Sampling the string: differences between single coil and humbuckers

[bbsailor]

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.

[ATTACH=CONFIG]15835[/ATTACH]

Mike,

The distance between typical humbucking coils is 0.75 inch or exactly 1/34 of a 25.5 inch string length. Although 1/34 string length represents a very high harmonic that would cancel out any harmonics where that harmonic string motion is moving up over one coil and down over the other coil. However this small 0.75 inch separation also allows for partial phase cancellation for lower harmonics where the phase cancellation is less than 180 degrees and would reflect adding or subtracting amplitude of various lower harmonics. An easy way to prove this is to plot out the harmonic structure (as you did in the graphic) but with humbucker coils spaced 1.5 inches apart and see if you can infer an new set of harmonic structures. I suspect that you could anticipate the harmonic structure at any specified coil distance. As an alternative you could use a humbucker single coil footprint pickup with the coils spaced about .375 inches apart.


It is interesting to note that the fret spacing between the 11th and 12th frets is 0.75 inches wide (on a 25.5" scale) and this might have some musical or harmonic relationship between notes/harmonics cancelled or added.


This may be a new level of research (short coil spacing) that I have not seen done before. Tillman (http://www.till.com/articles/PickupResponse/index.html) did show the harmonic effects of pickups spaced a few inches apart where the fundamentals or lower harmonics would add or cancel. The spacing between the neck and center pickups on a Stratocaster is 2.375 inches or 1/10.736 of the open string length.

Thanks

Joseph Rogowski

[Mike Sulzer]

Nice Graph!
Terry

Thanks. I am working on the E1 string now, and have a plot to show out to 20 KHz when the text is done.

[Mike Sulzer]

Mike,

The distance between typical humbucking coils is 0.75 inch or exactly 1/34 of a 25.5 inch string length. Although 1/34 string length represents a very high harmonic that would cancel out any harmonics where that harmonic string motion is moving up over one coil and down over the other coil. However this small 0.75 inch separation also allows for partial phase cancellation for lower harmonics where the phase cancellation is less than 180 degrees and would reflect adding or subtracting amplitude of various lower harmonics. An easy way to prove this is to plot out the harmonic structure (as you did in the graphic) but with humbucker coils spaced 1.5 inches apart and see if you can infer an new set of harmonic structures. I suspect that you could anticipate the harmonic structure at any specified coil distance. As an alternative you could use a humbucker single coil footprint pickup with the coils spaced about .375 inches apart.


It is interesting to note that the fret spacing between the 11th and 12th frets is 0.75 inches wide (on a 25.5" scale) and this might have some musical or harmonic relationship between notes/harmonics cancelled or added.


This may be a new level of research (short coil spacing) that I have not seen done before. Tillman (Response Effects of Guitar Pickup Position and Width) did show the harmonic effects of pickups spaced a few inches apart where the fundamentals or lower harmonics would add or cancel. The spacing between the neck and center pickups on a Stratocaster is 2.375 inches or 1/10.736 of the open string length.

Thanks

Joseph Rogowski

Thanks Joseph. I do not know if these measurements are new, but I am pretty sure of the reason that Tillman did not compute with coils as close as humbucker spacing. If you look towards the bottom of the article that you referred to, you see a section on pickup width effects. He assumes that a pickup samples across the whole coil, or a humbucker across both coils. This is a common assumption, although its origin is not clear. A look at the theory of how pickups works indicates that the sampling width should be more like a pole width, as others assume or perhaps have computed or measured.

In any case, it is important to get measurements that test predictions. The results for the E6 string above show that the aperture is narrow, but do it in an indirect way. By comparing the response of a single coil with that of the two coil humbucker, we see that measurement and sampling theory agree much better for a narrow sampling region for each coil than for a continuous sampling across the whole of both coils. I think there might be a discrepancy between his and my calculations for that latter case regarding the location of the null, and so I have to check mine. However, the recovery after the null (about -13db) is of course the standard number for a sinx/x (box car) filter and we both get that. That number alone is sufficient to show that the model with two narrow apertures is closer to correct.

