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-~~18 16~~:20:14 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-19 22:46:13 UTC</tt>.<br>

: The original revision id was <tt>~~287212438~~</tt>.<br>

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: The revision comment was: <tt></tt><br>

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=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 [[undecimal marvel chords]]. ~~Finally,~~ there are the three listed above.

[[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 [[undecimal marvel chords]]. Then there are the three listed above, ad ten essentially miracle chords.

Three chords may not seem to be 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. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 74, pentads: 32, and hexads: 10. There are therefore actually more essentially tempered chords than just ones.

Three chords may not seem to be 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. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 76, pentads: 38, and hexads: 12. There are therefore actually more essentially tempered chords than just ones.

EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.

EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.</pre></div>

</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 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 />

<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 <a class="wiki_link" href="/undecimal%20marvel%20chords">undecimal marvel chords</a>. ~~Finally,~~ there are the three listed above.<br />

<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 <a class="wiki_link" href="/undecimal%20marvel%20chords">undecimal marvel chords</a>. Then there are the three listed above, ad ten essentially miracle chords.<br />

<br />

Three chords may not seem to be 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. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 74, pentads: 32, and hexads: 10. There are therefore actually more essentially tempered chords than just ones.<br />

Three chords may not seem to be 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. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 76, pentads: 38, and hexads: 12. There are therefore actually more essentially tempered chords than just ones.<br />

<br />

EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.</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:genewardsmith|genewardsmith]] and made on <tt>2011-12-18 16:20:14 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-19 22:46:13 UTC</tt>.<br>
-: The original revision id was <tt>287212438</tt>.<br>
+: The original revision id was <tt>287557282</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 9: / Line 9: @@
 =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 [[undecimal marvel chords]]. Finally, there are the three listed above.
+[[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 [[undecimal marvel chords]]. Then there are the three listed above, ad ten essentially miracle chords.
-Three chords may not seem to be 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. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 74, pentads: 32, and hexads: 10. There are therefore actually more essentially tempered chords than just ones.
+Three chords may not seem to be 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. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 76, pentads: 38, and hexads: 12. There are therefore actually more essentially tempered chords than just ones.
-EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.
+EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.</pre></div>
-</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 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;
 &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 &lt;a class="wiki_link" href="/undecimal%20marvel%20chords"&gt;undecimal marvel chords&lt;/a&gt;. Finally, there are the three listed above.&lt;br /&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 &lt;a class="wiki_link" href="/undecimal%20marvel%20chords"&gt;undecimal marvel chords&lt;/a&gt;. Then there are the three listed above, ad ten essentially miracle chords.&lt;br /&gt;
 &lt;br /&gt;
-Three chords may not seem to be 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. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 74, pentads: 32, and hexads: 10. There are therefore actually more essentially tempered chords than just ones.&lt;br /&gt;
+Three chords may not seem to be 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. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 76, pentads: 38, and hexads: 12. There are therefore actually more essentially tempered chords than just ones.&lt;br /&gt;
 &lt;br /&gt;
 EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.&lt;/body&gt;&lt;/html&gt;</pre></div>