Armodue theory: Difference between revisions
Wikispaces>hstraub **Imported revision 240977343 - Original comment: ** |
Wikispaces>hstraub **Imported revision 240978573 - 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>2011-07-12 09: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-12 09:48:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>240978573</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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One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling temperaments#Valentine|valentine temperament]]. Similarly we might use three steps of [[46edo]], 3\46, 78.26 cents, or five steps of [[77edo]], 77.92 cents. | One step of 16edo (75 cents) is nearly equal to two steps (2\31) of [[31edo]] (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of [[Starling temperaments#Valentine|valentine temperament]]. Similarly we might use three steps of [[46edo]], 3\46, 78.26 cents, or five steps of [[77edo]], 77.92 cents. | ||
Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals (intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged).</pre></div> | Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals (intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged). | ||
||~ Armodue note ||~ cents (16edo) ||~ cents (semi-equalized Armodue based on [[31edo]]) || | |||
|| 1 || 0 || 0 || | |||
|| 1# || 75 || 77.42 || | |||
|| 2 || 150 || 154.84 || | |||
|| 2# || 225 || 232.26 || | |||
|| 3 || 300 || 309.68 || | |||
|| 3# || 375 || 387.10 || | |||
|| 4 || 450 || 464.52 || | |||
|| 5 || 525 || 541.94 || | |||
|| 5# || 600 || 619.35 || | |||
|| 6 || 675 || 696.77 || | |||
|| 6# || 750 || 774.19 || | |||
|| 7 || 825 || 851.61 || | |||
|| 7# || 900 || 929.03 || | |||
|| 8 || 975 || 967.74 || | |||
|| 8# || 1050 || 1045.16 || | |||
|| 9 || 1125 || 1122.58 ||</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>Armodue theory</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="#Armodue Theory of 16EDO">Armodue Theory of 16EDO</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Armodue just intonation - connection to Lou Harrison and Andrián Pertout">Armodue just intonation - connection to Lou Harrison and Andrián Pertout</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Semi-equalized Armodue">Semi-equalized Armodue</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | <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>Armodue theory</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="#Armodue Theory of 16EDO">Armodue Theory of 16EDO</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Armodue just intonation - connection to Lou Harrison and Andrián Pertout">Armodue just intonation - connection to Lou Harrison and Andrián Pertout</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Semi-equalized Armodue">Semi-equalized Armodue</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
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<td><!-- ws:start:WikiTextRemoteImageRule: | <td><!-- ws:start:WikiTextRemoteImageRule:353:&lt;img src=&quot;http://www.armodue.com/TETR-%5B1%5D.jpg&quot; alt=&quot;copyright Armodue, used with permission&quot; title=&quot;copyright Armodue, used with permission&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="http://www.armodue.com/TETR-%5B1%5D.jpg" alt="copyright Armodue, used with permission" title="copyright Armodue, used with permission" /></td></tr><tr><td class="imageCaption">copyright Armodue, used with permission</td></tr></table><!-- ws:end:WikiTextRemoteImageRule:353 --><br /> | ||
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<td><!-- ws:start:WikiTextRemoteImageRule: | <td><!-- ws:start:WikiTextRemoteImageRule:354:&lt;img src=&quot;http://www.armodue.com/Chiave.gif&quot; alt=&quot;copyright Armodue, used with permission&quot; title=&quot;copyright Armodue, used with permission&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="http://www.armodue.com/Chiave.gif" alt="copyright Armodue, used with permission" title="copyright Armodue, used with permission" /></td></tr><tr><td class="imageCaption">copyright Armodue, used with permission</td></tr></table><!-- ws:end:WikiTextRemoteImageRule:354 --><br /> | ||
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<td><!-- ws:start:WikiTextRemoteImageRule: | <td><!-- ws:start:WikiTextRemoteImageRule:355:&lt;img src=&quot;http://www.armodue.com/Tastiera.jpg&quot; alt=&quot;copyright Armodue, used by permission&quot; title=&quot;copyright Armodue, used by permission&quot; /&gt; --><table class="captionBox"><tr><td class="captionedImage"><img src="http://www.armodue.com/Tastiera.jpg" alt="copyright Armodue, used by permission" title="copyright Armodue, used by permission" /></td></tr><tr><td class="imageCaption">copyright Armodue, used by permission</td></tr></table><!-- ws:end:WikiTextRemoteImageRule:355 --><br /> | ||
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<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:352:&lt;img src=&quot;/file/view/Armodue_Neck.PNG/215944122/640x126/Armodue_Neck.PNG&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 126px; width: 640px;&quot; /&gt; --><img src="/file/view/Armodue_Neck.PNG/215944122/640x126/Armodue_Neck.PNG" alt="Armodue_Neck.PNG" title="Armodue_Neck.PNG" style="height: 126px; width: 640px;" /><!-- ws:end:WikiTextLocalImageRule:352 --><br /> | ||
Armodue Neck Inlays<br /> | Armodue Neck Inlays<br /> | ||
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One step of 16edo (75 cents) is nearly equal to two steps (2\31) of <a class="wiki_link" href="/31edo">31edo</a> (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of <a class="wiki_link" href="/Starling%20temperaments#Valentine">valentine temperament</a>. Similarly we might use three steps of <a class="wiki_link" href="/46edo">46edo</a>, 3\46, 78.26 cents, or five steps of <a class="wiki_link" href="/77edo">77edo</a>, 77.92 cents.<br /> | One step of 16edo (75 cents) is nearly equal to two steps (2\31) of <a class="wiki_link" href="/31edo">31edo</a> (77.42 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes '7#' and '8'). leading to the 16 note MOS Valentine[16] of <a class="wiki_link" href="/Starling%20temperaments#Valentine">valentine temperament</a>. Similarly we might use three steps of <a class="wiki_link" href="/46edo">46edo</a>, 3\46, 78.26 cents, or five steps of <a class="wiki_link" href="/77edo">77edo</a>, 77.92 cents.<br /> | ||
<br /> | <br /> | ||
Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals (intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged).</body></html></pre></div> | Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals (intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged).<br /> | ||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>Armodue note<br /> | |||
</th> | |||
<th>cents (16edo)<br /> | |||
</th> | |||
<th>cents (semi-equalized Armodue based on <a class="wiki_link" href="/31edo">31edo</a>)<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>0<br /> | |||
</td> | |||
<td>0<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1#<br /> | |||
</td> | |||
<td>75<br /> | |||
</td> | |||
<td>77.42<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>150<br /> | |||
</td> | |||
<td>154.84<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2#<br /> | |||
</td> | |||
<td>225<br /> | |||
</td> | |||
<td>232.26<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>300<br /> | |||
</td> | |||
<td>309.68<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3#<br /> | |||
</td> | |||
<td>375<br /> | |||
</td> | |||
<td>387.10<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>450<br /> | |||
</td> | |||
<td>464.52<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>525<br /> | |||
</td> | |||
<td>541.94<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5#<br /> | |||
</td> | |||
<td>600<br /> | |||
</td> | |||
<td>619.35<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>675<br /> | |||
</td> | |||
<td>696.77<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6#<br /> | |||
</td> | |||
<td>750<br /> | |||
</td> | |||
<td>774.19<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>825<br /> | |||
</td> | |||
<td>851.61<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7#<br /> | |||
</td> | |||
<td>900<br /> | |||
</td> | |||
<td>929.03<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>975<br /> | |||
</td> | |||
<td>967.74<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8#<br /> | |||
</td> | |||
<td>1050<br /> | |||
</td> | |||
<td>1045.16<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>1125<br /> | |||
</td> | |||
<td>1122.58<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
</body></html></pre></div> | |||