Augmented family: Difference between revisions

Revision as of 00:51, 12 January 2011

IMPORTED REVISION FROM WIKISPACES

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This revision was by author genewardsmith and made on 2011-01-12 00:51:34 UTC.

The original revision id was 192638858.

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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

The 5-limit parent comma for the augmented family is 128/125, the diesis. Its [[monzo]] is |7 0 -3>, and flipping that yields <<3 0 -7|| for the [[wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator]] can be taken as a fifth or a semitone, and [[12edo]], with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. 

==Seven limit children==
The second comma of the [[Normal lists|normal comma list]] defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, and hemiaug 245/243. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.

==August==
Commas: 36/35, 128/125

[[POTE tuning|POTE generator]]: 696.011

Map: [<3 0 7 -1|, <0 1 0 2|]
Wedgie: <<3 0 6 -7 1 14||
EDOs: [[9edo|9]], [[12edo|12]], [[69edo|69]], [[81edo|81]]
Badness: 0.0265

==Augene==
Commas: 64/63, 126/125

[[POTE tuning|POTE generator]]: 709.257

Map: [<3 0 7 18|, <0 1 0 -2|]
Wedgie: <<3 0 -6 -7 -18 -14||
EDOs: [[12edo|12]], [[27edo|27]], [[66edo|66]]
Badness: 0.0248

==Hexe==
Commas: 50/49, 128/125

[[POTE tuning|POTE generator]]: 710.963

Map: [<6 0 14 17|, <0 1 0 0|]
Wedgie: <<6 0 0 -14 -17 0||
EDOs: [[6edo|6]], [[12edo|12]], [[54edo|54]]
Badness: 0.0577

==Hemiaug==
Commas: 128/125, 245/243

[[POTE tuning|POTE generator]]: 445.118

Map: [<3 1 7 -1|, <0 2 0 5|]
Wedgie: <<6 0 15 -14 7 35||
EDOs: [[24edo|24]], [[27edo|27]]
Badness: 0.0705

Original HTML content:

<html><head><title>Augmented family</title></head><body>The 5-limit parent comma for the augmented family is 128/125, the diesis. Its <a class="wiki_link" href="/monzo">monzo</a> is |7 0 -3&gt;, and flipping that yields &lt;&lt;3 0 -7|| for the <a class="wiki_link" href="/wedgie">wedgie</a>. Hence the period is 1/3 octave, and this is what is used for a major third. The <a class="wiki_link" href="/generator">generator</a> can be taken as a fifth or a semitone, and <a class="wiki_link" href="/12edo">12edo</a>, with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. <br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h2>
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which 7-limit family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, and hemiaug 245/243. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-August"></a><!-- ws:end:WikiTextHeadingRule:2 -->August</h2>
Commas: 36/35, 128/125<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 696.011<br />
<br />
Map: [&lt;3 0 7 -1|, &lt;0 1 0 2|]<br />
Wedgie: &lt;&lt;3 0 6 -7 1 14||<br />
EDOs: <a class="wiki_link" href="/9edo">9</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/69edo">69</a>, <a class="wiki_link" href="/81edo">81</a><br />
Badness: 0.0265<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-Augene"></a><!-- ws:end:WikiTextHeadingRule:4 -->Augene</h2>
Commas: 64/63, 126/125<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 709.257<br />
<br />
Map: [&lt;3 0 7 18|, &lt;0 1 0 -2|]<br />
Wedgie: &lt;&lt;3 0 -6 -7 -18 -14||<br />
EDOs: <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/27edo">27</a>, <a class="wiki_link" href="/66edo">66</a><br />
Badness: 0.0248<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-Hexe"></a><!-- ws:end:WikiTextHeadingRule:6 -->Hexe</h2>
Commas: 50/49, 128/125<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 710.963<br />
<br />
Map: [&lt;6 0 14 17|, &lt;0 1 0 0|]<br />
Wedgie: &lt;&lt;6 0 0 -14 -17 0||<br />
EDOs: <a class="wiki_link" href="/6edo">6</a>, <a class="wiki_link" href="/12edo">12</a>, <a class="wiki_link" href="/54edo">54</a><br />
Badness: 0.0577<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-Hemiaug"></a><!-- ws:end:WikiTextHeadingRule:8 -->Hemiaug</h2>
Commas: 128/125, 245/243<br />
<br />
<a class="wiki_link" href="/POTE%20tuning">POTE generator</a>: 445.118<br />
<br />
Map: [&lt;3 1 7 -1|, &lt;0 2 0 5|]<br />
Wedgie: &lt;&lt;6 0 15 -14 7 35||<br />
EDOs: <a class="wiki_link" href="/24edo">24</a>, <a class="wiki_link" href="/27edo">27</a><br />
Badness: 0.0705</body></html>

