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16edo: Difference between revisions

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**Imported revision 161330031 - Original comment: **
Wikispaces>hstraub
**Imported revision 161348181 - Original comment: Separate pages for Armodue theory**
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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:tetraF|tetraF]] and made on <tt>2010-09-09 03:57:14 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-09-09 07:16:19 UTC</tt>.<br>
: The original revision id was <tt>161330031</tt>.<br>
: The original revision id was <tt>161348181</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt>Separate pages for Armodue theory</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>
<h4>Original Wikitext content:</h4>
<h4>Original Wikitext content:</h4>
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=**Armodue theory**=  
=**Armodue theory**=  
//(summary translation from the italian site)//


Not only referring to the 16-edo equal temperament, but also to half-equal and Lou Harrison's Just intonation 16 note scale, natural octave division of &lt;span style="font-family: Verdana; font-size: small; line-height: normal;"&gt;Andrián Pertout, &lt;/span&gt;
[[http://www.armodue.com/ricerche.htm|Armodue]]: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions.
&lt;span style="font-family: Verdana; font-size: small; line-height: normal;"&gt;and 16-to-31 overtone scale, &lt;/span&gt;Armodue is proposed as __totally new notation and theory system__.


Attempting of making much easy as possible the approach to Armodue, but conscious they had to give new names to the notes that constitutes the system,
Here are translations of parts of the Armodue pages:
the italian creators of &lt;span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;"&gt;[[@http://armodue.com|Armodue]]&lt;/span&gt; system called them numbering from 1 to 9:


1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9
[[Armodue theory]] //(summary translation from the italian site//)
[[Armodue armonia|Armodue: basic elements of harmony]]


Consequently, the interval between a note at frequency n and other at frequency 2n is called **tenth**.
For composing in Armodue it's useful using a **tetragram** (staff with 4 lines)
[[image:http://www.armodue.com/TETR-[1].jpg caption="copyright Armodue, used with permission"]]
In a musical piece, for which esecution, if we need to write on two o more tetragrams, the notes will be written in the same way for every tetragram.
In other words, the "1" note will be written immediately under the first line __in every tenth__.
In Armodue we have only a numeric clef, that show us the tenth:
[[image:http://www.armodue.com/Chiave.gif caption="copyright Armodue, used with permission"]]
The clefs 1,2,3... refers to the tenths: first, second, third...
So, in the illustrated example above, first tetragram (from top) refers to the 3rd tenth (central tenth, corresponding at equivalent octave C3-C4),
the second tetragram to the 5th tenth and the third to the 2nd. If we need to write simultaneously on several staves, we will draws normal braces.
The keyboard conceived by Armodue authors has the same disposition of the Goldsmith's one (except the curvature):
[[image:http://www.armodue.com/Tastiera.jpg caption="copyright Armodue, used by permission"]]
=External theory links=
[[http://www.armodue.com/ricerche.htm|Armodue]]: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions - translation, anyone?


