Harmonics

[Ross C]

I see from the forum that I’m not the first, but I still haven’t quite sussed where harmonics come from.. I keep thinking I’ve got it, and then get confused again.

Are they just from the physical vibration of the vocal folds, the same as in a guitar string or the Millennium Bridge? As in, it’s got an F0 derived from its length (and density, tautness, etc), a harmonic derived from half its length, another harmonic derived from a third of its length, etc? (Though those would actually be resonances of the string/bridge/vocal fold, right?)

It seems like conceptually we always quickly skip from F0 (which I get) to resonances (which I get) and I haven’t got an idea of what harmonics actually physically are, on their own (before they get altered by resonance), with reference to air particles and so on.

Or are they not physically real, just a useful concept in a Fourier analysis?

[Simon]

Yes, harmonics originate in the physical behaviour of the vocal folds. They are real, not just a concept. Of course, they are much, much easier to see and understand in the frequency domain than in the time domain.

You are trying to find the origin of harmonics in the time-domain, which is a good idea, but is never going to be simple. I think the place to start is to convince yourself that any periodic signal that is not a pure tone must have harmonics. This tool is my favourite.

A guitar string, the Millennium Bridge, or (even more spectacularly) the Tacoma Narrows Bridge, all exhibit resonance. In other words, they are filters that selectively amplify some of the input signal (which can be called the source, or the excitation) and produce a very large output signal at certain frequencies.

What is the source in each of these cases?

1. a guitar string making a musical note
2. a piano string making a musical note
3. the Millennium Bridge swaying
4. the Tacoma Narrows Bridge oscillating with a twisting motion

[Author]

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