S-expression/Advanced results: Difference between revisions
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== Using S-factorizations to understand the significance of S-expressions == | == Using S-factorizations to understand the significance of S-expressions == | ||
This section deals with the forms of the main infinite comma families listed on | This section deals with the forms of the main infinite comma families listed on the main [[S-expression]] page as expressed in terms of nearby harmonics in the harmonic series and as related to square-particulars; note that this uses a mathematical notation of [a, b, c, ...]^[x, y, z, ...] to denote a^x * b^y * c^z * ... | ||
If instead of working through things algebraically we look at square-particulars as describing a relationship between adjacent harmonics, we can use this to understand why certain simplifications and equivalences exist in a way that is equivalent to the sometimes harder-to-understand usual algebraic form: | If instead of working through things algebraically we look at square-particulars as describing a relationship between adjacent harmonics, we can use this to understand why certain simplifications and equivalences exist in a way that is equivalent to the sometimes harder-to-understand usual algebraic form: | ||
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While the question of where it is most appropriate and accurate to equate ultraparticulars is beyond the scope of this section, it nonetheless shows that the 2D comma family Ss''a''/Ss''b'' has utility. | While the question of where it is most appropriate and accurate to equate ultraparticulars is beyond the scope of this section, it nonetheless shows that the 2D comma family Ss''a''/Ss''b'' has utility. | ||
[[Category:Elementary math]] | |||
[[Category:Pages with proofs]] | |||