Prodigy chords: 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:genewardsmith|genewardsmith]] and made on <tt>2011-12-16 23:31:49 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-17 16:49:42 UTC</tt>.<br>

: The original revision id was <tt>~~287010650~~</tt>.<br>

: The original revision id was <tt>287090848</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">A //prodigy chord// is an 11 odd limit [[Dyadic chord|essentially tempered chord]] in [[~~http://xenharmonic.wikispaces.com/~~Marvel+family#Prodigy|prodigy temperament]]. Since 441/440 is tempered out in prodigy, [[werckismic chords]] are also prodigy chords, and since 225/224 is tempered out, the 9 odd limit marvel chords are prodigy chords. Aside from these, there are three more prodigy chords: a 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8 and a pair of inversely related pentads, 1-5/4-7/5-8/5-16/9 with steps 5/4-9/8-8/7-10/9-9/8 and 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.

<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">A //prodigy chord// is an 11 odd limit [[Dyadic chord|essentially tempered chord]] in [[Marvel family#Prodigy|prodigy temperament]]. Since 441/440 is tempered out in prodigy, [[werckismic chords]] are also prodigy chords, and since 225/224 is tempered out, the 9 odd limit marvel chords are prodigy chords. Aside from these, there are three more prodigy chords: a 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8 and a pair of inversely related pentads, 1-5/4-7/5-8/5-16/9 with steps 5/4-9/8-8/7-10/9-9/8 and 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.

Equal divisions with prodigy chords include 12, 29, 31, 41, 43, 72, 74, 84, 103, 175, 197, 247c, 3129bcde, 391bcde and 463bcde.</pre></div>

Equal divisions with prodigy chords include 12, 29, 31, 41, 43, 72, 74, 84, 103, 175, 197, 247c, 3129bcde, 391bcde and 463bcde.

=Miracle essentially tempered chords=

[[Gamelismic clan#Miracle|11-limit miracle temperament]] tempers out an astonishing five commas which allow essential tempering: 540/539, 441/440, 385/384, 243/242 and 225/224, and hence has all of the essentially tempered chords of each of them. Further chords come from [[Breed family#Jove, aka Wonder|jove]] and 9- and 11-marvel chords. Finally, there are the three listed above.

Three chords may not seem by many, but consider this: the POTE tuning for prodigy shrinks 540/539 and 243/242 to a third of a cent, and 385/384 to -1/3 cent. Other optimizations are similar. Hence, the miracle essentially tempered chords are already available in prodigy, we just aren't counting them; in effect, we can more or less equate prodigy with miracle.</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>prodigy chords</title></head><body>A <em>prodigy chord</em> is an 11 odd limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered chord</a> in <a href="~~http://xenharmonic.wikispaces.com~~/Marvel~~+family~~#Prodigy">prodigy temperament</a>. Since 441/440 is tempered out in prodigy, <a class="wiki_link" href="/werckismic%20chords">werckismic chords</a> are also prodigy chords, and since 225/224 is tempered out, the 9 odd limit marvel chords are prodigy chords. Aside from these, there are three more prodigy chords: a 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8 and a pair of inversely related pentads, 1-5/4-7/5-8/5-16/9 with steps 5/4-9/8-8/7-10/9-9/8 and 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.<br />

<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>prodigy chords</title></head><body>A <em>prodigy chord</em> is an 11 odd limit <a class="wiki_link" href="/Dyadic%20chord">essentially tempered chord</a> in <a class="wiki_link" href="/Marvel%20family#Prodigy">prodigy temperament</a>. Since 441/440 is tempered out in prodigy, <a class="wiki_link" href="/werckismic%20chords">werckismic chords</a> are also prodigy chords, and since 225/224 is tempered out, the 9 odd limit marvel chords are prodigy chords. Aside from these, there are three more prodigy chords: a 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8 and a pair of inversely related pentads, 1-5/4-7/5-8/5-16/9 with steps 5/4-9/8-8/7-10/9-9/8 and 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.<br />

<br />

Equal divisions with prodigy chords include 12, 29, 31, 41, 43, 72, 74, 84, 103, 175, 197, 247c, 3129bcde, 391bcde and 463bcde.<br />

<br />

<h1 id="toc0"><a name="Miracle essentially tempered chords"></a>Miracle essentially tempered chords</h1>

<a class="wiki_link" href="/Gamelismic%20clan#Miracle">11-limit miracle temperament</a> tempers out an astonishing five commas which allow essential tempering: 540/539, 441/440, 385/384, 243/242 and 225/224, and hence has all of the essentially tempered chords of each of them. Further chords come from <a class="wiki_link" href="/Breed%20family#Jove, aka Wonder">jove</a> and 9- and 11-marvel chords. Finally, there are the three listed above.<br />

<br />

~~Equal divisions with prodigy~~ chords ~~include 12~~, 29, 31, 41, 43, ~~72, 74, 84, 103, 175, 197, 247c, 3129bcde, 391bcde and 463bcde~~.</body></html></pre></div>

Three chords may not seem by many, but consider this: the POTE tuning for prodigy shrinks 540/539 and 243/242 to a third of a cent, and 385/384 to -1/3 cent. Other optimizations are similar. Hence, the miracle essentially tempered chords are already available in prodigy, we just aren't counting them; in effect, we can more or less equate prodigy with miracle.</body></html></pre></div>

