If a guitar is playing the A string, its fundamental frequency is 110Hz.
The second harmonic would be at 220Hz and the third harmonic would be at 330Hz.
What’s a partial?
Instruments like bells, drums, synths sometimes produce frequencies that aren’t integer multiples (2x, 3x, 4x, etc) of the fundamental.
Bells in particular are pretty “out” — the relationship of the frequency components to the percieved fundamental is unclear or muddy.
In that case, the frequencies are usually referred to as partials instead of harmonics.
If they aren’t “in harmony” with the fundamental, we can’t call them harmonics! They are just “a part” of the sound — a partial.
You can think of partials as being a superset of harmonics. It’s all the frequencies in a note, whether or not they are harmonic (integer multiple of fundamental) or inharmonic (strange frequency!).
What’s an overtone?
We have a mistranslation of Helmholtz to thank for this additional piece of jargon.
Basically, an overtone is “a tone above the fundamental”. Pretty simple.
It gets annoying because people sometimes refer to harmonics in terms of overtones.
In the case of the A guitar note, the fundamental is 110Hz.
The second harmonic is 220Hz. Well, because 220Hz is the first frequency above/over the fundamental, then it’s the first overtone.
You might see daunting looking charts trying to equate partials vs. overtones. This is all unnecessary — just remember that the “over” in “overtone” means that it excludes the fundamental.
The 3rd harmonic is the 2nd overtone. The 125th harmonic is the 124th overtone. An overtone is just harmonic number - 1, because we don’t count the fundamental. Not tooooo difficult in the end!
That’s the last you’ll hear of overtones in this manual!
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