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: $\frac{e}{a}=\frac{\frac{5}{4}}{\frac{5}{3}}=\frac{3}{4}$. 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: Set up the proportion

We have the proportion $\frac{3}{4}=\frac{E}{440}$, where $E$ is the frequency of the $E$ - note and 440 is the frequency of the $A$ - note.

Step2: Cross - multiply

Cross - multiplying gives us $3\times440 = 4\times E$.
So, $1320 = 4E$.

Step3: Solve for $E$

Dividing both sides of the equation $1320 = 4E$ by 4, we get $E=\frac{1320}{4}=330$ Hz. In fraction form, $E = \frac{330}{1}$ Hz.

Answer:

$\frac{330}{1}$ Hz