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.