Armodue theory: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2011-07-06 11:48:10 UTC</tt>.<br>

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-06 11:49:45 UTC</tt>.<br>

: The original revision id was <tt>~~240209767~~</tt>.<br>

: The original revision id was <tt>240210005</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>

<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">[[toc|flat]]

=Armodue Theory of 16EDO=

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Not only referring to the [[16edo|16-edo equal temperament]], but also to half-equal and [[http://en.wikipedia.org/wiki/Lou_Harrison|Lou Harrison]]'s [[JustIntonation|Just intonation]] 16 note scale, the natural octave division by <span style="font-family: Verdana; font-size: small; line-height: normal;">[[http://www.pertout.com/|Andrián Pertout]] and the 16-to-31 [[OverToneSeries|overtone scale]], </span>Armodue is proposed as **totally new notation and theory system**.

~~( ? What does Armodue have to do with Lou Harrison's Just Intonation 16 tone scale ?)~~

Attempting of making the approach to Armodue as easy as possible, but conscious they had to give new names to the notes that constitute the system, the italian creators of the <span style="background-position: 100% 50%; cursor: pointer; padding-right: 10px;">[[@http://armodue.com/|Armodue]]</span> system named them numbering from 1 to 9:

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=Armodue just intonation - connection to Lou Harrison and Andrián Pertout=

Armodue Just Intonation is nothing else ~~then~~ the 16-note scale by 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 but the 16-note scale by 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]])

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<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><a href="#Armodue Theory of 16EDO">Armodue Theory of 16EDO</a> | <a href="#Armodue just intonation - connection to Lou Harrison and Andrián Pertout">Armodue just intonation - connection to Lou Harrison and Andrián Pertout</a> | <a href="#Semi-equalized Armodue">Semi-equalized Armodue</a>

~~<br />~~

<h1 id="toc0"><a name="Armodue Theory of 16EDO"></a>Armodue Theory of 16EDO</h1>

<h1 id="toc0"><a name="Armodue Theory of 16EDO"></a>Armodue Theory of 16EDO</h1>

<br />

<em>(summary translation from the italian site</em> <a class="wiki_link_ext" href="http://www.armodue.com/ricerche.htm" rel="nofollow">Armodue</a> )<br />

<br />

Not only referring to the <a class="wiki_link" href="/16edo">16-edo equal temperament</a>, but also to half-equal and <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lou_Harrison" rel="nofollow">Lou Harrison</a>'s <a class="wiki_link" href="/JustIntonation">Just intonation</a> 16 note scale, the natural octave division by <span style="font-family: Verdana; font-size: small; line-height: normal;"><a class="wiki_link_ext" href="http://www.pertout.com/" rel="nofollow">Andrián Pertout</a> and the 16-to-31 <a class="wiki_link" href="/OverToneSeries">overtone scale</a>, </span>Armodue is proposed as <strong>totally new notation and theory system</strong>.<br />

~~<br />~~

~~( ? What does Armodue have to do with Lou Harrison's Just Intonation 16 tone scale ?)<br />~~

<br />

Attempting of making the approach to Armodue as easy as possible, but conscious they had to give new names to the notes that constitute the system, the italian creators of the <span style="background-position: 100% 50%; cursor: pointer; padding-right: 10px;"><a class="wiki_link_ext" href="http://armodue.com/" rel="nofollow" target="_blank">Armodue</a></span> system named them numbering from 1 to 9:<br />

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<h1 id="toc1"><a name="Armodue just intonation - connection to Lou Harrison and Andrián Pertout"></a>Armodue just intonation - connection to Lou Harrison and Andrián Pertout</h1>

<br />

Armodue Just Intonation is nothing else ~~then~~ the 16-note scale by Lou Harrison 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 but the 16-note scale by Lou Harrison 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 />

