Maqamat in maqamic temperament: Difference between revisions
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Maqamat (singular "maqam") are scale-like abstractions in [[Arabic, Turkish, Persian|Arabic, Turkish, and Persian]] music. This article, for the most part, treats maqamat simply as scales and disregards everything else about them (emotional connotation, melodic idioms, emphasized pitches...). Also note that in performance, depending on the instrument, a wide variety of subtle microtonal inflections may be used, rather than sticking rigidly to the pitches of a scale. This article deals with only the "central" or "canonical" pitches for each note of a maqam. See http://launch.groups.yahoo.com/group/tuning/message/101523 for an explanation of the level of abstraction being used here. | Maqamat (singular "maqam") are scale-like abstractions in [[Arabic, Turkish, Persian|Arabic, Turkish, and Persian]] music. This article, for the most part, treats maqamat simply as scales and disregards everything else about them (emotional connotation, melodic idioms, emphasized pitches...). Also note that in performance, depending on the instrument, a wide variety of subtle microtonal inflections may be used, rather than sticking rigidly to the pitches of a scale. This article deals with only the "central" or "canonical" pitches for each note of a maqam. See http://launch.groups.yahoo.com/group/tuning/message/101523 for an explanation of the level of abstraction being used here. | ||
Other theorists have developed completely different and often very complicated regular temperament structures to accomodate maqamat. This article is based on a simple rank-2 temperament known variously as "2.3.5.11 maqamic", or "2.3.5.11 mohajira", or "[[Chromatic pairs#Mohaha|mohaha]]". Whatever its name, it is the 2.3.5.11 temperament that tempers out 81/80, 121/120, and 243/242. This means that every other note in the generator chain is meantone, and the fifth generator is split into two equal "neutral thirds" that represent 11/9. An interval is 5-limit if and only if the number of generators needed to reach it is even. Therefore "quarter tones" (i.e. intervals outside meantone) and "intervals outside the 5 limit" are identified in this temperament. See [[Neutral third scales]] for more information. | Other theorists have developed completely different and often very complicated regular temperament structures to accomodate maqamat. This article is based on a simple rank-2 temperament known variously as "2.3.5.11 [[maqamic]]", or "2.3.5.11 [[Meantone family#Mohajira|mohajira]]", or "[[Chromatic pairs#Mohaha|mohaha]]". Whatever its name, it is the 2.3.5.11 temperament that tempers out 81/80, 121/120, and 243/242. This means that every other note in the generator chain is meantone, and the fifth generator is split into two equal "neutral thirds" that represent 11/9. An interval is 5-limit if and only if the number of generators needed to reach it is even. Therefore "quarter tones" (i.e. intervals outside meantone) and "intervals outside the 5 limit" are identified in this temperament. See [[Neutral third scales]] for more information. | ||
Note that, because the fifth is divided into two equal parts, the chromatic semitone (aka apotome, the interval by which sharps and flats alter pitches) is also divided into two equal parts. Therefore, although "quarter tone" is a misnomer because 9/8 is not divided into four equal parts (except in the particular tuning of [[24edo]]), "half flat" and "half sharp" are perfectly accurate. This is helpful in notating maqamic temperament because two new accidentals can be introduced (this article uses ^ and v) that obey the equations ^^ = # and vv = b. | Note that, because the fifth is divided into two equal parts, the chromatic semitone (aka apotome, the interval by which sharps and flats alter pitches) is also divided into two equal parts. Therefore, although "quarter tone" is a misnomer because 9/8 is not divided into four equal parts (except in the particular tuning of [[24edo]]), "half flat" and "half sharp" are perfectly accurate. This is helpful in notating maqamic temperament because two new accidentals can be introduced (this article uses ^ and v) that obey the equations ^^ = # and vv = b. | ||
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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>Maqamat in maqamic temperament</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1> | <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>Maqamat in maqamic temperament</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1> | ||
