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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|128}}It is notable because it is 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)
=== Prime harmonics ===
{{Harmonics in equal|128}}
{{Harmonics in equal|128}}
It 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. Being the power of two closest to division of the octave by the Germanic [[Wikipedia: long hundred| long hundred]], it has a unit step which is the binary (fine) relative cent (or relative heptamu in MIDI terms) of [[1edo]].


See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)
=== 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-1 center-2 center-3"
{| class="wikitable center-all left-5"
|+Rank-2 temperaments
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
!Periods
|-
per octave
! Periods<br>per 8ve
!Generator
! Generator*
(reduced)
! Cents*
!Cents
! Associated<br>ratio*
(reduced)
! Temperaments
!Associated
Ratio
!Temperaments
|-
|-
|1
| 1
|25\128
| 25\128
|234.375
| 234.375
|8/7
| 8/7
|[[Rodan]]
| [[Rodan]]
|-
|-
|1
| 1
|29\128
| 29\128
|271.875
| 271.875
|75/64
| 75/64
|[[Orson]]
| [[Orson]]
|-
|-
|1
| 1
|33\128
| 33\128
|309.375
| 309.375
|448/375
| 448/375
|[[Triwell]]
| [[Triwell]]
|-
|-
|1
| 1
|53\128
| 53\128
|496.875
| 496.875
|4/3
| 4/3
|[[Undecental]]
| [[Undecental]]
|-
|-
|2
| 2
|13\128
| 13\128
|121.875
| 121.875
|15/14
| 15/14
|[[Gamelismic clan#Lagaca|Lagaca]]
| [[Lagaca]]
|-
|-
|2
| 2
|15\128
| 15\128
|140.625
| 140.625
|27/25
| 13/12
|[[Fifive]]
| [[Fifive]]
|-
|-
|4
| 4
|15\128
| 11\128
|140.625
| 103.125
|27/25
| 625/588
|[[Fifive family#Fourfives|Fourfives]]
| [[Undim]] (7-limit)
|-
|-
|4
| 4
|53\128
| 15\128
(11\128)
| 140.625
|496.875
| 13/12
 
| [[Fourfives]]
(103.125)
|4/3
|[[Undim]] (7-limit)
|}
|}
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]


== Scales ==
== Scales ==
* [[Radon5]]
* [[Radon11]]
* [[Radon16]]


* [[radon5]]
* [[radon11]]
* [[radon16]]
[[Category:128edo| ]] <!-- main article -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Rodan]]
[[Category:Rodan]]
[[Category:Fifive]]
[[Category:Fourfives]]
Retrieved from "https://en.xen.wiki/w/128edo"