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'Euclid's Algorithm and Musical Intervals' printed from https://nrich.maths.org/
See the problem
Tuning and Ratio
in which you have to find a decimal approximation for this
ratio using logarithms. Here you must find an approximation in the
form of a ratio of two integers without using logarithms.
You could use the same method as given for finding rational
approximations to $\pi$ in the article
Approximations, Euclid's Algorithm and Continued
Fractions.