Maqamat (singular &quot;maqam&quot;) are scale-like abstractions in <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic, Turkish, and Persian</a> music. This article, for the most part, treats maqamat simply as scales and disregards everything else about them (emotional connotation, melodic idioms, emphasized pitches...). Also note that in performance, depending on the instrument, a wide variety of subtle microtonal inflections may be used, rather than sticking rigidly to the pitches of a scale. This article deals with only the &quot;central&quot; or &quot;canonical&quot; pitches for each note of a maqam. See <!-- ws:start:WikiTextUrlRule: | Maqamat (singular &quot;maqam&quot;) are scale-like abstractions in <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic, Turkish, and Persian</a> music. This article, for the most part, treats maqamat simply as scales and disregards everything else about them (emotional connotation, melodic idioms, emphasized pitches...). Also note that in performance, depending on the instrument, a wide variety of subtle microtonal inflections may be used, rather than sticking rigidly to the pitches of a scale. This article deals with only the &quot;central&quot; or &quot;canonical&quot; pitches for each note of a maqam. See <!-- ws:start:WikiTextUrlRule:174:http://launch.groups.yahoo.com/group/tuning/message/101523 --><a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/101523" rel="nofollow">http://launch.groups.yahoo.com/group/tuning/message/101523</a><!-- ws:end:WikiTextUrlRule:174 --> for an explanation of the level of abstraction being used here.<br /> | ||
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Other theorists have developed completely different and often very complicated regular temperament structures to accomodate maqamat. This article is based on a simple rank-2 temperament known variously as &quot;2.3.5.11 maqamic&quot;, or &quot;2.3.5.11 mohajira&quot;, or &quot;<a class="wiki_link" href="/Chromatic%20pairs#Mohaha">mohaha</a>&quot;. Whatever its name, it is the 2.3.5.11 temperament that tempers out 81/80, 121/120, and 243/242. This means that every other note in the generator chain is meantone, and the fifth generator is split into two equal &quot;neutral thirds&quot; that represent 11/9. An interval is 5-limit if and only if the number of generators needed to reach it is even. Therefore &quot;quarter tones&quot; (i.e. intervals outside meantone) and &quot;intervals outside the 5 limit&quot; are identified in this temperament. See <a class="wiki_link" href="/Neutral%20third%20scales">Neutral third scales</a> for more information.<br /> | Other theorists have developed completely different and often very complicated regular temperament structures to accomodate maqamat. This article is based on a simple rank-2 temperament known variously as &quot;2.3.5.11 <a class="wiki_link" href="/maqamic">maqamic</a>&quot;, or &quot;2.3.5.11 <a class="wiki_link" href="/Meantone%20family#Mohajira">mohajira</a>&quot;, or &quot;<a class="wiki_link" href="/Chromatic%20pairs#Mohaha">mohaha</a>&quot;. Whatever its name, it is the 2.3.5.11 temperament that tempers out 81/80, 121/120, and 243/242. This means that every other note in the generator chain is meantone, and the fifth generator is split into two equal &quot;neutral thirds&quot; that represent 11/9. An interval is 5-limit if and only if the number of generators needed to reach it is even. Therefore &quot;quarter tones&quot; (i.e. intervals outside meantone) and &quot;intervals outside the 5 limit&quot; are identified in this temperament. See <a class="wiki_link" href="/Neutral%20third%20scales">Neutral third scales</a> for more information.<br /> | ||
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Note that, because the fifth is divided into two equal parts, the chromatic semitone (aka apotome, the interval by which sharps and flats alter pitches) is also divided into two equal parts. Therefore, although &quot;quarter tone&quot; is a misnomer because 9/8 is not divided into four equal parts (except in the particular tuning of <a class="wiki_link" href="/24edo">24edo</a>), &quot;half flat&quot; and &quot;half sharp&quot; are perfectly accurate. This is helpful in notating maqamic temperament because two new accidentals can be introduced (this article uses ^ and v) that obey the equations ^^ = # and vv = b.<br /> | Note that, because the fifth is divided into two equal parts, the chromatic semitone (aka apotome, the interval by which sharps and flats alter pitches) is also divided into two equal parts. Therefore, although &quot;quarter tone&quot; is a misnomer because 9/8 is not divided into four equal parts (except in the particular tuning of <a class="wiki_link" href="/24edo">24edo</a>), &quot;half flat&quot; and &quot;half sharp&quot; are perfectly accurate. This is helpful in notating maqamic temperament because two new accidentals can be introduced (this article uses ^ and v) that obey the equations ^^ = # and vv = b.<br /> | ||