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.

{{ED intro}} 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 {{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 ===

=== Subsets and supersets ===

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== Regular temperament properties ==

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

|+~~Rank~~-2 temperaments by ~~generators~~

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Periods per 8ve

|-

! Generator~~ (Reduced)~~

! Periods per 8ve

! Cents~~ (Reduced)~~

! Generator*

! Associated ~~Ratio~~

! Cents*

! Associated ratio*

! Temperaments

|-

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|-

| 4

| 53\128 (11\128)

| 53\128 (11\128)

| 496.875 (103.125)

| 496.875 (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 ==

@@ 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.
+{{ED intro}} 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 {{nowrap|41 &amp; 87}} temperament, as well as for 7-limit [[fourfives]], the {{nowrap|60 &amp; 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 15: / Line 15: @@
 == Regular temperament properties ==
 {| class="wikitable center-all left-5"
-|+Rank-2 temperaments by generators
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
-! Generator<br>(Reduced)
+! Periods<br />per 8ve
-! Cents<br>(Reduced)
+! Generator*
-! Associated<br>Ratio
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 65: / Line 66: @@
 |-
 | 4
-| 53\128<br>(11\128)
+| 53\128<br />(11\128)
-| 496.875<br>(103.125)
+| 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 ==