16edo: Difference between revisions
Wikispaces>hstraub **Imported revision 441449938 - Original comment: That link, despite the name "Ron Sword", had nothing to do with microtones** |
Wikispaces>hstraub **Imported revision 445231992 - 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:hstraub|hstraub]] and made on <tt>2013- | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2013-08-17 10:47:31 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>445231992</tt>.<br> | ||
: The revision comment was: <tt> | : 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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
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**Mavila** | **Mavila** | ||
[5]: 5 2 5 2 2 | || [5]: || 5 2 5 2 2 || || | ||
[7]: 3 2 2 3 2 2 2 | || [7]: || 3 2 2 3 2 2 2 || [[media type="file" key="MavilaAntidiatonic16edo.mp3"]] || | ||
[9]: 1 2 2 2 1 2 2 2 2 | || [9]: || 1 2 2 2 1 2 2 2 2 || [[media type="file" key="MavilaSuperdiatonic16edo.mp3"]] || | ||
**Diminished** | **Diminished** | ||
[8]: 1 3 1 3 1 3 1 3 | [8]: 1 3 1 3 1 3 1 3 | ||
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[[http://micro.soonlabel.com/simultaneous-tunings/20130607_thin_ice_christiane.mp3|Thin Ice]] by [[Chris Vaisvil]] [[http://chrisvaisvil.com/thin-ice-for-alto-female-choir-harp-and-percussion-in-adaptive-ji-16-edo-and-8-edo/|information on the composition]]</pre></div> | [[http://micro.soonlabel.com/simultaneous-tunings/20130607_thin_ice_christiane.mp3|Thin Ice]] by [[Chris Vaisvil]] [[http://chrisvaisvil.com/thin-ice-for-alto-female-choir-harp-and-percussion-in-adaptive-ji-16-edo-and-8-edo/|information on the composition]]</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>16edo</title></head><body><!-- ws:start:WikiTextTocRule: | <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>16edo</title></head><body><!-- ws:start:WikiTextTocRule:16:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><a href="#Hexadecaphonic Octave Theory">Hexadecaphonic Octave Theory</a><!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --> | <a href="#Hexadecaphonic Notation:">Hexadecaphonic Notation:</a><!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --> | <a href="#Rank two temperaments">Rank two temperaments</a><!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --> | <a href="#Armodue Theory (4-line staff)">Armodue Theory (4-line staff)</a><!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --> | <a href="#Books/Literature">Books/Literature</a><!-- ws:end:WikiTextTocRule:22 --><!-- ws:start:WikiTextTocRule:23: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:23 --><!-- ws:start:WikiTextTocRule:24: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:24 --><hr /> | ||
<strong>16-EDO</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into sixteen narrow chromatic semitones each of 75 <a class="wiki_link" href="/cent">cent</a>s exactly. It is not especially good at representing most low-integer musical intervals, but it has a <a class="wiki_link" href="/7_4">7/4</a> which is six cents sharp, and a <a class="wiki_link" href="/5_4">5/4</a> which is eleven cents flat. Four steps of it gives the 300 cent minor third interval, the same of that 12-EDO, giving it four diminished seventh chords exactly like those of <a class="wiki_link" href="/12edo">12-EDO</a>, and a diminished triad on each scale step.<br /> | <strong>16-EDO</strong> is the <a class="wiki_link" href="/equal%20division%20of%20the%20octave">equal division of the octave</a> into sixteen narrow chromatic semitones each of 75 <a class="wiki_link" href="/cent">cent</a>s exactly. It is not especially good at representing most low-integer musical intervals, but it has a <a class="wiki_link" href="/7_4">7/4</a> which is six cents sharp, and a <a class="wiki_link" href="/5_4">5/4</a> which is eleven cents flat. Four steps of it gives the 300 cent minor third interval, the same of that 12-EDO, giving it four diminished seventh chords exactly like those of <a class="wiki_link" href="/12edo">12-EDO</a>, and a diminished triad on each scale step.<br /> | ||
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*based on treating 16-EDO as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible.<br /> | *based on treating 16-EDO as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="Hexadecaphonic Octave Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Hexadecaphonic Octave Theory</h1> | ||
<br /> | <br /> | ||
