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For questions on mathematical problems arising from music theory, e.g. scales, harmonies, rhythms, and compositional techniques (such as dodecaphony or minimalism).

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Powers of $3$ close to powers of $2$

The musical scale of $5$ fifths has good temperament because $3^5$ is quite close to a power of $2$, namely $2^8-3^5=13$, and I suspect that in the subsequent powers of $3$ none is so close to a power …