3136/3125: Difference between revisions

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Then we can optionally replace S4 with a nontrivial equivalent S-expression, S4 = [[36/35|S6]]*[[49/48|S7]]*[[64/63|S8]] = ([[6/5]])/([[9/8]]); substituting this in and simplifying yields:
Then we can optionally replace S4 with a nontrivial equivalent S-expression, S4 = [[36/35|S6]]*[[49/48|S7]]*[[64/63|S8]] = ([[6/5]])/([[9/8]]); substituting this in and simplifying yields:


S6*S7*S8*S7/S5<sup>2</sup> from which we can obtain an alternative equivalence 3136/3125 = ([[49/45]])/([[25/24]])<sup>2</sup>, meaning we split [[49/45]] into two [[25/24]]'s in the resulting temperament.
S6*S7<sup>2</sup>*S8/S5<sup>2</sup> from which we can obtain an alternative equivalence 3136/3125 = ([[49/45]])/([[25/24]])<sup>2</sup>, meaning we split [[49/45]] into two [[25/24]]'s in the resulting temperament.


== Temperaments ==
== Temperaments ==