[bbsailor]

Thanks Joseph. I do not know if these measurements are new, but I am pretty sure of the reason that Tillman did not compute with coils as close as humbucker spacing. If you look towards the bottom of the article that you referred to, you see a section on pickup width effects. He assumes that a pickup samples across the whole coil, or a humbucker across both coils. This is a common assumption, although its origin is not clear. A look at the theory of how pickups works indicates that the sampling width should be more like a pole width, as others assume or perhaps have computed or measured.

In any case, it is important to get measurements that test predictions. The results for the E6 string above show that the aperture is narrow, but do it in an indirect way. By comparing the response of a single coil with that of the two coil humbucker, we see that measurement and sampling theory agree much better for a narrow sampling region for each coil than for a continuous sampling across the whole of both coils. I think there might be a discrepancy between his and my calculations for that latter case regarding the location of the null, and so I have to check mine. However, the recovery after the null (about -13db) is of course the standard number for a sinx/x (box car) filter and we both get that. That number alone is sufficient to show that the model with two narrow apertures is closer to correct.

Mike,

It is very important to isolate variables to eliminate any coincident effects that might creep into your observed measurements. The most obvious coincident effect could be the pickup self resonance that affects a range of harmonics within the bandwidth of the resonant peak. Try measuring the same pickup with the coils in series (like a traditional humbucker) and parallel which will produce a different resonant peak due to the lower inductance of the parallel coil connection. Also, try putting the coils out of phase to pickup only the harmonic content that is detected by the space displacement between the coil poles. This should produce a cancellation of most fundamentals leaving only a very weak coil difference signal consisting of upper harmonics.

Here is another way to isolate this resonance variables. Use an 8 ohm to 20K (or higher) matching transformer with the 8 ohm side attached across a single string. Then mount two round magnets 0.75 inches apart and hold these magnets under the string in the same position as a humbucker would be located along the string length somewhat near the 24th fret. See if the harmonic content of the humbucker output compares with the direct string output of the transformer secondary (20K ohms side) with two magnets spaced 0.75 inches apart. This direct string approach could eliminate or minimize any resonant effects of using humbucking pickup coils. Plus you can easily change the spacing of the two magnets and see if there are any spacings that produce more dramatic harmonic effects or even match Tillman's results.

I believe the experiment described above, eliminating the resonance effect, is plowing new ground.

Thanks

Joseph Rogowski

[Mike Sulzer]

Mike,

It is very important to isolate variables to eliminate any coincident effects that might creep into your observed measurements. The most obvious coincident effect could be the pickup self resonance that affects a range of harmonics within the bandwidth of the resonant peak. Try measuring the same pickup with the coils in series (like a traditional humbucker) and parallel which will produce a different resonant peak due to the lower inductance of the parallel coil connection. Also, try putting the coils out of phase to pickup only the harmonic content that is detected by the space displacement between the coil poles. This should produce a cancellation of most fundamentals leaving only a very weak coil difference signal consisting of upper harmonics.

Here is another way to isolate this resonance variables. Use an 8 ohm to 20K (or higher) matching transformer with the 8 ohm side attached across a single string. Then mount two round magnets 0.75 inches apart and hold these magnets under the string in the same position as a humbucker would be located along the string length somewhat near the 24th fret. See if the harmonic content of the humbucker output compares with the direct string output of the transformer secondary (20K ohms side) with two magnets spaced 0.75 inches apart. This direct string approach could eliminate or minimize any resonant effects of using humbucking pickup coils. Plus you can easily change the spacing of the two magnets and see if there are any spacings that produce more dramatic harmonic effects or even match Tillman's results.

I believe the experiment described above, eliminating the resonance effect, is plowing new ground.

Thanks

Joseph Rogowski

Joseph,

I have already taken care to handle the effect of pickup resonance. Each coil has a capacitor across it to set the resonance at a frequency that would be typical of normal use with a cable. Either coil or the series combination is run to a very high impedance buffer. Gain and frequency response are very close as shown in the post "The pickups used in...."


