Xenharmonic Wiki

128edo: Difference between revisions

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**Imported revision 214083274 - Original comment: **
 
Cleanup; + category
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}} It is notable for being the equal division corresponding to a standard [[MIDI]] piano roll of 128 notes.  
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-03-25 16:55:52 UTC</tt>.<br>
 
: The original revision id was <tt>214083274</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
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.  
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
See also [https://www.youtube.com/watch?v=lGa66qHzKME 128 notes per octave on Alto Saxophone] (Demo by Philipp Gerschlauer)
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">The 128 equal division divides the octave into 128 equal parts of exactly 9.375 cents each. It is the [[optimal patent val]] for 7-limit [[Gamelismic clan|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.</pre></div>
 
<h4>Original HTML content:</h4>
=== Prime harmonics ===
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;128edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 128 equal division divides the octave into 128 equal parts of exactly 9.375 cents each. It is the &lt;a class="wiki_link" href="/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for 7-limit &lt;a class="wiki_link" href="/Gamelismic%20clan"&gt;rodan temperament&lt;/a&gt;. 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.&lt;/body&gt;&lt;/html&gt;</pre></div>
{{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 ==
{| 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
| 25\128
| 234.375
| 8/7
| [[Rodan]]
|-
| 1
| 29\128
| 271.875
| 75/64
| [[Orson]]
|-
| 1
| 33\128
| 309.375
| 448/375
| [[Triwell]]
|-
| 1
| 53\128
| 496.875
| 4/3
| [[Undecental]]
|-
| 2
| 13\128
| 121.875
| 15/14
| [[Lagaca]]
|-
| 2
| 15\128
| 140.625
| 13/12
| [[Fifive]]
|-
| 4
| 11\128
| 103.125
| 625/588
| [[Undim]] (7-limit)
|-
| 4
| 15\128
| 140.625
| 13/12
| [[Fourfives]]
|}
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]]
 
== Scales ==
* [[Radon5]]
* [[Radon11]]
* [[Radon16]]
 
[[Category:Rodan]]
[[Category:Fifive]]
[[Category:Fourfives]]
Retrieved from "https://en.xen.wiki/w/128edo"