S-expression: Difference between revisions

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<math>\displaystyle \frac {k^2}{k^2 - 1} = \frac {k/(k - 1)}{(k + 1)/k} </math>

which is square-(super)particular ''k'' for a given integer {{nowrap|''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 {{nowrap|S2 {{=}} [[4/3]]}} is the first musically meaningful square-particular, as {{nowrap|1=S1 = [[1/0]]}}.

which is square-(super)particular ''k'' for a given integer {{nowrap|''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 {{nowrap|S2 {{=}} [[4/3]]}} is the first musically meaningful square-particular, as {{nowrap|S1 {{=}} 1/0}}.

Also note that we use the notation S''k''''p'' to mean (S''k'')''p'' rather than S(''k''''p'') for convenience in the practical analysis of regular temperaments using [[S-expression]]s.

@@ Line 15: / Line 15: @@
 <math>\displaystyle \frac {k^2}{k^2 - 1} = \frac {k/(k - 1)}{(k + 1)/k} </math>
-which is square-(super)particular ''k'' for a given integer {{nowrap|''k'' &gt; 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 {{nowrap|S2 {{=}} [[4/3]]}} is the first musically meaningful square-particular, as {{nowrap|1=S1 = [[1/0]]}}.
+which is square-(super)particular ''k'' for a given integer {{nowrap|''k'' &gt; 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 {{nowrap|S2 {{=}} [[4/3]]}} is the first musically meaningful square-particular, as {{nowrap|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.