Horseshoe pickups: what do they do that's "different"?

[Joe Gwinn]

From the description for the pickup:

The usual practice is to allow considerable leeway in advertising, and I consider the claims just that, not necessarily the result of extensive research into the matter. It is advertised as an exact copy, and but that does not imply that the reason for building an exact copy of this original is because his research showed that it is technically the right thing to do. Usually you build exact copies because guitarists want them. You have to have a market for what you make.

The bolded statement could be interpreted as meaning "It makes the field close to constant in region where the strings are", but but is that really is what he means?

That's how I read it.

I am sure it is a great pickup, but not at all sure about what makes it so. It would be interesting to know. One way would be to use a different method of making the field nearly constant in the region of the strings (as I suggested) and see how that compares.

Jason has golden ears, and tests lots of stuff. His theory of operation may be nonsense, but it doesn't matter.

[bbsailor]

Well, I asked the question because that Lollar pickup is what's on the "Coodercaster" that Blake MIlls is playing here: https://www.youtube.com/watch?v=g1i8dnAi3X4

I don't know how else to describe it but that it feels like being able to get 30 more points out of your Scrabble letters when you only have 4 or 5 tiles left. There's more expression left far along in the note, when you would normally feel it going limp.

Mark,

The best way to test this, vice simply listening is to isolate the variables and see how the following changes in magnetic field configurations produces measurable differences. Plunk a string in a controlled manner and measure the time it takes for the string output to drop to a level near and slightly above the noise level.

1. No magnets near strings (record output on a contact microphone)
2. Traditional under-string single coil pickup (measure with contact microphone and pickup output)
3. A ferrous metal plate over the top of the pickup to focus the magnetic field (measure with contact microphone and pickup output)
4. Add an over-string single coil pickup with the opposite polarity wired and tested in both series and parallel modes (and measure with contact microphone also).

Plunk the strings in the following ways to collect a significant amount of data:
1. All six strings open
2. All six strings fretted at the 12 fret
3. All six strings fretted at the highest fret.

I suspect that the magnetic field will have some damping effect as evidenced by having shorter decay times to objectively prove what some have reported by listening tests. Also as the strings are pressed to the frets on the higher portions of the neck the strings will get about .0625 inches lower (depending on the guitar action/setup) and be closer to the magnets. I also suspect that with the over-string pickup added, any decrease in vibration time (damping effect of magnetic field) of the under-string pickup versus no magnets near the strings will be eliminated or reduced and the output would be more symmetrical.

Other variables to consider include:
1. The effect of the action/friction of the slide on the guitar to extract string motion even without plucking/struming the strings.
2. The location of the guitar amplifier relative to the guitar location, amplification level and energy being absorbed by the guitar/strings to create a longer sustain (less decay).

Note: Carlos Santana would mark the floor during rehersal to find the sweet spot on stage where certain notes related to his signature playing style would ring out and sustain.

I hope this puts your question in the proper perspective so we can collectively arrive at an answer that meets the listeners criteria as well as the scientific criteria.

Joseph Rogowski

[rjb]

Just out of curiosity, does anyone know if there is a patent for the Valco through-string pickup?
I haven't been able to find one online.
It's not this one: Patent US2683388 - Pickup device for stringed instruments - Google Patents

[bbsailor]

Well, I asked the question because that Lollar pickup is what's on the "Coodercaster" that Blake MIlls is playing here: https://www.youtube.com/watch?v=g1i8dnAi3X4

I don't know how else to describe it but that it feels like being able to get 30 more points out of your Scrabble letters when you only have 4 or 5 tiles left. There's more expression left far along in the note, when you would normally feel it going limp.

Mark and all,

Check out this web link for a revised 1 July 2014 document called: "The Science of Electric Guitars and Guitar Electronics" that is 615 pages of very technical reading. Paragraph 3.2.3 contains terms like this: " magnetic charge density, which is taken as a constant in this case due to the assumption of uniform density". Here is where what is easily observed with an oscilloscope (asymetrical peaks on the first few tenths of a second srting vibration) that get lost in the modeling process. http://www.guitarscience.net/papers/guibook.pdf

The article notes that the Horton reference 40 is an over simplification model of the situation.

