2.3.7.11.13 subgroup: Difference between revisions
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It is an extension of the [[2.3.7.11 subgroup]]. Notably, it is the subgroup of the [[parapyth]] temperament [[tempering out]] the commas [[352/351]], [[364/363]], and [[896/891]], which maps [[14/11]] to the diatonic major third and [[13/11]] to the diatonic minor third. | It is an extension of the [[2.3.7.11 subgroup]]. Notably, it is the subgroup of the [[parapyth]] temperament [[tempering out]] the commas [[352/351]], [[364/363]], and [[896/891]], which maps [[14/11]] to the diatonic major third and [[13/11]] to the diatonic minor third. | ||
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[[Category:Just intonation subgroups|#]] <!-- 1-digit number --> | |||
[[Category:Rank-5 temperaments|#]] | |||
[[Category:13-limit|#]] | |||
Latest revision as of 07:56, 22 May 2026
The 2.3.7.11.13 subgroup (zalatha in color notation) is a just intonation subgroup where 2, 3, 7, 11, and 13 are the only allowable prime factors, so that every such interval may be written as a ratio of integers which are products of 2, 3, 7, and 11. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the octave include 3/2, 7/4, 14/11, 13/11, and so on.
It is an extension of the 2.3.7.11 subgroup. Notably, it is the subgroup of the parapyth temperament tempering out the commas 352/351, 364/363, and 896/891, which maps 14/11 to the diatonic major third and 13/11 to the diatonic minor third.
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