Essential tempering comma: Difference between revisions
Wikispaces>genewardsmith **Imported revision 287490140 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 338009346 - 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>2012-05-21 14:40:00 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>338009346</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">Suppose S is a set of JI intervals i including 1 and 2 with 1 | <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">Suppose S is a set of JI intervals i including 1 and 2 with 1 ≤ i ≤ 2 such | ||
that if i is in S, so is 2/i. S is intended to represent a set of pitch classes | that if i is in S, so is 2/i. S is intended to represent a set of pitch classes | ||
defining "consonance". A JI interval c is an essential tempering comma for S if: | defining "consonance". A JI interval c is an essential tempering comma for S if: | ||
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members of S | members of S | ||
2. There are three intervals i, j, and k in S such that c = | 2. There are three intervals i, j, and k in S such that c = ij/k | ||
For various odd limit diamonds, we get the following essential tempering commas: | For various odd limit diamonds, we get the following essential tempering commas: | ||
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We don't need to use the full q-limit diamond; from Diamond([1,3,5,7,9,11,15]) | We don't need to use the full q-limit diamond; from Diamond([1,3,5,7,9,11,15]) | ||
we get: 540/539, 441/440, 385/384, 3388/3375, 243/242 | we get: 540/539, 441/440, 385/384, 3388/3375, 243/242</pre></div> | ||
</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>Essential tempering commas</title></head><body>Suppose S is a set of JI intervals i including 1 and 2 with 1 | <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>Essential tempering commas</title></head><body>Suppose S is a set of JI intervals i including 1 and 2 with 1 ≤ i ≤ 2 such<br /> | ||
that if i is in S, so is 2/i. S is intended to represent a set of pitch classes<br /> | that if i is in S, so is 2/i. S is intended to represent a set of pitch classes<br /> | ||
defining &quot;consonance&quot;. A JI interval c is an essential tempering comma for S if:<br /> | defining &quot;consonance&quot;. A JI interval c is an essential tempering comma for S if:<br /> | ||
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members of S<br /> | members of S<br /> | ||
<br /> | <br /> | ||
2. There are three intervals i, j, and k in S such that c = | 2. There are three intervals i, j, and k in S such that c = ij/k<br /> | ||
<br /> | <br /> | ||
For various odd limit diamonds, we get the following essential tempering commas:<br /> | For various odd limit diamonds, we get the following essential tempering commas:<br /> | ||