S-expression: Difference between revisions
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A '''square superparticular''', or ''square-particular'' for short, is a [[superparticular]] [[interval]] whose numerator is a square number, which is to say, a superparticular of the form | A '''square superparticular''', or ''square-particular'' for short, is a [[superparticular]] [[interval]] whose numerator is a square number, which is to say, a superparticular of the form | ||
<math>\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. Note that this means S2 = [[4/3]] is the first musically meaningful square-particular, as S1 = 1/0. | ||