7/4: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 164972615 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 164985767 - 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:xenwolf|xenwolf]] and made on <tt>2010-09-23 16:25:44 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>164985767</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> | ||
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Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents -- about 22 cents flat of 7:4, and so less effective as a consonance. | Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents -- about 22 cents flat of 7:4, and so less effective as a consonance. | ||
See: [[http://en.wikipedia.org/wiki/Septimal_meantone_temperament|Septimal Meantone Temperament on Wikipedia]].</pre></div> | See: [[http://en.wikipedia.org/wiki/Septimal_meantone_temperament|Septimal Meantone Temperament on Wikipedia]]. | ||
=Approximations= | |||
Edos containing good approximations of the interval 7:4 are: | |||
* [[5edo]] (8.8259 ct), [[26edo]] (0.40486 ct), ...</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>7_4</title></head><body>Frequency ratio 7:4, measuring approximately 968.8259064691249 cents, has been given the name &quot;harmonic seventh.&quot; It represents the interval between the 4th and 7th harmonics in the <a class="wiki_link" href="/OverToneSeries">overtone series</a>. It is also called a &quot;septimal subminor seventh&quot; -- the word &quot;septimal&quot; referring to the presence of a 7 as the highest prime in the ratio, and the word &quot;subminor&quot; referring to the harmonic seventh's narrowness compared with a traditional minor seventh (such as <a class="wiki_link" href="/9_5">9:5</a> or <a class="wiki_link" href="/16_9">16:9</a>, <a class="wiki_link" href="/12edo">12edo</a>'s 1000-cent interval, or a minor seventh found in a meantone system).<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>7_4</title></head><body>Frequency ratio 7:4, measuring approximately 968.8259064691249 cents, has been given the name &quot;harmonic seventh.&quot; It represents the interval between the 4th and 7th harmonics in the <a class="wiki_link" href="/OverToneSeries">overtone series</a>. It is also called a &quot;septimal subminor seventh&quot; -- the word &quot;septimal&quot; referring to the presence of a 7 as the highest prime in the ratio, and the word &quot;subminor&quot; referring to the harmonic seventh's narrowness compared with a traditional minor seventh (such as <a class="wiki_link" href="/9_5">9:5</a> or <a class="wiki_link" href="/16_9">16:9</a>, <a class="wiki_link" href="/12edo">12edo</a>'s 1000-cent interval, or a minor seventh found in a meantone system).<br /> | ||
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Note that a good approximation of the harmonic seventh is not available in every meantone system. In <a class="wiki_link" href="/19edo">19edo</a> (aurally identical, more or less, to 1/3-comma meantone), the &quot;augmented sixth&quot; is an interval of 947 cents -- about 22 cents flat of 7:4, and so less effective as a consonance.<br /> | Note that a good approximation of the harmonic seventh is not available in every meantone system. In <a class="wiki_link" href="/19edo">19edo</a> (aurally identical, more or less, to 1/3-comma meantone), the &quot;augmented sixth&quot; is an interval of 947 cents -- about 22 cents flat of 7:4, and so less effective as a consonance.<br /> | ||
<br /> | <br /> | ||
See: <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_meantone_temperament" rel="nofollow">Septimal Meantone Temperament on Wikipedia</a>.</body></html></pre></div> | See: <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_meantone_temperament" rel="nofollow">Septimal Meantone Temperament on Wikipedia</a>.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Approximations"></a><!-- ws:end:WikiTextHeadingRule:4 -->Approximations</h1> | |||
Edos containing good approximations of the interval 7:4 are:<br /> | |||
<ul><li><a class="wiki_link" href="/5edo">5edo</a> (8.8259 ct), <a class="wiki_link" href="/26edo">26edo</a> (0.40486 ct), ...</li></ul></body></html></pre></div> | |||