Sampling the string: differences between single coil and humbuckers

[Mike Sulzer]

Well Mike, some people, including myself, feel that it's the change in reluctance as the string disturbs the static field that causes the current to flow, and not so much the magnetized string. When everything is at rest the reluctance and the flux are constant.

Not going there again beyond this: Variable reluctance uses a mathematical analogy to make certain kinds of calculations easier. It is not something that happens in addition to the string magnetization. It does not predict anything different from the more straight forward use of the law of induction. I have explained this before several times, and referred you to a Wikipedia page.

[David Schwab]

Not going there again beyond this: Variable reluctance uses a mathematical analogy to make certain kinds of calculations easier. It is not something that happens in addition to the string magnetization. It does not predict anything different from the more straight forward use of the law of induction. I have explained this before several times, and referred you to a Wikipedia page.

And this is what you say, and I know others well versed in this that don't agree. Somehow you always come off as trying to be the authority on these matters.

Clearly this entire "experiment" is because you don't believe that different magnetic field shapes affect the tone of pickups. It's the case of "it can't be, so it isn't, so it must be something else."

Meanwhile there have been pickups made for many years using these different approaches.

What you should do is make some different pickups with different width magnets as cores, and then report back to us.

Or reconstruct that Attila Zollar pickup—with ceramic magnets—and see what it does.

[RedHouse]

...Somehow you always come off as trying to be the authority on these matters...

"Trying" is the operative word to be sure, hopefully someday Mike will give us all a rest and think of another approach to stimulate discussion.

[MrCandy]

There are shifts that literally are so small that they won't show up on an overlay graphic such as the ones you've posted, but make a difference in significant things like whether it's easier for me to get pinch harmonics, or the way one pickup interacts with another (passively of course)

I would like to share some thoughts on the subject you are discussing.
Coils interaction in passive mode (when one coil is connected and another dont) can be significant, but it depends of each coil frequency characteristics individually and degree of coils interaction in system.
Even when on spectrogram we dont see significant difference (coils are very similar by their AFC) there could be huge impact on tone due to phase and intermodulation distortions.
In U.S. Patent No. 4,501,185 they tried to solve the problem of these distortions, but the problem was partly solved because they overlooked Q-factor.

We want to show you how passive coils(same DCR,NT,wire gauge) interaction could mirror on AFC spectrogram.
Coils were measured individually. First coil was connected, second dont and vice versa.

Spec1:

Spec2:

[Mike Sulzer]

Coils interaction in passive mode (when one coil is connected and another dont) can be significant, but it depends of each coil frequency characteristics individually and degree of coils interaction in system....

If no current flows in the unconnected coil, then there can be no interaction, but you never can achieve that exactly because of the coil's self-capacitance. So if you have a coil not connected you tend to get some interaction at the coil's natural resonance because that is the frequency range where the most current can flow.

In the experiments here, when listening to or measuring one coil, the other is left open. Measured results are are shown only out to about 5 KHz in order to stay away from the resonant region (above 20 KHz with this pickup.)

There is also some coupling from one coil to the core of the other. That is, even if the coil is taken away, leaving the core behind, there is an effect. This is kind of a much weaker version of what Mark was mentioning when you connect the cores together with steel.

I am not sure what you mean about intermodulation distortion. There are non-linearities associated with sensing the string vibration, but I do not know of any in the pickup itself.

[fieldwrangler]

If you do couple the coils in this way with high permeability material, this material responds to stray fields and couples them through the coils with opposite phase since the coils are on opposite ends of the coupler.

Hmmm... So in a sidewinder does the permeable common core couple the stray field through the coils in a possibly even more nefarious way?

[Mike Sulzer]

Hmmm... So in a sidewinder does the permeable common core couple the stray field through the coils in a possibly even more nefarious way?

Apparently something like that does limit the hum rejection of a sidewinder. I think I mentioned that in a discussion of sidewinders.

[Mike Sulzer]

Measured spectral results with both coils compared to a simple model

The second figure shows a spectrum (with both coils on) measured by picking the no. 6 E string once. The red line is the spectrum with both coils; the blue line is that with one coil for reference. The first figure shows a model made by assuming that the aperture consists of two very narrow regions separated by the spacing between the two sets of screws. The details of a picked spectrum are of course very complicated and cannot be exactly predicted. The lower harmonics depend on where one picks and the higher harmonics decay away for various reasons. However there are some general features that show very good agreement between the two. Both decay gradually showing a very deep null at just over 2600 Hz, and then recover as the frequency increases. In the case of the measured spectrum, it is necessary to compare the spectrum with one coil (blue) with that of both coils (red). This recovery is a result of summing two narrow apertures. The recovery is not perfect in the measured case. Also both spectra have a less deep null at about 1750 Hz. I will described how the model was made in a later post.

