S-expression: Difference between revisions
m →hk = 2k + 1: correction as per Frostburn's discovery |
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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 | This section deals with the forms of the main infinite comma families listed on this 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 * ... | ||
<nowiki>*</nowiki> except [[lopsided comma]]s which are dealt with in their respective subsection of the page. | |||
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: | ||