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16edt: Difference between revisions

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**Imported revision 277238938 - Original comment: **
 
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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}}
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-11-19 14:33:23 UTC</tt>.<br>
 
: The original revision id was <tt>277238938</tt>.<br>
== Properties ==
: The revision comment was: <tt></tt><br>
As the double of [[8edt|8EDT]], this division of the tritave is harmonically fraternal to [[10edo|10EDO]]. Its unit step is ~1.128{{c}} flat of 1\10EDO. Unlike 10EDO, it does not really have a 7 or 13 because it is not using its approximation of 2 as equivalent though the accumulated flatness of a stack of its unit step leads to an excellent [[21/13|13:21]] and a decent [[13/7|7:13]]. When twos are admitted, it turns into a tritave-repeating version of Blackwood 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>
== 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;white-space: pre-wrap ! important" class="old-revision-html">
{{Harmonics in equal
=Music=
| steps = 16
[[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3|A Short Tune in 16EDT]] by [[Peter 'Rush' Kosmorsky]]</pre></div>
| num = 3
<h4>Original HTML content:</h4>
| denom = 1
<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;16edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;br /&gt;
| intervals = odd
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Music&lt;/h1&gt;
}}
&lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3" rel="nofollow"&gt;A Short Tune in 16EDT&lt;/a&gt; by &lt;a class="wiki_link" href="/Peter%20%27Rush%27%20Kosmorsky"&gt;Peter 'Rush' Kosmorsky&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Harmonics in equal
| steps = 16
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = odd
}}
 
== Intervals ==
 
{| class="wikitable"
|-
! rowspan="2" | Degree
! colspan="2" | Size in
|-
! [[Cents]]
! Hekts
|-
| style="text-align: center;" | 1
| style="text-align: right;" | 118.87219
| 81.25
|-
| style="text-align: center;" | 2
| style="text-align: right;" | 237.74438
| 162.5
|-
| style="text-align: center;" | 3
| style="text-align: right;" | 356.61656
| 243.75
|-
| style="text-align: center;" | 4
| style="text-align: right;" | 475.48875
| 325
|-
| style="text-align: center;" | 5
| style="text-align: right;" | 594.36094
| 406.25
|-
| style="text-align: center;" | 6
| style="text-align: right;" | 713.23312
| 487.5
|-
| style="text-align: center;" | 7
| style="text-align: right;" | 832.10531
| 568.75
|-
| style="text-align: center;" | 8
| style="text-align: right;" | 950.9775
| 650
|-
| style="text-align: center;" | 9
| style="text-align: right;" | 1069.84969
| 731.25
|-
| style="text-align: center;" | 10
| style="text-align: right;" | 1188.72188
| 812.5
|-
| style="text-align: center;" | 11
| style="text-align: right;" | 1307.59406
| 893.75
|-
| style="text-align: center;" | 12
| style="text-align: right;" | 1426.46625
| 975
|-
| style="text-align: center;" | 13
| style="text-align: right;" | 1545.33844
| 1056.25
|-
| style="text-align: center;" | 14
| style="text-align: right;" | 1664.21063
| 1137.5
|-
| style="text-align: center;" | 15
| style="text-align: right;" | 1783.08281
| 1218.75
|-
| style="text-align: center;" | 16
| style="text-align: right;" | 1901.955
| 1300
|}
 
== Related temperament ==
16EDT is also be thought of as a generator of the ''subsedia'' temperament, which is a [[cluster temperament]] with 10 clusters of notes in an octave.
 
=== [[Mirkwai clan #Subsedia|Subsedia]] (10 &amp; 111) ===
==== 7-limit ====
Comma list: 16875/16807, 65536/64827
 
Mapping: [{{val|1 0 5 4}}, {{val|0 16 -27 -12}}]
 
POTE generator: ~15/14 = 118.965
 
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d}}
 
Badness: 0.157658
 
==== 11-limit ====
Comma list: 540/539, 1375/1372, 65536/64827
 
Mapping: [{{val|1 0 5 4 -1}}, {{val|0 16 -27 -12 45}}]
 
POTE generator: ~15/14 = 118.968
 
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d}}
 
Badness: 0.066838
 
==== 13-limit ====
Comma list: 352/351, 540/539, 676/675, 1375/1372
 
Mapping: [{{val|1 0 5 4 -1 4}}, {{val|0 16 -27 -12 45 -3}}]
 
POTE generator: ~15/14 = 118.968
 
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d}}
 
Badness: 0.031635
 
==== 17-limit ====
Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
 
Mapping: [{{val|1 0 5 4 -1 4 3}}, {{val|0 16 -27 -12 45 -3 11}}]
 
POTE generator: ~15/14 = 118.968
 
{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232dg}}
 
Badness: 0.019707
 
== Music ==
[http://soonlabel.com/xenharmonic/wp-content/uploads/2011/11/16-edt.mp3 A Short Tune in 16EDT] by [[Peter_'Rush'_Kosmorsky|Peter 'Rush' Kosmorsky]]
 
[[Category:Macrotonal]]
{{todo|expand}}
Retrieved from "https://en.xen.wiki/w/16edt"