Page 190 "...notes played on the electric guitar will be slightly distorted for a few tenths of a second after which the amplitude of the string vibration will decay to a displacement level where the pickup gives an almost linear response to the played note".

My observation is that this also indicates that the neck pickup with more string movement overhead will exhibit more initial non linearity than the bridge pickup having less string movement.

I hope the MEF members enjoy reading this and adding it to their personal library.

Joseph Rogowski

[Mike Sulzer]

Mark and all,

Check out this web link for a revised 1 July 2014 document called:

...

The article notes that the Horton reference 40 is an over simplification model of the situation.

The Horton reference can be found here:

http://scholarship.rollins.edu/cgi/viewcontent.cgi?article=1014&context=stud_fac

Read it instead. "The Science of Electric Guitars and Guitar Electronics" contains no original work on guitar pickup theory, directly copying the material from Horton et al. without understanding it. The couple of references do not indicate how much it depends on it, but the real problem is that it is not correct. For example, as far as I can see, in deriving the field of a cylindrical magnet, it completely leaves out the disk of negative magnetic charge at the opposite end of the magnet that complements the positive charge. This is necessary to make the model of the cylindrical magnet valid. Horton is understandable and correct.

[David Schwab]

Please try to understand. Magnetization refers to lining up the magnetic domains, partially or completely, temporarily or permanently. It is happens when you put a ferromagnetic material in a magnetic field. Therefore it happens when you put a pickup with a magnet on a guitar and install strings over it. It is not open to question, and there is no other physical effect that allows a vibrating string to induce a time varying field through a coil. It is essential to the operation of the pickup, whether the magnet is part of the pickup or located somewhere else.

Variable reluctance does not offer a different physical effect to explain the operation of a pickup. It is a method of explaining some magnetic phenomena by making an analogy to voltage and resistance. Just a different way of explaining what happens. And it is a terrible way except in certain simple cases. Guitar pickups are not one of them. In my previous message I asked Joe to attempt a similar analysis to what the Princeton researcher did but using variable reluctance. He has not responded. There is no simple way to do it. The standard way is the right way. This researcher put the string in a magnetic field, computed the resulting field, and then computed how much flux changed through the coil when the string was moved relative to the coil. The analysis has some significant approximations, and so it is not completely realistic, but it is pretty good, and it is much easier than trying to do it by variable reluctance, which would require computing the field everywhere and defining some complicated 3D path. In fact in attempting the reluctance solution, you would already have solved the problem the easier way and could stop.

You have some fundamental misconceptions about electromagnetism. Please drop them and learn how it really works.

Whatever Mike. Go back a couple of years and read your posts here. You didn't know much about magnetism either.

I'm actually designing and building pickups. How about you?

I stand by what I said. You can remove the magnet from the pickup and it will produce sound, but the magnetized strings with no permanent magnet is very inefficient. Plus it would be very impractical. The fact that it doesn't work well indicates that you need the magnet to constantly magnetize the strings, etc. Also the fact that you can swap of different strength/type magnets to affect the tone indicates the magnet is doing more than just charging the strings, all things being equal.

If it worked, people would have been doing it that way all these years.

Not counting this patent:

RE20070_Lesti (electromagnet).pdf

[Mike Sulzer]

Horton has interesting results that relate to the topic of this discussion. Here is a brief description of one thing.

Horton has made very careful high quality measurements. What he measures is the sum of the field of the permanent magnet and the very small field from the magnetized string. This difficult to do because the second one is so small. Figure 9 shows the relative change in this total field for changing height of the string above the pickup. The numbers are very small, but they agree well with the results of his calculations.

The meaning of the curve is this:

1. The slope of the curve gives the sensitivity of the pickup to string vibration at that point.
2. The curvature is related to the amount of distortion.

These two things vary differently with height. In figure 12 he has shown a waveform from vertical vibration that is quite distorted. The resting position of the vibrating string is 4 mm from the top of the magnet. This is on the high side: an often used distance is 3/32", or about 2.4 mm. The distortion is less there.

It would be interesting to take a more detailed look at this later.

