Question

to calculate the frequency of a note on a piano in the same octave or a different octave, the hertz (hz) of a particular note can be multiplied by the ratio of change in the octave between the original note and the new note to indicate the hz. when not starting at c major for an octave, the ratio would need to be calculated using a formula. for example, moving from a to e on the same octave would be done with a ratio derived from: $\frac{e}{a}=\frac{\frac{3}{4}}{\frac{5}{5}}=\frac{3}{4}$. thus, a note at a would be a different hz value on the same octave at e based on the ratio multiplier as indicated above between the notes on the same octave as follows: $\frac{3}{4}=\frac{e}{440}$. what would the hz be at e if the a note is 440 hz (convert to an equivalent fraction)?

Explanation:

Step1: Cross - multiply the equation

Given $\frac{3}{4}=\frac{E}{440}$, cross - multiplying gives $3\times440 = 4\times E$.

Step2: Solve for E

$E=\frac{3\times440}{4}$. Simplify the right - hand side: $3\times110=\frac{1320}{1}$.

Answer:

$\frac{1320}{1}$