The eventempered musical scale is the modern standard tuning

The “even-tempered” musical scale is the modern standard tuning, as discussed in class. This scale produces notes with pitches (frequencies) given by: f (N) = 27.5 x 2^(N/12) where f is frequency and N is the piano key number. The frequency f (N) is the fundamental frequency of vibration of the strings struck by piano key N. d) Recalling that strings also tend to vibrate at integer multiples of the fundamental, what would you expect to be the first four additional frequencies (overtones, or harmonics) produced by key #12?

Solution

given N=12, substituting in the above expression we get f(12) =55Hz and additional 4 frequencies are 55*2,55*3,55*4,55*5 = 110Hz,165Hz,220Hz,275Hz