Armodue harmony: Difference between revisions
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
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: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-09-09 | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-09-09 09:33:06 UTC</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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==The intervals of 6 eka and 10 eka== | ==The intervals of 6 eka and 10 eka== | ||
The interval of 6 eka is particularly striking, with its complement of 10 eka. 6 eka is located exactly at the point of equidistance between the major third and the perfect fourth of the tempered system, while 12 eka is the average between a perfect fifth and a minor sixth. | |||
This property constitutes the most interesting point of the intervals examined so far. The interval of 6 eka joins the concise color of the major third with the propulsion and the dynamism of the perfect fourth, the interval of 10 eka combines the twilight character of the minor sixth with the staticity and the balance of the perfect fifth. | |||
In the tempered system, thirds and sixths give color to the chords, while the base tones of the same chords are concatenated in jumps of perfect fourths and fifths. In Armodue, the ambiguity of the "neutral" intervals that mediate between third and fourth as between fifth and sixth makes them suitable for use both in the construction of the chords and in the concatenation XXX of the base tones. | |||
Like the intervals of 2 and 14 eka (which are also "neutral": the first halfway between minor and major second and the second equidistant from minor and major seventh), the intervals of 6 and 10 eka are unfamiliar to the western ear (excluding those accustomed to the quarter-tone). | |||
The intervals of 6 and 10 eka are classified as neutral consonances. | |||
==The intervals of 7 eka and 9 eka== | |||
The intervals corresponding to the perfect fourth and and the perfect fifth in Armodue are the intervals of 7 and 9 eka, the first one quantifies in a slightly shaprened fourth, the second in a slightly flattened fifth. | |||
These Armodue intervals, however, are incompatible with the concept of the cycle of the fifth that is on the base of the dodecatonic system. Especially with the intervals of 7 and 9 eka, Armodue shows an entirely new and different system, compared to the ruling dodecatonic system. | |||
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 belöng to the open consonances. | |||
==The interval of 8 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:34:&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:34 --><!-- ws:start:WikiTextTocRule:35: --><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:35 --><!-- ws:start:WikiTextTocRule:36: --><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:36 --><!-- ws:start:WikiTextTocRule:37: --><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:37 --><!-- ws:start:WikiTextTocRule:38: --><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:38 --><!-- ws:start:WikiTextTocRule:39: --><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:39 --><!-- ws:start:WikiTextTocRule:40: --><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:40 --><!-- ws:start:WikiTextTocRule:41: --><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:41 --><!-- ws:start:WikiTextTocRule:42: --><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:42 --><!-- ws:start:WikiTextTocRule:43: --><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:43 --><!-- ws:start:WikiTextTocRule:44: --><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:44 --><!-- ws:start:WikiTextTocRule:45: --><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:45 --><!-- ws:start:WikiTextTocRule:46: --><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:46 --><!-- ws:start:WikiTextTocRule:47: --><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:47 --><!-- ws:start:WikiTextTocRule:48: --><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:48 --><!-- ws:start:WikiTextTocRule:49: --><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:49 --><!-- ws:start:WikiTextTocRule:50: --><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:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 1em;"><a href="#Chapter 5: &quot;elastic&quot; chords">Chapter 5: &quot;elastic&quot; chords</a></div> | ||
<!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --></div> | |||
<!-- ws:end:WikiTextTocRule:52 --><!-- 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: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> | <!-- 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 /> | |||
The interval of 6 eka is particularly striking, with its complement of 10 eka. 6 eka is located exactly at the point of equidistance between the major third and the perfect fourth of the tempered system, while 12 eka is the average between a perfect fifth and a minor sixth.<br /> | |||
<br /> | |||
This property constitutes the most interesting point of the intervals examined so far. The interval of 6 eka joins the concise color of the major third with the propulsion and the dynamism of the perfect fourth, the interval of 10 eka combines the twilight character of the minor sixth with the staticity and the balance of the perfect fifth.<br /> | |||
<br /> | |||
In the tempered system, thirds and sixths give color to the chords, while the base tones of the same chords are concatenated in jumps of perfect fourths and fifths. In Armodue, the ambiguity of the &quot;neutral&quot; intervals that mediate between third and fourth as between fifth and sixth makes them suitable for use both in the construction of the chords and in the concatenation XXX of the base tones.<br /> | |||
<br /> | |||
Like the intervals of 2 and 14 eka (which are also &quot;neutral&quot;: the first halfway between minor and major second and the second equidistant from minor and major seventh), the intervals of 6 and 10 eka are unfamiliar to the western ear (excluding those accustomed to the quarter-tone).<br /> | |||
<br /> | |||
The intervals of 6 and 10 eka are classified as neutral consonances.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Chapter 2: The interval table-The intervals of 7 eka and 9 eka"></a><!-- ws:end:WikiTextHeadingRule:24 -->The intervals of 7 eka and 9 eka</h2> | |||
<br /> | |||
The intervals corresponding to the perfect fourth and and the perfect fifth in Armodue are the intervals of 7 and 9 eka, the first one quantifies in a slightly shaprened fourth, the second in a slightly flattened fifth.<br /> | |||
<br /> | |||
These Armodue intervals, however, are incompatible with the concept of the cycle of the fifth that is on the base of the dodecatonic system. Especially with the intervals of 7 and 9 eka, Armodue shows an entirely new and different system, compared to the ruling dodecatonic system.<br /> | |||
<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 /> | |||
As for the classification, 7 and 9 eka belöng to the open consonances.<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> | |||
<br /> | <br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:28:&lt;h1&gt; --><h1 id="toc14"><a name="Chapter 3: Creating scales with Armodue: modal systems"></a><!-- ws:end:WikiTextHeadingRule:28 -->Chapter 3: Creating scales with Armodue: modal systems</h1> | ||
<br /> | <br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:30:&lt;h1&gt; --><h1 id="toc15"><a name="Chapter 4: &quot;Geometric&quot; harmonic constructions with Armodue"></a><!-- ws:end:WikiTextHeadingRule:30 -->Chapter 4: &quot;Geometric&quot; harmonic constructions with Armodue</h1> | ||
<br /> | <br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h1&gt; --><h1 id="toc16"><a name="Chapter 5: &quot;elastic&quot; chords"></a><!-- ws:end:WikiTextHeadingRule:32 -->Chapter 5: &quot;elastic&quot; chords</h1> | ||
<br /> | <br /> | ||
XXX</body></html></pre></div> | XXX</body></html></pre></div> | ||