User:Fastaro/Generalized Pythagorean tuning: Difference between revisions
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== Implications and applications == | == Implications and applications == | ||
The generalized Pythagorean tuning provides a more versatile framework for musical tuning, allowing composers and musicians to explore scales and harmonies beyond the traditional limits. This approach can lead to new musical expressions and better alignment with various musical traditions and instruments. | The generalized Pythagorean tuning provides a more versatile framework for musical tuning, allowing composers and musicians to explore scales and harmonies beyond the traditional limits. This approach can lead to new musical expressions and better alignment with various musical traditions and instruments. | ||
=== 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. | |||
<nowiki> | |||
\[ S_{p_5} = \left\{ R_{x_1} \mid x \in \mathbb{Z}, 0 \leq x \leq k \right\} \] | |||
\[ S_{p_4} = \left\{ R_{x_2} \mid x \in \mathbb{Z}, 0 \leq x \leq k \right\} \] | |||
</nowiki> | |||
== See also == | == See also == | ||