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...that we put into these amps. So let's look at the spectrum of the guitar signal. It is a good idea to first derive certain geometry related properties to compare with the measured spectrum so that we can be sure that it is the guitar harmonics that we are measuring. The first attachment shows the results of what are usually known as Tillman type computations: the relative levels of the set of harmonics taking into account just the location of the pickup and its aperture. We use a neck pickup because the pattern is distinctive: if the pickup is located one quarter of the scale length from the bridge, then all multiples of the fourth harmonic are zero. W look at the open E6 string since it has the most harmonics within the system bandwidth. The guitar used in these measurements has the neck pickup located 6.0625 inches from the bridge and the scale length is 25.5 inches, and we assume a .2 inch aperture. This is not quite a quarter of the way, and so we must compute the pattern and look for the distinctive variations from the simple case.
The three up, one down pattern shifts at the 28th-29th harmonics, and resumes with an odd harmonic down. In the real world, he string stiffness is an important factor; two major effects are changing the frequency of the harmonics, and also a slight change in effective scale length as the harmonic number increases.
The measured is shown in the second attachment.
It is a 16384 point spectrum taken over about 1.5 seconds. The string was excited very close to the bridge to produce a spectrum of harmonics that is reasonably flat so that the pattern is most visible. The higher harmonics are down ,quite a bit, but they are clearly visible. These harmonics decay very quickly, and so their peak power is much higher than the average power over the integration period since they exist only a short time. That, and the fact that human hearing peaks in sensitivity near 3 KHz, means that these harmonics are very audible. They are the spectral representation of the picking transient, an important part of what makes the electric guitar sound the way it does.
We see the predicted pattern up to about the 29th harmonic, and although the 3 up, 1 down pattern exists above that, it is not the same as the prediction. This is probably a result of a shift in the effective scale length from the string stiffness. Also, the frequencies shift well off the values predicted for a perfectly flexible string.
The three up, one down pattern shifts at the 28th-29th harmonics, and resumes with an odd harmonic down. In the real world, he string stiffness is an important factor; two major effects are changing the frequency of the harmonics, and also a slight change in effective scale length as the harmonic number increases.
The measured is shown in the second attachment.
It is a 16384 point spectrum taken over about 1.5 seconds. The string was excited very close to the bridge to produce a spectrum of harmonics that is reasonably flat so that the pattern is most visible. The higher harmonics are down ,quite a bit, but they are clearly visible. These harmonics decay very quickly, and so their peak power is much higher than the average power over the integration period since they exist only a short time. That, and the fact that human hearing peaks in sensitivity near 3 KHz, means that these harmonics are very audible. They are the spectral representation of the picking transient, an important part of what makes the electric guitar sound the way it does.
We see the predicted pattern up to about the 29th harmonic, and although the 3 up, 1 down pattern exists above that, it is not the same as the prediction. This is probably a result of a shift in the effective scale length from the string stiffness. Also, the frequencies shift well off the values predicted for a perfectly flexible string.