@@ 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>2011-01-12 00:35:04 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-01-12 00:51:34 UTC</tt>.<br>
-: The original revision id was <tt>192637528</tt>.<br>
+: The original revision id was <tt>192638858</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 29: / Line 29: @@
 Wedgie: &lt;&lt;3 0 -6 -7 -18 -14||
 EDOs: [[12edo|12]], [[27edo|27]], [[66edo|66]]
-Badness: 0.0248</pre></div>
+Badness: 0.0248
+==Hexe==
+Commas: 50/49, 128/125
+[[POTE tuning|POTE generator]]: 710.963
+Map: [&lt;6 0 14 17|, &lt;0 1 0 0|]
+Wedgie: &lt;&lt;6 0 0 -14 -17 0||
+EDOs: [[6edo|6]], [[12edo|12]], [[54edo|54]]
+Badness: 0.0577
+==Hemiaug==
+Commas: 128/125, 245/243
+[[POTE tuning|POTE generator]]: 445.118
+Map: [&lt;3 1 7 -1|, &lt;0 2 0 5|]
+Wedgie: &lt;&lt;6 0 15 -14 7 35||
+EDOs: [[24edo|24]], [[27edo|27]]
+Badness: 0.0705</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;Augmented family&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 5-limit parent comma for the augmented family is 128/125, the diesis. Its &lt;a class="wiki_link" href="/monzo"&gt;monzo&lt;/a&gt; is |7 0 -3&amp;gt;, and flipping that yields &amp;lt;&amp;lt;3 0 -7|| for the &lt;a class="wiki_link" href="/wedgie"&gt;wedgie&lt;/a&gt;. Hence the period is 1/3 octave, and this is what is used for a major third. The &lt;a class="wiki_link" href="/generator"&gt;generator&lt;/a&gt; can be taken as a fifth or a semitone, and &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, with its excellent fifth, is an obvious tuning for 5-limit augmented, though a sharper fifth might be preferred to go with the sharp third. &lt;br /&gt;
@@ Line 54: / Line 74: @@
 Wedgie: &amp;lt;&amp;lt;3 0 -6 -7 -18 -14||&lt;br /&gt;
 EDOs: &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;, &lt;a class="wiki_link" href="/66edo"&gt;66&lt;/a&gt;&lt;br /&gt;
-Badness: 0.0248&lt;/body&gt;&lt;/html&gt;</pre></div>
+Badness: 0.0248&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Hexe"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Hexe&lt;/h2&gt;
+Commas: 50/49, 128/125&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 710.963&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;6 0 14 17|, &amp;lt;0 1 0 0|]&lt;br /&gt;
+Wedgie: &amp;lt;&amp;lt;6 0 0 -14 -17 0||&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/6edo"&gt;6&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12&lt;/a&gt;, &lt;a class="wiki_link" href="/54edo"&gt;54&lt;/a&gt;&lt;br /&gt;
+Badness: 0.0577&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x-Hemiaug"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Hemiaug&lt;/h2&gt;
+Commas: 128/125, 245/243&lt;br /&gt;
+&lt;br /&gt;
+&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 445.118&lt;br /&gt;
+&lt;br /&gt;
+Map: [&amp;lt;3 1 7 -1|, &amp;lt;0 2 0 5|]&lt;br /&gt;
+Wedgie: &amp;lt;&amp;lt;6 0 15 -14 7 35||&lt;br /&gt;
+EDOs: &lt;a class="wiki_link" href="/24edo"&gt;24&lt;/a&gt;, &lt;a class="wiki_link" href="/27edo"&gt;27&lt;/a&gt;&lt;br /&gt;
+Badness: 0.0705&lt;/body&gt;&lt;/html&gt;</pre></div>

Augmented family: Difference between revisions

Revision as of 00:51, 12 January 2011

IMPORTED REVISION FROM WIKISPACES

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