That is a very interesting idea about using spaced magnets!

[Mike Sulzer]

Improving the electronics

The measurements so far have used a series connection of the two coils into a high impedance buffer for the two coil tests. This keeps the setup as much as possible like the normal humbucker connection. However, the lack of symmetry with respect to ground can cause problems with the high frequency response, in particular, bumps in the baseline of the frequency response. In order to look at the details of string sampling at high frequencies on the higher frequency strings, it is necessary to do better.

The circuit shown in the attachment takes care of these problems.

It is a unity gain three op amp instrumentation amplifier which can be split apart with the switch in order to give a gain of two with either coil alone so that the signal level is the same in all three positions. In the humbucker position it cancels magnetic hum, but it also cancels electric hum to the extent that the same electric field occurs across both coils. The EMG differential amp does this as well, of course, which assures that no string ground is necessary. I prefer to use the instrumentation amp with the high impedance buffers into the diff amp because the eddy currents in the steel cores and the base plate provide sufficient damping of the resonance.

This circuit also provides the possibility of inserting a buffered dummy coil at the switch terminals that are grounded. This would make it easy to test dummy coils and circuits, especially whether there is any change in the single coil sound. The buffered dummy coil signal also could be inserted on the other side by lifting the resistor from ground using another switch section.

[Mike Sulzer]

A plot with the new electronics using data from all six strings

The plot in the attachment has spectra from all six strings, arranged vertically, with the prediction below.

The prediction is for two narrow regions separated by .75 inches. The graph is a bit different from before because I have make small corrections in the measured distances. The horizontal axis is harmonic number, not frequency; the frequencies for each spectrum are divided by the fundamental in order to get the harmonic number. The string fundamentals cover a range of two octaves, but the harmonics that are attenuated are always the same. Thus, presenting the data in this manner makes it easy to see the spectra for all strings behave as expected.

As before, the plot of predictions tells how much the spectra with two coils should be attenuated below the spectra for the single coil. Most of the attenuation should occur between the 30th and 40th harmonics. It does, but there are some irregularities; picking a string does not give perfect results. Data were collected for .5 second with 20 spectra of 2000 points averaged. The string was picked three times quickly. The data for the E1 and B2 strings are not as good as the others; the relevant harmonics are at quite high frequencies where the pickup response is significantly attenuated. These measurements could probably be improved by removing the capacitors across the coils.

The boundary between the white and gray area on each individual spectral plot occurs at 5 KHz. The boundary moves to lower harmonic number as the frequency of the string increases. This means that the attenuated region moves towards higher frequencies. 5 KHz has been taken as a reasonable indicator of the range of the instrument because pickups usually fall off at or below this frequency, and most guitar speakers have rapidly falling response above 5 KHz.

Here is a review of the conclusions from these observations:

1. The roughly constant locations of the attenuated regions (expressed in harmonic number) and agreement of the predictions for the sampling effect imply that the reason for the attenuation is string sampling.

2. The recovery of the spectrum after the minimum (that is, as harmonic number increases) means that the two sampling regions are narrow. The predictions were computed for a region of .1 inch. A significantly larger region means that the spectrum does not fully recover at frequencies above the minimum.

3. The difference between the sound of single coil and double coil sampling should be heard most on the lower frequency strings, and should be a much smaller effect on the highest frequency strings as the attenuated harmonics move out of the range of the instrument.

The attenuated region on the E6 string falls near the middle of the range where human hearing is most sensitive. To me, the difference between single and double coil is a loss of definition, and not so much as a loss of high frequencies. Such al sound is neither good nor bad, but rather is useful for some purposes and not others.

[fieldwrangler]

The attenuated region on the E6 string falls near the middle of the range where human hearing is most sensitive. To me, the difference between single and double coil is a loss of definition, and not so much as a loss of high frequencies. Such al sound is neither good nor bad, but rather is useful for some purposes and not others.

Man... I just couldn't agree more.

Bob Palmieri

[Mike Sulzer]

Here is a brief sound sample with all six strings showing how the effect decreases with increases string frequency.
sixStrings.mp3