Armodue theory: Difference between revisions
Wikispaces>Osmiorisbendi **Imported revision 240255593 - Original comment: ** |
Wikispaces>hstraub **Imported revision 240977343 - 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> | ||
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Armodue Just Intonation is nothing else than the 16-note scale by[[http://en.wikipedia.org/wiki/Lou_Harrison| Lou Harrison]] based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the "natural" or "Zarlinian" scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in addtion to the tritone and four other intervals that are based on the harmonic seventh (the ratios 8/7, 7/6, 12/7, 7/4). | Armodue Just Intonation is nothing else than the 16-note scale by[[http://en.wikipedia.org/wiki/Lou_Harrison| Lou Harrison]] based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the "natural" or "Zarlinian" scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in addtion to the tritone and four other intervals that are based on the harmonic seventh (the ratios 8/7, 7/6, 12/7, 7/4). | ||
The composer Andrián Pertout used a very similar scale in his composition "Sonus dulcis" ([[http://web.archive.org/web/20040511172650/http://www.users.bigpond.com/apertout/Sonus.htm|article on archive.org]]) | The composer Andrián Pertout used a very similar scale in his composition "Sonus dulcis" ([[http://web.archive.org/web/20040511172650/http://www.users.bigpond.com/apertout/Sonus.htm|article on archive.org]]), namely the following (according to [[http://www.armodue.com/risorse.htm|Armodue]]): | ||
||~ Armodue note ||~ Interval ||~ Ratio ||~ Cents || | |||
|| 1 || unison || 1/1 || 0 || | |||
|| 1# || major half-tone || 16/15 || 112 || | |||
|| 2 || minor tone || 10/9 || 182 || | |||
|| 2# || major tone || 9/8 || 204 || | |||
|| 3 || minor third || 6/5 || 316 || | |||
|| 3# || major third || 5/5 || 386 || | |||
|| 4 || fourth || 4/3 || 498 || | |||
|| 5 || harmonic tritone || 45/32 || 590 || | |||
|| 5# || cyclic tritone || 64/45 || 610 || | |||
|| 6 || fifth || 3/2 || 702 || | |||
|| 6# || diminished sixth || 8/5 || 814 || | |||
|| 7 || harmonic sixth || 5/3 || 884 || | |||
|| 7# || harmonic minor seventh || 7/4 || 969 || | |||
|| 8 || minor seventh || 16/9 || 996 || | |||
|| 8# || minor seventh || 9/5 || 1018 || | |||
|| 9 || major seventh || 15/8 || 1088 || | |||
XXX | XXX | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td><!-- ws:start:WikiTextRemoteImageRule: | <td><!-- ws:start:WikiTextRemoteImageRule:215:&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:215 --><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td><!-- ws:start:WikiTextRemoteImageRule: | <td><!-- ws:start:WikiTextRemoteImageRule:216:&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:216 --><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td><!-- ws:start:WikiTextRemoteImageRule: | <td><!-- ws:start:WikiTextRemoteImageRule:217:&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:217 --><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:214:&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:214 --><br /> | ||
Armodue Neck Inlays<br /> | Armodue Neck Inlays<br /> | ||
<br /> | <br /> | ||
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Armodue Just Intonation is nothing else than the 16-note scale by<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lou_Harrison" rel="nofollow"> Lou Harrison</a> based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the &quot;natural&quot; or &quot;Zarlinian&quot; scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in addtion to the tritone and four other intervals that are based on the harmonic seventh (the ratios 8/7, 7/6, 12/7, 7/4).<br /> | Armodue Just Intonation is nothing else than the 16-note scale by<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lou_Harrison" rel="nofollow"> Lou Harrison</a> based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the &quot;natural&quot; or &quot;Zarlinian&quot; scale (the semitone 16/15, the minor wholetone 10/9, the minor third 6/5, the major third 5/4, the pure forth and fifth 4/3 and 3/2, the minor sixth 8/5, the major sixth 5/3, the minor seventh that is the complement of the minor wholetone 9/5, the major seventh 15/8) in addtion to the tritone and four other intervals that are based on the harmonic seventh (the ratios 8/7, 7/6, 12/7, 7/4).<br /> | ||
<br /> | <br /> | ||
The composer Andrián Pertout used a very similar scale in his composition &quot;Sonus dulcis&quot; (<a class="wiki_link_ext" href="http://web.archive.org/web/20040511172650/http://www.users.bigpond.com/apertout/Sonus.htm" rel="nofollow">article on archive.org</a>)<br /> | The composer Andrián Pertout used a very similar scale in his composition &quot;Sonus dulcis&quot; (<a class="wiki_link_ext" href="http://web.archive.org/web/20040511172650/http://www.users.bigpond.com/apertout/Sonus.htm" rel="nofollow">article on archive.org</a>), namely the following (according to <a class="wiki_link_ext" href="http://www.armodue.com/risorse.htm" rel="nofollow">Armodue</a>):<br /> | ||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>Armodue note<br /> | |||
</th> | |||
<th>Interval<br /> | |||
</th> | |||
<th>Ratio<br /> | |||
</th> | |||
<th>Cents<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>unison<br /> | |||
</td> | |||
<td>1/1<br /> | |||
</td> | |||
<td>0<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1#<br /> | |||
</td> | |||
<td>major half-tone<br /> | |||
</td> | |||
<td>16/15<br /> | |||
</td> | |||
<td>112<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>minor tone<br /> | |||
</td> | |||
<td>10/9<br /> | |||
</td> | |||
<td>182<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2#<br /> | |||
</td> | |||
<td>major tone<br /> | |||
</td> | |||
<td>9/8<br /> | |||
</td> | |||
<td>204<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>minor third<br /> | |||
</td> | |||
<td>6/5<br /> | |||
</td> | |||
<td>316<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3#<br /> | |||
</td> | |||
<td>major third<br /> | |||
</td> | |||
<td>5/5<br /> | |||
</td> | |||
<td>386<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>fourth<br /> | |||
</td> | |||
<td>4/3<br /> | |||
</td> | |||
<td>498<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>harmonic tritone<br /> | |||
</td> | |||
<td>45/32<br /> | |||
</td> | |||
<td>590<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5#<br /> | |||
</td> | |||
<td>cyclic tritone<br /> | |||
</td> | |||
<td>64/45<br /> | |||
</td> | |||
<td>610<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>fifth<br /> | |||
</td> | |||
<td>3/2<br /> | |||
</td> | |||
<td>702<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6#<br /> | |||
</td> | |||
<td>diminished sixth<br /> | |||
</td> | |||
<td>8/5<br /> | |||
</td> | |||
<td>814<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>harmonic sixth<br /> | |||
</td> | |||
<td>5/3<br /> | |||
</td> | |||
<td>884<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7#<br /> | |||
</td> | |||
<td>harmonic minor seventh<br /> | |||
</td> | |||
<td>7/4<br /> | |||
</td> | |||
<td>969<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>minor seventh<br /> | |||
</td> | |||
<td>16/9<br /> | |||
</td> | |||
<td>996<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8#<br /> | |||
</td> | |||
<td>minor seventh<br /> | |||
</td> | |||
<td>9/5<br /> | |||
</td> | |||
<td>1018<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>major seventh<br /> | |||
</td> | |||
<td>15/8<br /> | |||
</td> | |||
<td>1088<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | <br /> | ||
XXX<br /> | XXX<br /> | ||