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 />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-07-06 11:48:10 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-06 11:49:45 UTC</tt>.<br>
-: The original revision id was <tt>240209767</tt>.<br>
+: The original revision id was <tt>240210005</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>
 <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">[[toc|flat]]
 =Armodue Theory of 16EDO=
@@ Line 13: / Line 12: @@
 Not only referring to the [[16edo|16-edo equal temperament]], but also to half-equal and [[http://en.wikipedia.org/wiki/Lou_Harrison|Lou Harrison]]'s [[JustIntonation|Just intonation]] 16 note scale, the natural octave division by &lt;span style="font-family: Verdana; font-size: small; line-height: normal;"&gt;[[http://www.pertout.com/|Andrián Pertout]] and the 16-to-31 [[OverToneSeries|overtone scale]], &lt;/span&gt;Armodue is proposed as **totally new notation and theory system**.
-( ? What does Armodue have to do with Lou Harrison's Just Intonation 16 tone scale ?)
 Attempting of making the approach to Armodue as easy as possible, but conscious they had to give new names to the notes that constitute the system, the italian creators of the &lt;span style="background-position: 100% 50%; cursor: pointer; padding-right: 10px;"&gt;[[@http://armodue.com/|Armodue]]&lt;/span&gt; system named them numbering from 1 to 9:
@@ Line 54: / Line 51: @@
 =Armodue just intonation - connection to Lou Harrison and Andrián Pertout=
-Armodue Just Intonation is nothing else then the 16-note scale by 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 but the 16-note scale by 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]])
@@ Line 69: / Line 66: @@
 <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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Armodue theory&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:6:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:6 --&gt;&lt;!-- ws:start:WikiTextTocRule:7: --&gt;&lt;a href="#Armodue Theory of 16EDO"&gt;Armodue Theory of 16EDO&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:7 --&gt;&lt;!-- ws:start:WikiTextTocRule:8: --&gt; | &lt;a href="#Armodue just intonation - connection to Lou Harrison and Andrián Pertout"&gt;Armodue just intonation - connection to Lou Harrison and Andrián Pertout&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:8 --&gt;&lt;!-- ws:start:WikiTextTocRule:9: --&gt; | &lt;a href="#Semi-equalized Armodue"&gt;Semi-equalized Armodue&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:9 --&gt;&lt;!-- ws:start:WikiTextTocRule:10: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;br /&gt;
+&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Armodue Theory of 16EDO"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Armodue Theory of 16EDO&lt;/h1&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Armodue Theory of 16EDO"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Armodue Theory of 16EDO&lt;/h1&gt;
   &lt;br /&gt;
 &lt;em&gt;(summary translation from the italian site&lt;/em&gt; &lt;a class="wiki_link_ext" href="http://www.armodue.com/ricerche.htm" rel="nofollow"&gt;Armodue&lt;/a&gt; )&lt;br /&gt;
 &lt;br /&gt;
 Not only referring to the &lt;a class="wiki_link" href="/16edo"&gt;16-edo equal temperament&lt;/a&gt;, but also to half-equal and &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lou_Harrison" rel="nofollow"&gt;Lou Harrison&lt;/a&gt;'s &lt;a class="wiki_link" href="/JustIntonation"&gt;Just intonation&lt;/a&gt; 16 note scale, the natural octave division by &lt;span style="font-family: Verdana; font-size: small; line-height: normal;"&gt;&lt;a class="wiki_link_ext" href="http://www.pertout.com/" rel="nofollow"&gt;Andrián Pertout&lt;/a&gt; and the 16-to-31 &lt;a class="wiki_link" href="/OverToneSeries"&gt;overtone scale&lt;/a&gt;, &lt;/span&gt;Armodue is proposed as &lt;strong&gt;totally new notation and theory system&lt;/strong&gt;.&lt;br /&gt;
-&lt;br /&gt;
-( ? What does Armodue have to do with Lou Harrison's Just Intonation 16 tone scale ?)&lt;br /&gt;
 &lt;br /&gt;
 Attempting of making the approach to Armodue as easy as possible, but conscious they had to give new names to the notes that constitute the system, the italian creators of the &lt;span style="background-position: 100% 50%; cursor: pointer; padding-right: 10px;"&gt;&lt;a class="wiki_link_ext" href="http://armodue.com/" rel="nofollow" target="_blank"&gt;Armodue&lt;/a&gt;&lt;/span&gt; system named them numbering from 1 to 9:&lt;br /&gt;
@@ Line 149: / Line 143: @@
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Armodue just intonation - connection to Lou Harrison and Andrián Pertout"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Armodue just intonation - connection to Lou Harrison and Andrián Pertout&lt;/h1&gt;
   &lt;br /&gt;
-Armodue Just Intonation is nothing else then the 16-note scale by Lou Harrison 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 but the 16-note scale by Lou Harrison 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;
 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;