20ed5: Difference between revisions

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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>2011-09-02 00:48~~:38~~ UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-02 12:52:48 UTC</tt>.<br>

: The original revision id was <tt>~~250237560~~</tt>.<br>

: The original revision id was <tt>250338240</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>

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<span class="commentBody">‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents.</span>

<span class="commentBody">One ~~component of its essence, or one~~ way of looking at it~~, is~~ constructing it by four tempered 3/2 each of which is divided</span> ~~in 5~~ tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on 5/1 ~~the pentave~~. ~~So calling~~ it ~~some kind~~ of ~~quintuple non-octave meantone makes a certain sense but it goes beyond~~ that, as a temperament ~~making use of the 2nd~~, ~~3rd~~, ~~5th~~, ~~7th, 11th, 13th harmonic factors and probably many more~~.</pre></div>

<span class="commentBody">One way of looking at it comes by constructing it via four tempered 3/2 each of which is divided</span> into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the "pentave", 5/1. Adding octaves makes it [[Meantone family#Jerome]] temperament, with generator a meantone fifth divided in five, and Hieronymus is the generators of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, 17, 19 or even 23 limit system.</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"><html><head><title>20ed5</title></head><body>20th root of 5 &quot;Hieronymus' Tuning&quot;<br />

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<span class="commentBody">‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents.</span><br />

<br />

<span class="commentBody">One ~~component of its essence, or one~~ way of looking at it~~, is~~ constructing it by four tempered 3/2 each of which is divided</span> ~~in 5~~ tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on 5/1 ~~the pentave~~. ~~So calling~~ it ~~some kind~~ of ~~quintuple non-octave meantone makes a certain sense but it goes beyond~~ that, as a temperament ~~making use of the 2nd~~, ~~3rd~~, ~~5th~~, ~~7th, 11th, 13th harmonic factors and probably many more~~.</body></html></pre></div>

<span class="commentBody">One way of looking at it comes by constructing it via four tempered 3/2 each of which is divided</span> into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the &quot;pentave&quot;, 5/1. Adding octaves makes it <a class="wiki_link" href="/Meantone%20family#Jerome">Meantone family</a> temperament, with generator a meantone fifth divided in five, and Hieronymus is the generators of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, 17, 19 or even 23 limit system.</body></html></pre></div>

@@ Line 1: / Line 1: @@
 <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>2011-09-02 00:48:38 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-02 12:52:48 UTC</tt>.<br>
-: The original revision id was <tt>250237560</tt>.<br>
+: The original revision id was <tt>250338240</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 11: / Line 11: @@
 &lt;span class="commentBody"&gt;‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents.&lt;/span&gt;
-&lt;span class="commentBody"&gt;One component of its essence, or one way of looking at it, is constructing it by four tempered 3/2 each of which is divided&lt;/span&gt; in 5 tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on 5/1 the pentave. So calling it some kind of quintuple non-octave meantone makes a certain sense but it goes beyond that, as a temperament making use of the 2nd, 3rd, 5th, 7th, 11th, 13th harmonic factors and probably many more.</pre></div>
+&lt;span class="commentBody"&gt;One way of looking at it comes by constructing it via four tempered 3/2 each of which is divided&lt;/span&gt; into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the "pentave", 5/1. Adding octaves makes it [[Meantone family#Jerome]] temperament, with generator a meantone fifth divided in five, and Hieronymus is the generators of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, 17, 19 or even 23 limit system.</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;20ed5&lt;/title&gt;&lt;/head&gt;&lt;body&gt;20th root of 5 &amp;quot;Hieronymus' Tuning&amp;quot;&lt;br /&gt;
@@ Line 18: / Line 18: @@
 &lt;span class="commentBody"&gt;‎8, 12 (or 61), 23, 27, 32, 44, 48, 52, 56, 66, 71, 77, etc. within 20 cents.&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span class="commentBody"&gt;One component of its essence, or one way of looking at it, is constructing it by four tempered 3/2 each of which is divided&lt;/span&gt; in 5 tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on 5/1 the pentave. So calling it some kind of quintuple non-octave meantone makes a certain sense but it goes beyond that, as a temperament making use of the 2nd, 3rd, 5th, 7th, 11th, 13th harmonic factors and probably many more.&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;span class="commentBody"&gt;One way of looking at it comes by constructing it via four tempered 3/2 each of which is divided&lt;/span&gt; into five tones, which in turn approximate 11/8 13/8 7/6 etc., and themselves end up on the &amp;quot;pentave&amp;quot;, 5/1. Adding octaves makes it &lt;a class="wiki_link" href="/Meantone%20family#Jerome"&gt;Meantone family&lt;/a&gt; temperament, with generator a meantone fifth divided in five, and Hieronymus is the generators of that. Jerome/Hieronymus only really comes into its own as a higher limit temperament, as a 13, 17, 19 or even 23 limit system.&lt;/body&gt;&lt;/html&gt;</pre></div>