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In music theory, an octave is an interval in frequency, from a frequency $f$ to frequency $2f$. For example "an octave higher" means "twice the frequency". Expressed as wavelength inversely proportional to frequency, $\lambda \propto \frac{1}{f}$, an octave would be the interval from a $\lambda$ to $\frac{1}{2}\lambda$. In the SIFT paper'...