S-expression: Difference between revisions
→Using S-factorizations to understand the significance of S-expressions: document important equivalence that can be understood most intuitively in terms of S-factorizations |
m →Sk (square-particulars): clarify usage |
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<math>\Large \frac {k^2}{k^2 - 1} = \frac {k/(k - 1)}{(k + 1)/k}</math> | <math>\Large \frac {k^2}{k^2 - 1} = \frac {k/(k - 1)}{(k + 1)/k}</math> | ||
which is square-(super)particular ''k'' for a given integer ''k > 1''. A suggested shorthand for this interval is '''S''k''''' for the ''k''-th square superparticular, where the ''S'' stands for "(Shorthand for) Second-order/Square Superparticular". This will be used later in this article. Note that this means S2 = [[4/3]] is the first musically meaningful square-particular, as S1 = 1/0. | which is square-(super)particular ''k'' for a given integer ''k > 1''. A suggested shorthand for this interval is '''S''k''''' for the ''k''-th square superparticular, where the ''S'' stands for "(Shorthand for) Second-order/Square Superparticular". This will be used later in this article as the notation will prove powerful in understanding the commas and implied tempered structures of [[regular temperament]]s. Note that this means S2 = [[4/3]] is the first musically meaningful square-particular, as S1 = 1/0. | ||
Also note that we use the notation S''k''<sup>''p''</sup> to mean (S''k'')<sup>''p''</sup> rather than S(''k''<sup>''p''</sup>) for convenience in the practical analysis of regular temperaments using [[S-expression]]s. | |||
=== Significance/motivation === | === Significance/motivation === | ||