Armodue harmony: Difference between revisions
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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:hstraub|hstraub]] and made on <tt>2010-09-10 | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-09-10 04:11:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>161608705</tt>.<br> | ||
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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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==Modal systems based on hexachords== | ==Modal systems based on hexachords== | ||
The tetrachords and pentachords treated so far are focused on the characteristic interval of 7eka, the Armodue equivalent of the diatessaron in the greek modal system (the perfect fourth, five tempered semitones wide). | |||
In Armodue, however, there is another very significant interval that deserves to function as pivotal interval: that of 13 eka - whose width is very close to the natural minor seventh (the frequency ratio between the seventh and the fourth harmonic of the overtone series). | |||
Assuming the interval of 13 eka as delimiting interval (that includes the notes 1-8 of the standard tenth 1 to 1), the following partitions with hexachords stand out as important (many other divisions are possible, of course): | |||
Hexachordal interval partition: 1 + 3 + 3 + 3 + 3 eka | |||
1, 3, 3, 3, 3 | |||
3, 1, 3, 3, 3 | |||
3, 3, 1, 3, 3 | |||
3, 3, 3, 1, 3 | |||
3, 3, 3, 3, 1 | |||
For example, taking the formula 3, 1, 3, 3, 3 we get a scale formed by the notes: 1, # 2, 3, 5, 6 #, 8 to which we can add the note 9 as leading tone. | |||
==Other modal systems and various considerations on the scales in Armodue== | |||
XXX | XXX | ||
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XXX</pre></div> | XXX</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"><html><head><title>Armodue armonia</title></head><body><!-- ws:start:WikiTextTocRule: | <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 armonia</title></head><body><!-- ws:start:WikiTextTocRule:44:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 1em;"><a href="#Armodue: basic elements of harmony">Armodue: basic elements of harmony</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 1em;"><a href="#Two theses supporting the system">Two theses supporting the system</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 2em;"><a href="#Two theses supporting the system-The supremacy of the fifth and and the seventh harmonic in Armodue">The supremacy of the fifth and and the seventh harmonic in Armodue</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 2em;"><a href="#Two theses supporting the system-The triple mean of the double diagonal / side of the square">The triple mean of the double diagonal / side of the square</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 1em;"><a href="#The interval table">The interval table</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 2em;"><a href="#The interval table-Qualitative categories of intervals">Qualitative categories of intervals</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 2em;"><a href="#The interval table-The intervals of 1 eka and 15 eka">The intervals of 1 eka and 15 eka</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><div style="margin-left: 2em;"><a href="#The interval table-The intervals of 2 eka and 14 eka">The intervals of 2 eka and 14 eka</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 2em;"><a href="#The interval table-The intervals of 3 eka and 13 eka">The intervals of 3 eka and 13 eka</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 2em;"><a href="#The interval table-The intervals of 4 eka and 12 eka">The intervals of 4 eka and 12 eka</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><div style="margin-left: 2em;"><a href="#The interval table-The intervals of 5 eka and 11 eka">The intervals of 5 eka and 11 eka</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><div style="margin-left: 2em;"><a href="#The interval table-The intervals of 6 eka and 10 eka">The intervals of 6 eka and 10 eka</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><div style="margin-left: 2em;"><a href="#The interval table-The intervals of 7 eka and 9 eka">The intervals of 7 eka and 9 eka</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><div style="margin-left: 2em;"><a href="#The interval table-The interval of 8 eka">The interval of 8 eka</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><div style="margin-left: 2em;"><a href="#The interval table-Gradation of harmonic tensions">Gradation of harmonic tensions</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><div style="margin-left: 2em;"><a href="#The interval table-Arrangement of tones in the chords">Arrangement of tones in the chords</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --><div style="margin-left: 1em;"><a href="#Creating scales with Armodue: modal systems">Creating scales with Armodue: modal systems</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:61 --><!-- ws:start:WikiTextTocRule:62: --><div style="margin-left: 2em;"><a href="#Creating scales with Armodue: modal systems-Modal systems based on tetrachords and pentachords">Modal systems based on tetrachords and pentachords</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:62 --><!-- ws:start:WikiTextTocRule:63: --><div style="margin-left: 2em;"><a href="#Creating scales with Armodue: modal systems-Modal systems based on hexachords">Modal systems based on hexachords</a></div> | ||
