User:Fastaro/Generalized Pythagorean tuning: Difference between revisions
Created page with "= Generalized Pythagorean Tuning = == Introduction == Generalized Pythagorean Tuning is an extension of the traditional Pythagorean tuning method, which is based on chains of..." |
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== Generating Tuple of Ratios == | == Generating Tuple of Ratios == | ||
Using the derived value of 'n', we can generate a tuple of ratios \[ R_{x_1} \ | <nowiki>Using the derived value of 'n', we can generate a tuple of ratios \[ R_{x_1} \text and\ R_{x_2} \], 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 \[ R_{x_1} \text and\ R_{x_2} \] for all 'x' from 0 to 'k' yields the series:</nowiki> | ||
\[ \prod_{x=0}^{k} R_{x_1} \cdot R_{x_2} = q^{k+1} \] | \[ \prod_{x=0}^{k} R_{x_1} \cdot R_{x_2} = q^{k+1} \] | ||