[MrCandy]

If no current flows in the unconnected coil, then there can be no interaction, but you never can achieve that exactly because of the coil's self-capacitance. So if you have a coil not connected you tend to get some interaction at the coil's natural resonance because that is the frequency range where the most current can flow.

In the experiments here, when listening to or measuring one coil, the other is left open. Measured results are are shown only out to about 5 KHz in order to stay away from the resonant region (above 20 KHz with this pickup.)

There is also some coupling from one coil to the core of the other. That is, even if the coil is taken away, leaving the core behind, there is an effect. This is kind of a much weaker version of what Mark was mentioning when you connect the cores together with steel.

I am not sure what you mean about intermodulation distortion. There are non-linearities associated with sensing the string vibration, but I do not know of any in the pickup itself.

Good work you ve done and shared in this thread.
About current flow in unconnected coil I can say that this coil we can review as oscillatory circuit because it has its own capacity. Thats why this coil by means of inductive coupling
it directly affects the frequency characteristics of the other coil and the more closely the inductive coupling the more significant these changes are. Particularly noticeable in rail pickups.
About intermodulation distortions when 2 coils are very similar by its phase characteristics for better understanding you can can hear sound samples here,
sample number 2 have less int. dis. that manifest in other samples as muddy tone.

The second figure shows a spectrum (with both coils on) measured by picking the no. 6 E string once. The red line is the spectrum with both coils; the blue line is that with one coil for reference. The first figure shows a model made by assuming that the aperture consists of two very narrow regions separated by the spacing between the two sets of screws. The details of a picked spectrum are of course very complicated and cannot be exactly predicted. The lower harmonics depend on where one picks and the higher harmonics decay away for various reasons. However there are some general features that show very good agreement between the two. Both decay gradually showing a very deep null at just over 2600 Hz, and then recover as the frequency increases. In the case of the measured spectrum, it is necessary to compare the spectrum with one coil (blue) with that of both coils (red). This recovery is a result of summing two narrow apertures. The recovery is not perfect in the measured case. Also both spectra have a less deep null at about 1750 Hz. I will described how the model was made in a later post.

Some thoughts about decay. This affect is common to all humbucker pickups and due to the distance between the cores of the two coils it will fall on different frequencies.
We are working on active soupbar pickups for bass now, and we want to do hum canceling without this effect with 3d zonding.
First results:

[Mike Sulzer]

String sampling theory

We need to look at the response of a higher frequency string in order to verify that the response described in my previous outer level post (Measured spectral…) really is the result of how the string is sampled rather than some other cause. But before doing that, it is necessary to look at the theory of how this works: what harmonic pattern results from locating a pickup coil in a particular place?

Let's start with some very basic physics about vibrating strings, stuff everyone knows, but useful to review to get on the same page. When you pick a string you have the potential to excite vibration over a continuous wide range of frequencies. However, the physics constrains the string to move at a certain set of (nearly) harmonically related frequencies, each of which has a different sinusoidal pattern of motion given by sin(pi*n*x/l_s,) where n is the harmonic number, L_s is the length of the string, and x is the position along the string). The string does not move at the ends, and so it is constrained to move in sinusoidal patterns that have zero displacement at the ends and at evenly spaced intervals along the string depending on n. The fundamental moves the most at the center; the second harmonic has a null at the center, and so on.

Suppose we have a pickup with the poles pieces located a distance L_m from the bridge. Then if we substitute L_m in for x in the equation, this gives us the relative string displacement over the pickup poles for the fundamental and each harmonic (simply vary n), assuming the sampling region is small and can be adequately. represented by a single number. The first figure shows the first five harmonics from bridge to nut. This is a 25.5" scale guitar, with the actual scale length for the no. 6 E string about 1/8" longer. The vertical lines show the locations of the centers of the two pickups coils, and so the amplitudes of the harmonics where they intersect the lines show the relative strengths of these harmonics. Using the above equation, you can compute the harmonic strength for many harmonics.

harms1Through5_5.6875.pdf

A more complete description of the string vibration includes the fact that there are two independent kinds of motion (call them vertical and horizontal if you like). Any harmonic of either degree of freedom can be positive or negative. That can be represented by the direction of motion near the bridge with respect to the fundamental. (They are all shown positive in the figure.)

