Armodue theory is a xenharmonic notation and theory system for 16-note tuning, not only in the sense of [[16edo|16-tone equal temperament]], but also regarding half-equal tuning, [[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]].
//(summary translation from the italian site// [[http://www.armodue.com/ricerche.htm|Armodue]] )
== Notation ==
In order to make Armodue approachable, while also making its notation distinct from Western diatonic notation, the Italian creators of the [http://armodue.com/ Armodue] system named the notes using numbers from 1 to 9:
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 ?)
This is the recommended system for Armodue theory, though in technicality any notation system can be used.
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:
Relative notation is simply done by specifying the number of edosteps, in order to support alternative scale constructions. For example, one refers not to the perfect fourth or fifth (at least in the specific sense of Armodue intervals) but to the intervals of 7-eka and 9-eka.
However, the interval between a note at frequency n and other at frequency 2n is called a ''tenth,'' ''decave,'' or ''decim'', as it is the tenth note of the Mavila[9] scale.
Consequently, the interval between a note at frequency n and other at frequency 2n is called **tenth**.
The basic semitone of Armodue, whatever concrete temperament is used, is always called '''eka''' (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes.
The basic (micro-)tone of Armodue, whatever concrete temperament is used, is always called **eka** (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes.
The standard staff notation for Armodue uses 4 lines, so that 1 is always found below the first line, and 9 above the last line.
For composing in Armodue it's useful to use a **tetragram** (staff with 4 lines)
|| [[image:http://www.armodue.com/TETR-%5B1%5D.jpg caption="copyright Armodue, used with permission"]] ||
|| copyright Armodue, used with permission ||
The notes without accidentals form a [[Mavila|Mavila]] [[7L_2s|armotonic scale (7L 2s)]].
If for the execution of a musical piece we need to write on two or more tetragrams, the notes will be written in the same way for every tetragram.
This notation is similar to the KISS notation using numbers for this scale, except with the staff laid out differently (i.e. in KISS, the standard treble and bass clefs are used, and the staff has 6 lines instead of 4)
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:
When multiple staves are necessary, the notes will be written in the same way in every staff.
|| [[image:http://www.armodue.com/Chiave.gif caption="copyright Armodue, used with permission"]] ||
In other words, the "1" note will be written immediately under the first line <u>in every tenth</u>.
|| copyright Armodue, used with permission ||
In Armodue we have only a numeric clef, that shows us the tenth:
=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).
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]])
XXX
=Semi-equalized Armodue=
One step of 16edo (75 cents) is nearly equal to two steps of [[31edo]] (77.4 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes # 7 and 8).
XXX According to the 31EDO site, this is called "Valentine temperament"...
Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals (intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged).</pre></div>
<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><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#Armodue Theory of 16EDO">Armodue Theory of 16EDO</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#Armodue just intonation - connection to Lou Harrison and Andrián Pertout">Armodue just intonation - connection to Lou Harrison and Andrián Pertout</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Semi-equalized Armodue">Semi-equalized Armodue</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: -->
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Armodue Theory of 16EDO"></a><!-- ws:end:WikiTextHeadingRule:0 -->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 />
Consequently, the interval between a note at frequency n and other at frequency 2n is called <strong>tenth</strong>.<br />
<br />
The basic (micro-)tone of Armodue, whatever concrete temperament is used, is always called <strong>eka</strong> (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes.<br />
<br />
For composing in Armodue it's useful to use a <strong>tetragram</strong> (staff with 4 lines)<br />
<br />
<table class="wiki_table">
<tr>
<td><!-- ws:start:WikiTextRemoteImageRule:42:&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:42 --><br />
</td>
</tr>
<tr>
<td>copyright Armodue, used with permission<br />
</td>
</tr>
</table>
<br />
So, in the illustrated example above, the first staff (from top) refers to the 3rd tenth (central tenth, corresponding to the 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 draw normal braces.
<br />
If for the execution of a musical piece we need to write on two or more tetragrams, the notes will be written in the same way for every tetragram.<br />
In other words, the &quot;1&quot; note will be written immediately under the first line <u>in every tenth</u>.<br />
<br />
In Armodue we have only a numeric clef, that show us the tenth:<br />
<br />
Note that you cannot connect staves like in standard notation, because the lines are offset from one decave to the next.
