16edo: Difference between revisions

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If we take the 300-cent minor third as an approximation of the harmonic 19th (19/16, approximately 297.5 cents), that adds another overtone which can combine with the approximation of the harmonic seventh to form a 16:19:28 triad. The interval between the 28th &amp; 19th overtones, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's "narrow fifth". Example on Goldsmith board: [[image:http://www.ronsword.com/161928%20copy.jpg width="158" height="92"]]Another voicing for this chord is 14:16:19, which features 19:14 as the outer interval (528.7 cents just, 525.0 cents in 16edo). A perhaps more consonant open voicing is 7:16:19.

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In 16-edo diatonic scales are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth / poor 3/2 approximation. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales an alternative temperament families like the "Anti-Diatonic" Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be more interesting and suitable:

=Hexadecaphonic Notation:=  

=**Armodue theory**=  

If we take the 300-cent minor third as an approximation of the harmonic 19th (19/16, approximately 297.5 cents), that adds another overtone which can combine with the approximation of the harmonic seventh to form a 16:19:28 triad. The interval between the 28th &amp;amp; 19th overtones, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's &amp;quot;narrow fifth&amp;quot;. Example on Goldsmith board: &lt;!-- ws:start:WikiTextRemoteImageRule:21:&amp;lt;img src=&amp;quot;http://www.ronsword.com/161928%20copy.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 92px; width: 158px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://www.ronsword.com/161928%20copy.jpg" alt="external image 161928%20copy.jpg" title="external image 161928%20copy.jpg" style="height: 92px; width: 158px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:21 --&gt;Another voicing for this chord is 14:16:19, which features 19:14 as the outer interval (528.7 cents just, 525.0 cents in 16edo). A perhaps more consonant open voicing is 7:16:19.&lt;br /&gt;

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In 16-edo diatonic scales are dissonant because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth / poor 3/2 approximation. The septimal semi diminished fourth can be more desirable. Perhaps using Moment of Symmetry Scales an alternative temperament families like the &amp;quot;Anti-Diatonic&amp;quot; Mavila (which reverses step sizes of diatonic), Diminished, Happy, Rice, Grumpy, Mosh, Magic, Lemba, Cynder, and Decatonic can be more interesting and suitable:&lt;br /&gt;

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&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Armodue theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;strong&gt;Armodue theory&lt;/strong&gt;&lt;/h1&gt;