Question

The frequency of the musical note E3 is about 164.81 Hz.

what is the frequency of the note a perfect fifth above E3.

Answer 1

Answer: 247.215 Hz

Explanation:

We know that in music theory, a perfect fifth is a musical interval having inverse perfect fourth that corresponds a pair of pitches with a frequency ratio of 3:2.

Let the frequency of the note a perfect fifth above
`E_3` be x, then we have the following proportion.

`x:164.81::3:2\\\\\Rightarrow x=(3*164.81)/(2)=247.215`

Hence, the frequency of the note a perfect fifth above
`E_3` is 247.215 Hz.

Answer 2

A perfect fifth above a note has a frequency ratio of 3 to 2.
Therefore, we can set the proportion:
164.81 : x = 2 : 3

which gives:
x = 164.81 × 3 ÷ 2
= 247.21

Hence, the perfect fifth above E₃ will have a frequency of 247.21Hz which corresponds to a B₃.