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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox ET}} |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-11-01 15:16:55 UTC</tt>.<br>
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| : The original revision id was <tt>270764670</tt>.<br>
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| : The revision comment was: <tt></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>
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| <h4>Original Wikitext content:</h4>
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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;white-space: pre-wrap ! important" class="old-revision-html">=10 equal divisions of the 5th harmonic=
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| Well, as [[17ed5|hyperpyth]] is based on the chord 5:9:13:17:(21):25 there ought to be a companion system which emphasizes ratios of 7 and 11. 11/5 is ~30 cents away from the square root of five, so barring a relatively large and complex temperament with 60-80 cent intervals, the square root of five is an adequate approximation. 10ed5 approximates the 7/5 slightly sharp (merging it with 11/8) such that the 77/25 - an important orgone structural element, is within 3 cents of just. This is no coincidence.
| | In general, 10ed5 is simply a smashing tuning. The relatively large small steps, about the size of a minor third or an orwell generator, actually work for melodies, and it's harmonies while strange have no lack of impact. It can be used such that the fifth harmonic is equivalent, but of course, doesn't have to. |
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| Though it has a step size of around 273 cents it has a weird musical sound.</pre></div>
| | It is especially important as a structural framework for the [[5.7.11.13 subgroup]]. |
| <h4>Original HTML content:</h4>
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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>10ed5</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x10 equal divisions of the 5th harmonic"></a><!-- ws:end:WikiTextHeadingRule:0 -->10 equal divisions of the 5th harmonic</h1>
| | == Harmonics == |
| <br />
| | {{Harmonics in equal |
| Well, as <a class="wiki_link" href="/17ed5">hyperpyth</a> is based on the chord 5:9:13:17:(21):25 there ought to be a companion system which emphasizes ratios of 7 and 11. 11/5 is ~30 cents away from the square root of five, so barring a relatively large and complex temperament with 60-80 cent intervals, the square root of five is an adequate approximation. 10ed5 approximates the 7/5 slightly sharp (merging it with 11/8) such that the 77/25 - an important orgone structural element, is within 3 cents of just. This is no coincidence.<br />
| | | steps = 10 |
| <br />
| | | num = 5 |
| Though it has a step size of around 273 cents it has a weird musical sound.</body></html></pre></div>
| | | denom = 1 |
| | }} |
| | {{Harmonics in equal |
| | | steps = 10 |
| | | num = 5 |
| | | denom = 1 |
| | | start = 12 |
| | | collapsed = 1 |
| | }} |
| | |
| | == Intervals == |
| | {| class="wikitable" |
| | |+ |
| | !Degree |
| | !Cents |
| | !5.7.11.13 intervals |
| | |- |
| | |0 |
| | |0.000 |
| | |1/1 |
| | |- |
| | |1 |
| | |278.631 |
| | |13/11, 55/49 |
| | |- |
| | |2 |
| | |557.263 |
| | |7/5 |
| | |- |
| | |3 |
| | |835.894 |
| | |11/7 |
| | |- |
| | |4 |
| | |1114.525 |
| | |13/7, 25/13 |
| | |- |
| | |5 |
| | |1393.157 |
| | |11/5, 25/11 |
| | |- |
| | |6 |
| | |1671.788 |
| | |13/5, 35/13 |
| | |- |
| | |7 |
| | |1950.420 |
| | |35/11 |
| | |- |
| | |8 |
| | |2229.051 |
| | |49/13 |
| | |- |
| | |9 |
| | |2507.682 |
| | |49/11 |
| | |- |
| | |10 |
| | |2786.314 |
| | |5/1 |
| | |} |
| | |
| | == Subsets and supersets == |
| | Half of [[20ed5]]. |
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| | As 5ed5 is the simplest [[hyperpyth]] tuning (analogous to [[5edo]] and [[4edt]] in their own spheres) this, its double, can be compared structurally to [[10edo]]. While its approximations of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals. |
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| | Octaves can be added by dividing the step in three to get [[13edo]] with octaves 7 cents sharp. If octaves are instead made just, prime 7 becomes very flat, as well as prime 5 to a lesser extent. Alternatively, the step can be divided in ten to get [[43edo]]. |
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| | == Music == |
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| | [http://www.youtube.com/watch?v=tjD7Es05zuI Weird Blues] -- Kosmorsky |
| | [[Category:5th_harmonic]] |