2.3.7.11 subgroup
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- This revision was by author genewardsmith and made on 2013-12-17 14:08:14 UTC.
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Original Wikitext content:
* Genus(3*7*11) 12/11, 14/11, 21/16, 16/11, 3/2, 7/4, 21/11, 2
* Genus(3*7^2*11) 49/48, 49/44, 7/6, 14/11, 4/3, 16/11, 49/33, 49/32, 56/33, 7/4, 64/33, 2
* Ptolemy's Intense Chromatic at 1/1 22/21 8/7 4/3 3/2 11/7 12/7 2/1 (disjunct form)
* a conjunct Rast: 1/1 9/8 27/22 4/3 3/2 11/8 16/9 2/1 (note: actually 2.3.11 subgroup)
* Qutb al-Din al-Shirazi's version of Hijaz: 1/1-12/11-14/11-4/3 (12:11-7:6-22:21), itself a permutation of Ptolemy's Intense Chromatic
** [[Margo Schulter]] notes: "A modern form of Maqam Hijaz based on this tuning might be 1/1-12/11-14/11-4/3-32-18/11-16/9-2/1 ascending, and 1/1-12/11-14/11-4/3-3/2-128/81-16/9-2/1 descending (with the minor sixth maybe a bit smaller, say 11/7 or the like)."
* a septimal flavor of Sazkar, which has a minor third above the 1/1 ascending but a tone descending: thus ascending 1/1-7/6-11/9-4/3-3/2-27/16-11/6-2/1, and descending 1/1-9/8-11/9-4/3-3/2-27/16-11/6-2/1
** Margo Schulter adds: "I should caution that an Arab Rast, of which Sazkar is an offshoot, might usually have a Zalzalian third more like 27/22 or 16/13 rather than 11/9, so this may be more of a new tuning than a traditional Arab Sazkar."
* The 1-3-7-9-11 [[Combination product sets|2(5 Dekany]] within a 12-tone [[Periodic scale#Constant Structure|constant structure]] (see [[http://anaphoria.com/dekanyconstantstructures.pdf|link]]): 1*3, 9*11, 3*9, 1*7, 3*7*11, 7*9, 3*11, 1*9, 3*9*11, 7*11, 3*7, 1*11.
* A 12f, {352/351, 364/363} 2.3.7.11.13 elf transversal: 28/27-9/8-13/11-9/7-4/3-11/8-3/2-14/9-22/13-16/9-27/14-2Original HTML content:
<html><head><title>Gallery of 2.3.7.11 Subgroup Scales</title></head><body><ul><li>Genus(3*7*11) 12/11, 14/11, 21/16, 16/11, 3/2, 7/4, 21/11, 2</li><li>Genus(3*7^2*11) 49/48, 49/44, 7/6, 14/11, 4/3, 16/11, 49/33, 49/32, 56/33, 7/4, 64/33, 2</li><li>Ptolemy's Intense Chromatic at 1/1 22/21 8/7 4/3 3/2 11/7 12/7 2/1 (disjunct form)</li><li>a conjunct Rast: 1/1 9/8 27/22 4/3 3/2 11/8 16/9 2/1 (note: actually 2.3.11 subgroup)</li><li>Qutb al-Din al-Shirazi's version of Hijaz: 1/1-12/11-14/11-4/3 (12:11-7:6-22:21), itself a permutation of Ptolemy's Intense Chromatic<ul><li><a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a> notes: "A modern form of Maqam Hijaz based on this tuning might be 1/1-12/11-14/11-4/3-32-18/11-16/9-2/1 ascending, and 1/1-12/11-14/11-4/3-3/2-128/81-16/9-2/1 descending (with the minor sixth maybe a bit smaller, say 11/7 or the like)."</li></ul></li><li>a septimal flavor of Sazkar, which has a minor third above the 1/1 ascending but a tone descending: thus ascending 1/1-7/6-11/9-4/3-3/2-27/16-11/6-2/1, and descending 1/1-9/8-11/9-4/3-3/2-27/16-11/6-2/1<ul><li>Margo Schulter adds: "I should caution that an Arab Rast, of which Sazkar is an offshoot, might usually have a Zalzalian third more like 27/22 or 16/13 rather than 11/9, so this may be more of a new tuning than a traditional Arab Sazkar."</li></ul></li><li>The 1-3-7-9-11 <a class="wiki_link" href="/Combination%20product%20sets">2(5 Dekany</a> within a 12-tone <a class="wiki_link" href="/Periodic%20scale#Constant Structure">constant structure</a> (see <a class="wiki_link_ext" href="http://anaphoria.com/dekanyconstantstructures.pdf" rel="nofollow">link</a>): 1*3, 9*11, 3*9, 1*7, 3*7*11, 7*9, 3*11, 1*9, 3*9*11, 7*11, 3*7, 1*11.</li><li>A 12f, {352/351, 364/363} 2.3.7.11.13 elf transversal: 28/27-9/8-13/11-9/7-4/3-11/8-3/2-14/9-22/13-16/9-27/14-2</li></ul></body></html>