The scale supports the diminished temperament with its 1/4 octave period, though its generator size, equal to its step size of 75 cents, is smaller than ideal. Its very flat 3/2 of 675 cents supports Mavila temperament, where the mapping of major and minor is reversed. The temperament could be popular for its 150-cent &quot;3/4-tone&quot; equal division of the traditional 300-cent minor third.<br /> | The scale supports the diminished temperament with its 1/4 octave period, though its generator size, equal to its step size of 75 cents, is smaller than ideal. Its very flat 3/2 of 675 cents supports Mavila temperament, where the mapping of major and minor is reversed. The temperament could be popular for its 150-cent &quot;3/4-tone&quot; equal division of the traditional 300-cent minor third.<br /> | ||
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Another interesting approach can include two interwoven <a class="wiki_link" href="/8edo">8-EDO</a> scales (narrow 12/11 neutral seconds). There are two major seventh intervals, a harmonic seventh at step 13\16, a 7/4 ratio approximation, sharp by 6.174 cents, followed by an undecimal 11/6 ratio or neutral seventh (which is mapped in 16's <strong>Mavila</strong> as a major seventh).<br /> | Another interesting approach can include two interwoven <a class="wiki_link" href="/8edo">8-EDO</a> scales (narrow 12/11 neutral seconds). There are two major seventh intervals, a harmonic seventh at step 13\16, a 7/4 ratio approximation, sharp by 6.174 cents, followed by an undecimal 11/6 ratio or neutral seventh (which is mapped in 16's <strong>Mavila</strong> as a major seventh).<br /> | ||
If we take the 300-cent minor third as an approximation of the harmonic 19th (<a class="wiki_link" href="/19_16">19/16</a>, 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 (pictured below).<br /> | If we take the 300-cent minor third as an approximation of the harmonic 19th (<a class="wiki_link" href="/19_16">19/16</a>, 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 (pictured below).<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:563:&lt;img src=&quot;http://www.ronsword.com/161928%20copy.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 179px; width: 316px;&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: 179px; width: 316px;" /><!-- ws:end:WikiTextRemoteImageRule:563 --><br /> | ||
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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;. 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 /> | 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;. 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: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc1"><a name="Hexadecaphonic Notation:"></a><!-- ws:end:WikiTextHeadingRule:4 -->Hexadecaphonic Notation:</h1> | ||
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16-EDO notation can be easy utilizing Goldsmith's Circle of keys, Nominals, and respective Notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon<br /> | 16-EDO notation can be easy utilizing Goldsmith's Circle of keys, Nominals, and respective Notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon<br /> | ||
additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO.<br /> | additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO.<br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:564:&lt;img src=&quot;http://ronsword.com/DSgoldsmith_piece.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 342px; width: 1008px;&quot; /&gt; --><img src="http://ronsword.com/DSgoldsmith_piece.jpg" alt="external image DSgoldsmith_piece.jpg" title="external image DSgoldsmith_piece.jpg" style="height: 342px; width: 1008px;" /><!-- ws:end:WikiTextRemoteImageRule:564 --><br /> | ||
<hr /> | <hr /> | ||
In 16-EDO diatonic scales are dissonant and &quot;shimmery&quot; because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth / poor 3/2 approximation. Scales like the Harmonic Minor scale in 16-EDO require 4 step sizes.<br /> | In 16-EDO diatonic scales are dissonant and &quot;shimmery&quot; because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth / poor 3/2 approximation. Scales like the Harmonic Minor scale in 16-EDO require 4 step sizes.<br /> | ||
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unison vector from Fokker periodicity blocks.Only in 16-EDO, that unison vector is 135:128, instead of 81:80.&quot;<br /> | unison vector from Fokker periodicity blocks.Only in 16-EDO, that unison vector is 135:128, instead of 81:80.&quot;<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="Rank two temperaments"></a><!-- ws:end:WikiTextHeadingRule:6 -->Rank two temperaments</h1> | ||
<a class="wiki_link" href="/List%20of%2016et%20rank%20two%20temperaments%20by%20badness">List of 16et rank two temperaments by badness</a><br /> | <a class="wiki_link" href="/List%20of%2016et%20rank%20two%20temperaments%20by%20badness">List of 16et rank two temperaments by badness</a><br /> | ||