[Mike Sulzer]

In this discussion we are trying to understand why an "over the top" pickup might have a distinct sound. Very brief summary of some comments so far: One possible reason is that the permanent magnetic field has little "vertical" variation, and therfore there is less "string pull". However, the implications of the more constant field could extend beyond this. Both the Horton and "Princeton" papers discussed here conclude that the pickup response is nonlinear, but the analyses are different. The latter assumes that the string is in a constant field, and the non linearity then results from the rapid variation with distance of the field caused by the magnetization in the vibrating string. The former includes the variation with height of the permanent field.


Looking at figure 6 in Horton, it appears that a +/- 1 mm movement of the string would result in only about a +/- 13% change in the field, suggesting a small contribution to the nonlinearity. However, the magnet used here is larger than normally used in pickups near the string. Could this be a problem?


I like Horton's charge model for computing the magnetic field, but as he points out, you have to be a bit careful because it is not accurate if you get too close to the magnet. Looking at Figure 11a confirms this. I want to look 3/32" (2.38mm) from the top face of the magnet, and the computation and the measurement do not agree well there. I am going to use a smaller magnet; that helps keep it accurate, but you want to be careful, especially since you have to allow for a 1mm motion of the string so its gets down to 1.38mm.


So, to keep the spirit of Horton's method, I have represented a magnetic dipole with closely spaced + and - magnetic charges, and then added to a cylinder the size of the magnet many dipoles (about 50,000 or more), randomly located. This is a good analog of how a magnet works, but of course the number of little dipoles is many many times more in the physical case. My computer takes about 10 seconds to compute the resulting total field, but it does not mind all the work.


(Joe Gwinn will appreciate the power of randomly located dipoles since I am sure he is familiar with the high quality antenna beams than can be obtained with random locations for the elements of an antenna array.)


The results need to be checked. There is a classic analytic equation that gives the field of a cylinder magnet (or solenoid of surface current), but only along the axis, that is up from the top face of the magnet, centered. We need the magnetic field at other places as well, but if we get agreement between the random dipole dipole model and the classic equation along the axis, we can be sure that the former is accurate not too off axis as well, and probably anywhere except very close to the magnet.


Results for two magnet sizes are shown in the attached figures, one for approximately Fender sized magnets, and the other for humbucker pole pieces, which become very much like cylinder magnets when magnetized by the flat magnet below. Shown is the vertical variation of the centered vertical component of the field.


BzovermagFen.pdf Bzovermag.pdf


Each plot has two lines, one for the random dipole calculation, the other for the classic equation. It is hard to see the difference. A quick look at these plots verifies that the field variation +/- 1mm from a position 2.38 mm above the magnet is a few times, not 13%!


However, this is not the whole story since it is not just the bit of string over the center of the magnet that counts. Thus we need to look off center as well, out to where the field component is small. It is convenient to look at the results of a sinusoidal variation. The next figure shows the field that results from a sinusoidal movement of the string, resting 2.38mm (3/32") above the magnet and moving 1mm up and down.

Bzhor0-4.pdf

In this figure the curve on top is for the bit of string centered over the magnet, and each lower one is moved .2mm horizontally away from the center. The lowest curve is for 4mm. About 2mm from the center the field decreases to about .707 times the value at the center, reducing the signal to about half the power compared to the center. At the edge of the magnet the field is down about a factor of two, and so the power is down about a fator of four. The sampling window is essentially defined by the diameter of the magnet.


Not only does the field at the resting part get smaller, but also the relative fluctuation decreases. Thus, the non-centered bits of string contribute less nonlinearity than the center, but the average effect is still large. Joseph is correct when he says that the variation of the field matters; my instincts were more like the Horton results, and that is too small.


A later post will look at the other source of non linearity, the one caused by the rapid variation with distance of the field from the magnetized string.

[Joe Gwinn]

You can remove the magnet from the pickup and it will produce sound, but the magnetized strings with no permanent magnet is very inefficient. Plus it would be very impractical. The fact that it doesn't work well indicates that you need the magnet to constantly magnetize the strings, etc. Also the fact that you can swap of different strength/type magnets to affect the tone indicates the magnet is doing more than just charging the strings, all things being equal.

There is a simple explanation for this observed behavior: Steel strings are softer magnetically than alnico and the like, and so don't make very good permanent magnets.

