Vals and tuning space: Difference between revisions
Wikispaces>genewardsmith **Imported revision 250543814 - Original comment: ** |
Wikispaces>mbattaglia1 **Imported revision 250543972 - 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:mbattaglia1|mbattaglia1]] and made on <tt>2011-09-03 20:01:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>250543972</tt>.<br> | ||
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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.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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(Caveat: a more formal definition for a val is that it maps JI intervals onto a certain number of equally tempered "steps," which may or may not reflect an EDO in its intuitive sense at all, but rather steps of a much larger generator. This definition, while being perhaps less intuitive, is more applicable in some of the deeper implications of vals in regular temperament theory, which are not dealt with in this abstract.) | (Caveat: a more formal definition for a val is that it maps JI intervals onto a certain number of equally tempered "steps," which may or may not reflect an EDO in its intuitive sense at all, but rather steps of a much larger generator. This definition, while being perhaps less intuitive, is more applicable in some of the deeper implications of vals in regular temperament theory, which are not dealt with in this abstract.) | ||
See also: [[Monzos and Interval Space]], [[Patent val]] | |||
=Definition= | =Definition= | ||
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[[math]] | [[math]] | ||
which is approximately <31.000 30.916 31.009 30.990|. The standard Euclidean norm would then be the square root of the sum of squares of this vector, which is approximately sqrt(3838.694), or 61.957. To use the RMS we divide that by sqrt(4)=2, giving 30.976 for the TE norm. Note that the TE norm for this val is approximately 31. | which is approximately <31.000 30.916 31.009 30.990|. The standard Euclidean norm would then be the square root of the sum of squares of this vector, which is approximately sqrt(3838.694), or 61.957. To use the RMS we divide that by sqrt(4)=2, giving 30.976 for the TE norm. Note that the TE norm for this val is approximately 31.</pre></div> | ||
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<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>Vals and Tuning Space</title></head><body><!-- ws:start:WikiTextTocRule:12:&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:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Abstract">Abstract</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Definition">Definition</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Vals and Monzos">Vals and Monzos</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Example">Example</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <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>Vals and Tuning Space</title></head><body><!-- ws:start:WikiTextTocRule:12:&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:12 --><!-- ws:start:WikiTextTocRule:13: --><a href="#Abstract">Abstract</a><!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --> | <a href="#Definition">Definition</a><!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --> | <a href="#Vals and Monzos">Vals and Monzos</a><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --> | <a href="#Example">Example</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | ||
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(Caveat: a more formal definition for a val is that it maps JI intervals onto a certain number of equally tempered &quot;steps,&quot; which may or may not reflect an EDO in its intuitive sense at all, but rather steps of a much larger generator. This definition, while being perhaps less intuitive, is more applicable in some of the deeper implications of vals in regular temperament theory, which are not dealt with in this abstract.)<br /> | (Caveat: a more formal definition for a val is that it maps JI intervals onto a certain number of equally tempered &quot;steps,&quot; which may or may not reflect an EDO in its intuitive sense at all, but rather steps of a much larger generator. This definition, while being perhaps less intuitive, is more applicable in some of the deeper implications of vals in regular temperament theory, which are not dealt with in this abstract.)<br /> | ||
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See also: <a class="wiki_link" href="/Monzos%20and%20Interval%20Space">Monzos and Interval Space</a>, <a class="wiki_link" href="/Patent%20val">Patent val</a><br /> | |||
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