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<strong>Mavila</strong><br /> | <strong>Mavila</strong><br /> | ||
[5]: 5 2 5 2 2<br /> | |||
[7]: 3 2 2 3 2 2 2<br /> | |||
[9]: 1 2 2 2 1 2 2 2 2<br /> | <table class="wiki_table"> | ||
<tr> | |||
<td>[5]:<br /> | |||
</td> | |||
<td>5 2 5 2 2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>[7]:<br /> | |||
</td> | |||
<td>3 2 2 3 2 2 2<br /> | |||
</td> | |||
<td><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/MavilaAntidiatonic16edo.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;MavilaAntidiatonic16edo.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FMavilaAntidiatonic16edo.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:0 --><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>[9]:<br /> | |||
</td> | |||
<td>1 2 2 2 1 2 2 2 2<br /> | |||
</td> | |||
<td><!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/MavilaSuperdiatonic16edo.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;MavilaSuperdiatonic16edo.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FMavilaSuperdiatonic16edo.mp3?file_extension=mp3&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:1 --><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<strong>Diminished</strong><br /> | <strong>Diminished</strong><br /> | ||
[8]: 1 3 1 3 1 3 1 3<br /> | [8]: 1 3 1 3 1 3 1 3<br /> | ||
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135/128 (the difference between 16/15 and 9/8) is tempered out....&quot;<br /> | 135/128 (the difference between 16/15 and 9/8) is tempered out....&quot;<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc3"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:8 -->Commas</h1> | ||
16 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes <a class="wiki_link" href="/val">val</a> &lt; 16 25 37 45 55 59 |.)<br /> | 16 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes <a class="wiki_link" href="/val">val</a> &lt; 16 25 37 45 55 59 |.)<br /> | ||
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<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc4"><a name="Armodue Theory (4-line staff)"></a><!-- ws:end:WikiTextHeadingRule:10 --><strong>Armodue Theory (4-line staff)</strong></h1> | ||
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<a class="wiki_link_ext" href="http://www.armodue.com/ricerche.htm" rel="nofollow">Armodue</a>: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions.<br /> | <a class="wiki_link_ext" href="http://www.armodue.com/ricerche.htm" rel="nofollow">Armodue</a>: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions.<br /> | ||
Translations of parts of the Armodue pages can be found <a class="wiki_link" href="/Armodue">here</a> on this wiki..<br /> | Translations of parts of the Armodue pages can be found <a class="wiki_link" href="/Armodue">here</a> on this wiki..<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc5"><a name="Books/Literature"></a><!-- ws:end:WikiTextHeadingRule:12 -->Books/Literature</h1> | ||
<br /> | <br /> | ||
Sword, Ronald. &quot;Thesaurus of Melodic Patterns and Intervals for 16-Tones&quot; IAAA Press, USA. First Ed: August, 2011<br /> | Sword, Ronald. &quot;Thesaurus of Melodic Patterns and Intervals for 16-Tones&quot; IAAA Press, USA. First Ed: August, 2011<br /> | ||
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Sword, Ronald. &quot;Esadekaphonic Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: April, 2009. (semi-diminished fourth tuning)<br /> | Sword, Ronald. &quot;Esadekaphonic Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: April, 2009. (semi-diminished fourth tuning)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc6"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:14 -->Compositions</h1> | ||
<a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=660895&amp;songID=12370649&amp;showPlayer=true" rel="nofollow" target="_blank">Prenestyna Highway</a> by <a class="wiki_link_ext" href="http://fiale.tk" rel="nofollow" target="_blank">Fabrizio Fulvio Fausto Fiale</a><br /> | <a class="wiki_link_ext" href="http://www.soundclick.com/bands/page_songInfo.cfm?bandID=660895&amp;songID=12370649&amp;showPlayer=true" rel="nofollow" target="_blank">Prenestyna Highway</a> by <a class="wiki_link_ext" href="http://fiale.tk" rel="nofollow" target="_blank">Fabrizio Fulvio Fausto Fiale</a><br /> | ||
<a class="wiki_link_ext" href="http://lastsacrament.bandcamp.com/album/enantiodromia" rel="nofollow" target="_blank">Enantiodromia (album)</a> by Last Sacrament<br /> | <a class="wiki_link_ext" href="http://lastsacrament.bandcamp.com/album/enantiodromia" rel="nofollow" target="_blank">Enantiodromia (album)</a> by Last Sacrament<br /> | ||