User:Fastaro/Generalized Pythagorean tuning: Difference between revisions
m Fastaro moved page User:Fastaro/Generalized Pythagorean Tuning to Generalized Pythagorean Tuning: The people who read it appreciated it and it dosn't have to be under my name like it was - I think it should be its own page so anyone feels free to add / edit it |
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== Generating Tuple of Ratios == | == Generating Tuple of Ratios == | ||
<nowiki>Using the derived value of 'n', we can generate a tuple of ratios \[ R_{x_1} \text and\ R_{x_2} \ | <nowiki>Using the derived value of 'n', we can generate a tuple of ratios \[ R_{x_1} \text {and}\ R_{x_2} \text{ , where } R_{x_1} = \frac{p^x}{q^n} \text { and}\ R_{x_2} = \frac{q^{n+1}}{p^x} \]. This pair of ratios represents the upper and lower bounds of a frequency range for a given 'x'. The product of \[ R_{x_1} \cdot R_{x_2} \] for all 'x' from 0 to 'k' yields the result:</nowiki> | ||
\[ \prod_{x=0}^{k} R_{x_1} \cdot R_{x_2} = q^{k+1} \] | \[ \prod_{x=0}^{k} R_{x_1} \cdot R_{x_2} = q^{k+1} \] | ||