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I've been researching Physical Modeling lately, and so far pretty much everything makes sense from a physical/logical perspective.

The one thing that I haven't yet found a proper explanation on is the difference in overtones between soft and hard materials. I've seen it mentioned in a few places that this stiffness is the parameter which defines the difference between metallic and nylon string on a guitar, for instance. I've also caught that one of the two directions (hard vs soft) "spreads the harmonics." But that's all I've got.

So, what are these differences in overtones for rigid materials? They seem to be more spread out, I've come to recognize metallic sounds as being rather comb like. But I'm trying to eventually write code to synthesize these sounds, and need to know some details as to the way they are spread.

Also, here's a great video in which most other aspects of physical modeling are pretty well explained, as well as the mention of more spread out overtones for harder materials (though I don't remember at what time): https://www.youtube.com/watch?v=dUcNzPhZdwk

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I am not sure if this is exactly answering your question but it may help you in your modeling efforts. The metallic strings are going to be fairly simple to model in that the differential equations you use will be only dependent on the shape of string at any given time and the tensile strength of the string.

The nylon strings exhibit non-linear viscoelastic behavior which has a time dependent component to it. That means that is has a memory and the local velocity of the string will be important. By memory I mean there is residual strain built in once plucked and the time for recovery will be much greater than the frequency of motion. I believe this is what gives it a “softer” sound. Classically viscoelastic materials are modeled with a spring and damper in parallel.

Descretizing the string over a number of elements and using a divided differences approach to approximate the differential equations you should be able to get a theoretical sense of how these differences affect the observed signal.

Hope that is helpful for you in thinking about your problem.

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  • $\begingroup$ Can you please provide one or two indicative papers on the topic where the OP could potentially find more about it? Or maybe add some more specific details from your own experience (?). Interesting point by the way. $\endgroup$ – A_A Dec 8 '17 at 9:13
  • $\begingroup$ This is definitely helpful, though my current grasp of it seemingly implies the opposite of what I'm used to. I tend to think of metallic as being more twangy, or high pitch. An increase in tension in nylon strings seems like it would create even higher pitches. Then again, perhaps the FM movement of the fundamental keeps any of these higher pitches from resonating, thus dulling the twang? $\endgroup$ – Seph Reed Dec 8 '17 at 19:26
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    $\begingroup$ Regarding "memory", the residual strain is introduced due to the phenomena of creep and stress-relaxation. The initial pluck of the string will introduce residual strain through creep and instantaneously over time, additional strain will be introduced through dynamic loading of the string changing direction as it vibrates. All the while, the residual strain will be trying to recover. $\endgroup$ – Inflexionist Dec 9 '17 at 16:18
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    $\begingroup$ These residual strain components will be fighting against the want for the string to recover and slow the recovery process at a decaying rate because over time the amplitude of the vibration reduces thus reducing the dynamic loading. $\endgroup$ – Inflexionist Dec 9 '17 at 16:18
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    $\begingroup$ How long the residual strain will last is a function of the material. once the string is not in motion, recovery will continue, but if plucked again before full recovery is acheived, a different response should be observed. There is also limit to how much residual strain can be introduced. Microscopically this is a result of secondary intramolecular bonds being broken as the plastic material "unfolds" carbon chain. The fully recovered (no residual) strain material will have the carbon backbone folded up again reestablishing secondary intramolecular bonds in the polymer chain. $\endgroup$ – Inflexionist Dec 9 '17 at 16:22

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