Question

On a piano, the formula to determine the frequency mc021-1.jpg of any pitch relative to the A above middle C (A440) is given by the expression mc021-2.jpg, where x represents the the number of half-steps above or below A440. Which of the following is equivalent to mc021-3.jpg?
mc021-4.jpg
mc021-5.jpg
mc021-6.jpg
mc021-7.jpg

Answer 1

The frequency formula is f(x) = 440·2^(x/12). Using exponent rules this is equivalent to

- 440·(2^(1/12))^x (since 2^(x/12) = (2^(1/12))^x), and
- 440·e^{(ln 2)(x/12)} = 440·e^{(x ln 2)/12}.

So pick the choice that reads 440·(2^(1/12))^x (or the one that reads 440·e^{(x ln 2)/12}). The choice (440·2^x)/12 is not equivalent.