128edo: Difference between revisions

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{{EDO intro|128}} It is notable for being 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~~ [[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.

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 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)

=== Prime harmonics ===

=== Subsets and supersets ===

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|+Rank-2 temperaments by generators

! Periods per 8ve

! Generator~~ (Reduced)~~

! Generator*

! Cents~~ (Reduced)~~

! Cents*

! Associated Ratio

! Associated Ratio*

! Temperaments

|-

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| [[Undim]] (7-limit)

|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct

== Scales ==

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|128}} It is notable for being 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 [[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.
+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 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)
 === Prime harmonics ===
-{{Harmonics in equal|128|columns=11}}
+{{Harmonics in equal|128}}
 === Subsets and supersets ===
@@ Line 17: / Line 17: @@
 |+Rank-2 temperaments by generators
 ! Periods<br>per 8ve
-! Generator<br>(Reduced)
+! Generator*
-! Cents<br>(Reduced)
+! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-
@@ Line 70: / Line 70: @@
 | [[Undim]] (7-limit)
 |}
+<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
 == Scales ==