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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.
Euclid's Algorithm and Musical Intervals
Age 16 to 18
Challenge Level 
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.
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There's a Limit
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Not Continued Fractions
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