<table class="wiki_table">
This is a keyboard layout for Armodue, which can also be seen as a standard mavila keyboard layout for 16edo.
<tr>
<td><!-- ws:start:WikiTextRemoteImageRule:43:&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:43 --><br />
</td>
</tr>
<tr>
<td>copyright Armodue, used with permission<br />
The clefs 1,2,3... refers to the tenths: first, second, third...<br />
So, in the illustrated example above, the first tetragram (from top) refers to the 3rd tenth (central tenth, corresponding to the octave C3-C4),<br />
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.<br />
<br />
The keyboard conceived by Armodue authors has the same disposition as Goldsmith's one (except the curvature):<br />
<table class="wiki_table">
The white keys, corresponding to the notes without accidentals in the notation system, form again a [[Mavila|Mavila]] [[7L_2s|superdiatonic scale (7L 2s).]]
<tr>
<td><!-- ws:start:WikiTextRemoteImageRule:44:&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:44 --><br />
</td>
</tr>
<tr>
<td>copyright Armodue, used by permission<br />
</td>
</tr>
</table>
<br />
[[file:Armodue_Neck.PNG|frame|none|Dot-Pattern inlays, by Armodue]]
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Armodue just intonation - connection to Lou Harrison and Andrián Pertout"></a><!-- ws:end:WikiTextHeadingRule:2 -->Armodue just intonation - connection to Lou Harrison and Andrián Pertout</h1>
[[Category:Valentine]]
<br />
[[Category:Method]]
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 />
[[Category:Approaches to tuning systems]]
<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 />
One step of 16edo (75 cents) is nearly equal to two steps of <a class="wiki_link" href="/31edo">31edo</a> (77.4 cents). If we take the latter as a base, we get semi-equalized Armodue. In this temperament there is inevitably a smaller microtone (eka between the notes # 7 and 8).<br />
<br />
XXX According to the 31EDO site, this is called &quot;Valentine temperament&quot;...<br />
<br />
Semi-equalized Armodue provides a balance between the symmetry of the equalized system and the purity of natural intervals (intervals of semi-equalized Armodue are very pure, and at the same time it preserves the symmetry of the equalized system and its interval sizes almost unchanged).</body></html></pre></div>
Latest revision as of 01:42, 11 April 2025
(summary translation from the Italian language siteArmodue)
In order to make Armodue approachable, while also making its notation distinct from Western diatonic notation, the Italian creators of the Armodue system named the notes using numbers from 1 to 9:
This is the recommended system for Armodue theory, though in technicality any notation system can be used.
Relative notation is simply done by specifying the number of edosteps, in order to support alternative scale constructions. For example, one refers not to the perfect fourth or fifth (at least in the specific sense of Armodue intervals) but to the intervals of 7-eka and 9-eka.
However, the interval between a note at frequency n and other at frequency 2n is called a tenth,decave, or decim, as it is the tenth note of the Mavila[9] scale.
The basic semitone of Armodue, whatever concrete temperament is used, is always called eka (from Sanskrit eka: one, unit). In the chromatic Armodue scale, one eka always corresponds to the interval between any two consecutive notes.
The standard staff notation for Armodue uses 4 lines, so that 1 is always found below the first line, and 9 above the last line.
This notation is similar to the KISS notation using numbers for this scale, except with the staff laid out differently (i.e. in KISS, the standard treble and bass clefs are used, and the staff has 6 lines instead of 4)
When multiple staves are necessary, the notes will be written in the same way in every staff.
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 shows us the tenth:
The clefs 1,2,3... refers to the tenths: first, second, third...
So, in the illustrated example above, the first staff (from top) refers to the 3rd tenth (central tenth, corresponding to the 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 draw normal braces.
Note that you cannot connect staves like in standard notation, because the lines are offset from one decave to the next.
This is a keyboard layout for Armodue, which can also be seen as a standard mavila keyboard layout for 16edo.
