Question

(a) Find the frequency ratio between the two frequencies fi =256 Hz and f2 = 320 Hz. (b) Add the interval of a fifth to f2 to obtain fs, and find the frequency ratio fs/fi. (c) Find the frequency of f3.

Answer 1

(a) The frequency ratio between the two frequencies fi = 256 Hz and f2 = 320 Hz is:

`(f_2)/(f_i) = (320)/(256) = (5)/(4) = 1.25`

So the frequency ratio is 1.25.

(b) Adding the interval of a fifth to f2 = 320 Hz gives:

fs = f2 * (3/2) = 320 * (3/2) = 480 Hz

The frequency ratio fs/fi is:

`(f_s)/(f_i) = (480)/(256) = (15)/(8) = 1.875`

So the frequency ratio is 1.875.

(c) To find the frequency of f3, we need to add the interval of a fourth to f2:

f3 = f2 * (4/3) = 320 * (4/3) = 426.67 Hz

Therefore, the frequency of f3 is 426.67 Hz.