Well, maybe tit is a good to look at the properties of this signal...

[Mike Sulzer]

...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. WE 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. 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.

[Malcolm Irving]

It’s interesting that the second harmonic is stronger than the fundamental in both the theoretical and measured results (if I am reading the graphs right). I believe that is found in many musical instruments. The brain is good at ‘hearing’ the note as the fundamental, based on hearing the harmonics. Perhaps another reason why guitar amps can get away with small output transformers.

In theory (and probably of no practical importance whatsoever) to detect all the harmonics a pickup needs to be at an ‘irrational’ position along the string 1/sqrt(17) or somewhere like that.

The higher frequency harmonics are relatively more attenuated in the measurements than in the theory (again – if I’m reading the graphs right). Perhaps another effect of the string not being perfectly flexible?

[nickb]

Interesting. Of course, the nice 4n harmonic nulls would go away as soon as you fret a note, to a lesser or greater extent.

I see matplotlib strikes again.

[Mike Sulzer]

It’s interesting that the second harmonic is stronger than the fundamental in both the theoretical and measured results (if I am reading the graphs right). I believe that is found in many musical instruments. The brain is good at ‘hearing’ the note as the fundamental, based on hearing the harmonics. Perhaps another reason why guitar amps can get away with small output transformers.

In theory (and probably of no practical importance whatsoever) to detect all the harmonics a pickup needs to be at an ‘irrational’ position along the string 1/sqrt(17) or somewhere like that.

The higher frequency harmonics are relatively more attenuated in the measurements than in the theory (again – if I’m reading the graphs right). Perhaps another effect of the string not being perfectly flexible?

Yes, I do not think there need be any fundamental at all. The brain is apparently looking for patterns in the detected outputs versus time of the set of fairly broad filters.

The bridge pickup has less fundamental than the neck:

Yes, string stiffness results in higher harmonics going away faster. Merlinb was probably referring to that in that other discussion, but I think his assumption that they are therefore insignificant is not correct.

[Mike Sulzer]

Interesting. Of course, the nice 4n harmonic nulls would go away as soon as you fret a note, to a lesser or greater extent.

I see matplotlib strikes again.

Yes, they do, but I wanted a distinctive pattern so we could be sure be sure we are measuring the harmonics.

I think an interesting next step would be to look at the spectral widths of the higher harmonics in order to measure how fast they decay.

[darkfenriz]

There will be nulls and boosts of harmonics as a function of the pick plucking position versus the vibrating string length.
Guitar sound in general has very little to do with a specific harmonics structure, contrary to mythology. It has more to do with how the harmonics decay versus each other.

[Mike Sulzer]

There will be nulls and boosts of harmonics as a function of the pick plucking position versus the vibrating string length.
Guitar sound in general has very little to do with a specific harmonics structure, contrary to mythology. It has more to do with how the harmonics decay versus each other.

The bridge and neck pickups sound very different because they sense different relative levels of harmonics. Guitar sound has everything to do with specific harmonic structure, along with other factors.

[darkfenriz]

Probably we talk apples and oranges here.
Hammer the string with a mallet or apply a quick attack with a violin bow. Does it sound like a guitar?

Change the pickup, pickup position, add some eq and distortion and it still does, hah?

Harmonic structure does apply a flavour but it is not exactly and excursively what makes guitar sound like it does... is what I was trying to say.

P.S. handy applet: http://www.till.com/articles/PickupR...emo/index.html

[Mike Sulzer]

Probably we talk apples and oranges here.
Hammer the string with a mallet or apply a quick attack with a violin bow. Does it sound like a guitar?

Change the pickup, pickup position, add some eq and distortion and it still does, hah?

Harmonic structure does apply a flavour but it is not exactly and excursively what makes guitar sound like it does... is what I was trying to say.

P.S. handy applet: Guitar Pickup Response Demonstration

I see what you mean, but I think when you pick, hammer, or bow you excite different harmonic structures that decay as the physics of the string and guitar control.

[Mike Sulzer]

The string is excited with the nail of the forefinger after the sampling is started. Approximately the first 0.1 second is shown in the attachment. Remember that guitar pickups sense the velocity of the string, but modified by the resonance. In this case the resonance is about 6 KHz, and the Q is higher than normal for a single coil sized pickup. The first spike spike is the velocity (with extra signal in the region of the resonance) of the string from a sharp displacement that travels from near the bridge (and includes reflection from the bridge) and passes over the neck pickup. This deflection transient travels to the nut, is reflected with reverse polarity and passes over the pickup causing the first negative transient. It proceeds to the bridge, and reflects with reverse polarity causing the second positive spike, and so on. The negative transients are followed closely by positive ones because the distance from the bridge to the neck pickup is about one third of that from the nut to the neck pickup We see some evolution immediately as the highest harmonics are attenuated. But I think more is going on. The excitement is nearly parallel with the top of the guitar, but the pickup is most sensitive to motion perpendicular to that, along the axis of the coil. But rotation occurs, and I believe some of what we are seeing is a result of that change in the direction of the deflection.

[darkfenriz]

Hmm... is that open low E string?
Aren't the positive spikes roughly 1/82 second apart?

I'm leaning to see it more in fourier terms ...

[Mike Sulzer]

Hmm... is that open low E string?
Aren't the positive spikes roughly 1/82 second apart?

I'm leaning to see it more in fourier terms ...

Yes, it is the open E6 string. Next, will be an attempt to look the the decay of the various harmonics.

[Mike Sulzer]

Fundamental through 15th harmonic



This is the same neck pickup signal. The waveforms are plotted, starting with the fundamental. They appear as solid colors since there are so many zero crossings in the (modulated) sine waves. The higher number harmonics go on top, which means they are mostly visible. Not visible are harmonics 4,5, 8,9, 12,13 since they are smaller than the next higher number.

These all appear quite significant, as are additional higher numbered harmonics. I will plot more later when I have time, and, for the engineers and signal processors, explain how the harmonics were extracted from the signal. (The rise time in the leading edge of the signals is a result of the filter bandwidth, which is thus too wide to affect the decay time.)

[SoulFetish]

Perhaps it goes without saying, but I wanted to double check that all other strings except the low E were muted during each test, correct?

[Mike Sulzer]

Perhaps it goes without saying, but I wanted to double check that all other strings except the low E were muted during each test, correct?

NO, forgot to put in the Swiffer Duster pad. Easily redone. Note the different time scale; I did it a bit longer this time since stuff sticks around a bit longer than I initially expected. We have higher amplitude on the high harmonics, and more consistency from harmonic to harmonic.