User:Fastaro/Generalized Pythagorean tuning: Difference between revisions

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=== Chain of fifths / fourths ===
=== Chain of fifths / fourths ===
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 or it's octave complement, the chain of fourths.
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\[ S_{p_5} = \left\{ \frac{p^{x}}{q^n}  \mid x \in \mathbb{Z}, 0 \leq x \leq k \right\} \]
\[ S_{p_5} = \left\{ \frac{p^{x}}{q^n}  \mid x \in \mathbb{Z}, 0 \leq x \leq k \right\} \]