What makes a guitar "twang" when it is plucked very hard?

[mikejm]

I've been working for quite some time on/off on plucked string (guitar) modeling using modal synthesis (resonant bandpass array, one bandpass per partial). I've come to understand and capture most of what makes a guitar a guitar. But I can't figure out for the life of me what makes a guitar "twang."

What I am referring to is when you pluck a guitar string very hard, it gives a very clear almost formant-like effect that sounds to me a bit like "BAUWWWWWW". I can't figure out exactly how this is being generated or where it is coming from. If I can't figure out where it's coming from, I can't emulate it.

Attached is a zip containing a flac of a strongly plucked guitar string, and this pluck windowed down to 800 Hz to 1.4 kHz using Izotope Rx (a narrow range which still represents the twang effect a bit):



The twang seems to not come as much from below 800 Hz or so. If you window to that region you don't hear it much. I would think of it as a pitch bend effect but I'm having trouble grasping what's happening. If you just run a pitch bend you don't get this type of effect on its own. Maybe it's that each partial is bending more and more the more you go up in frequencies? That's my best suspicion but I've had trouble replicating the sonic effect so I'm not sure.

This has been stumping me for a while now. Any thoughts or ideas? Thanks.

[EvilDragon]

It's the sound of the string hitting the frets when you pluck 'em hard.

[noizebox]

The strings hitting the frets is one part of the sound, that gives a metallic buzzing sound. But it doesn't sound like that is what's happening in the audio clip above, to my ears. That clip is just the normal twang of a guitar string picked hard. I think the baaaoouuww sound comes from the higher harmonics decaying faster than the lower harmonics and the origin of the pitch bend effect is that the displacement of the string when plucked hard is so large that it actually raises the pitch of the string temporarily.

[resynthesis]

Some useful stuff in here:

http://digitool.library.mcgill.ca/webcl ... 961709~451

[Music Engineer]

from this book, page 145: https://www.amazon.com/Physics-Musical- ... 441931201/

in the course of vibration, the string is displaced from its initial straight configuration and its length increases. The string tension therefore increases by an amount which involves both a steady and an oscillating term. ... the effect of principal musical significance is the quasi steady increase in tension ... [the other term] gives a further frequency shift for the mode of frequency w_n only. ... this second contribution to the frequency shift destroys harmonicity ...as the free excitation decays with time, the pitch glides back toward its small-amplitude value ... the effect is generally an unpleasant "twang"

...so, it seems we have a combination of a pitch envelope (initial pitch higher) and an initial inharmonicity. well - that's what the theory says - although the spectrogram doesn't really show such things. dunno - maybe the frequency resolution is too bad?

edit: looking at the cycle lengths of your sample, there seems to be no such thing as a pitch glide. ...hmmm

[Music Engineer]

here is also an article from one the authors of the book - below Eq. 10.4, it gives similar explanations:
http://phys.unsw.edu.au/music/people/pu ... r1999a.pdf

[kryptonaut]

There are a few things that might be worth considering.

If a string is vibrating hard, its average tension over the course of a cycle is increased so the frequency of vibration is slightly higher than for a gently plucked string. As the amplitude decays, the average tension is reduced and the frequency drops slightly. This is the 'pitch-bend' effect.

Higher frequency partials decay more rapidly than lower frequency partials, giving that 'filter-sweep' effect.

For a wirewound string, if the pluck also 'strokes' the string longitudinally then you get a lot of high frequency oscillations which might be a combination of transverse and longitudinal vibrations of the string. To me this sounds almost like a hardsync effect, and can also be quite formant-like.

[JCJR]

I wonder if this has anything to do with the phenomena: Long ago one bane of my clumsy attempts at filter + time-domain guitar and electric bass pitch tracking, were the common "temporary DC shifts" at note-starts.

Has been some years since I last studied on guitar/bass wave plots and maybe I remember wrong. It is just that auto-correlation was not very good when DC level is changing from one wave period to the next and it seemed non-trivial to filter out those temporary DC shifts.

Maybe it was an artifact of assymetrical waveforms interacting with multiple layers of AC coupling between guitar/bass and final capture into the computer? Or maybe the temp DC shift is a "real" characteristic of the plucked string, dunno. Picked note-starts, for the first few wave cycles would have a temporary DC shift, presumably caused by the pick moving the string far enough away from the center line that it takes a few cycles to get back to a DC center.

If that is actually what happens-- That a string can go thru several initial wave cycles while the "center of movement" is returning back to the DC baseline-- Then the assymetrical string tension, assymetrical wave shape, might get close indeed to a synth "sync oscillator sweep" sound.

[DaveClark]

Hi all,

David Politzer of Caltech studied banjos and wrote up an article published at arxiv.org that attributes the characteristic twang of banjos to string stretching and frequency modulation. This seems quite reasonable physically speaking. Many of the explanations of guitar twang on Internet forums do not really explain anything at all, instead being claims about correlations: scale length, pickup placement especially near metal, changes in magnetic fields, and so on. These people could be said to be doing nothing more than describing a Telecaster. Politzer's article, in sharp contrast, offers a truly physical explanation:

https://arxiv.org/pdf/1406.4907.pdf

See also:

https://physicsworld.com/a/how-the-banj ... -and-more/

Regards,
Dave Clark

[mdstudio]

I tried to resynthesize it in Icarus and slow it down so that we could see how the waveform and harmonics change. Hope that helps:

​​​​​​https://www.youtube.com/watch?v=m9y0Cwwg-0o

[liqih]

Yes it's a combination: string stretching (tension modulation) gives frequency modulation and inharmonicity modulation,
partials start much further up and unrelated and distant, then fall back unlinearly in their harmonic places, but slower that the pitch bending (depends on the diameter of the strings also). Also the guitar neck curves (especially in telecaster and in banjo neck and skin) and contributes to the non-linear fall back of the harmonics pitch.