Harmonics and Overtones

## Question:

What are the differences between harmonic and overtone? Is there
any cases where there is only harmonic but no overtone or vice
versa?
If there is a sound of fundamental frequency fo, how will the
sound of its harmonics and overtones be different from it? Will
the intensity change? Or just the pitch be different? Is there
any mathematical formular to show it?

## Answer:

I have some vague memory of a subtle difference between harmonics
and overtones but it may be only different terms to express the
same idea, depending on whether you are talking to a physicist or
a musician. You will find that to be the case sometimes. I think
if you have the one you have the other.
Harmonics or overtones are multiples of the fundamental
frequency. The amplitude or intensity of each harmonic will in
general be different from that of the fundamental. Pitch is
usually meant to be the perceived frequency of a sound wave, and
that is set by the fundamental frequency. The harmonics are not
heard separately. If we could separate out a single harmonic, it
would be some number of whole octaves above the fundamental
frequency. The mathematical expression for complex periodic
functions like waves with harmonics is called the Fourier series.
It is an infinite series of all the harmonics each with its own
amplitude and phase.