To take things to the extreme, consider a string made of dead soft pure iron (never mind that this wouldn't work mechanically - the string would stretch like taffy). Such a string has essentially no residual magnetism after an external field is removed. Such a string would work just fine with a standard pickup (energized by permanent magnets), and would be just about useless when the permanent magnet is removed or degaussed.

A magnetically soft string will be energized in proportion to the driving external field, until the string material saturates magnetically.


An ideal variable-reluctance transducer has a magnetically dead soft moving part. The simplest variable-reluctance transducer is a coil of wire with a movable hunk of soft iron nearby. There is a DC current through the coil (or a permanent magnet nearby), thus generating the static magnetic field.

If the static or quasi-static location of the iron piece is to be measured, the AC inductance of the coil is measured. This inductance will vary with the location of the iron piece. Lamination of the hunk may be helpful, depending on the AC test frequency

If only motion of the iron piece is to be sensed, the equipment to measure AC inductance is omitted, and AC voltages induced in the coil are instead measured. Lamination of the hunk may be helpful, depending on frequency of motion.

[Mike Sulzer]

Joe, thank you for a good explanation of how magnetization can be both temporary or "permanent", as I said in the comment DS was responding to, but I did not say it so well.


This sentence still needs a response:

Also the fact that you can swap of different strength/type magnets to affect the tone indicates the magnet is doing more than just charging the strings, all things being equal.

The magnetic function of the permanent magnet is to make a field that matters only at the strings, but the magnet can also affect the electrical operation of the circuit due to its conductivity or permeability. That is, it causes eddy currents, or alters the inductance, etc. I have posted several times impedance measurements showing the effects of different cores having different electrical properties while using the same coil.

The strength of the magnet affects the sound in particular when the amp is overdriven. A stronger magnet, with the volume controls in the same position, causes more overdrive and thus a different sound.

[Joe Gwinn]

This sentence [from David Schwab] still needs a response:

"Also the fact that you can swap of different strength/type magnets to affect the tone indicates the magnet is doing more than just charging the strings, all things being equal."

The magnetic function of the permanent magnet is to make a field that matters only at the strings, but the magnet can also affect the electrical operation of the circuit due to its [own] conductivity or permeability. That is, it causes eddy currents, or alters the inductance, etc. I have posted several times impedance measurements showing the effects of different cores having different electrical properties while using the same coil.

The strength of the magnet affects the sound in particular when the amp is overdriven. A stronger magnet, with the volume controls in the same position, causes more overdrive and thus a different sound.

Is there anything to dispute here? You are saying that the magnet itself changes the sound by its own magnetic permeability and electrical conductivity; this is certainly true. And is exactly what David Schwab is saying.


To clarify the issue, it's best to simplify the model (even if the resulting model is too simple to be a practical pickup). The simpler the model, the cleaner the arguments. (This is why I went to the coil of wire with a nearby movable hunk of iron.)

The simplest model that seems to capture the issues in debate consists of a coil, a nearby stationary hunk of permanent magnet, and a nearby moveable hunk of soft iron.

If the permanent magnet is ceramic, there will be little electrical effect on the coil. If alnico, there will be some effect. If alnico plus soft iron pole-pieces and maybe a baseplate, more effect. And so on.

[Mike Sulzer]

You are saying that the magnet itself changes the sound by its own magnetic permeability and electrical conductivity; this is certainly true. And is exactly what David Schwab is saying.

I think DS is disagreeing with what I am saying, not saying the same thing. He objects to my statement that the permanent magnetic field only matters where the strings are because all the permanent field does is to magnetize the strings, and as evidence he says that the magnet has other effects. Of course, these effects have nothing directly to do with the permanent field, and so they actually do not contradict what I am saying.

[rjb]

The lousy former student raises his hand

[ATTACH]32030[/ATTACH]

In this figure the curve on top is for the bit of string centered over the magnet, and each lower one is moved .2mm horizontally away from the center

Just checking if I understand the lecture. Is this right?:
> This figure shows the magnetic field at various points along the string (vs time).
> The pickup's output voltage is proportional not to the field at the string, but to the rate of change of flux through the coil (the source of changing magnetic field being the vector sum of the points along the string... if that makes sense).
> Noting that all but the weakest few magnetic field vs time curves have essentially the same shape, can we get a rough idea of the predicted waveform of the pickup's output voltage by linearly summing the curves, then taking d/dt (i.e., plotting the slope vs time) of the result? (Or should you plot d/dt for each of the curves first, then add them?) Or, to make life simpler, just plot d/dt of the top curve?

