Otonality and utonality: Difference between revisions
Wikispaces>genewardsmith **Imported revision 303823170 - Original comment: ** |
Wikispaces>hstraub **Imported revision 570739099 - 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: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2015-12-24 13:11:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>570739099</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|flat]] | <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"><span style="text-align: right; | ||
display: block;">[[OtonalityとUtonality|日本語]]</span> | |||
[[toc|flat]] | |||
=Introduction= | =Introduction= | ||
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=Essentially tempered chords= | =Essentially tempered chords= | ||
This kind of reduction can also be used to analyze [[Dyadic chord|essentially tempered chords]]. Consider for example the [[sinbadmic tetrad]], which is the 1001/1000-tempering of 1-11/10-13/10-10/7. The reduction of the JI version of this chord is {25, 35, 77, 91}; discarding the lowest number, 25, and reducing again gives {5, 11, 13}. This tells us the chord can be analyzed as an otonbal 1-11/10-13/10 chord plus a 10/7 addition requiring essential tempering.</pre></div> | This kind of reduction can also be used to analyze [[Dyadic chord|essentially tempered chords]]. Consider for example the [[sinbadmic tetrad]], which is the 1001/1000-tempering of 1-11/10-13/10-10/7. The reduction of the JI version of this chord is {25, 35, 77, 91}; discarding the lowest number, 25, and reducing again gives {5, 11, 13}. This tells us the chord can be analyzed as an otonbal 1-11/10-13/10 chord plus a 10/7 addition requiring essential tempering.ed </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>Otonality and utonality</title></head><body><!-- ws:start:WikiTextTocRule:18:&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:18 --><!-- ws:start:WikiTextTocRule:19: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Precise definitions">Precise definitions</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Properties of types of chords">Properties of types of chords</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Ambitonal chord theorem">Ambitonal chord theorem</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Essentially tempered chords">Essentially tempered chords</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | <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>Otonality and utonality</title></head><body><span style="text-align: right; | ||
display: block;"><a class="wiki_link" href="/Otonality%E3%81%A8Utonality">日本語</a></span><br /> | |||
<!-- ws:start:WikiTextTocRule:18:&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:18 --><!-- ws:start:WikiTextTocRule:19: --><a href="#Introduction">Introduction</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Precise definitions">Precise definitions</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Properties of types of chords">Properties of types of chords</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --> | <a href="#Ambitonal chord theorem">Ambitonal chord theorem</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --> | <a href="#Scales">Scales</a><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Essentially tempered chords">Essentially tempered chords</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --> | |||
<!-- ws:end:WikiTextTocRule:28 --><br /> | <!-- ws:end:WikiTextTocRule:28 --><br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Essentially tempered chords"></a><!-- ws:end:WikiTextHeadingRule:16 -->Essentially tempered chords</h1> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="Essentially tempered chords"></a><!-- ws:end:WikiTextHeadingRule:16 -->Essentially tempered chords</h1> | ||
This kind of reduction can also be used to analyze <a class="wiki_link" href="/Dyadic%20chord">essentially tempered chords</a>. Consider for example the <a class="wiki_link" href="/sinbadmic%20tetrad">sinbadmic tetrad</a>, which is the 1001/1000-tempering of 1-11/10-13/10-10/7. The reduction of the JI version of this chord is {25, 35, 77, 91}; discarding the lowest number, 25, and reducing again gives {5, 11, 13}. This tells us the chord can be analyzed as an otonbal 1-11/10-13/10 chord plus a 10/7 addition requiring essential tempering.</body></html></pre></div> | This kind of reduction can also be used to analyze <a class="wiki_link" href="/Dyadic%20chord">essentially tempered chords</a>. Consider for example the <a class="wiki_link" href="/sinbadmic%20tetrad">sinbadmic tetrad</a>, which is the 1001/1000-tempering of 1-11/10-13/10-10/7. The reduction of the JI version of this chord is {25, 35, 77, 91}; discarding the lowest number, 25, and reducing again gives {5, 11, 13}. This tells us the chord can be analyzed as an otonbal 1-11/10-13/10 chord plus a 10/7 addition requiring essential tempering.ed</body></html></pre></div> | ||