being the equal division corresponding to a standard MIDI piano roll of 128 notes.

== Theory ==

128edo ~~is the [[optimal patent val]] for [[7-limit]] [[Rodan]] temperament. It~~ [[tempers out]] 2109375/2097152 in the [[5-limit]]; 245/243, 1029/1024 and 5120/5103 in the 7-limit; 385/384 and 441/440 in the limit.

128edo [[tempers out]] 2109375/2097152 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 41 & 87 temperament, as well as for 7-limit [[fourfives]], the 60 & 68 temperament.

See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)

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=== Prime harmonics ===

=== Subsets and supersets ===

Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs| 2, 4, 8, 16, 32, and 64 }}.

=== Miscellaneous properties ===

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== Regular temperament properties ==

{| class="wikitable center-~~1 center~~-~~2 center-3~~"

{| class="wikitable center-all left-5"

|+Rank-2 temperaments

|+Rank-2 temperaments by generators

! Periods<br>per 8ve

! Generator<br>(Reduced)

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== Scales ==

* [[~~radon5~~]]

* [[Radon5]]

* [[~~radon11~~]]

* [[Radon11]]

* [[~~radon16~~]]

* [[Radon16]]

~~[[Category:128edo| ]] ~~

~~[[Category:Equal divisions of the octave|###]] ~~

[[Category:Rodan]]

[[Category:Fourfives]]

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 {{Infobox ET}}
-{{EDO intro|128}}It is notable because it is the equal division corresponding to a standard MIDI piano roll of 128 notes.
+{{EDO intro|128}} It is notable for being the equal division corresponding to a standard MIDI piano roll of 128 notes.
 == Theory ==
-edo is the [[optimal patent val]] for [[7-limit]] [[Rodan]] temperament. It [[tempers out]] 2109375/2097152 in the [[5-limit]]; 245/243, 1029/1024 and 5120/5103 in the 7-limit; 385/384 and 441/440 in the limit.
+edo [[tempers out]] 2109375/2097152 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 41 & 87 temperament, as well as for 7-limit [[fourfives]], the 60 & 68 temperament.
 See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)
@@ Line 9: / Line 9: @@
 === Prime harmonics ===
 {{Harmonics in equal|128|columns=11}}
+=== Subsets and supersets ===
+Since 128 factors into 2<sup>7</sup>, 128edo has subset edos {{EDOs| 2, 4, 8, 16, 32, and 64 }}.
 === Miscellaneous properties ===
@@ Line 14: / Line 17: @@
 == Regular temperament properties ==
-{| class="wikitable center-1 center-2 center-3"
+{| class="wikitable center-all left-5"
-|+Rank-2 temperaments
+|+Rank-2 temperaments by generators
 ! Periods<br>per 8ve
 ! Generator<br>(Reduced)
@@ Line 72: / Line 75: @@
 == Scales ==
-* [[radon5]]
+* [[Radon5]]
-* [[radon11]]
+* [[Radon11]]
-* [[radon16]]
+* [[Radon16]]
-[[Category:128edo| ]] <!-- main article -->
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Rodan]]
+[[Category:Fourfives]]