What characteristics of a single-coil (Telecaster) sound to consider for simulation?

Question

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

Answer 1

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.

Answer 2

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.

Answer 3

"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.