Although sampling at a point might be a good approximation, real pickups sample over one or more finite length regions. You can compute at a number of closely spaced points in the interval and add the results. For example, the second figure shows the result of an interval covering the full width of both humbucker coils. The frequency scale is computed by starting with the harmonic numbers and multiplying by the fundamental frequency.
HBWideSam.pdf
The full width humbucker sampling mode shows poor agreement with the measurements . There is a null, but it is at the wrong frequency. Also, the recovery after the null is only within about 13 db of the low frequency level while the data show a stronger recovery. Thus it appears that the model with two narrow samples is much better, but it is not perfect either.

[David Schwab]

The full width humbucker sampling mode shows poor agreement with the measurements . There is a null, but it is at the wrong frequency. Also, the recovery after the null is only within about 13 db of the low frequency level while the data show a stronger recovery. Thus it appears that the model with two narrow samples is much better, but it is not perfect either.

Mike, what I was trying to point out is that with a humbucker you are sampling the string at two discrete locations, and then summing that signals together. The nature of the pickup also samples the string in a differential manner. While the string is moving down over one pole, it might be moving up over another. But they sum together more-or-less, higher harmonics notwithstanding.

Now if you make a wide aperture single coil, you are now sampling a larger area of the string, but at a single wide area, and not two small areas summed together.

So if you really want to test this, you need a single coil doing this and not a humbucker. The humbucker (or any two coils summed) reinforces some frequencies and attenuates others. A wide single coil will behave differently. If you try making one you will hear the difference.

[Mike Sulzer]

Mike, what I was trying to point out is that with a humbucker you are sampling the string at two discrete locations, and then summing that signals together.

You are telling me this, but I have just shown it to be true. Some people think that a humbucker samples across the whole width of both coils, but that is not correct.

The nature of the pickup also samples the string in a differential manner. While the string is moving down over one pole, it might be moving up over another. But they sum together more-or-less, higher harmonics notwithstanding.

At low harmonic numbers the string moves in the same direction with the same amplitude and the signals add. At higher harmonic numbers, the amplitudes are not the same, and at still higher numbers the signals tend to cancel because one string is moving towards the pole and the other away. At the null, they move in opposite directions with the same amplitude. At still higher harmonics, the amplitudes differ, and the cancellation is gradually lost.

Now if you make a wide aperture single coil, you are now sampling a larger area of the string, but at a single wide area, and not two small areas summed together.

So if you really want to test this, you need a single coil doing this and not a humbucker. The humbucker (or any two coils summed) reinforces some frequencies and attenuates others. A wide single coil will behave differently. If you try making one you will hear the difference.

I think that I am on the right track to showing what the title of this discussion implies. You need a very wide aperture on a single coil to get a significant effect on audible harmonics, but I agree it can be done.

[Mike Sulzer]

Is it string sampling or something else?

Anyone experienced at making measurements and finding explanations concerning music electronics and instruments might suggest that if we have choices A and B, one might predominate, but if we say A, then B will be there too, as well as C, D, And E…. But in any case, the agreement between the measured string response and the string sampling model suggests looking for more evidence that reinforces that interpretation, and maybe show the extent to which it is true.

What should happen if we look at the response of the A string? The cancellation of harmonics should still be the same, but the fundamental is five half steps higher, and so the frequency pattern should move up by a factor of 2 raised to the 5/12 power. That is, instead of 2600Hz, we should have just under 3500 Hz.

The figure shows the results. There is no null at 2600; the response is starting to fall off and it is very small at about 3500 Hz. So it looks as though we have string sampling. But it is not the same a the E6 string just displaced up in frequency. So there are probably other things going on too.

[Mike Sulzer]

The D string

The figure shows the response of the D string. The null should be just under 4700 HZ since it is about 2630 on the E6 string, and so on the D string it is at about 2630 times 2 raised to the 10/12 power. The humbucker response does drop a lot near that frequency although it is already down quite a bit below the SC response. It does not recover very much. The response is shown to 8 KHz rather than 5 KHz to show this. As pointed out before, there is something more going on than just simple string sampling issues. But string sampling is important, and we see that there is a decreasing effect as we look at the E6, A5, and D4 strings. This must continue to decree: the E1 string would have a null at about 10,500 Hx, twice the frequency where a guitar speaker takes a dive in frequency response. Nonetheless, there still could be other effects on the E1 string.

[big_teee]

Nice Graph!
Terry