Armodue harmony: Difference between revisions
Wikispaces>hstraub **Imported revision 161360407 - Original comment: ** |
Wikispaces>hstraub **Imported revision 161364741 - Original comment: ** |
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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 08: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-09-09 08:58:20 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>161364741</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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This is a translation of an article by Luca Attanasio. Original page in italian: [[http://www.armodue.com/armonia.htm]] | This is a translation of an article by Luca Attanasio. Original page in italian: [[http://www.armodue.com/armonia.htm]] | ||
//Note: This is a preliminary tranlsation. Parts that are still "under construction" are marked with "XXX".// | //Note: This is a preliminary tranlsation. Parts that are still "under construction" are marked with "XXX".// | ||
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==The intervals of 4 eka and 12 eka== | ==The intervals of 4 eka and 12 eka== | ||
With the intervals of 4 and 12 eka we have two intervals that are very popular and familiar to the ear translated into Armodue. Indeed 4 eka and 12 eka correspond exactly to the minor third and the major sixth in the dodecatonic system. Therefore, there is the evident possibility of evoking major and minor triads with Armodue (the minor triad is created in stacking 4 eka and 5 eka on a base tone, the major triad stacking 5 eka and 4 eka). The perfect equivalence of the two considered intervals in the dodecatonic system and in Armodue is a crucial point in the inevitable interaction that the ear of a western listener will establish between the two different tunings. In fact, listening to the intervals of 4 and 12 eka, the ear will immediately associate these Armodue intervals to two already familiar ones (the minor third and the major sixth). For this reason, many of the other intervals present - in an Armodue environment - in a context to those of 4 and 12 eka are likely to be felt by the ear as abnormal and unknown. The composers will give much attention every time they use one of these two intervals, trying to predict the reactions of an ear used to the dodecaphonic system. | |||
In a particular and interesting case, a composer could also decide not to use the intervals giving the color to the harmonies - minor and major thirds and sixths transferred in Armodue: intervals of 4, 5, 11 and 12 eka. Excluding these four types of intervals in the texture of the chords, the ear probably will realize at once that it is in a new and unknown musical environment. | |||
Moreover, the exclusion of minor and major thirds and sixths in the dodecatonic system has already been successfully tested by several composers; from an aesthetic point of view, the lack of colour and the openness of sounds that are feeled then are particularly significant and expressive. | |||
Another interval of Armodue perfectly equivalent to an interval of the dodecatonic system is the one of 8 eka, whose width is found to be equal to that of the tritone. However, the restless nature of that interval makes it unique and not comparable to the intervals just treated. | |||
The intervals of 4 and 12 eka belong without doubt - being of equivalent size - to the same category that includes the minor third and the major sixth: that of sweet consonances. | |||
==The intervals of 5 eka and 11 eka== | |||
The interval of 5 eka is very close to the natural major third that appears as the ratio between the fourth and fifth harmonic of the overtone series. The major third of the dodecatonic system is not so close to the natural major third as the interval of 5 eka. | |||
The complement of 5 eka is the interval of 11 eka, very close to the natural minor sixth that occurs between the fifth and eighth harmonic. Since the intervals of 5 and 11 eka are associated to the tempered third and sixth, the same considerations hold that were made in the previous paragraph about the intervals of 4 and 12 eka. They too are classified as sweet consonances. | |||
==The intervals of 6 eka and 10 eka== | |||
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:30:&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:30 --><!-- ws:start:WikiTextTocRule:31: --><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:31 --><!-- ws:start:WikiTextTocRule:32: --><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:32 --><!-- ws:start:WikiTextTocRule:33: --><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:33 --><!-- ws:start:WikiTextTocRule:34: --><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:34 --><!-- ws:start:WikiTextTocRule:35: --><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:35 --><!-- ws:start:WikiTextTocRule:36: --><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:36 --><!-- ws:start:WikiTextTocRule:37: --><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:37 --><!-- ws:start:WikiTextTocRule:38: --><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:38 --><!-- ws:start:WikiTextTocRule:39: --><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:39 --><!-- ws:start:WikiTextTocRule:40: --><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:40 --><!-- ws:start:WikiTextTocRule:41: --><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:41 --><!-- ws:start:WikiTextTocRule:42: --><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:42 --><!-- ws:start:WikiTextTocRule:43: --><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:43 --><!-- ws:start:WikiTextTocRule:44: --><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:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 1em;"><a href="#Chapter 5: &quot;elastic&quot; chords">Chapter 5: &quot;elastic&quot; chords</a></div> | ||
