Breedsmic temperaments: Difference between revisions

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>2012-01-~~17 21~~:54:51 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-27 07:43:39 UTC</tt>.<br>

: The original revision id was <tt>~~293077668~~</tt>.<br>

: The original revision id was <tt>295856398</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 247:

EDOs: 72, 311, 694, 1005c, 1699cd

Badness: 0.0209

=Newt=

Commas: 2401/2400, 33554432/33480783

POTE generator: ~49/40 = 351.113

Map: [<1 1 19 11|, <0 2 -57 -28|]

Wedgie: <<2 -57 -28 -95 -50 95||

EDOs: 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bc

Badness: 0.0419

==11-limit==

Commas: 2401/2400, 3025/3024, 19712/19683

POTE generator: ~49/40 = 351.115

Map: [<1 1 19 11 -10|, <0 2 -57 -28 46|]

EDOs: 41, 188, 229, 270, 581, 851, 1121, 1972, 3093b, 4214b

Badness: 0.0195

==13-limit==

Commas: 2080/2079, 2401/2400, 3025/3024, 4096/4095

POTE genertaor: ~49/40 = 351.117

Map: [<1 1 19 11 -10 -20|, <0 2 -57 -28 46 81|]

EDOs: 41, 229, 270, 581, 851, 2283b, 3134b

Badness: 0.0138

</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>Breedsmic temperaments</title></head><body><a href="#Hemififths">Hemififths</a> | <a href="#Tertiaseptal">Tertiaseptal</a> | <a href="#Harry">Harry</a> | <a href="#Quasiorwell">Quasiorwell</a> | <a href="#Decoid">Decoid</a> | <a href="#Neominor">Neominor</a> | <a href="#Emmthird">Emmthird</a> | <a href="#Quinmite">Quinmite</a> | <a href="#Unthirds">Unthirds</a>

<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><a href="#Hemififths">Hemififths</a> | <a href="#Tertiaseptal">Tertiaseptal</a> | <a href="#Harry">Harry</a> | <a href="#Quasiorwell">Quasiorwell</a> | <a href="#Decoid">Decoid</a> | <a href="#Neominor">Neominor</a> | <a href="#Emmthird">Emmthird</a> | <a href="#Quinmite">Quinmite</a> | <a href="#Unthirds">Unthirds</a> | <a href="#Newt">Newt</a>

<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 />

Line 491:

Line 521:

Map: [&lt;1 29 33 25 25 99|, &lt;0 -42 -47 -34 -33 -146|]<br />

EDOs: 72, 311, 694, 1005c, 1699cd<br />

Badness: 0.0209</body></html></pre></div>

Badness: 0.0209<br />

<br />

<h1 id="toc23"><a name="Newt"></a>Newt</h1>

Commas: 2401/2400, 33554432/33480783<br />

<br />

POTE generator: ~49/40 = 351.113<br />

<br />

Map: [&lt;1 1 19 11|, &lt;0 2 -57 -28|]<br />

Wedgie: &lt;&lt;2 -57 -28 -95 -50 95||<br />

EDOs: 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bc<br />

Badness: 0.0419<br />

<br />

<h2 id="toc24"><a name="Newt-11-limit"></a>11-limit</h2>

Commas: 2401/2400, 3025/3024, 19712/19683<br />

<br />

POTE generator: ~49/40 = 351.115<br />

<br />

Map: [&lt;1 1 19 11 -10|, &lt;0 2 -57 -28 46|]<br />

EDOs: 41, 188, 229, 270, 581, 851, 1121, 1972, 3093b, 4214b<br />

Badness: 0.0195<br />

<br />

<h2 id="toc25"><a name="Newt-13-limit"></a>13-limit</h2>

Commas: 2080/2079, 2401/2400, 3025/3024, 4096/4095<br />

<br />

POTE genertaor: ~49/40 = 351.117<br />

<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 />

Badness: 0.0138</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>2012-01-17 21:54:51 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-27 07:43:39 UTC</tt>.<br>
-: The original revision id was <tt>293077668</tt>.<br>
+: The original revision id was <tt>295856398</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 247: / Line 247: @@
 EDOs: 72, 311, 694, 1005c, 1699cd
 Badness: 0.0209
+=Newt=
+Commas: 2401/2400, 33554432/33480783
+POTE generator: ~49/40 = 351.113
+Map: [&lt;1 1 19 11|, &lt;0 2 -57 -28|]
+Wedgie: &lt;&lt;2 -57 -28 -95 -50 95||
+EDOs: 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bc
+Badness: 0.0419
+==11-limit==
+Commas: 2401/2400, 3025/3024, 19712/19683
+POTE generator: ~49/40 = 351.115
+Map: [&lt;1 1 19 11 -10|, &lt;0 2 -57 -28 46|]
+EDOs: 41, 188, 229, 270, 581, 851, 1121, 1972, 3093b, 4214b
+Badness: 0.0195
+==13-limit==
+Commas: 2080/2079, 2401/2400, 3025/3024, 4096/4095
+POTE genertaor: ~49/40 = 351.117
+Map: [&lt;1 1 19 11 -10 -20|, &lt;0 2 -57 -28 46 81|]
+EDOs: 41, 229, 270, 581, 851, 2283b, 3134b
+Badness: 0.0138
 </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;Breedsmic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:46:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;a href="#Hemififths"&gt;Hemififths&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt; | &lt;a href="#Tertiaseptal"&gt;Tertiaseptal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt; | &lt;a href="#Harry"&gt;Harry&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Quasiorwell"&gt;Quasiorwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Decoid"&gt;Decoid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Neominor"&gt;Neominor&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt; | &lt;a href="#Emmthird"&gt;Emmthird&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt; | &lt;a href="#Quinmite"&gt;Quinmite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt; | &lt;a href="#Unthirds"&gt;Unthirds&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;
+<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;Breedsmic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:52:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;a href="#Hemififths"&gt;Hemififths&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt; | &lt;a href="#Tertiaseptal"&gt;Tertiaseptal&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;!-- ws:end:WikiTextTocRule:58 --&gt;&lt;!-- ws:start:WikiTextTocRule:59: --&gt; | &lt;a href="#Harry"&gt;Harry&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:59 --&gt;&lt;!-- ws:start:WikiTextTocRule:60: --&gt;&lt;!-- ws:end:WikiTextTocRule:60 --&gt;&lt;!-- ws:start:WikiTextTocRule:61: --&gt;&lt;!-- ws:end:WikiTextTocRule:61 --&gt;&lt;!-- ws:start:WikiTextTocRule:62: --&gt; | &lt;a href="#Quasiorwell"&gt;Quasiorwell&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:62 --&gt;&lt;!-- ws:start:WikiTextTocRule:63: --&gt;&lt;!-- ws:end:WikiTextTocRule:63 --&gt;&lt;!-- ws:start:WikiTextTocRule:64: --&gt;&lt;!-- ws:end:WikiTextTocRule:64 --&gt;&lt;!-- ws:start:WikiTextTocRule:65: --&gt; | &lt;a href="#Decoid"&gt;Decoid&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:65 --&gt;&lt;!-- ws:start:WikiTextTocRule:66: --&gt;&lt;!-- ws:end:WikiTextTocRule:66 --&gt;&lt;!-- ws:start:WikiTextTocRule:67: --&gt;&lt;!-- ws:end:WikiTextTocRule:67 --&gt;&lt;!-- ws:start:WikiTextTocRule:68: --&gt; | &lt;a href="#Neominor"&gt;Neominor&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:68 --&gt;&lt;!-- ws:start:WikiTextTocRule:69: --&gt;&lt;!-- ws:end:WikiTextTocRule:69 --&gt;&lt;!-- ws:start:WikiTextTocRule:70: --&gt;&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;!-- ws:start:WikiTextTocRule:71: --&gt; | &lt;a href="#Emmthird"&gt;Emmthird&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:71 --&gt;&lt;!-- ws:start:WikiTextTocRule:72: --&gt; | &lt;a href="#Quinmite"&gt;Quinmite&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:72 --&gt;&lt;!-- ws:start:WikiTextTocRule:73: --&gt; | &lt;a href="#Unthirds"&gt;Unthirds&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:73 --&gt;&lt;!-- ws:start:WikiTextTocRule:74: --&gt;&lt;!-- ws:end:WikiTextTocRule:74 --&gt;&lt;!-- ws:start:WikiTextTocRule:75: --&gt;&lt;!-- ws:end:WikiTextTocRule:75 --&gt;&lt;!-- ws:start:WikiTextTocRule:76: --&gt; | &lt;a href="#Newt"&gt;Newt&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:76 --&gt;&lt;!-- ws:start:WikiTextTocRule:77: --&gt;&lt;!-- ws:end:WikiTextTocRule:77 --&gt;&lt;!-- ws:start:WikiTextTocRule:78: --&gt;&lt;!-- ws:end:WikiTextTocRule:78 --&gt;&lt;!-- ws:start:WikiTextTocRule:79: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:70 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:79 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&amp;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.&lt;br /&gt;
@@ Line 491: / Line 521: @@
 Map: [&amp;lt;1 29 33 25 25 99|, &amp;lt;0 -42 -47 -34 -33 -146|]&lt;br /&gt;
 EDOs: 72, 311, 694, 1005c, 1699cd&lt;br /&gt;
-Badness: 0.0209&lt;/body&gt;&lt;/html&gt;</pre></div>
+Badness: 0.0209&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc23"&gt;&lt;a name="Newt"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Newt&lt;/h1&gt;
+Commas: 2401/2400, 33554432/33480783&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~49/40 = 351.113&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 1 19 11|, &amp;lt;0 2 -57 -28|]&lt;br /&gt;
+Wedgie: &amp;lt;&amp;lt;2 -57 -28 -95 -50 95||&lt;br /&gt;
+EDOs: 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bc&lt;br /&gt;
+Badness: 0.0419&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Newt-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;11-limit&lt;/h2&gt;
+Commas: 2401/2400, 3025/3024, 19712/19683&lt;br /&gt;
+&lt;br /&gt;
+POTE generator: ~49/40 = 351.115&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 1 19 11 -10|, &amp;lt;0 2 -57 -28 46|]&lt;br /&gt;
+EDOs: 41, 188, 229, 270, 581, 851, 1121, 1972, 3093b, 4214b&lt;br /&gt;
+Badness: 0.0195&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Newt-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;13-limit&lt;/h2&gt;
+Commas: 2080/2079, 2401/2400, 3025/3024, 4096/4095&lt;br /&gt;
+&lt;br /&gt;
+POTE genertaor: ~49/40 = 351.117&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;1 1 19 11 -10 -20|, &amp;lt;0 2 -57 -28 46 81|]&lt;br /&gt;
+EDOs: 41, 229, 270, 581, 851, 2283b, 3134b&lt;br /&gt;
+Badness: 0.0138&lt;/body&gt;&lt;/html&gt;</pre></div>