16edo: Difference between revisions
Wikispaces>hstraub **Imported revision 161348181 - Original comment: Separate pages for Armodue theory** |
Wikispaces>guest **Imported revision 162575909 - 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> | ||
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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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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16-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most low-integer musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step. | 16-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most low-integer musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step. | ||
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 & 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. | |||
=Hexadecaphonic Octave Theory= | =Hexadecaphonic Octave Theory= | ||
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16-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most low-integer musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.<br /> | 16-edo equal temperament is the division of the octave into sixteen narrow chromatic semitones each of 75 cents exactly. It is not especially good at representing most low-integer musical intervals, but it has a 7/4 which is six cents sharp, and a 5/4 which is eleven cents flat. Four steps of it gives the 300 cent minor third interval identical to that of 12-edo, giving it four diminished seventh chords exactly like those of 12-edo, and a diminished triad on each scale step.<br /> | ||
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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 &quot;narrow fifth&quot;. Example on Goldsmith board: <!-- ws:start:WikiTextRemoteImageRule:22:&lt;img src=&quot;http://www.ronsword.com/161928%20copy.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 92px; width: 158px;&quot; /&gt; --><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;" /><!-- ws:end:WikiTextRemoteImageRule:22 -->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.<br /> | |||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Hexadecaphonic Octave Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Hexadecaphonic Octave Theory</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Hexadecaphonic Octave Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Hexadecaphonic Octave Theory</h1> | ||