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 d to b on the same octave would be done with a ratio derived from:
\\(\frac{b}{d}=\frac{\frac{15}{8}}{\frac{9}{8}} = \frac{15}{9}=\frac{5}{3}\\)
thus, a note at d would be a different hz value on the same octave at b based on the ratio multiplier as indicated above between the notes on the same octave as follows:
\\(\frac{5}{3}=\frac{b}{300}\\)
what would the hz be at b if the d note is 300 hz (convert to an equivalent fraction)?

Explanation:

Step1: Set up the proportion

We have the proportion $\frac{5}{3}=\frac{B}{300}$, where $B$ is the frequency of the $B$ - note and 300 is the frequency of the $D$ - note.

Step2: Cross - multiply

Cross - multiplying gives us $3\times B = 5\times300$.
So, $3B=1500$.

Step3: Solve for $B$

Dividing both sides of the equation $3B = 1500$ by 3, we get $B=\frac{1500}{3}=500$. In fraction form, $B = \frac{1500}{3}$.

Answer:

$\frac{1500}{3}$