16edo: Difference between revisions
Wikispaces>guest **Imported revision 152834133 - Original comment: ** |
Wikispaces>hstraub **Imported revision 152851969 - 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: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-07-16 04:07:46 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>152851969</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : 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> | ||
<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"> | <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">[[toc|flat]] | ||
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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 just 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 just 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. | ||
=Hexadecaphonic Octave Theory= | |||
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 "blown fifth" of 675 cents means it works as a mavila temperament tuning. For a 16-edo version of Indonesian music, four small steps of 225 cents and one large one of 300 cents gives a [[MOSScales|MOS]] version of the Slendro scale, and five small steps of 150 cents with two large ones of 225 steps a Pelog-like MOS. The temperament could be popular for its easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones. The 25 cent difference in the steps can have a similar effect the [[scales of Olympos have]] with buried enharmonic genera. | 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 "blown fifth" of 675 cents means it works as a mavila temperament tuning. For a 16-edo version of Indonesian music, four small steps of 225 cents and one large one of 300 cents gives a [[MOSScales|MOS]] version of the Slendro scale, and five small steps of 150 cents with two large ones of 225 steps a Pelog-like MOS. The temperament could be popular for its easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones. The 25 cent difference in the steps can have a similar effect the [[scales of Olympos have]] with buried enharmonic genera. | ||
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=External theory links= | |||
[[http://www.armodue.com/ricerche.htm|Armodue]]: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions - translation, anyone? | [[http://www.armodue.com/ricerche.htm|Armodue]]: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions - translation, anyone? | ||
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Sword, Ronald. "Esadekaphonic Scales for Guitar." IAAA Press, UK-USA. First Ed: April, 2009. (semi-diminished fourth tuning) | Sword, Ronald. "Esadekaphonic Scales for Guitar." IAAA Press, UK-USA. First Ed: April, 2009. (semi-diminished fourth tuning) | ||
=Compositions= | |||
[[http://www.io.com/%7Ehmiller/midi/16tet.mid|Etude in 16-tone equal tuning]] by Herman Miller | [[http://www.io.com/%7Ehmiller/midi/16tet.mid|Etude in 16-tone equal tuning]] by Herman Miller | ||
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[[@http://www.ronsword.com/sounds/ronsword_miracle528_part3.mp3|16-tet Magic Drone]] by Ron Sword</pre></div> | [[@http://www.ronsword.com/sounds/ronsword_miracle528_part3.mp3|16-tet Magic Drone]] by Ron Sword</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: | <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:6:&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:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#Hexadecaphonic Octave Theory">Hexadecaphonic Octave Theory</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#External theory links">External theory links</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Compositions">Compositions</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | ||
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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 just 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 just 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 /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Hexadecaphonic Octave Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->Hexadecaphonic Octave Theory</h1> | ||
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 &quot;blown fifth&quot; of 675 cents means it works as a mavila temperament tuning. For a 16-edo version of Indonesian music, four small steps of 225 cents and one large one of 300 cents gives a <a class="wiki_link" href="/MOSScales">MOS</a> version of the Slendro scale, and five small steps of 150 cents with two large ones of 225 steps a Pelog-like MOS. The temperament could be popular for its easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones. The 25 cent difference in the steps can have a similar effect the <a class="wiki_link" href="/scales%20of%20Olympos%20have">scales of Olympos have</a> with buried enharmonic genera.<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 &quot;blown fifth&quot; of 675 cents means it works as a mavila temperament tuning. For a 16-edo version of Indonesian music, four small steps of 225 cents and one large one of 300 cents gives a <a class="wiki_link" href="/MOSScales">MOS</a> version of the Slendro scale, and five small steps of 150 cents with two large ones of 225 steps a Pelog-like MOS. The temperament could be popular for its easy manageability of 150 cent intervals 3/4, 9/4 and 21/4-tones. The 25 cent difference in the steps can have a similar effect the <a class="wiki_link" href="/scales%20of%20Olympos%20have">scales of Olympos have</a> with buried enharmonic genera.<br /> | ||
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< | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="External theory links"></a><!-- ws:end:WikiTextHeadingRule:2 -->External theory links</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 - translation, anyone?<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 - translation, anyone?<br /> | ||
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<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:12:&lt;img src=&quot;http://ronsword.com/images/ESG_sm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 161px; width: 120px;&quot; /&gt; --><img src="http://ronsword.com/images/ESG_sm.jpg" alt="external image ESG_sm.jpg" title="external image ESG_sm.jpg" style="height: 161px; width: 120px;" /><!-- ws:end:WikiTextRemoteImageRule:12 --><br /> | ||
Sword, Ronald. &quot;Hexadecaphonic Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: Feb, 2010. (superfourth tuning).<br /> | Sword, Ronald. &quot;Hexadecaphonic Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: Feb, 2010. (superfourth tuning).<br /> | ||
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 /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt; | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:4 -->Compositions</h1> | ||
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<a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/16tet.mid" rel="nofollow">Etude in 16-tone equal tuning</a> by Herman Miller<br /> | <a class="wiki_link_ext" href="http://www.io.com/%7Ehmiller/midi/16tet.mid" rel="nofollow">Etude in 16-tone equal tuning</a> by Herman Miller<br /> | ||