|
|
| (14 intermediate revisions by 6 users not shown) |
| Line 1: |
Line 1: |
| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A '''prodigy chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in [[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, with a palindromic tetrad: |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | * 1–5/4–7/5–16/9 with steps 5/4, 9/8, 14/11, 9/8; |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-12-17 20:12:52 UTC</tt>.<br>
| |
| : The original revision id was <tt>287106236</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 [[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.
| | 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 its inverse |
| | * 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 == |
| [[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.
| | {{Main| Miracle chords }} |
|
| |
|
| 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.
| | 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, and ten essentially miracle chords. |
|
| |
|
| EDOs supporting prodigy/miracle include 31, 41, 72, 216c, 247c, 319bcde, 391bcde, 463bcde.</pre></div>
| | 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. |
| <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 />
| | EDOs supporting prodigy/miracle include {{EDOs| 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde }}. |
| <br />
| | |
| Equal divisions with prodigy chords include 12, 29, 31, 41, 43, 72, 74, 84, 103, 175, 197, 247c, 3129bcde, 391bcde and 463bcde.<br />
| | == See also == |
| <br />
| | * [[Chords of miracle]] |
| <!-- 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>
| | |
| <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 />
| | [[Category:11-odd-limit chords]] |
| <br />
| | [[Category:Essentially tempered chords]] |
| 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 /> | | [[Category:Marvel]] |
| <br />
| | [[Category:Prodigy]] |
| EDOs supporting prodigy/miracle include 31, 41, 72, 216c, 247c, 319bcde, 391bcde, 463bcde.</body></html></pre></div> | | [[Category:Miracle]] |