Also:
If we pass Below-String Pickups, will there be a class on String-Through Pickups next semester?

[Mike Sulzer]

Yes, that is the vertical component of the field at various points along the string as a function of height, and therefore time.

The idea here is to determine which factors are important in determining the changing flux through the coil. For example, with the horseshoe pickup, we expect the permanent field to be almost spatially constant. The question we are looking at is this: is it close to spatially constant for a normal pickup. If not, the changing field strength will modulate the signal, producing a variation that is not in the output of the horseshoe pickup, and therefore be a possible cause of differences in sound between the two. This variation would be called "nonlinear", contributing to a signal shape that is not a sinusoid for a sinusoidal vibration, resulting in extra harmonics. The output should be the sum from all the little bits of vibrating string, yes, and therefore it is important to check for this variation along the string.

This variation is just one "secondary" factor; we still have to look at the main variations caused by the vertical motion of the field of the "string" magnet. How much does the approximate 1/r^3 variation of this field contribute to nonlinearity? Both the horse shoe and normal pickup have this.

The attached plot is a vertically squashed 3D plot of the location of the random dipoles in the magnet with a piece of string above. This could help in visualizing the situation.

magandstring.pdf

Just checking if I understand the lecture. Is this right?:
> This figure shows the magnetic field at various points along the string (vs time).
> The pickup's output voltage is proportional not to the field at the string, but to the rate of change of flux through the coil (the source of changing magnetic field being the vector sum of the points along the string... if that makes sense).
> Noting that all but the weakest few magnetic field vs time curves have essentially the same shape, can we get a rough idea of the predicted shape of the pickup's output voltage by linearly adding the curves together, then taking d/dt (i.e., plotting the slope vs time) of the result? (Or should you plot d/dt for each of the curves first, then add them?) Or, to make life simpler, just plot d/dt of the top curve?

Also:
If we pass Below-String Pickups, will there be a class on String-Through Pickups next semester?

[bbsailor]

Yes, that is the vertical component of the field at various points along the string as a function of height, and therefore time.

The idea here is to determine which factors are important in determining the changing flux through the coil. For example, with the horseshoe pickup, we expect the permanent field to be almost spatially constant. The question we are looking at is this: is it close to spatially constant for a normal pickup. If not, the changing field strength will modulate the signal, producing a variation that is not in the output of the horseshoe pickup, and therefore be a possible cause of differences in sound between the two. This variation would be called "nonlinear", contributing to a signal shape that is not a sinusoid for a sinusoidal vibration, resulting in extra harmonics. The output should be the sum from all the little bits of vibrating string, yes, and therefore it is important to check for this variation along the string.

This variation is just one "secondary" factor; we still have to look at the main variations caused by the vertical motion of the field of the "string" magnet. How much does the approximate 1/r^3 variation of this field contribute to nonlinearity? Both the horse shoe and normal pickup have this.

The attached plot is a vertically squashed 3D plot of the location of the random dipoles in the magnet with a piece of string above. This could help in visualizing the situation.

[ATTACH]32048[/ATTACH]

Mike and all,

Since we are talking about the sound difference that we can hear between an under string magnet/coil pickup and an over/under magnet and coil pickup, we also need to look at how the ear perceives short transients that represent the initial string attack of the first 200 milli seconds. See this web link: http://wiki.dxarts.washington.edu/sa...oustics%29.pdf

Page 59 discusses how the ear responds to transients of short duration. This is critical for us humans to be able to accurately hear words that have only a short difference in sound. This also applies to the initial nonlinearity of the initial guitar string transient that we have been decomposing to find a common understanding of why the magnetic field adds to the perception of the sound. See Figure 3-12 where the non-linearity of the graph starts at 200 milli-seconds and that is where the greatest asymmetry of the signal occurs with under-string magnet/coil pickups. The ear is the final arbitrator of sound quality, the physics allows us to understand what forces are related to what we hear and allows us to change things and better understand the probable effect.

Mike, thanks for your detailed analysis.

Joseph Rogowski