Tetrachord: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>~~2012~~-07-~~17 06~~:29:24 UTC</tt>.<br>

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-27 21:57:47 UTC</tt>.<br>

: The original revision id was <tt>~~353481628~~</tt>.<br>

: The original revision id was <tt>597354074</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>

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John Chalmers, in [[http://eamusic.dartmouth.edu/%7Elarry/published_articles/divisions_of_the_tetrachord/index.html|Divisions of the Tetrachord]], tells us:

//Tetrachords are modules from which more complex scalar and harmonic structures may be built. These structures range from the simple heptatonic scales known to the classical civilizations of the eastern ~~Medditterranean~~ to experimental gamuts with many tones. Furthermore, the traditional scales of much of the world's music, including that of Europe, the [[Arabic, Turkish, Persian|Near East]], the Catholic and Orthodox churches, Iran and India, are still based on tetrachords. Tetrachords are thus basic to an understanding of much of the world's music.//

//Tetrachords are modules from which more complex scalar and harmonic structures may be built. These structures range from the simple heptatonic scales known to the classical civilizations of the eastern Mediterranean to experimental gamuts with many tones. Furthermore, the traditional scales of much of the world's music, including that of Europe, the [[Arabic, Turkish, Persian|Near East]], the Catholic and Orthodox churches, Iran and India, are still based on tetrachords. Tetrachords are thus basic to an understanding of much of the world's music.//

Related pages: [[22edo tetrachords]], [[17edo tetrachords]], [[Tricesimoprimal Tetrachordal Tesseract]], [[Armodue armonia#Creating%20scales%20with%20Armodue:%20modal%20systems-Modal%20systems%20based%20on%20tetrachords%20and%20pentachords|16edo tetrachords]], [[Gallery of Wakalixes#Divisions%20of%20the%20Tetrachord|Wakalix tetrachords]]

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The CI (and the other intervals) approximates a "tone," measuring less than 250 cents.

==~~Ptolomy~~'s Catalog==

==Ptolemy's Catalog==

In the //Harmonics//, ~~Ptolomy~~ catalogs several historical tetrachords and attributes them to particular theorists.

In the //Harmonics//, Ptolemy catalogs several historical tetrachords and attributes them to particular theorists.

||||||~ Archytas's Genera ||

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John Chalmers, in <a class="wiki_link_ext" href="http://eamusic.dartmouth.edu/%7Elarry/published_articles/divisions_of_the_tetrachord/index.html" rel="nofollow">Divisions of the Tetrachord</a>, tells us:<br />

<br />

<em>Tetrachords are modules from which more complex scalar and harmonic structures may be built. These structures range from the simple heptatonic scales known to the classical civilizations of the eastern ~~Medditterranean~~ to experimental gamuts with many tones. Furthermore, the traditional scales of much of the world's music, including that of Europe, the <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Near East</a>, the Catholic and Orthodox churches, Iran and India, are still based on tetrachords. Tetrachords are thus basic to an understanding of much of the world's music.</em><br />

<em>Tetrachords are modules from which more complex scalar and harmonic structures may be built. These structures range from the simple heptatonic scales known to the classical civilizations of the eastern Mediterranean to experimental gamuts with many tones. Furthermore, the traditional scales of much of the world's music, including that of Europe, the <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Near East</a>, the Catholic and Orthodox churches, Iran and India, are still based on tetrachords. Tetrachords are thus basic to an understanding of much of the world's music.</em><br />

<br />

Related pages: <a class="wiki_link" href="/22edo%20tetrachords">22edo tetrachords</a>, <a class="wiki_link" href="/17edo%20tetrachords">17edo tetrachords</a>, <a class="wiki_link" href="/Tricesimoprimal%20Tetrachordal%20Tesseract">Tricesimoprimal Tetrachordal Tesseract</a>, <a class="wiki_link" href="/Armodue%20armonia#Creating%20scales%20with%20Armodue:%20modal%20systems-Modal%20systems%20based%20on%20tetrachords%20and%20pentachords">16edo tetrachords</a>, <a class="wiki_link" href="/Gallery%20of%20Wakalixes#Divisions%20of%20the%20Tetrachord">Wakalix tetrachords</a><br />

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The CI (and the other intervals) approximates a &quot;tone,&quot; measuring less than 250 cents.<br />

<br />

<h2 id="toc5"><a name="Ancient Greek Genera-~~Ptolomy~~'s Catalog"></a>~~Ptolomy~~'s Catalog</h2>

<h2 id="toc5"><a name="Ancient Greek Genera-Ptolemy's Catalog"></a>Ptolemy's Catalog</h2>

<br />

In the <em>Harmonics</em>, ~~Ptolomy~~ catalogs several historical tetrachords and attributes them to particular theorists.<br />

In the <em>Harmonics</em>, Ptolemy catalogs several historical tetrachords and attributes them to particular theorists.<br />

