Breedsmic temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 300719476 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 300877698 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2012-02- | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-12 02:35:43 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>300877698</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> | ||
| Line 293: | Line 293: | ||
EDOs: 41, 229, 270, 581, 851, 2283b, 3134b | EDOs: 41, 229, 270, 581, 851, 2283b, 3134b | ||
Badness: 0.0138 | Badness: 0.0138 | ||
=Amicable= | |||
Commas: 2401/2400, 1600000/1594323 | |||
POTE generator: ~21/20 = 84.880 | |||
Map: [<1 3 6 5|, <0 -20 -52 -31|] | |||
Wedgie: <<20 52 31 36 -7 -74|| | |||
EDOs: 99, 212, 311, 410, 1131, 1541b | |||
Badness: 0.0455 | |||
| Line 299: | Line 311: | ||
</pre></div> | </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>Breedsmic temperaments</title></head><body><!-- ws:start:WikiTextTocRule: | <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>Breedsmic temperaments</title></head><body><!-- ws:start:WikiTextTocRule:58:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><a href="#Hemififths">Hemififths</a><!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --> | <a href="#Semihemi">Semihemi</a><!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --> | <a href="#Tertiaseptal">Tertiaseptal</a><!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --> | <a href="#Harry">Harry</a><!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextTocRule:68: --><!-- ws:end:WikiTextTocRule:68 --><!-- ws:start:WikiTextTocRule:69: --><!-- ws:end:WikiTextTocRule:69 --><!-- ws:start:WikiTextTocRule:70: --> | <a href="#Quasiorwell">Quasiorwell</a><!-- ws:end:WikiTextTocRule:70 --><!-- ws:start:WikiTextTocRule:71: --><!-- ws:end:WikiTextTocRule:71 --><!-- ws:start:WikiTextTocRule:72: --><!-- ws:end:WikiTextTocRule:72 --><!-- ws:start:WikiTextTocRule:73: --> | <a href="#Decoid">Decoid</a><!-- ws:end:WikiTextTocRule:73 --><!-- ws:start:WikiTextTocRule:74: --><!-- ws:end:WikiTextTocRule:74 --><!-- ws:start:WikiTextTocRule:75: --><!-- ws:end:WikiTextTocRule:75 --><!-- ws:start:WikiTextTocRule:76: --> | <a href="#Neominor">Neominor</a><!-- ws:end:WikiTextTocRule:76 --><!-- ws:start:WikiTextTocRule:77: --><!-- ws:end:WikiTextTocRule:77 --><!-- ws:start:WikiTextTocRule:78: --><!-- ws:end:WikiTextTocRule:78 --><!-- ws:start:WikiTextTocRule:79: --> | <a href="#Emmthird">Emmthird</a><!-- ws:end:WikiTextTocRule:79 --><!-- ws:start:WikiTextTocRule:80: --> | <a href="#Quinmite">Quinmite</a><!-- ws:end:WikiTextTocRule:80 --><!-- ws:start:WikiTextTocRule:81: --> | <a href="#Unthirds">Unthirds</a><!-- ws:end:WikiTextTocRule:81 --><!-- ws:start:WikiTextTocRule:82: --><!-- ws:end:WikiTextTocRule:82 --><!-- ws:start:WikiTextTocRule:83: --><!-- ws:end:WikiTextTocRule:83 --><!-- ws:start:WikiTextTocRule:84: --> | <a href="#Newt">Newt</a><!-- ws:end:WikiTextTocRule:84 --><!-- ws:start:WikiTextTocRule:85: --><!-- ws:end:WikiTextTocRule:85 --><!-- ws:start:WikiTextTocRule:86: --><!-- ws:end:WikiTextTocRule:86 --><!-- ws:start:WikiTextTocRule:87: --> | <a href="#Amicable">Amicable</a><!-- ws:end:WikiTextTocRule:87 --><!-- ws:start:WikiTextTocRule:88: --> | ||
< | <!-- ws:end:WikiTextTocRule:88 --><br /> | ||
<br /> | <br /> | ||
Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<br /> | Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<br /> | ||
| Line 585: | Line 597: | ||
Map: [&lt;1 1 19 11 -10 -20|, &lt;0 2 -57 -28 46 81|]<br /> | Map: [&lt;1 1 19 11 -10 -20|, &lt;0 2 -57 -28 46 81|]<br /> | ||
EDOs: 41, 229, 270, 581, 851, 2283b, 3134b<br /> | EDOs: 41, 229, 270, 581, 851, 2283b, 3134b<br /> | ||
Badness: 0.0138</body></html></pre></div> | Badness: 0.0138<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:56:&lt;h1&gt; --><h1 id="toc28"><a name="Amicable"></a><!-- ws:end:WikiTextHeadingRule:56 -->Amicable</h1> | |||
Commas: 2401/2400, 1600000/1594323<br /> | |||
<br /> | |||
POTE generator: ~21/20 = 84.880<br /> | |||
<br /> | |||
Map: [&lt;1 3 6 5|, &lt;0 -20 -52 -31|]<br /> | |||
Wedgie: &lt;&lt;20 52 31 36 -7 -74||<br /> | |||
EDOs: 99, 212, 311, 410, 1131, 1541b<br /> | |||
Badness: 0.0455</body></html></pre></div> | |||