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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