Armodue theory: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-~~13 05~~:03:51 UTC</tt>.

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-15 02:44:18 UTC</tt>.

: The original revision id was <tt>~~241131115~~</tt>.

: The original revision id was <tt>241450791</tt>.

: The revision comment was: <tt></tt>

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//(summary translation from the italian site// [[http://www.armodue.com/ricerche.htm|Armodue]] )

Referring not only 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 [[http://www.pertout.com/|Andrián Pertout]] and the 16-to-31 [[OverToneSeries|overtone scale]], Armodue has been proposed as a new notation and theory system.

Referring not only to the [[16edo|16-edo equal temperament]], but also to half-equal and [[Lou Harrison]]'s [[JustIntonation|Just intonation]] 16 note scale, the natural octave division by [[http://www.pertout.com/|Andrián Pertout]] and the 16-to-31 [[OverToneSeries|overtone scale]], Armodue has been proposed as a new notation and theory system.

Desiring to make the approach to Armodue as easy as possible, but conscious that they had to give new names to the notes that constitute the system, the Italian creators of the [[@http://armodue.com/|Armodue]] 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 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[[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]]), namely the following (according to [[http://www.armodue.com/risorse.htm|Armodue]]):

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

Referring not only 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 <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>, Armodue has been proposed as a new notation and theory system.

Referring not only to the <a class="wiki_link" href="/16edo">16-edo equal temperament</a>, but also to half-equal and <a class="wiki_link" href="/Lou%20Harrison">Lou Harrison</a>'s <a class="wiki_link" href="/JustIntonation">Just intonation</a> 16 note scale, the natural octave division by <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>, Armodue has been proposed as a new notation and theory system.

Desiring to make the approach to Armodue as easy as possible, but conscious that they had to give new names to the notes that constitute the system, the Italian creators of the <a class="wiki_link_ext" href="http://armodue.com/" rel="nofollow" target="_blank">Armodue</a> system named them numbering from 1 to 9:

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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>

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).

Armodue Just Intonation is nothing else than the 16-note scale by<a class="wiki_link" href="/Lou%20Harrison"> 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).

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>):

@@ 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>2011-07-13 05:03:51 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-07-15 02:44:18 UTC</tt>.<br>
-: The original revision id was <tt>241131115</tt>.<br>
+: The original revision id was <tt>241450791</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>
@@ Line 13: / Line 13: @@
 //(summary translation from the italian site// [[http://www.armodue.com/ricerche.htm|Armodue]] )
-Referring not only 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 has been proposed as a new notation and theory system.
+Referring not only to the [[16edo|16-edo equal temperament]], but also to half-equal and [[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 has been proposed as a new notation and theory system.
 Desiring to make the approach to Armodue as easy as possible, but conscious that 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 53: / Line 53: @@
 =Armodue just intonation - connection to Lou Harrison and Andrián Pertout=
-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[[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]]), namely the following (according to [[http://www.armodue.com/risorse.htm|Armodue]]):
@@ Line 108: / Line 108: @@
 &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;
-Referring not only 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 has been proposed as a new notation and theory system.&lt;br /&gt;
+Referring not only 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" href="/Lou%20Harrison"&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 has been proposed as a new notation and theory system.&lt;br /&gt;
 &lt;br /&gt;
 Desiring to make the approach to Armodue as easy as possible, but conscious that 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 181: / Line 181: @@
 &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 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" href="/Lou%20Harrison"&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;
 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;