User:Fastaro/Generalized Pythagorean tuning: Difference between revisions
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The original pythagorean tuning using the ratios from the chain of fifths and chain of fourths in a tuple. The generalized pythagorean ratios shows us how you can generate a scale of kth EDO with only the chain of fifths. | The original pythagorean tuning using the ratios from the chain of fifths and chain of fourths in a tuple. The generalized pythagorean ratios shows us how you can generate a scale of kth EDO with only the chain of fifths. | ||
<nowiki> | <nowiki> | ||
\[ S_{p_5} = \left\{ | \[ S_{p_5} = \left\{ \frac{p^{x}}{q^n} \mid x \in \mathbb{Z}, 0 \leq x \leq k \right\} \] | ||
\[ S_{p_4} = \left\{ | \[ S_{p_4} = \left\{ \frac{q^{n+1}}{p^x} \mid x \in \mathbb{Z}, 0 \leq x \leq k \right\} \] | ||
</nowiki> | </nowiki> | ||