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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:genewardsmith|genewardsmith]] and made on <tt>2011-12-16 23:31:49 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-17 16:49:42 UTC</tt>.<br>
-: The original revision id was <tt>287010650</tt>.<br>
+: The original revision id was <tt>287090848</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">A //prodigy chord// is an 11 odd limit [[Dyadic chord|essentially tempered chord]] in [[http://xenharmonic.wikispaces.com/Marvel+family#Prodigy|prodigy temperament]]. Since 441/440 is tempered out in prodigy, [[werckismic chords]] are also prodigy chords, and since 225/224 is tempered out, the 9 odd limit marvel chords are prodigy chords. Aside from these, there are three more prodigy chords: a 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8 and a pair of inversely related pentads, 1-5/4-7/5-8/5-16/9 with steps 5/4-9/8-8/7-10/9-9/8 and 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.
+<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">A //prodigy chord// is an 11 odd limit [[Dyadic chord|essentially tempered chord]] in [[Marvel family#Prodigy|prodigy temperament]]. Since 441/440 is tempered out in prodigy, [[werckismic chords]] are also prodigy chords, and since 225/224 is tempered out, the 9 odd limit marvel chords are prodigy chords. Aside from these, there are three more prodigy chords: a 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8 and a pair of inversely related pentads, 1-5/4-7/5-8/5-16/9 with steps 5/4-9/8-8/7-10/9-9/8 and 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.
-Equal divisions with prodigy chords include 12, 29, 31, 41, 43, 72, 74, 84, 103, 175, 197, 247c, 3129bcde, 391bcde and 463bcde.</pre></div>
+Equal divisions with prodigy chords include 12, 29, 31, 41, 43, 72, 74, 84, 103, 175, 197, 247c, 3129bcde, 391bcde and 463bcde.
+=Miracle essentially tempered chords=
+[[Gamelismic clan#Miracle|11-limit miracle temperament]] tempers out an astonishing five commas which allow essential tempering: 540/539, 441/440, 385/384, 243/242 and 225/224, and hence has all of the essentially tempered chords of each of them. Further chords come from [[Breed family#Jove, aka Wonder|jove]] and 9- and 11-marvel chords. Finally, there are the three listed above.
+Three chords may not seem by many, but consider this: the POTE tuning for prodigy shrinks 540/539 and 243/242 to a third of a cent, and 385/384 to -1/3 cent. Other optimizations are similar. Hence, the miracle essentially tempered chords are already available in prodigy, we just aren't counting them; in effect, we can more or less equate prodigy with miracle.</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;prodigy chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;prodigy chord&lt;/em&gt; is an 11 odd limit &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;essentially tempered chord&lt;/a&gt; in &lt;a href="http://xenharmonic.wikispaces.com/Marvel+family#Prodigy"&gt;prodigy temperament&lt;/a&gt;. Since 441/440 is tempered out in prodigy, &lt;a class="wiki_link" href="/werckismic%20chords"&gt;werckismic chords&lt;/a&gt; are also prodigy chords, and since 225/224 is tempered out, the 9 odd limit marvel chords are prodigy chords. Aside from these, there are three more prodigy chords: a 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8 and a pair of inversely related pentads, 1-5/4-7/5-8/5-16/9 with steps 5/4-9/8-8/7-10/9-9/8 and 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.&lt;br /&gt;
+<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;prodigy chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A &lt;em&gt;prodigy chord&lt;/em&gt; is an 11 odd limit &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;essentially tempered chord&lt;/a&gt; in &lt;a class="wiki_link" href="/Marvel%20family#Prodigy"&gt;prodigy temperament&lt;/a&gt;. Since 441/440 is tempered out in prodigy, &lt;a class="wiki_link" href="/werckismic%20chords"&gt;werckismic chords&lt;/a&gt; are also prodigy chords, and since 225/224 is tempered out, the 9 odd limit marvel chords are prodigy chords. Aside from these, there are three more prodigy chords: a 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8 and a pair of inversely related pentads, 1-5/4-7/5-8/5-16/9 with steps 5/4-9/8-8/7-10/9-9/8 and 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.&lt;br /&gt;
+&lt;br /&gt;
+Equal divisions with prodigy chords include 12, 29, 31, 41, 43, 72, 74, 84, 103, 175, 197, 247c, 3129bcde, 391bcde and 463bcde.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Miracle essentially tempered chords"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Miracle essentially tempered chords&lt;/h1&gt;
+&lt;a class="wiki_link" href="/Gamelismic%20clan#Miracle"&gt;11-limit miracle temperament&lt;/a&gt; tempers out an astonishing five commas which allow essential tempering: 540/539, 441/440, 385/384, 243/242 and 225/224, and hence has all of the essentially tempered chords of each of them. Further chords come from &lt;a class="wiki_link" href="/Breed%20family#Jove, aka Wonder"&gt;jove&lt;/a&gt; and 9- and 11-marvel chords. Finally, there are the three listed above.&lt;br /&gt;
 &lt;br /&gt;
-Equal divisions with prodigy chords include 12, 29, 31, 41, 43, 72, 74, 84, 103, 175, 197, 247c, 3129bcde, 391bcde and 463bcde.&lt;/body&gt;&lt;/html&gt;</pre></div>
+Three chords may not seem by many, but consider this: the POTE tuning for prodigy shrinks 540/539 and 243/242 to a third of a cent, and 385/384 to -1/3 cent. Other optimizations are similar. Hence, the miracle essentially tempered chords are already available in prodigy, we just aren't counting them; in effect, we can more or less equate prodigy with miracle.&lt;/body&gt;&lt;/html&gt;</pre></div>