The formula for determining the frequency, f , of a note on a piano is f is equal to 440 times 2 raised to the h over 12 power , where h is the number of half-steps from the cap A above middle C on the keyboard. A note is six half-steps away from the cap A above middle C The frequency of the cap A above middle C is 440 Hz. How much greater is the frequency of the new note compared with the frequency of the cap A above middle C ?
For six half-steps, the frequency is 440 × 2^(6/12) = 440 × √2, which is about 622.3 Hz. The increase over 440 Hz is about 622.3 − 440 = 182.3 Hz. As a percentage of the original frequency, 182.3 ÷ 440 × 100% is about 41.4%, so the frequency is 41.4% greater.
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