<!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --></div> | |||
<!-- ws:end:WikiTextTocRule:46 --><!-- 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 /> | ||
<em>Note: This is a preliminary tranlsation. Parts that are still &quot;under construction&quot; are marked with &quot;XXX&quot;.</em><br /> | <em>Note: This is a preliminary tranlsation. Parts that are still &quot;under construction&quot; are marked with &quot;XXX&quot;.</em><br /> | ||
<br /> | <br /> | ||
<hr /> | <hr /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Chapter 2: The interval table-The intervals of 4 eka and 12 eka"></a><!-- ws:end:WikiTextHeadingRule:18 -->The intervals of 4 eka and 12 eka</h2> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Chapter 2: The interval table-The intervals of 4 eka and 12 eka"></a><!-- ws:end:WikiTextHeadingRule:18 -->The intervals of 4 eka and 12 eka</h2> | ||
<br /> | |||
With the intervals of 4 and 12 eka we have two intervals that are very popular and familiar to the ear translated into Armodue. Indeed 4 eka and 12 eka correspond exactly to the minor third and the major sixth in the dodecatonic system. Therefore, there is the evident possibility of evoking major and minor triads with Armodue (the minor triad is created in stacking 4 eka and 5 eka on a base tone, the major triad stacking 5 eka and 4 eka). The perfect equivalence of the two considered intervals in the dodecatonic system and in Armodue is a crucial point in the inevitable interaction that the ear of a western listener will establish between the two different tunings. In fact, listening to the intervals of 4 and 12 eka, the ear will immediately associate these Armodue intervals to two already familiar ones (the minor third and the major sixth). For this reason, many of the other intervals present - in an Armodue environment - in a context to those of 4 and 12 eka are likely to be felt by the ear as abnormal and unknown. The composers will give much attention every time they use one of these two intervals, trying to predict the reactions of an ear used to the dodecaphonic system.<br /> | |||
<br /> | |||
In a particular and interesting case, a composer could also decide not to use the intervals giving the color to the harmonies - minor and major thirds and sixths transferred in Armodue: intervals of 4, 5, 11 and 12 eka. Excluding these four types of intervals in the texture of the chords, the ear probably will realize at once that it is in a new and unknown musical environment.<br /> | |||
<br /> | |||
Moreover, the exclusion of minor and major thirds and sixths in the dodecatonic system has already been successfully tested by several composers; from an aesthetic point of view, the lack of colour and the openness of sounds that are feeled then are particularly significant and expressive.<br /> | |||
<br /> | |||
Another interval of Armodue perfectly equivalent to an interval of the dodecatonic system is the one of 8 eka, whose width is found to be equal to that of the tritone. However, the restless nature of that interval makes it unique and not comparable to the intervals just treated.<br /> | |||
The intervals of 4 and 12 eka belong without doubt - being of equivalent size - to the same category that includes the minor third and the major sixth: that of sweet consonances.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Chapter 2: The interval table-The intervals of 5 eka and 11 eka"></a><!-- ws:end:WikiTextHeadingRule:20 -->The intervals of 5 eka and 11 eka</h2> | |||
<br /> | |||
The interval of 5 eka is very close to the natural major third that appears as the ratio between the fourth and fifth harmonic of the overtone series. The major third of the dodecatonic system is not so close to the natural major third as the interval of 5 eka.<br /> | |||
<br /> | |||
The complement of 5 eka is the interval of 11 eka, very close to the natural minor sixth that occurs between the fifth and eighth harmonic. Since the intervals of 5 and 11 eka are associated to the tempered third and sixth, the same considerations hold that were made in the previous paragraph about the intervals of 4 and 12 eka. They too are classified as sweet consonances.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Chapter 2: The interval table-The intervals of 6 eka and 10 eka"></a><!-- ws:end:WikiTextHeadingRule:22 -->The intervals of 6 eka and 10 eka</h2> | |||
<br /> | <br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:24:&lt;h1&gt; --><h1 id="toc12"><a name="Chapter 3: Creating scales with Armodue: modal systems"></a><!-- ws:end:WikiTextHeadingRule:24 -->Chapter 3: Creating scales with Armodue: modal systems</h1> | ||
<br /> | <br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:26:&lt;h1&gt; --><h1 id="toc13"><a name="Chapter 4: &quot;Geometric&quot; harmonic constructions with Armodue"></a><!-- ws:end:WikiTextHeadingRule:26 -->Chapter 4: &quot;Geometric&quot; harmonic constructions with Armodue</h1> | ||
<br /> | <br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Chapter 5: &quot;elastic&quot; chords"></a><!-- ws:end:WikiTextHeadingRule:28 -->Chapter 5: &quot;elastic&quot; chords</h1> | ||
<br /> | <br /> | ||
XXX</body></html></pre></div> | XXX</body></html></pre></div> | ||