<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2012-07-17 06:29:24 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-27 21:57:47 UTC</tt>.<br>
-: The original revision id was <tt>353481628</tt>.<br>
+: The original revision id was <tt>597354074</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>
@@ Line 10: / Line 10: @@
 John Chalmers, in [[http://eamusic.dartmouth.edu/%7Elarry/published_articles/divisions_of_the_tetrachord/index.html|Divisions of the Tetrachord]], tells us:
-//Tetrachords are modules from which more complex scalar and harmonic structures may be built. These structures range from the simple heptatonic scales known to the classical civilizations of the eastern Medditterranean to experimental gamuts with many tones. Furthermore, the traditional scales of much of the world's music, including that of Europe, the [[Arabic, Turkish, Persian|Near East]], the Catholic and Orthodox churches, Iran and India, are still based on tetrachords. Tetrachords are thus basic to an understanding of much of the world's music.//
+//Tetrachords are modules from which more complex scalar and harmonic structures may be built. These structures range from the simple heptatonic scales known to the classical civilizations of the eastern Mediterranean to experimental gamuts with many tones. Furthermore, the traditional scales of much of the world's music, including that of Europe, the [[Arabic, Turkish, Persian|Near East]], the Catholic and Orthodox churches, Iran and India, are still based on tetrachords. Tetrachords are thus basic to an understanding of much of the world's music.//
 Related pages: [[22edo tetrachords]], [[17edo tetrachords]], [[Tricesimoprimal Tetrachordal Tesseract]], [[Armodue armonia#Creating%20scales%20with%20Armodue:%20modal%20systems-Modal%20systems%20based%20on%20tetrachords%20and%20pentachords|16edo tetrachords]], [[Gallery of Wakalixes#Divisions%20of%20the%20Tetrachord|Wakalix tetrachords]]
@@ Line 33: / Line 33: @@
 The CI (and the other intervals) approximates a "tone," measuring less than 250 cents.
-==Ptolomy's Catalog==
+==Ptolemy's Catalog==
-In the //Harmonics//, Ptolomy catalogs several historical tetrachords and attributes them to particular theorists.
+In the //Harmonics//, Ptolemy catalogs several historical tetrachords and attributes them to particular theorists.
 ||||||~ Archytas's Genera ||
@@ Line 161: / Line 161: @@
 John Chalmers, in &lt;a class="wiki_link_ext" href="http://eamusic.dartmouth.edu/%7Elarry/published_articles/divisions_of_the_tetrachord/index.html" rel="nofollow"&gt;Divisions of the Tetrachord&lt;/a&gt;, tells us:&lt;br /&gt;
 &lt;br /&gt;
-&lt;em&gt;Tetrachords are modules from which more complex scalar and harmonic structures may be built. These structures range from the simple heptatonic scales known to the classical civilizations of the eastern Medditterranean to experimental gamuts with many tones. Furthermore, the traditional scales of much of the world's music, including that of Europe, the &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Near East&lt;/a&gt;, the Catholic and Orthodox churches, Iran and India, are still based on tetrachords. Tetrachords are thus basic to an understanding of much of the world's music.&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;Tetrachords are modules from which more complex scalar and harmonic structures may be built. These structures range from the simple heptatonic scales known to the classical civilizations of the eastern Mediterranean to experimental gamuts with many tones. Furthermore, the traditional scales of much of the world's music, including that of Europe, the &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Near East&lt;/a&gt;, the Catholic and Orthodox churches, Iran and India, are still based on tetrachords. Tetrachords are thus basic to an understanding of much of the world's music.&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
 Related pages: &lt;a class="wiki_link" href="/22edo%20tetrachords"&gt;22edo tetrachords&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo%20tetrachords"&gt;17edo tetrachords&lt;/a&gt;, &lt;a class="wiki_link" href="/Tricesimoprimal%20Tetrachordal%20Tesseract"&gt;Tricesimoprimal Tetrachordal Tesseract&lt;/a&gt;, &lt;a class="wiki_link" href="/Armodue%20armonia#Creating%20scales%20with%20Armodue:%20modal%20systems-Modal%20systems%20based%20on%20tetrachords%20and%20pentachords"&gt;16edo tetrachords&lt;/a&gt;, &lt;a class="wiki_link" href="/Gallery%20of%20Wakalixes#Divisions%20of%20the%20Tetrachord"&gt;Wakalix tetrachords&lt;/a&gt;&lt;br /&gt;
@@ Line 184: / Line 184: @@
   The CI (and the other intervals) approximates a &amp;quot;tone,&amp;quot; measuring less than 250 cents.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Ancient Greek Genera-Ptolomy's Catalog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Ptolomy's Catalog&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Ancient Greek Genera-Ptolemy's Catalog"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Ptolemy's Catalog&lt;/h2&gt;
   &lt;br /&gt;
-In the &lt;em&gt;Harmonics&lt;/em&gt;, Ptolomy catalogs several historical tetrachords and attributes them to particular theorists.&lt;br /&gt;
+In the &lt;em&gt;Harmonics&lt;/em&gt;, Ptolemy catalogs several historical tetrachords and attributes them to particular theorists.&lt;br /&gt;
 &lt;br /&gt;