17/15: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 283156728 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 342111626 - 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:genewardsmith|genewardsmith]] and made on <tt>2012-06-02 21:35:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>342111626</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">In [[17-limit]] [[Just Intonation]], 17/15 is the "septendecimal whole tone" measuring about 216.687¢. It is the [[mediant]] between [[9_8|9/8]] and [[8_7|8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[11edo]]'s second degree, measuring approximately 218.182¢, is close in size 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo. | <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">In [[17-limit]] [[Just Intonation]], 17/15 is the "septendecimal whole tone" measuring about 216.687¢. It is the [[mediant]] between [[9_8|9/8]] and [[8_7|8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[11edo]]'s second degree, measuring approximately 218.182¢, is close in size 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo. | ||
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard.) | |||
See: [[Gallery of Just Intervals]]</pre></div> | See: [[Gallery of Just Intervals]]</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>17_15</title></head><body>In <a class="wiki_link" href="/17-limit">17-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 17/15 is the &quot;septendecimal whole tone&quot; measuring about 216.687¢. It is the <a class="wiki_link" href="/mediant">mediant</a> between <a class="wiki_link" href="/9_8">9/8</a> and <a class="wiki_link" href="/8_7">8/7</a>, as it is (9+8)/(8+7). It is found in the <a class="wiki_link" href="/OverToneSeries">harmonic series</a> between the 17th and 15th overtones. <a class="wiki_link" href="/11edo">11edo</a>'s second degree, measuring approximately 218.182¢, is close in size 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.<br /> | <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>17_15</title></head><body>In <a class="wiki_link" href="/17-limit">17-limit</a> <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a>, 17/15 is the &quot;septendecimal whole tone&quot; measuring about 216.687¢. It is the <a class="wiki_link" href="/mediant">mediant</a> between <a class="wiki_link" href="/9_8">9/8</a> and <a class="wiki_link" href="/8_7">8/7</a>, as it is (9+8)/(8+7). It is found in the <a class="wiki_link" href="/OverToneSeries">harmonic series</a> between the 17th and 15th overtones. <a class="wiki_link" href="/11edo">11edo</a>'s second degree, measuring approximately 218.182¢, is close in size 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.<br /> | ||
<br /> | |||
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard.)<br /> | |||
<br /> | <br /> | ||
See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | See: <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | ||