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I've always called the overtones one can play on, say, guitar, harmonics, but some say the fundamental is also a harmonic. Which means my 1st harmonic is their 2nd harmonic. Confusing - to both of us, at least.

Why would the fundamental (usually an open string, but could be anywhere) ever be termed the 1st harmonic, since in my mind a harmonic is a note produced by splitting the fundamental into integral parts?

Partials is another term that is heard - but all harmonics are partials, and not all partials are harmonics...the plot thickens.

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    …or does it just depend on whether you're using a zero- or one-based counting system? eg, in the UK if you go in the front door & up one flight of stairs you're on the first floor. In the US, you're on the second.
    – Tetsujin
    Aug 19, 2022 at 8:06
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    @Tetsujin Using your building and stairs analogy from what I’ve learned the UK is overtones and the US is harmonics. The first floor UK (overtone) is the second floor US (harmonic).
    – John Belzaguy
    Aug 19, 2022 at 15:15
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    and what about instruments that produce inharmonic partials (timpani, gongs, marimbas, vibraphones, etc) or aperiodic sounds (cymbals, snakes, etc)?
    – thrig
    Aug 19, 2022 at 15:35
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    @thrig Lot of these can actually be described by the sum of two harmonics series which can be written for instance (2,3) : second harmonic of the first fundamental mode and third of the second. Similarly the naming problem arises also. For completely inharmonic light white noise, the notion of overtones is irrelevant
    – Tom
    Aug 19, 2022 at 15:54
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    "Carilloneurs have long observed that carillons are not well suited to contrapuntal writing" (David Huron, Voice Leading) so wedging not-harmonics into some harmonic system might be of dubious merit. Maybe doable if the partials are not too terrible, but then "nope" as things become more snake-like. Where the "nope" happens could depend on the culture or individual composer...
    – thrig
    Aug 19, 2022 at 17:22

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The standard terminology that I learned in school was that the octave is the first overtone, the second harmonic. The numbering for harmonics is standard in physics, perhaps because it yields the convenient property that the frequency of the Nth harmonic is N multiplied by the fundamental frequency. The numbering for overtones follows from the fact that the fundamental isn't higher than itself, so the second harmonic is the first one that can be described as an overtone.

The Wikipedia article is unfortunately light on source citations, but a web search such as harmonic vs overtone site:.edu turns up some relatively authoritative university physics materials. I hesitate to link to any of these because of the possibility of link rot.

Another difference is that overtones may be non-harmonic (or "inharmonic"), as in a bell.

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Yes, there are two systems of counting. You'll see the fundamental described as the first harmonic, you'll also see that label used for the first overtone, an octave above. (Well, not necessarily an octave above, but that's a whole other topic.)

Both systems are currently used. Same way that 'Middle C', MIDI note 60, 256Hz, is labelled 'C4' - unless you're Yamaha when it's 'C3'.

And here's a 'medical' tuning fork that thinks 512hz is 'C2'.

It's a jungle out there.

enter image description here

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  • So much for a scientific approach. For C2, it should be at least a foot long.
    – Tim
    Aug 19, 2022 at 16:28
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    I learned something today: apparently a tuning fork can help diagnose broken bones (maybe a quick triage in lieu of an x-ray), by putting the fork and one end and a stethoscope at the other and seeing whether the bone transmits the pitch.
    – Andy Bonner
    Aug 19, 2022 at 16:34
  • That C2 was probably meant to be c'', using Helmholtz notation. Name C2 comes from scientific notation, and that's 3 octaves lower
    – user1079505
    Aug 19, 2022 at 18:03
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A physicist might say:
If you try to excite for example a string under tension, at an arbitrary frequency – it probably won't generate a stable waveform. However there are certain frequencies that will be stable.

The lowest frequency that will produce a standing wave on the string is called the 1st harmonic or fundamental frequency. This is because this frequency will resonate "in harmony" with the system.

The next highest frequency that produces a standing wave is called the 2nd harmonic or 1st overtone. Other energy levels that will generate a stable waveform are found with the harmonic series. Superposition blah blah blah...

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