143edo: Difference between revisions

Wikispaces>Andrew_Heathwaite
**Imported revision 264954242 - Original comment: **
 
m Sectioning following similar pages and misc. improvements
 
(15 intermediate revisions by 9 users not shown)
Line 1: Line 1:
<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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-10-14 21:55:50 UTC</tt>.<br>
: The original revision id was <tt>264954242</tt>.<br>
: The revision comment was: <tt></tt><br>
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>
<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">143edo is a scale which divides the [[octave]] into 143 equal divisions of approximately 8.392¢.


As 143 is 11*13, 143edo allows the [[polymicrotonality|polymicrotonal]] juxtaposition of [[11edo]] and [[13edo]]:
== Theory ==
143edo is only [[consistent]] to the [[5-odd-limit]], and the error of the [[harmonic]] [[3/1|3]] is quite large. With the patent sharp fifth and flat 7, it supports a sharp form of [[slendric]] and [[hemithirds]] through to the [[13-limit]], while the 143b val provides a tuning almost identical with that of the [[POTE tuning]] for 7-limit [[meantone]].


[[image:13_against_11.gif width="800" height="312"]]
=== Odd harmonics ===
{{Harmonics in equal|143}}


If the 11edo and 13edo sub-scales share one tone (as in the diagram above), the resulting scale would have 23 tones in the octave; otherwise, it would have 24.</pre></div>
=== Subsets and supersets ===
<h4>Original HTML content:</h4>
As 143 is {{nowrap| 11 × 13 }}, 143edo allows the [[polymicrotonality|polymicrotonal juxtaposition]] of [[11edo]] and [[13edo]]:
<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;143edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;143edo is a scale which divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 143 equal divisions of approximately 8.392¢.&lt;br /&gt;
 
&lt;br /&gt;
[[File:13_against_11.gif|alt=13_against_11.gif|800x312px|13_against_11.gif]]
As 143 is 11*13, 143edo allows the &lt;a class="wiki_link" href="/polymicrotonality"&gt;polymicrotonal&lt;/a&gt; juxtaposition of &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt; and &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;:&lt;br /&gt;
 
&lt;br /&gt;
If the 11edo and 13edo subsets are analyzed as two scales that share the [[tonic]] and are then combined (as in the diagram above), the resulting scale would have 23 tones in the octave; otherwise, it would have 24.
&lt;!-- ws:start:WikiTextLocalImageRule:0:&amp;lt;img src=&amp;quot;/file/view/13_against_11.gif/264953770/800x312/13_against_11.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 312px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/13_against_11.gif/264953770/800x312/13_against_11.gif" alt="13_against_11.gif" title="13_against_11.gif" style="height: 312px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:0 --&gt;&lt;br /&gt;
 
&lt;br /&gt;
== Intervals ==
If the 11edo and 13edo sub-scales share one tone (as in the diagram above), the resulting scale would have 23 tones in the octave; otherwise, it would have 24.&lt;/body&gt;&lt;/html&gt;</pre></div>
{{Interval table}}