<!-- ws:end:WikiTextTocRule:63 --><!-- ws:start:WikiTextTocRule:64: --><div style="margin-left: 2em;"><a href="#Creating scales with Armodue: modal systems-Other modal systems and various considerations on the scales in Armodue">Other modal systems and various considerations on the scales in Armodue</a></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:64 --><!-- ws:start:WikiTextTocRule:65: --><div style="margin-left: 1em;"><a href="#x&quot;Geometric&quot; harmonic constructions with Armodue">&quot;Geometric&quot; harmonic constructions with Armodue</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:65 --><!-- ws:start:WikiTextTocRule:66: --><div style="margin-left: 1em;"><a href="#x&quot;Elastic&quot; chords">&quot;Elastic&quot; chords</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:66 --><!-- ws:start:WikiTextTocRule:67: --></div> | ||
<!-- ws:end:WikiTextTocRule:67 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Armodue: basic elements of harmony"></a><!-- ws:end:WikiTextHeadingRule:0 --><strong>Armodue: basic elements of harmony</strong></h1> | |||
<br /> | <br /> | ||
This is a translation of an article by Luca Attanasio. Original page in italian: <a class="wiki_link_ext" href="http://www.armodue.com/armonia.htm" rel="nofollow">http://www.armodue.com/armonia.htm</a><br /> | This is a translation of an article by Luca Attanasio. Original page in italian: <a class="wiki_link_ext" href="http://www.armodue.com/armonia.htm" rel="nofollow">http://www.armodue.com/armonia.htm</a><br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Creating scales with Armodue: modal systems-Modal systems based on hexachords"></a><!-- ws:end:WikiTextHeadingRule:36 -->Modal systems based on hexachords</h2> | <!-- ws:start:WikiTextHeadingRule:36:&lt;h2&gt; --><h2 id="toc18"><a name="Creating scales with Armodue: modal systems-Modal systems based on hexachords"></a><!-- ws:end:WikiTextHeadingRule:36 -->Modal systems based on hexachords</h2> | ||
<br /> | |||
The tetrachords and pentachords treated so far are focused on the characteristic interval of 7eka, the Armodue equivalent of the diatessaron in the greek modal system (the perfect fourth, five tempered semitones wide).<br /> | |||
<br /> | |||
In Armodue, however, there is another very significant interval that deserves to function as pivotal interval: that of 13 eka - whose width is very close to the natural minor seventh (the frequency ratio between the seventh and the fourth harmonic of the overtone series).<br /> | |||
<br /> | |||
Assuming the interval of 13 eka as delimiting interval (that includes the notes 1-8 of the standard tenth 1 to 1), the following partitions with hexachords stand out as important (many other divisions are possible, of course):<br /> | |||
<br /> | |||
Hexachordal interval partition: 1 + 3 + 3 + 3 + 3 eka<br /> | |||
1, 3, 3, 3, 3<br /> | |||
3, 1, 3, 3, 3<br /> | |||
3, 3, 1, 3, 3<br /> | |||
3, 3, 3, 1, 3<br /> | |||
3, 3, 3, 3, 1<br /> | |||
<br /> | |||
For example, taking the formula 3, 1, 3, 3, 3 we get a scale formed by the notes: 1, # 2, 3, 5, 6 #, 8 to which we can add the note 9 as leading tone.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:38:&lt;h2&gt; --><h2 id="toc19"><a name="Creating scales with Armodue: modal systems-Other modal systems and various considerations on the scales in Armodue"></a><!-- ws:end:WikiTextHeadingRule:38 -->Other modal systems and various considerations on the scales in Armodue</h2> | |||
<br /> | <br /> | ||
XXX<br /> | XXX<br /> | ||
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<hr /> | <hr /> | ||
Chapter 4: <br /> | Chapter 4: <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:40:&lt;h1&gt; --><h1 id="toc20"><a name="x&quot;Geometric&quot; harmonic constructions with Armodue"></a><!-- ws:end:WikiTextHeadingRule:40 -->&quot;Geometric&quot; harmonic constructions with Armodue</h1> | ||
<br /> | <br /> | ||
XXX<br /> | XXX<br /> | ||
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<hr /> | <hr /> | ||
Chapter 5: <br /> | Chapter 5: <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:42:&lt;h1&gt; --><h1 id="toc21"><a name="x&quot;Elastic&quot; chords"></a><!-- ws:end:WikiTextHeadingRule:42 -->&quot;Elastic&quot; chords</h1> | ||
<br /> | <br /> | ||
XXX</body></html></pre></div> | XXX</body></html></pre></div> | ||