ED5: Difference between revisions

Revision as of 14:53, 25 October 2011

IMPORTED REVISION FROM WIKISPACES

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This revision was by author Kosmorsky and made on 2011-10-25 14:53:13 UTC.

The original revision id was 268461362.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

=Division of the Fifth Harmonic (5/1) into n equal parts= 

The fifth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at most) ~4.3 pentaves within human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, </span>this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see [[17ed5]]). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus ([[20ed5]]) which itself is a zeta peak tuning (not "no-fives", full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.


3ed5 [[orwell]] generator (with octaves)
4ed5 [[meantone]] generator (with octaves)
5ed5 [[2L 7s|thuja]] generator (with octaves)

[[10ed5]]
[[11ed5]]
[[17ed5]]
[[20ed5]] (Hieronymus Tuning)
[[25ed5]] (Stockhausen, McLaren)
[[39ed5]]

[[http://www.nonoctave.com/tuning/fifth_harmonic.html]]

Original HTML content:

<html><head><title>ed5</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Division of the Fifth Harmonic (5/1) into n equal parts"></a><!-- ws:end:WikiTextHeadingRule:0 -->Division of the Fifth Harmonic (5/1) into n equal parts</h1>
 <br />
The fifth harmonic is particularly wide as far as equivalences go.<span class="commentBody"> There are (at most) ~4.3 pentaves within human hearing range; imagine if that were the case with octaves. If one does indeed deal with pentave equivalence, </span>this fact shapes one's musical approach dramatically. Following this, the quintessential example of a pentave based tuning is hyperpyth (see <a class="wiki_link" href="/17ed5">17ed5</a>). However, perhaps the more common reason to use these scales is in approximation with lower harmonic factors than 5. This approach is highlighted by Hieronymus (<a class="wiki_link" href="/20ed5">20ed5</a>) which itself is a zeta peak tuning (not &quot;no-fives&quot;, full on zeta). Other reasons for taking the nth root of 5 include finding temperaments like orwell, meantone, and thuja. This approach can of course be used indiscriminately.<br />
<br />
<br />
3ed5 <a class="wiki_link" href="/orwell">orwell</a> generator (with octaves)<br />
4ed5 <a class="wiki_link" href="/meantone">meantone</a> generator (with octaves)<br />
5ed5 <a class="wiki_link" href="/2L%207s">thuja</a> generator (with octaves)<br />
<br />
<a class="wiki_link" href="/10ed5">10ed5</a><br />
<a class="wiki_link" href="/11ed5">11ed5</a><br />
<a class="wiki_link" href="/17ed5">17ed5</a><br />
<a class="wiki_link" href="/20ed5">20ed5</a> (Hieronymus Tuning)<br />
<a class="wiki_link" href="/25ed5">25ed5</a> (Stockhausen, McLaren)<br />
<a class="wiki_link" href="/39ed5">39ed5</a><br />
<br />
<a class="wiki_link_ext" href="http://www.nonoctave.com/tuning/fifth_harmonic.html" rel="nofollow">http://www.nonoctave.com/tuning/fifth_harmonic.html</a></body></html>

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 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-25 14:45:58 UTC</tt>.<br>
+: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-25 14:53:13 UTC</tt>.<br>
-: The original revision id was <tt>268458094</tt>.<br>
+: The original revision id was <tt>268461362</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>
@@ Line 20: / Line 20: @@
 [[20ed5]] (Hieronymus Tuning)
 [[25ed5]] (Stockhausen, McLaren)
-[[39ed5]]</pre></div>
+[[39ed5]]
+[[http://www.nonoctave.com/tuning/fifth_harmonic.html]]</pre></div>
 <h4>Original HTML 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;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;ed5&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Division of the Fifth Harmonic (5/1) into n equal parts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Division of the Fifth Harmonic (5/1) into n equal parts&lt;/h1&gt;
@@ Line 36: / Line 38: @@
 &lt;a class="wiki_link" href="/20ed5"&gt;20ed5&lt;/a&gt; (Hieronymus Tuning)&lt;br /&gt;
 &lt;a class="wiki_link" href="/25ed5"&gt;25ed5&lt;/a&gt; (Stockhausen, McLaren)&lt;br /&gt;
-&lt;a class="wiki_link" href="/39ed5"&gt;39ed5&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;a class="wiki_link" href="/39ed5"&gt;39ed5&lt;/a&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link_ext" href="http://www.nonoctave.com/tuning/fifth_harmonic.html" rel="nofollow"&gt;http://www.nonoctave.com/tuning/fifth_harmonic.html&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

ED5: Difference between revisions

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