100edo: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 585712975 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 585770669 - 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-17 | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-17 21:45:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>585770669</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> | ||
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=100bddd and the 22-note | =100bddd and the 22-note scales= | ||
The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo]] for [[pajara]] temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range [[http://www.anaphoria.com/Secor17puzzle.pdf|favored by George Secor]] for neomedieval compositions. | The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to [[22edo]] for [[pajara]] temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range [[http://www.anaphoria.com/Secor17puzzle.pdf|favored by George Secor]] for neomedieval compositions. | ||
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|| 21 || Augmented 10th<span style="vertical-align: sub;">10</span> | || 21 || Augmented 10th<span style="vertical-align: sub;">10</span> | ||
Diminished 11th<span style="vertical-align: sub;">10</span> || Major seventh || 1140¢ [12] || 1152¢ [10] || | Diminished 11th<span style="vertical-align: sub;">10</span> || Major seventh || 1140¢ [12] || 1152¢ [10] || | ||
|| 22 || 11th<span style="vertical-align: sub;">10</span> || Octave || 1200¢ [22] || N/A ||</pre></div> | || 22 || 11th<span style="vertical-align: sub;">10</span> || Octave || 1200¢ [22] || N/A || | ||
Alternatively, the unmodified, symmetrical 2MOS scale 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 4 5 could be used instead. This scale is very similar to the modified version except that it lacks dog tritones; every 6th<span style="vertical-align: sub;">10 </span>is exactly 600 cents. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they [[https://en.wikipedia.org/wiki/Augmented-fourths_tuning|are tuned in tritones]]. This makes guitar construction much easier compared to other non-equally-tempered scales.</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>100edo</title></head><body><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/youtube/shcrw2vtmJU?h=315&amp;w=560&quot; class=&quot;WikiMedia WikiMediaYoutube&quot; id=&quot;wikitext@@media@@type=&amp;quot;youtube&amp;quot; key=&amp;quot;shcrw2vtmJU&amp;quot; width=&amp;quot;560&amp;quot; height=&amp;quot;315&amp;quot;&quot; title=&quot;YouTube Video&quot;height=&quot;315&quot; width=&quot;560&quot;/&gt; --><iframe width="560" height="315" src="//www.youtube.com/embed/shcrw2vtmJU" frameborder="0" allowfullscreen></iframe><!-- ws:end:WikiTextMediaRule:0 --><br /> | <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>100edo</title></head><body><!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/youtube/shcrw2vtmJU?h=315&amp;w=560&quot; class=&quot;WikiMedia WikiMediaYoutube&quot; id=&quot;wikitext@@media@@type=&amp;quot;youtube&amp;quot; key=&amp;quot;shcrw2vtmJU&amp;quot; width=&amp;quot;560&amp;quot; height=&amp;quot;315&amp;quot;&quot; title=&quot;YouTube Video&quot;height=&quot;315&quot; width=&quot;560&quot;/&gt; --><iframe width="560" height="315" src="//www.youtube.com/embed/shcrw2vtmJU" frameborder="0" allowfullscreen></iframe><!-- ws:end:WikiTextMediaRule:0 --><br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><!-- ws:end:WikiTextHeadingRule:3 --> </h2> | <!-- ws:start:WikiTextHeadingRule:3:&lt;h2&gt; --><h2 id="toc1"><!-- ws:end:WikiTextHeadingRule:3 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="x100bddd and the 22-note | <!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc2"><a name="x100bddd and the 22-note scales"></a><!-- ws:end:WikiTextHeadingRule:5 -->100bddd and the 22-note scales</h1> | ||
<br /> | <br /> | ||
The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to <a class="wiki_link" href="/22edo">22edo</a> for <a class="wiki_link" href="/pajara">pajara</a> temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range <a class="wiki_link_ext" href="http://www.anaphoria.com/Secor17puzzle.pdf" rel="nofollow">favored by George Secor</a> for neomedieval compositions.<br /> | The 100bddd val (which maps 3/2 onto 59\100, 5/4 onto its patent value of 32\100, and 7/4 onto 82\100) is of special interest as it provides a good alternative to <a class="wiki_link" href="/22edo">22edo</a> for <a class="wiki_link" href="/pajara">pajara</a> temperament and for tuning Paul Erlich's decatonic scales, as well as diatonic scales (via superpyth temperament). This alternative tuning prioritizes the 3- and 5-limits over the 7-limit (although the latter is still within striking distance); its pure intervals are also all closer to their 12edo counterparts, and for both reasons it is much less xenharmonic overall. Melodically its properties are superior as well; decatonic scales are more expressive due to the larger difference between step sizes, and the superpyth diatonic scale has a minor second of 60¢ which just barely falls within the 60-80 cent range <a class="wiki_link_ext" href="http://www.anaphoria.com/Secor17puzzle.pdf" rel="nofollow">favored by George Secor</a> for neomedieval compositions.<br /> | ||
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</table> | </table> | ||
</body></html></pre></div> | <br /> | ||
Alternatively, the unmodified, symmetrical 2MOS scale 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 4 5 could be used instead. This scale is very similar to the modified version except that it lacks dog tritones; every 6th<span style="vertical-align: sub;">10 </span>is exactly 600 cents. Because it repeats every half-octave, this scale could be used to construct straight-fretted guitars as long as they <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Augmented-fourths_tuning" rel="nofollow">are tuned in tritones</a>. This makes guitar construction much easier compared to other non-equally-tempered scales.</body></html></pre></div> | |||