Hewuermera comma: Difference between revisions
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As a generalized lopsided comma, 589824/588245 has the S-expression of (S46 = [[2116/2115]]) × (S47 = [[2209/2208]])<sup>2</sup> × (S48 = [[2304/2303]])<sup>3</sup>. Equivalent factorizations include (S48 = 2304/2303) × (S(47/2) = [[2209/2205]]) and (S46×S47×S48 = [[736/735]]) × (S47×S48 = [[1128/1127]]) × (S48 = 2304/2303). | As a generalized lopsided comma, 589824/588245 has the S-expression of (S46 = [[2116/2115]]) × (S47 = [[2209/2208]])<sup>2</sup> × (S48 = [[2304/2303]])<sup>3</sup>. Equivalent factorizations include (S48 = 2304/2303) × (S(47/2) = [[2209/2205]]) and (S46×S47×S48 = [[736/735]]) × (S47×S48 = [[1128/1127]]) × (S48 = 2304/2303). | ||
The S-factorization indicates that 23 and 47 are particularly natural primes to incorporate into hewuermera temperaments (by tempering out S46, S47, and S48); in particular, three 8/7s reach a "[[ | The S-factorization indicates that 23 and 47 are particularly natural primes to incorporate into hewuermera temperaments (by tempering out S46, S47, and S48); in particular, three 8/7s reach a "[[1/2-comma meantone]] fifth" identified with [[70/47]][[~]][[94/63]]. | ||
== Temperaments == | == Temperaments == |