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>
: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-07-06 16:45:56 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-12 09:38:12 UTC</tt>.<br>
: The original revision id was <tt>240255593</tt>.<br>
: The original revision id was <tt>240977343</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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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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&lt;table class="wiki_table"&gt;
&lt;table class="wiki_table"&gt;
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         &lt;td&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:43:&amp;lt;img src=&amp;quot;http://www.armodue.com/TETR-%5B1%5D.jpg&amp;quot; alt=&amp;quot;copyright Armodue, used with permission&amp;quot; title=&amp;quot;copyright Armodue, used with permission&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://www.armodue.com/TETR-%5B1%5D.jpg" alt="copyright Armodue, used with permission" title="copyright Armodue, used with permission" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;copyright Armodue, used with permission&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:43 --&gt;&lt;br /&gt;
         &lt;td&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:215:&amp;lt;img src=&amp;quot;http://www.armodue.com/TETR-%5B1%5D.jpg&amp;quot; alt=&amp;quot;copyright Armodue, used with permission&amp;quot; title=&amp;quot;copyright Armodue, used with permission&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://www.armodue.com/TETR-%5B1%5D.jpg" alt="copyright Armodue, used with permission" title="copyright Armodue, used with permission" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;copyright Armodue, used with permission&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:215 --&gt;&lt;br /&gt;
&lt;/td&gt;
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&lt;table class="wiki_table"&gt;
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         &lt;td&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:44:&amp;lt;img src=&amp;quot;http://www.armodue.com/Chiave.gif&amp;quot; alt=&amp;quot;copyright Armodue, used with permission&amp;quot; title=&amp;quot;copyright Armodue, used with permission&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://www.armodue.com/Chiave.gif" alt="copyright Armodue, used with permission" title="copyright Armodue, used with permission" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;copyright Armodue, used with permission&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:44 --&gt;&lt;br /&gt;
         &lt;td&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:216:&amp;lt;img src=&amp;quot;http://www.armodue.com/Chiave.gif&amp;quot; alt=&amp;quot;copyright Armodue, used with permission&amp;quot; title=&amp;quot;copyright Armodue, used with permission&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://www.armodue.com/Chiave.gif" alt="copyright Armodue, used with permission" title="copyright Armodue, used with permission" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;copyright Armodue, used with permission&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:216 --&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;table class="wiki_table"&gt;
&lt;table class="wiki_table"&gt;
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         &lt;td&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:45:&amp;lt;img src=&amp;quot;http://www.armodue.com/Tastiera.jpg&amp;quot; alt=&amp;quot;copyright Armodue, used by permission&amp;quot; title=&amp;quot;copyright Armodue, used by permission&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://www.armodue.com/Tastiera.jpg" alt="copyright Armodue, used by permission" title="copyright Armodue, used by permission" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;copyright Armodue, used by permission&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:45 --&gt;&lt;br /&gt;
         &lt;td&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:217:&amp;lt;img src=&amp;quot;http://www.armodue.com/Tastiera.jpg&amp;quot; alt=&amp;quot;copyright Armodue, used by permission&amp;quot; title=&amp;quot;copyright Armodue, used by permission&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://www.armodue.com/Tastiera.jpg" alt="copyright Armodue, used by permission" title="copyright Armodue, used by permission" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;copyright Armodue, used by permission&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:217 --&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:42:&amp;lt;img src=&amp;quot;/file/view/Armodue_Neck.PNG/215944122/640x126/Armodue_Neck.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 126px; width: 640px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:42 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextLocalImageRule:214:&amp;lt;img src=&amp;quot;/file/view/Armodue_Neck.PNG/215944122/640x126/Armodue_Neck.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 126px; width: 640px;&amp;quot; /&amp;gt; --&gt;&lt;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;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:214 --&gt;&lt;br /&gt;
Armodue Neck Inlays&lt;br /&gt;
Armodue Neck Inlays&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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Armodue Just Intonation is nothing else than the 16-note scale by&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lou_Harrison" rel="nofollow"&gt; Lou Harrison&lt;/a&gt; based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the &amp;quot;natural&amp;quot; or &amp;quot;Zarlinian&amp;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).&lt;br /&gt;
Armodue Just Intonation is nothing else than the 16-note scale by&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lou_Harrison" rel="nofollow"&gt; Lou Harrison&lt;/a&gt; based on simple ratios and pure intervals. In this scale there are practically the same twelve intervals of the &amp;quot;natural&amp;quot; or &amp;quot;Zarlinian&amp;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).&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The composer Andrián Pertout used a very similar scale in his composition &amp;quot;Sonus dulcis&amp;quot; (&lt;a class="wiki_link_ext" href="http://web.archive.org/web/20040511172650/http://www.users.bigpond.com/apertout/Sonus.htm" rel="nofollow"&gt;article on archive.org&lt;/a&gt;)&lt;br /&gt;
The composer Andrián Pertout used a very similar scale in his composition &amp;quot;Sonus dulcis&amp;quot; (&lt;a class="wiki_link_ext" href="http://web.archive.org/web/20040511172650/http://www.users.bigpond.com/apertout/Sonus.htm" rel="nofollow"&gt;article on archive.org&lt;/a&gt;), namely the following (according to &lt;a class="wiki_link_ext" href="http://www.armodue.com/risorse.htm" rel="nofollow"&gt;Armodue&lt;/a&gt;):&lt;br /&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;th&gt;Armodue note&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Interval&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Ratio&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;unison&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;major half-tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;112&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;minor tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;182&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;major tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;204&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;minor third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;316&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;major third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;386&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;498&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;harmonic tritone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;45/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;590&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;cyclic tritone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;64/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;610&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;702&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;diminished sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;814&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;harmonic sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;884&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;harmonic minor seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;969&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;minor seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;996&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;minor seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1018&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;major seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1088&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;br /&gt;
XXX&lt;br /&gt;
XXX&lt;br /&gt;