These are the questions I read through before asking this:

What I'm trying to understand (generally) is the effects of a guitar body on sound. In particular, tones being played either into the cavity or onto the face.

Here's my questions:

  1. To what non-numerical degree are guitar bodies similar to formants? If one used a speaker to play pure tones into the cavity, would they find a meaningfully "bumpy" response? (in no way linear nor any other smooth function)

  2. If #1 is "depends on the guitar," is this the reason for its shape and the craftsmanship involved with instrument making?

  3. Does the non-linear response of the guitar body (and all physical bodies) create any overtones? If you took a surface transducer and played pure tones, would the non-linear response of the guitar body create any meaningful overtones?

For further insight into what I'm trying to answer, here's my intuition for the three above:

  1. yes there are "formants," if you tap on a guitar body, you'll hear a non-random sound. this is the frequency response.
  2. if you made a box guitar, the response would be even worse. the shape of guitars is such that the distance between each successive "bounce" of sound is different, so no "bounce" can get too comfortable. a box would have the same bounces in each dimension
  3. yes, non-linearity always introduces overtones, but given the tiny distance of movement this non-linearity is not particularly additive

1 Answer 1

  1. yes, there are in principle discrete (eigen-)frequencies which are amplified by the guitar body, and because these are damped (due to sound radiating through the hole in the body), the resonance lines are no longer infinitely tall (which could theoretically cause a resonance catastrophe) and get broadened (supposedly what you mean by "bumps") so that they can be excited more easily by frequencies that are off the resonance center; this is the same principle that causes the formants of vocal articulation, but for a guitar one desires a more "neutral", less "bumpy" character of the spectrum (an "aaa" or "ooo" sound would make a guitar sound interesting, but would restrict its application in general music pieces)
  2. a box guitar is possible, but there would be less (due to a phenomenon called degenerate eigen-values) and less fortunately distributed resonances, which would probably make the guitar sound too "regular", i.e. certain notes would almost be muted, while others would be quite loud; what is desirable is that the "bumpiness" of the guitar's response is as small as possible, such that every note sounds at about the same loudness when plucked with the same force; I suppose that is what craftsmanship for guitars (and probably all acoustic instruments) is mostly about
  3. there is (or should be) no noticeable nonlinear response of a guitar body; otherwise the sound would suffer intermodulation (which is what you hear with a distortion effect device) that sounds rather ugly to ears not wanting to listen to rock music; since the guitar body is a linear system to very good approximation, there are also no harmonic or non-harmonic overtones added, that are not already in the excitation (plucked string); that being said, there can be nonlinearity under special circumstances: if you pull a string really hard, you notice the "zzzaaaooouung" sound, which I think is a nonlinear response of the string (not the body!); also if the string hits the fingerboard; but normally you try to avoid those effects when you are playing music, although they are relatively "mildly" nonlinear because they only concern the single string

Be careful with the term "nonlinearity". The guitar as a vibrating system is linear, but the frequency response is of course not a linear function of frequency (which is a completely different thing than the system being nonlinear).

I know of no nonlinear musical instruments outside of electronic music, but that may be a limitation of my knowledge. In electronic music, the non-linearity is most often applied only to single voices, because otherwise it will often sound noisy. Intermodulation is characterized by not only adding overtones (whole multiples of the base frequency), but rather fractional multiples and sum/difference frequencies. This is what makes nonlinearity sound noisy when multiple tones are played at the same time.

  • $\begingroup$ For #3, would you mind helping me understand why you're saying "I know of no nonlinear musical instruments" and this answer elsewhere (music.stackexchange.com/a/114016/33785) is saying all instruments are non-linear? Is this a semantics thing? $\endgroup$
    – Seph Reed
    Jun 30, 2021 at 18:56
  • $\begingroup$ "I know of no nonlinear musical instruments outside of electronic music," - that is not at all true. Trivial example: the sound pressure levels within a brass instrument played loudly are sufficient to create shock waves in the air flow (and they have been observed with high-speed photography). Even for a simple "idealized" plucked-string instrument, the tension of the string varies at twice the vibration frequency because of the finite amplitude, causing non-sinusoidal vibrations whose fundamental frequency is amplitude-dependent. $\endgroup$
    – alephzero
    Jun 30, 2021 at 19:33
  • 1
    $\begingroup$ ... and ignoring such second (or higher) order effects is precisely why early attempts at synthesizing the sound of acoustic instruments were a failure. $\endgroup$
    – alephzero
    Jun 30, 2021 at 19:34
  • $\begingroup$ @alephzero, what's your take on #3? Is the guitar body likely to create any meaningful overtones? $\endgroup$
    – Seph Reed
    Jun 30, 2021 at 20:11
  • $\begingroup$ @alephzero: The OP asked about the guitar body which is definitely a linear system up to very strong excitations. Nevertheless I mentioned that the strings may behave nonlinearly at higher amplitude, which is actually no contradiction to the fact that they will behave linearly with smaller amplitude. As to the brass instruments: interesting to know. This is why I carefully referred to my knowledge. $\endgroup$
    – oliver
    Jun 30, 2021 at 22:51

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