Prodigy chords
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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. 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.
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 /> Equal divisions with prodigy chords include 12, 29, 31, 41, 43, 72, 74, 84, 103, 175, 197, 247c, 3129bcde, 391bcde and 463bcde.<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 9- and 11-marvel chords. 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.</body></html>