Armodue harmony: Difference between revisions
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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:hstraub|hstraub]] and made on <tt>2010-09-09 09: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-09-09 09:42:23 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>161375309</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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The Armodue "fourth" and "fifth" are euphonious and absolutely consonant, but in a radically different range from those of the dodecatonic system. It is suggested to use the intervals of 7 and 9 eka with caution, just to highlight the special significance that the "fourth" and "fifth" acquire in Armodue and not mislead the western ear deeply accustomed to the cycle of fifth. | The Armodue "fourth" and "fifth" are euphonious and absolutely consonant, but in a radically different range from those of the dodecatonic system. It is suggested to use the intervals of 7 and 9 eka with caution, just to highlight the special significance that the "fourth" and "fifth" acquire in Armodue and not mislead the western ear deeply accustomed to the cycle of fifth. | ||
As for the classification, 7 and 9 eka | As for the classification, 7 and 9 eka belong to the open consonances. | ||
==The interval of 8 eka== | ==The interval of 8 eka== | ||
The interval of 8 eka divides the Armodue tenth in half, just as the tritone halves the tempered octave. Indeed 8 eka correspond exactly to three wholetones, hence to an augmented fourth or diminished fifth. | |||
Being exactly half of 16 eka, the interval of 8 eka is its own complement; this feature makes it particularly uneasy and unstable - just like the tritone among the twelve intervals of the tempered system. | |||
When the interval of 8 eka is present in a chord, the entire chord becomes unstable; on the other hand, even the most dissonant chord comes out static and stabilized in the absence of that interval. | |||
The interval of 8 eka is the first axis of symmetry in Armodue: indeed in this system we proceed with progressive splittings of the tenth: 16 eka, 8 eka, 4 eka, 2 eka and 1 eka. As the tritone of the tempered system, the interval of 8 eka is an unstable dissonance. | |||
==Gradation of harmonic tensions== | |||
XXX | XXX | ||
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XXX</pre></div> | XXX</pre></div> | ||
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<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:36:&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:36 --><!-- ws:start:WikiTextTocRule:37: --><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:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 1em;"><a href="#Chapter 1: Two theses supporting the system">Chapter 1: Two theses supporting the system</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 2em;"><a href="#Chapter 1: 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:39 --><!-- ws:start:WikiTextTocRule:40: --><div style="margin-left: 2em;"><a href="#Chapter 1: 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:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 1em;"><a href="#Chapter 2: The interval table">Chapter 2: The interval table</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 2em;"><a href="#Chapter 2: The interval table-Qualitative categories of intervals">Qualitative categories of intervals</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 2em;"><a href="#Chapter 2: 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:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 2em;"><a href="#Chapter 2: 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:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 2em;"><a href="#Chapter 2: 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:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 2em;"><a href="#Chapter 2: 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:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 2em;"><a href="#Chapter 2: 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:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 2em;"><a href="#Chapter 2: 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:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 2em;"><a href="#Chapter 2: 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:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 2em;"><a href="#Chapter 2: The interval table-The interval of 8 eka">The interval of 8 eka</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 2em;"><a href="#Chapter 2: The interval table-Gradation of harmonic tensions">Gradation of harmonic tensions</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><div style="margin-left: 1em;"><a href="#Chapter 3: Creating scales with Armodue: modal systems">Chapter 3: Creating scales with Armodue: modal systems</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 1em;"><a href="#Chapter 4: &quot;Geometric&quot; harmonic constructions with Armodue">Chapter 4: &quot;Geometric&quot; harmonic constructions with Armodue</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 1em;"><a href="#Chapter 5: &quot;elastic&quot; chords">Chapter 5: &quot;elastic&quot; chords</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --></div> | ||
<!-- ws:end:WikiTextTocRule:55 --><!-- 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> | |||
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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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The Armodue &quot;fourth&quot; and &quot;fifth&quot; are euphonious and absolutely consonant, but in a radically different range from those of the dodecatonic system. It is suggested to use the intervals of 7 and 9 eka with caution, just to highlight the special significance that the &quot;fourth&quot; and &quot;fifth&quot; acquire in Armodue and not mislead the western ear deeply accustomed to the cycle of fifth.<br /> | The Armodue &quot;fourth&quot; and &quot;fifth&quot; are euphonious and absolutely consonant, but in a radically different range from those of the dodecatonic system. It is suggested to use the intervals of 7 and 9 eka with caution, just to highlight the special significance that the &quot;fourth&quot; and &quot;fifth&quot; acquire in Armodue and not mislead the western ear deeply accustomed to the cycle of fifth.<br /> | ||
<br /> | <br /> | ||
As for the classification, 7 and 9 eka | As for the classification, 7 and 9 eka belong to the open consonances.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Chapter 2: The interval table-The interval of 8 eka"></a><!-- ws:end:WikiTextHeadingRule:26 -->The interval of 8 eka</h2> | <!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Chapter 2: The interval table-The interval of 8 eka"></a><!-- ws:end:WikiTextHeadingRule:26 -->The interval of 8 eka</h2> | ||
<br /> | |||
The interval of 8 eka divides the Armodue tenth in half, just as the tritone halves the tempered octave. Indeed 8 eka correspond exactly to three wholetones, hence to an augmented fourth or diminished fifth.<br /> | |||
<br /> | |||
Being exactly half of 16 eka, the interval of 8 eka is its own complement; this feature makes it particularly uneasy and unstable - just like the tritone among the twelve intervals of the tempered system.<br /> | |||
<br /> | |||
When the interval of 8 eka is present in a chord, the entire chord becomes unstable; on the other hand, even the most dissonant chord comes out static and stabilized in the absence of that interval.<br /> | |||
<br /> | |||
The interval of 8 eka is the first axis of symmetry in Armodue: indeed in this system we proceed with progressive splittings of the tenth: 16 eka, 8 eka, 4 eka, 2 eka and 1 eka. As the tritone of the tempered system, the interval of 8 eka is an unstable dissonance.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h2&gt; --><h2 id="toc14"><a name="Chapter 2: The interval table-Gradation of harmonic tensions"></a><!-- ws:end:WikiTextHeadingRule:28 -->Gradation of harmonic tensions</h2> | |||
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XXX<br /> | XXX<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Chapter 3: Creating scales with Armodue: modal systems"></a><!-- ws:end:WikiTextHeadingRule:30 -->Chapter 3: Creating scales with Armodue: modal systems</h1> | ||
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XXX<br /> | XXX<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Chapter 4: &quot;Geometric&quot; harmonic constructions with Armodue"></a><!-- ws:end:WikiTextHeadingRule:32 -->Chapter 4: &quot;Geometric&quot; harmonic constructions with Armodue</h1> | ||
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XXX<br /> | XXX<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h1&gt; --><h1 id="toc17"><a name="Chapter 5: &quot;elastic&quot; chords"></a><!-- ws:end:WikiTextHeadingRule:34 -->Chapter 5: &quot;elastic&quot; chords</h1> | ||
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XXX</body></html></pre></div> | XXX</body></html></pre></div> | ||