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I am in the course of simulating a Telecaster guitar with supercollider, i.e. electronically. I started with the low E-String and results were satisfactory. Then I tried the high e-String and had nothing but trouble.

When I compare the synthesized high-e with a sampled high-e I noticed a number of differences:

  • The sampled string sounds like there is a light chorus effect applied. I had noticed this while live playing and it only happens when you use both pickups (the sample was taken with both pickups) and only on the higher strings. Adding a chorus is one of the easiest things to do, but in order to make it realistic, I would need to understand the physics behind it.

    I suspect that there are waves travelling up and down the string which reach the two pickups with a small delay, but for a chorus effect I would need a detune, which would not happen with a simple delay.

  • The sampled string sounds a lot brighter and exhibits the typical single-coil "twang" while the synthesized string sounds more like a nylon string. No matter how much EQ I applied, I didn't succeed in getting the twang into the synthesized sound. I could make it ultra-bright and it just sounded shitty and artificial.

So can anybody explain

  • the cause of the chorus effect?
  • why and how a steel string sounds different than a nylon string.
  • the characteristics of the single-coil twang
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Are you sure it is not just a non-uniform delay? the very short delays involved in a wave passing from one pickup to the other will produce (non-modulated) flanger-like notches in the spectrum. –  Dave Apr 13 at 20:25
    
The question is: why should the delay not be constant? For a chorus-like effect either the delay or the pitch needs to change ove time. Otherwise the notches stay at the same pace all the time –  Martin Drautzburg Apr 13 at 20:47
    
Non-uniform might not have been the right word. All of the delays are of constant latency, but there is more than one of them, and they all have different (short) delay times. –  Dave Apr 13 at 21:04
    
@MartinDrautzburg - if delay changes, it shouldn't alter the pitch. Digitally it won't, but if we're talking old tape echoes, changing the speed of the delay often changed the pitch. –  Tim Apr 14 at 6:39
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FFT FTW :-). Which is to say: generate graphs of the Fourier Transform of both the sample and synth, and see if some obvious peaks match or don't match between them. BTW, all frequencies a string generates are travelling waves. The standing waves are simply superpositions of travelling waves, and most certainly the various harmonics will have different phase relations at the physical location of the pickup. –  Carl Witthoft Apr 14 at 13:19

3 Answers 3

up vote 4 down vote accepted

Answering my own question after a fair amount of research.

A steel string sounds different than a nylon string

Unlike a nylon string, a steel string does not vibrate like an ideal string, because it has a significant inner stiffness. This has the effect, that the partials/harmonics are not exact multiples of the fundamental, but are shifted towards higher frequencies.

This is a well-known phenomenon and the reason why grand pianos are tuned in a "stretched" way, so the partials of the low strings coincide with the fundamentals of the higher strings.

This is well in line with my supercollider experiments, where detuning the partials indeed turns a nylon string into a steel string. See also Miguel Negaro's thesis.

The cause of the chorus effect

Now when there is some non-linearity involved, this will create partials, which are exact multiples of the fundamental (or exact multiples of another partial). In any case, the partials caused by non-linearity do not have the excact same pitch as the partials caused by the viabrating (stiff) string itself. Eh voila, you have a chorus effect.

Now where should a non-linearity come from? The thing is, a guitar pickup simply does not have to be linear with respect to a single string. You can add a fair amount of distortion to a single string, and you would only percieve a slightly increased brightess. It is the sum and difference frequencies which makes non-linearity sound unpleasant. This happens when you run the guitar through an "overdrive", but it doesn't happen, when you look at only one string.

A real pickup is close to six individual pickups, one for each string, because it has six individual magnets. So a pikckup has some non-linearity, simply because nobody bothered to make it super linear.

The only thing I cannot explain, is why the chorus effect is more pronounced when I use both pickups. It may simply be caused by cancellation effects (or the absence therof), but I am not sure.

The characteristics of the single-coil twang

Most of the information I found, suggest that the "twang" is not caused by single coil pickups, but by a particular playing style. The twang comes from your fingers and many insist, that humbuckers can twang as well, when played properly.

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Nice analysis! — "Unlike a nylon string"? I was always under the impression that nylon strings had stronger inharmonicity, have you measured otherwise? (Of course, on a nylon string the higher harmonics decay faster, so it might just be less noticable.) –  leftaroundabout Jun 17 at 9:04
    
No I dind't measure this. You may be right, that the inhamonicity simply decays faster on a nylon string and therefore it sounds more like an ideal string. –  Martin Drautzburg Jun 18 at 14:23

Just a thought. The neck pup on Telecasters is placed exactly under a harmonic node. I found this when I 'lost' the double octave on mine, playing the harmonic at that point (24th fret position - which, on Telecasters, obviously has no fret), When I changed from neck pup to bridge pup, the harmonic was audible again. It MAY be that as the neck pup and the bridge pup hear slightly different notes, or yours is out of intonation, a chorus effect is apparent. Try the top string on different frets - this phenomenon will only be there with an open string. - Or try using only one pup.

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Interesting point. Yesterday I added a Comb-filter to mimick the effect, that a pickup is at a certain position and thus may emphasize or deemphasize certain modes. When I modulate the frequencies of the comb filter I get this chorus effect, althought I feel like I am cheating. –  Martin Drautzburg Apr 14 at 6:43
    
I added the pickup position by adding a delay with 180 degree phaseshift. It lowers the frequency of the fundamental and this is a small step forwards. Still not as much twang as I had hoped for and no chorus at all (unless I fake it) –  Martin Drautzburg Apr 14 at 15:34
    
@MartinDrautzburg How does a delay (where?) change the input frequency? Are you sure you haven't just created a difference frequency output? –  Carl Witthoft Apr 14 at 20:03
    
The idea is that a wave along the string bounces back from the bridge with 180 degree phaseshift. I add the delayed signal to the original signal. If you are close to the bridge everything gets compeltely cancelled. As you move away from the bridge the higher frequencies will recover more quickly than the lower frequencies. Thus each spot below the strings has a characteristic frequency response. –  Martin Drautzburg Apr 15 at 16:26
    
I wonder if that's the reason why, when playing harmonics, they are easier to sound when you pluck very close to the bridge –  Tim Apr 15 at 16:51

"I suspect waves travelling reach the two pickups with a small delay"

Sounds plausible. Have you tried to verify the hypothesis? You could modify a guitar so as to make the pickups moveable, and then make multiple samples while varying the position of the pickups.

"why should the delay not be constant?"

waves of different freq travel at different speed. So it seems to me that, if your hypothesis is correct, this effect you're hearing would vary with the pitch. Naively I would say that the delay would become less and less as the pitch gets higher, since the wave nodes are closer to each other.

Another thought: if the hypothesis is correct, then perhaps you could synthesize the effect by making two samples, one for each pickup, and then mix those back together.

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Even if the delay depends on the frequency, I would still not get a chorus effect. For a chorus I need a delay which changes over time (not frequency). I did simulate the output of the two pickups and mixed them (though not by using samples, but with the Karplus Strong algorithm). I don't get a chorus effect and I wouldn't know why I should. –  Martin Drautzburg May 14 at 21:11

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