=External links=
[[image:http://ronsword.com/images/ESG_sm.jpg width="120" height="161"]]
[[image:http://ronsword.com/images/ESG_sm.jpg width="120" height="161"]]
Sword, Ronald. "Hexadecaphonic Scales for Guitar." IAAA Press, UK-USA. First Ed: Feb, 2010. (superfourth tuning).
Sword, Ronald. "Hexadecaphonic Scales for Guitar." IAAA Press, UK-USA. First Ed: Feb, 2010. (superfourth tuning).
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[[@http://www.soundclick.com/bands/page_songInfo.cfm?bandID=660895&amp;songID=7715803|Palestrina Morta, fantasia quasi una sonata]] by [[@http://fiale.tk|Fabrizio Fulvio Fausto Fiale]]</pre></div>
[[@http://www.soundclick.com/bands/page_songInfo.cfm?bandID=660895&amp;songID=7715803|Palestrina Morta, fantasia quasi una sonata]] by [[@http://fiale.tk|Fabrizio Fulvio Fausto Fiale]]</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">&lt;html&gt;&lt;head&gt;&lt;title&gt;16edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&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:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#Hexadecaphonic Octave Theory"&gt;Hexadecaphonic Octave Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#toc1"&gt; &lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Hexadecaphonic Notation:"&gt;Hexadecaphonic Notation:&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Armodue theory"&gt;Armodue theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#External theory links"&gt;External theory links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
<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;16edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:12:&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:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt;&lt;a href="#Hexadecaphonic Octave Theory"&gt;Hexadecaphonic Octave Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#toc1"&gt; &lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Hexadecaphonic Notation:"&gt;Hexadecaphonic Notation:&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt; | &lt;a href="#Armodue theory"&gt;Armodue theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;!-- ws:start:WikiTextTocRule:17: --&gt; | &lt;a href="#External links"&gt;External links&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:21:&amp;lt;img src=&amp;quot;http://ronsword.com/DSgoldsmith_piece.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 380px; width: 1120px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/DSgoldsmith_piece.jpg" alt="external image DSgoldsmith_piece.jpg" title="external image DSgoldsmith_piece.jpg" style="height: 380px; width: 1120px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:21 --&gt;&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextRemoteImageRule:21:&amp;lt;img src=&amp;quot;http://ronsword.com/DSgoldsmith_piece.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 380px; width: 1120px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/DSgoldsmith_piece.jpg" alt="external image DSgoldsmith_piece.jpg" title="external image DSgoldsmith_piece.jpg" style="height: 380px; width: 1120px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:21 --&gt;&lt;br /&gt;
&lt;hr /&gt;
&lt;hr /&gt;
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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Armodue theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;strong&gt;Armodue theory&lt;/strong&gt;&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Armodue theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&lt;strong&gt;Armodue theory&lt;/strong&gt;&lt;/h1&gt;
  &lt;em&gt;(summary translation from the italian site)&lt;/em&gt;&lt;br /&gt;
  &lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.armodue.com/ricerche.htm" rel="nofollow"&gt;Armodue&lt;/a&gt;: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions.&lt;br /&gt;
Not only referring to the 16-edo equal temperament, but also to half-equal and Lou Harrison's Just intonation 16 note scale, natural octave division of &lt;span style="font-family: Verdana; font-size: small; line-height: normal;"&gt;Andrián Pertout, &lt;/span&gt;&lt;br /&gt;
&lt;span style="font-family: Verdana; font-size: small; line-height: normal;"&gt;and 16-to-31 overtone scale, &lt;/span&gt;Armodue is proposed as &lt;u&gt;totally new notation and theory system&lt;/u&gt;.&lt;br /&gt;
&lt;br /&gt;
Attempting of making much easy as possible the approach to Armodue, but conscious they had to give new names to the notes that constitutes the system, &lt;br /&gt;
the italian creators of &lt;span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; 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 called them numbering from 1 to 9:&lt;br /&gt;
&lt;br /&gt;
1, 1#, 2, 2#, 3, 3#, 4, 5, 5#, 6, 6#, 7, 7#, 8, 8#, 9&lt;br /&gt;
&lt;br /&gt;
Consequently, the interval between a note at frequency n and other at frequency 2n is called &lt;strong&gt;tenth&lt;/strong&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For composing in Armodue it's useful using a &lt;strong&gt;tetragram&lt;/strong&gt; (staff with 4 lines)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[image:&lt;!-- ws:start:WikiTextUrlRule:155:http://www.armodue.com/TETR- --&gt;&lt;a class="wiki_link_ext" href="http://www.armodue.com/TETR-" rel="nofollow"&gt;http://www.armodue.com/TETR-&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:155 --&gt;[1].jpg caption=&amp;quot;copyright Armodue, used with permission&amp;quot;]]&lt;br /&gt;
Here are translations of parts of the Armodue pages:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In a musical piece, for which esecution, if we need to write on two o more tetragrams, the notes will be written in the same way for every tetragram.&lt;br /&gt;
&lt;a class="wiki_link" href="/Armodue%20theory"&gt;Armodue theory&lt;/a&gt; &lt;em&gt;(summary translation from the italian site&lt;/em&gt;)&lt;br /&gt;
In other words, the &amp;quot;1&amp;quot; note will be written immediately under the first line &lt;u&gt;in every tenth&lt;/u&gt;.&lt;br /&gt;
&lt;a class="wiki_link" href="/Armodue%20armonia"&gt;Armodue: basic elements of harmony&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In Armodue we have only a numeric clef, that show us the tenth:&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:23:&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:23 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The clefs 1,2,3... refers to the tenths: first, second, third...&lt;br /&gt;
So, in the illustrated example above, first tetragram (from top) refers to the 3rd tenth (central tenth, corresponding at equivalent octave C3-C4), &lt;br /&gt;
the second tetragram to the 5th tenth and the third to the 2nd. If we need to write simultaneously on several staves, we will draws normal braces.&lt;br /&gt;
&lt;br /&gt;
The keyboard conceived by Armodue authors has the same disposition of the Goldsmith's one (except the curvature):&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:24:&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:24 --&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="External theory links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;External theory links&lt;/h1&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.armodue.com/ricerche.htm" rel="nofollow"&gt;Armodue&lt;/a&gt;: Italian pages of theory for 16-tone (esadekaphonic) system, including compositions - translation, anyone?&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:25:&amp;lt;img src=&amp;quot;http://ronsword.com/images/ESG_sm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 161px; width: 120px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/images/ESG_sm.jpg" alt="external image ESG_sm.jpg" title="external image ESG_sm.jpg" style="height: 161px; width: 120px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:25 --&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;External links&lt;/h1&gt;
&lt;!-- ws:start:WikiTextRemoteImageRule:23:&amp;lt;img src=&amp;quot;http://ronsword.com/images/ESG_sm.jpg&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 161px; width: 120px;&amp;quot; /&amp;gt; --&gt;&lt;img src="http://ronsword.com/images/ESG_sm.jpg" alt="external image ESG_sm.jpg" title="external image ESG_sm.jpg" style="height: 161px; width: 120px;" /&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:23 --&gt;&lt;br /&gt;
Sword, Ronald. &amp;quot;Hexadecaphonic Scales for Guitar.&amp;quot; IAAA Press, UK-USA. First Ed: Feb, 2010. (superfourth tuning).&lt;br /&gt;
Sword, Ronald. &amp;quot;Hexadecaphonic Scales for Guitar.&amp;quot; IAAA Press, UK-USA. First Ed: Feb, 2010. (superfourth tuning).&lt;br /&gt;
Sword, Ronald. &amp;quot;Esadekaphonic Scales for Guitar.&amp;quot; IAAA Press, UK-USA. First Ed: April, 2009. (semi-diminished fourth tuning)&lt;br /&gt;
Sword, Ronald. &amp;quot;Esadekaphonic Scales for Guitar.&amp;quot; IAAA Press, UK-USA. First Ed: April, 2009. (semi-diminished fourth tuning)&lt;br /&gt;
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