Tetrachord: Difference between revisions
Wikispaces>genewardsmith **Imported revision 319999742 - Original comment: ** |
Wikispaces>hstraub **Imported revision 353481628 - Original comment: ** |
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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> | ||
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//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 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.// | ||
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 | 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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ssL, sLs, Lss | ssL, sLs, Lss | ||
And, if you have only one step size (as is the case in Porcupine temperament, for instance), you have an evenly-divided fourth, and only one possible rotation. (A tetrachord of this type can be found in [[22edo]] - see [[22edo tetrachords]].) | And, if you have only one step size (as is the case in [[Porcupine]] temperament, for instance), you have an evenly-divided fourth, and only one possible rotation. (A tetrachord of this type can be found in [[22edo]] - see [[22edo tetrachords]].) | ||
=Tetrachords in equal temperaments= | =Tetrachords in equal temperaments= | ||
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<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 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 /> | ||
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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 | 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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<!-- ws:start:WikiTextTocRule:30:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><a href="#Ancient Greek Genera">Ancient Greek Genera</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Ajnas (tetrachords in middle-eastern music)">Ajnas (tetrachords in middle-eastern music)</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Tetrachords Generalized">Tetrachords Generalized</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Tetrachords in equal temperaments">Tetrachords in equal temperaments</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Dividing Other-Than-Perfect Fourths">Dividing Other-Than-Perfect Fourths</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --> | <a href="#Tetrachords And Non-Octave Scales">Tetrachords And Non-Octave Scales</a><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <!-- ws:start:WikiTextTocRule:30:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><a href="#Ancient Greek Genera">Ancient Greek Genera</a><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --> | <a href="#Ajnas (tetrachords in middle-eastern music)">Ajnas (tetrachords in middle-eastern music)</a><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --> | <a href="#Tetrachords Generalized">Tetrachords Generalized</a><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --> | <a href="#Tetrachords in equal temperaments">Tetrachords in equal temperaments</a><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --> | <a href="#Dividing Other-Than-Perfect Fourths">Dividing Other-Than-Perfect Fourths</a><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --> | <a href="#Tetrachords And Non-Octave Scales">Tetrachords And Non-Octave Scales</a><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | ||
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ssL, sLs, Lss<br /> | ssL, sLs, Lss<br /> | ||
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And, if you have only one step size (as is the case in Porcupine temperament, for instance), you have an evenly-divided fourth, and only one possible rotation. (A tetrachord of this type can be found in <a class="wiki_link" href="/22edo">22edo</a> - see <a class="wiki_link" href="/22edo%20tetrachords">22edo tetrachords</a>.)<br /> | And, if you have only one step size (as is the case in <a class="wiki_link" href="/Porcupine">Porcupine</a> temperament, for instance), you have an evenly-divided fourth, and only one possible rotation. (A tetrachord of this type can be found in <a class="wiki_link" href="/22edo">22edo</a> - see <a class="wiki_link" href="/22edo%20tetrachords">22edo tetrachords</a>.)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Tetrachords in equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:22 -->Tetrachords in equal temperaments</h1> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Tetrachords in equal temperaments"></a><!-- ws:end:WikiTextHeadingRule:22 -->Tetrachords in equal temperaments</h1> | ||