When you pluck a single guitar string, several different frequencies/tones are produced at once. leftaroundbout's answer here does a great job of explaining why these higher harmonics are produced on a guitar: when you pull back the string, you produce a shape that does not match a simple sinusoidal shape and thus doesn't match a single frequency/pitch. Rather, the complex shape can only be created from a combination of simpler sinusoidal waves/pure pitches. These simpler sinusoidal waves that combine together to form the complex shape are the harmonic frequencies. Producing the complex shape in turn produces those harmonic frequencies, which we then hear as higher pitches.
As an example, we could give the string a shape that consists of:
- 50% of the fundamental frequency f1,
- 30% of the second harmonic f2,
- 15% of the third harmonic f3, and
5% of the fourth harmonic f4.
I'm making up these numbers. I imagine the true coefficients when plucking a string would be closer to a sawtooth waveform.
The percentages/weights (more formally called Fourier coefficients) determine how loud the harmonics are.
Presumably, there are other mechanisms which also determine how loud the harmonics are--mechanisms beyond just the starting shape of the string when plucked. I don't know what these other mechanisms are, but I'm imagining that the string vibrates slightly at its ends and interacts with the other parts of the guitar. I would expect that these sorts of interactions impact the strength (amplitude/intensity) of the harmonic frequencies. (For example, maybe certain frequencies are damped more strongly.)
My question isn't about the mechanisms--although folks are free to weigh in on those as well. Rather, here is my question: how much do the relative volumes of the harmonic frequencies vary when plucking a guitar string? Does plucking the guitar string at different locations along the string impact how loud certain harmonics are? I'm not talking about muting the fundamental--I'm referring to plucking a guitar string once and simply letting it ring.