Augmented family: Difference between revisions
Wikispaces>genewardsmith **Imported revision 277338212 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 289128299 - Original comment: ** |
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<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> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-02 17:16:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>289128299</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> | ||
<h4>Original Wikitext content:</h4> | <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">[[toc]] | <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">[[toc|flat]] | ||
The 5-limit parent comma for the **augmented family** is 128/125, the [[128_125|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. | The 5-limit parent comma for the **augmented family** is 128/125, the [[128_125|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, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones. | 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, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones. | ||
=August= | |||
[[Comma]]s: 36/35, 128/125 | [[Comma]]s: 36/35, 128/125 | ||
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[[Badness]]: 0.0265 | [[Badness]]: 0.0265 | ||
==11-limit== | |||
Commas: 36/35, 45/44, 56/55 | Commas: 36/35, 45/44, 56/55 | ||
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Badness: 0.0202 | Badness: 0.0202 | ||
==13-limit== | |||
Commas: 27/26, 36/35, 45/44, 56/55 | Commas: 27/26, 36/35, 45/44, 56/55 | ||
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Badness: 0.0184 | Badness: 0.0184 | ||
=Augene= | |||
Commas: 64/63, 126/125 | Commas: 64/63, 126/125 | ||
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Badness: 0.0248 | Badness: 0.0248 | ||
==11-limit== | |||
Commas: 56/55, 64/63, 100/99 | Commas: 56/55, 64/63, 100/99 | ||
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[[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]] by [[http://soundcloud.com/cityoftheasleep/sad-like-winter-trees|Igliashon Jones]] | [[http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3|Sad Like Winter Leaves]] by [[http://soundcloud.com/cityoftheasleep/sad-like-winter-trees|Igliashon Jones]] | ||
==Hexe | =Inflated= | ||
Commas: 28/27, 128/125 | |||
POTE generator: ~3/2 = 722.719 | |||
Map: [<3 0 7 -6|, <0 1 0 3|] | |||
Wedgie: <<3 0 9 -7 6 21|| | |||
EDOs: 15, 48bc, 63bc, 78bc | |||
Badness: 0.0547 | |||
==11-limit== | |||
Commas: 28/27, 55/54, 128/125 | |||
POTE generator: ~3/2 = 722.663 | |||
Map: [<3 0 7 -6|, <0 1 0 3|] | |||
EDOs: 15, 48bce, 63bce, 78bce | |||
Badness: 0.0312 | |||
=Hexe= | |||
Commas: 50/49, 128/125 | Commas: 50/49, 128/125 | ||
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Badness: 0.0577 | Badness: 0.0577 | ||
=Hemiaug= | |||
Commas: 128/125, 245/243 | Commas: 128/125, 245/243 | ||
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Badness: 0.0705 | Badness: 0.0705 | ||
=Triforce= | |||
Commas: 49/48, 128/125 | Commas: 49/48, 128/125 | ||
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[[image:triforce9.jpg]] | [[image:triforce9.jpg]] | ||
==11-limit== | |||
Commas: 56/55, 77/75, 128/125 | Commas: 56/55, 77/75, 128/125 | ||
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Badness: 0.0262 | Badness: 0.0262 | ||
==13-limit== | |||
Commas: 49/48, 56/55, 66/65, 77/75 | Commas: 49/48, 56/55, 66/65, 77/75 | ||
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[[triphi|Triforce(9) with L:s = phi]]</pre></div> | [[triphi|Triforce(9) with L:s = phi]]</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>Augmented family</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>Augmented family</title></head><body><!-- ws:start:WikiTextTocRule:26:&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:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#Seven limit children">Seven limit children</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <a href="#August">August</a><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --> | <a href="#Augene">Augene</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#Inflated">Inflated</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Hexe">Hexe</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Hemiaug">Hemiaug</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | <a href="#Triforce">Triforce</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | ||
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<!-- ws:end:WikiTextTocRule: | The 5-limit parent comma for the <strong>augmented family</strong> is 128/125, the <a class="wiki_link" href="/128_125">diesis</a>. 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 <a class="wiki_link" href="/5-limit">5-limit</a> augmented, though a sharper fifth might be preferred to go with the sharp third. <br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt; | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Seven limit children"></a><!-- ws:end:WikiTextHeadingRule:0 -->Seven limit children</h1> | ||
