We have seen that \(\log \left( \frac{3}{2} \right) \approx \frac{7}{12} \log 2 \), or in other words, \( \left( \frac{3}{2} \right)^{12} \approx 2^7 \). Since a perfect fifth has a pitch ratio of \( 3:2 \), and an octave has a ratio of \( 2:1 \), we could also express \( \left( \frac{3}{2} \right)^{12} \approx 2^7 \) as saying that “twelve fifths is almost seven octaves.”

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Fifths

Octaves