7/4: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 166037489 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 231889092 - 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-05-25 19:02:01 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>231889092</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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=Approximations= | =Approximations= | ||
Edos containing good approximations of the interval 7:4 are: | Edos containing good approximations of the interval 7:4 are: | ||
* [EDO; Delta; Multiples] | |||
* [ | |||
* [[11edo]], 12.9923 ct, [[22edo]] | * [[11edo]], 12.9923 ct, [[22edo]] | ||
* [[5edo]], -8.8259 ct, [[10edo]], [[15edo]], [[20edo]], [[25edo]] | |||
* [[16edo]], 6.1741 ct | * [[16edo]], 6.1741 ct | ||
* [[69edo]], 5.0871 ct | |||
* [[21edo]], 2.6026 ct | * [[21edo]], 2.6026 ct | ||
* [[ | * [[36edo]], -2.1592 ct, [[72edo]] | ||
* [[89edo]], 1.9606 ct | |||
* [[47edo]], 1.3868 ct, [[94edo]] | |||
* [[31edo]], 1.0839 ct | * [[31edo]], 1.0839 ct | ||
* [[ | * [[73edo]], 1.0371 ct | ||
* [[ | * [[88edo]], -0.6441 ct | ||
* [[57edo]], 0. | * [[26edo]], 0.40486 ct, [[78edo]] | ||
* [[57edo]], -0.40485 ct | |||
* [[83edo]], 0.1512 ct, [[166edo]] | * [[83edo]], -0.1512 ct, [[166edo]]</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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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Approximations"></a><!-- ws:end:WikiTextHeadingRule:4 -->Approximations</h1> | <!-- 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 /> | Edos containing good approximations of the interval 7:4 are:<br /> | ||
<ul><li> | <ul><li>[EDO; Delta; Multiples]</li><li><a class="wiki_link" href="/11edo">11edo</a>, 12.9923 ct, <a class="wiki_link" href="/22edo">22edo</a></li><li><a class="wiki_link" href="/5edo">5edo</a>, -8.8259 ct, <a class="wiki_link" href="/10edo">10edo</a>, <a class="wiki_link" href="/15edo">15edo</a>, <a class="wiki_link" href="/20edo">20edo</a>, <a class="wiki_link" href="/25edo">25edo</a></li><li><a class="wiki_link" href="/16edo">16edo</a>, 6.1741 ct</li><li><a class="wiki_link" href="/69edo">69edo</a>, 5.0871 ct</li><li><a class="wiki_link" href="/21edo">21edo</a>, 2.6026 ct</li><li><a class="wiki_link" href="/36edo">36edo</a>, -2.1592 ct, <a class="wiki_link" href="/72edo">72edo</a></li><li><a class="wiki_link" href="/89edo">89edo</a>, 1.9606 ct</li><li><a class="wiki_link" href="/47edo">47edo</a>, 1.3868 ct, <a class="wiki_link" href="/94edo">94edo</a></li><li><a class="wiki_link" href="/31edo">31edo</a>, 1.0839 ct</li><li><a class="wiki_link" href="/73edo">73edo</a>, 1.0371 ct</li><li><a class="wiki_link" href="/88edo">88edo</a>, -0.6441 ct</li><li><a class="wiki_link" href="/26edo">26edo</a>, 0.40486 ct, <a class="wiki_link" href="/78edo">78edo</a></li><li><a class="wiki_link" href="/57edo">57edo</a>, -0.40485 ct</li><li><a class="wiki_link" href="/83edo">83edo</a>, -0.1512 ct, <a class="wiki_link" href="/166edo">166edo</a></li></ul></body></html></pre></div> | ||