152edo: Difference between revisions

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The ''152 equal division'' divides the octave into 152 equally sized parts of 7.895 cents each. It is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It provides the [[Optimal_patent_val|optimal patent val]] for the 11-limit [[Mirkwai_clan|grendel]] and [[Mirkwai_clan|kwai]] linear temperaments, the 13-limit rank two temperament [[Ragismic_microtemperaments#Octoid-Octopus|octopus]], the planar temperament [[Hemifamity_family|laka]], and the rank five temperament tempering out 169/168. It tempers out 1600000/1594323, the amity comma, in the 5-limit; 4375/4374, 5120/5103, 6144/6125 and 16875/15807 in the 7-limit; 540/539, 1375/1372, 4000/3993, 5632/5625 and 9801/9800 in the 11-limit, and 169/168, 325/324, 351/350, 364/363, 1001/1000, and 4096/4095 in the 13-limit.

The '''152 equal division''' divides the octave into 152 equally sized parts of 7.895 cents each.

[[~~Paul_Erlich|Paul Erlich~~]] ~~has suggested that 152 could be considered a sort of~~ [~~http:~~//~~tech.dir.groups.yahoo.com~~/~~neo~~/~~groups~~/~~tuning-math~~/~~conversations~~/~~topics~~/~~3041 universal tuning~~].

152et is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323, the [[amity comma]], in the 5-limit; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[16875/16807]] in the 7-limit; [[540/539]], 1375/1372, [[4000/3993]], 5632/5625 and [[9801/9800]] in the 11-limit.

152 = 8 * 19, with divisors 2, 4, 8, 19, 38, 76.

It has two reasonable mappings for 13, with the 152f val scoring much better. The patent val tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], and [[4096/4095]]. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1575/1573]], [[1716/1715]] and [[2080/2079]].

It provides the [[optimal patent val]] for the 11-limit [[Mirkwai clan #Grendel|grendel]] and [[Mirkwai clan #Kwai|kwai]] linear temperaments, the 13-limit rank two temperament [[Ragismic microtemperaments #Octoid-Octopus|octopus]], the 11-limit planar temperament [[Hemifamity family #Laka|laka]], and the rank five temperament tempering out 169/168.

[[Paul Erlich]] has suggested that 152edo could be considered a sort of [http://tech.dir.groups.yahoo.com/neo/groups/tuning-math/conversations/topics/3041 universal tuning].

152 = 8 × 19, with divisors 2, 4, 8, 19, 38, 76.

[[Category:Equal divisions of the octave]]

[[Category:Grendel]]

[[Category:Kwai]]

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-The ''152 equal division'' divides the octave into 152 equally sized parts of 7.895 cents each. It is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It provides the [[Optimal_patent_val|optimal patent val]] for the 11-limit [[Mirkwai_clan|grendel]] and [[Mirkwai_clan|kwai]] linear temperaments, the 13-limit rank two temperament [[Ragismic_microtemperaments#Octoid-Octopus|octopus]], the planar temperament [[Hemifamity_family|laka]], and the rank five temperament tempering out 169/168. It tempers out 1600000/1594323, the amity comma, in the 5-limit; 4375/4374, 5120/5103, 6144/6125 and 16875/15807 in the 7-limit; 540/539, 1375/1372, 4000/3993, 5632/5625 and 9801/9800 in the 11-limit, and 169/168, 325/324, 351/350, 364/363, 1001/1000, and 4096/4095 in the 13-limit.
+The '''152 equal division''' divides the octave into 152 equally sized parts of 7.895 cents each.
-[[Paul_Erlich|Paul Erlich]] has suggested that 152 could be considered a sort of [http://tech.dir.groups.yahoo.com/neo/groups/tuning-math/conversations/topics/3041 universal tuning].
+et is a strong 11-limit system, with the 3, 5, 7, and 11 slightly sharp. It tempers out 1600000/1594323, the [[amity comma]], in the 5-limit; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[16875/16807]] in the 7-limit; [[540/539]], 1375/1372, [[4000/3993]], 5632/5625 and [[9801/9800]] in the 11-limit.
-= 8 * 19, with divisors 2, 4, 8, 19, 38, 76.
+It has two reasonable mappings for 13, with the 152f val scoring much better. The patent val tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], and [[4096/4095]]. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1575/1573]], [[1716/1715]] and [[2080/2079]].
+It provides the [[optimal patent val]] for the 11-limit [[Mirkwai clan #Grendel|grendel]] and [[Mirkwai clan #Kwai|kwai]] linear temperaments, the 13-limit rank two temperament [[Ragismic microtemperaments #Octoid-Octopus|octopus]], the 11-limit planar temperament [[Hemifamity family #Laka|laka]], and the rank five temperament tempering out 169/168.
+[[Paul Erlich]] has suggested that 152edo could be considered a sort of [http://tech.dir.groups.yahoo.com/neo/groups/tuning-math/conversations/topics/3041 universal tuning].
+= 8 × 19, with divisors 2, 4, 8, 19, 38, 76.
+[[Category:Equal divisions of the octave]]
+[[Category:Grendel]]
+[[Category:Kwai]]