Prodigy chords: Difference between revisions
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Wikispaces>genewardsmith **Imported revision 287124640 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 287125024 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | 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 03: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-18 03:12:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>287125024</tt>.<br> | ||
: The revision comment was: <tt></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> | 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> | <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 [[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. | ||
=Miracle essentially tempered chords= | =Miracle essentially tempered chords= | ||
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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. 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 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. 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. | ||
EDOs supporting prodigy/miracle include 31, 41, 72, 216c, 247c, 319bcde, 391bcde, 463bcde.</pre></div> | EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde. | ||
</pre></div> | |||
<h4>Original HTML content:</h4> | <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 /> | <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 /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Miracle essentially tempered chords"></a><!-- ws:end:WikiTextHeadingRule:0 -->Miracle essentially tempered chords</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Miracle essentially tempered chords"></a><!-- ws:end:WikiTextHeadingRule:0 -->Miracle essentially tempered chords</h1> | ||
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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. 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 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. 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 /> | ||
<br /> | <br /> | ||
EDOs supporting prodigy/miracle include 31, 41, 72, 216c, 247c, 319bcde, 391bcde, 463bcde.</body></html></pre></div> | EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.</body></html></pre></div> | ||
Revision as of 03:12, 18 December 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-12-18 03:12:41 UTC.
- The original revision id was 287125024.
- 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:
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. =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. 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. 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. EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.
Original HTML content:
<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 /> <!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Miracle essentially tempered chords"></a><!-- ws:end:WikiTextHeadingRule:0 -->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 /> <br /> 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. 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 /> <br /> EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.</body></html>