The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.<br /> | The second comma of the <a class="wiki_link" href="/Normal%20lists">normal comma list</a> defines which <a class="wiki_link" href="/7-limit">7-limit</a> family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt; | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="August"></a><!-- ws:end:WikiTextHeadingRule:2 -->August</h1> | ||
<a class="wiki_link" href="/Comma">Comma</a>s: 36/35, 128/125<br /> | <a class="wiki_link" href="/Comma">Comma</a>s: 36/35, 128/125<br /> | ||
<br /> | <br /> | ||
| Line 140: | Line 150: | ||
<a class="wiki_link" href="/Badness">Badness</a>: 0.0265<br /> | <a class="wiki_link" href="/Badness">Badness</a>: 0.0265<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt; | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="August-11-limit"></a><!-- ws:end:WikiTextHeadingRule:4 -->11-limit</h2> | ||
Commas: 36/35, 45/44, 56/55<br /> | Commas: 36/35, 45/44, 56/55<br /> | ||
<br /> | <br /> | ||
| Line 149: | Line 159: | ||
Badness: 0.0202<br /> | Badness: 0.0202<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt; | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="August-13-limit"></a><!-- ws:end:WikiTextHeadingRule:6 -->13-limit</h2> | ||
Commas: 27/26, 36/35, 45/44, 56/55<br /> | Commas: 27/26, 36/35, 45/44, 56/55<br /> | ||
<br /> | <br /> | ||
| Line 158: | Line 168: | ||
Badness: 0.0184<br /> | Badness: 0.0184<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt; | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Augene"></a><!-- ws:end:WikiTextHeadingRule:8 -->Augene</h1> | ||
Commas: 64/63, 126/125<br /> | Commas: 64/63, 126/125<br /> | ||
<br /> | <br /> | ||
| Line 168: | Line 178: | ||
Badness: 0.0248<br /> | Badness: 0.0248<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt; | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Augene-11-limit"></a><!-- ws:end:WikiTextHeadingRule:10 -->11-limit</h2> | ||
Commas: 56/55, 64/63, 100/99<br /> | Commas: 56/55, 64/63, 100/99<br /> | ||
<br /> | <br /> | ||
| Line 179: | Line 189: | ||
<a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow">Sad Like Winter Leaves</a> by <a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/sad-like-winter-trees" rel="nofollow">Igliashon Jones</a><br /> | <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3" rel="nofollow">Sad Like Winter Leaves</a> by <a class="wiki_link_ext" href="http://soundcloud.com/cityoftheasleep/sad-like-winter-trees" rel="nofollow">Igliashon Jones</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id=" | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Inflated"></a><!-- ws:end:WikiTextHeadingRule:12 -->Inflated</h1> | ||
Commas: 28/27, 128/125<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 722.719<br /> | |||
<br /> | |||
Map: [&lt;3 0 7 -6|, &lt;0 1 0 3|]<br /> | |||
Wedgie: &lt;&lt;3 0 9 -7 6 21||<br /> | |||
EDOs: 15, 48bc, 63bc, 78bc<br /> | |||
Badness: 0.0547<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Inflated-11-limit"></a><!-- ws:end:WikiTextHeadingRule:14 -->11-limit</h2> | |||
Commas: 28/27, 55/54, 128/125<br /> | |||
<br /> | |||
POTE generator: ~3/2 = 722.663<br /> | |||
<br /> | |||
Map: [&lt;3 0 7 -6|, &lt;0 1 0 3|]<br /> | |||
EDOs: 15, 48bce, 63bce, 78bce<br /> | |||
Badness: 0.0312<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Hexe"></a><!-- ws:end:WikiTextHeadingRule:16 -->Hexe</h1> | |||
Commas: 50/49, 128/125<br /> | Commas: 50/49, 128/125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0577<br /> | Badness: 0.0577<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h1&gt; --><h1 id="toc9"><a name="Hemiaug"></a><!-- ws:end:WikiTextHeadingRule:18 -->Hemiaug</h1> | ||
Commas: 128/125, 245/243<br /> | Commas: 128/125, 245/243<br /> | ||
<br /> | <br /> | ||
| Line 199: | Line 228: | ||
Badness: 0.0705<br /> | Badness: 0.0705<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Triforce"></a><!-- ws:end:WikiTextHeadingRule:20 -->Triforce</h1> | ||
Commas: 49/48, 128/125<br /> | Commas: 49/48, 128/125<br /> | ||
<br /> | <br /> | ||
| Line 209: | Line 238: | ||
Badness: 0.0202<br /> | Badness: 0.0202<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:41:&lt;img src=&quot;/file/view/triforce9.jpg/271381934/triforce9.jpg&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/triforce9.jpg/271381934/triforce9.jpg" alt="triforce9.jpg" title="triforce9.jpg" /><!-- ws:end:WikiTextLocalImageRule:41 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Triforce-11-limit"></a><!-- ws:end:WikiTextHeadingRule:22 -->11-limit</h2> | ||
Commas: 56/55, 77/75, 128/125<br /> | Commas: 56/55, 77/75, 128/125<br /> | ||
<br /> | <br /> | ||
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Badness: 0.0262<br /> | Badness: 0.0262<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Triforce-13-limit"></a><!-- ws:end:WikiTextHeadingRule:24 -->13-limit</h2> | ||
Commas: 49/48, 56/55, 66/65, 77/75<br /> | Commas: 49/48, 56/55, 66/65, 77/75<br /> | ||
<br /> | <br /> | ||