10ed5: Difference between revisions

Half of [[20ed5]] (obviously). But it has important characteristics of its own:

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.

Furthermore, 5ed5 is the simplest hyperpyth tuning, analogous to [[5edo]] and [[4edt]] in their own spheres. So, while the approximation of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals. I think this is a relatively important tuning as well, it would certainly do well on a harmonica. Though it has a step size of around 273 cents, strange melodies may still be crafted around it, however the main feature is likely to be its variety of chords and harmonies. This would be the perfect tuning for blues from outer space (perhaps from a gas giant somewhere).

Adding octaves, strangely enough, relates this tuning to [[53edo]].

<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;10ed5&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="x10 equal divisions of the 5th harmonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;10 equal divisions of the 5th harmonic&lt;/h1&gt;

Half of &lt;a class="wiki_link" href="/20ed5"&gt;20ed5&lt;/a&gt; (obviously). But it has important characteristics of its own:&lt;br /&gt;

Furthermore, 5ed5 is the simplest hyperpyth tuning, analogous to &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt; and &lt;a class="wiki_link" href="/4edt"&gt;4edt&lt;/a&gt; in their own spheres. So, while the approximation of 9/5, 17/5 and 21/5 are quite far off, these are still categorically important intervals. I think this is a relatively important tuning as well, it would certainly do well on a harmonica. Though it has a step size of around 273 cents, strange melodies may still be crafted around it, however the main feature is likely to be its variety of chords and harmonies. This would be the perfect tuning for blues from outer space (perhaps from a gas giant somewhere).&lt;br /&gt;

Adding octaves, strangely enough, relates this tuning to &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;.&lt;br /&gt;

1: 278.631 cents 13/11&lt;br /&gt;

6: 1671.788 cents 13/5&lt;br /&gt;

7: 1950.420 cents&lt;br /&gt;

8: 2229.051 cents &amp;quot;17/5&amp;quot;&lt;br /&gt;

9: 2507.682 cents 21/5&lt;br /&gt;

10: 5/1&lt;/body&gt;&lt;/html&gt;</pre></div>