# Emulating guitar pickup position with delays

If I have a vibrating string, then there will be no motion at the endpoints. If I move away a bit from an endpoint then I'll get a signal, but particularly the fundamental will still be attenuated. Higher modes may suffer less or even benefit. This explains why the bridge pickup (closer to the edge) of an electric guitar suppresses the fundamental more than the neck pickup and sounds "thinner".

The amplitude of the signal obviously depends on the position of the pickup and the frequency. The relationship is some $sin(\frac{\omega x}{c})$ function.

• The question is: if I have a string signal, can I emulate this position dependant behavior with delays?

Suppose the pickup is at $\frac 14$ of the string. I can then add a delay with an amplification of $-1$ which reflects (sic!) the wave bouncing back from the near edge of the string. I will get an attenuated fundamental and all that, but is it physically correct?

Why not do the same with the far end of the string and use a delay which stands for $\frac 34$ of the string. It will also attenuate the fundamental, but the notches will be at different frequencies.

Now I realize, that I am about to model the string itself. If this model was done correctly, I could excite the string and pick it up anywhere I want. But I already have a string signal (from a Karplus-Strong algorithm).

• What would I have to do, to add just the effect of the pickup position to this?
• What wiring of delays would produce this $sin(\frac{\omega x}{c})$ frequency response?

i won't divulge some proprietary information i have about how to do this, but i'll tell you this hint:

1. the vibrations on the guitar strings are standing waves.

2. standing waves as well as any waves on a string are made of of sinusoidal components with frequencies at harmonic intervals, that is each harmonic sinusoid has a frequency that is an integer multiple of the fundamental which is the frequency we will normally associate with the pitch of the note.

3. with standing waves, there are nodal points for each harmonic at distance that is a submultiple of the length of the string between the bridge on the right and the fret that is terminating the string on the left.

4. even-numbered harmonics will have a nodal point at the middle of the string and odd-numbered harmonics will not have a nodal point there.

5. there is a relationship between ration of the even-harmonic energy to the odd-harmonic energy and the position of the pickup and with the position of the pick.

have phun figgering it out.

• Is "plucked string" algorithm a reasonable choice for the original waveform generator? Apr 7, 2015 at 0:18
• i dunno. i thought this was about how to detect a plausible position of the pick on the string of, say, an electric guitar (but it could be something else, like a pedal-steel), based on the ratio of the odd-harmonic energy to the even (or to the total). i guess i'm curious, @YuriNenakhov, about what you mean. what is the "pluck string algorithm"? Apr 7, 2015 at 3:57
• I thought this was about making a guitar synthesizer, this topic is interesting to me and I thought maybe you're familiar with it. "Plucked string" is also known as Karplus–Strong string synthesis algorithm and is relatively easy way to synthesize a string-like sound. Buffer is filled with random samples and then repeated while continuously applying low-pass filter to it. Length of the buffer determines base pitch. Sometimes it's referred as "physical modelling synthesis". I thought maybe it's possible to achieve more natural results by combining it with physical model of a guitar pick-up. Apr 7, 2015 at 4:34
• you're right. so i dunno how to answer the original question exactly. maybe instead of filling the buffer with random numbers, like in K-S, maybe fill it with a triangle wave that has it's positive and negative peak corresponding to where the pick position is. (that would be the initial shape of the plucked string.) or, if you fill it with random numbers, pre-filter the random numbers to have a similar magnitude spectrum as does the above mentioned triangle wave. other than that, i dunno. Apr 7, 2015 at 14:28