Guitar Pickup Analysis Web Link

[bbsailor]

Below is a web link for a good technical analysis of guitar pickups.
http://www.moore.org.au/pick001.htm

Joseph Rogowski

[David Schwab]

Great info there!

[guitician]

Yeah, I was looking at the page titled "Unified Pickup Measurements" and noticed how he states that.......

"If you put a relatively powerful magnet near the strings, they may be very marginally pulled towards the magnet. The pitch is effectively not changed and the string still sustains as before."

I've always noticed a "Warble" when the pickup is too close to the strings. Am I just amagining this?

[bbsailor]

Yeah, I was looking at the page titled "Unified Pickup Measurements" and noticed how he states that.......

"If you put a relatively powerful magnet near the strings, they may be very marginally pulled towards the magnet. The pitch is effectively not changed and the string still sustains as before."

I've always noticed a "Warble" when the pickup is too close to the strings. Am I just amagining this?

guitician,

The warble is the caused by the magnet being too close to the strings. The up and down string motion is the only part of the string motion that generates a pickup voltage. Sideways string motion does not contribute to output, according to induction theory.

Typically, magnets that have more mass (diameter, length), magnet type, string diameter, string-to-pickup distance and string tension contribute to the "warble effect". Thicker strings are affected more than thinner strings. Loose strings are affected more than tighter strings.

The recommended maximum pickup height adjustment procedure is to move the pickup close enough to the strings to hear the warble than lower it until the warble stops. Then, adjust the low-E to high-E string balance or individual string balance to suite your ear.

Joseph Rogowski

[guitician]

Yeah, that's what I thought. I think the statement I quoted was refering to sustain and pitch, which is not the same as an attack distortion or warble. Thanks

[Mike Sulzer]

Yeah, that's what I thought. I think the statement I quoted was refering to sustain and pitch, which is not the same as an attack distortion or warble. Thanks

I think the quote is wrong. Think of the total motion of the string as divided into two modes, one in which it moves vertically, the other horizontally. A strong vertical B field affects the frequency of the vertical mode. But the modes are not completely independent; energy from one moves into the other. So the "beat" that you hear is from two nearly equal frequencies present at once.

If you use really strong magnets and light up the string just right, you can see the normally elliptical motion of the string become sort of wild. I am tempted so say "chaoitic", but I doubt that this really qualifies under the formal definition of chaos.

[guitician]

I guess that it pulls a discordant harmonic into the vibrating string.

[Mike Sulzer]

I guess that it pulls a discordant harmonic into the vibrating string.

I think the when the string moves vertically in the vertically-directed B field, the average tension on the string is altered as the force due to the field varies, thus changing the frequency. Horizontal motion, that is parallel to the field, does not result in a change in the force from the B field. With both motions present at once, the situation is nasty, resulting in a coupling of the two modes. I do not know the details, but this seems reasonable.

[Mal88]

Hi Mike

I used to think that the pickup picked up on vertical and horizontal motion relative to the strings but my experiments showed that relative horizontal motion gave very little output compared to the vertical relative motion - and that is why I wrote what vertical relative motion gets translated into electrical signal.

You are right that the string appears to move elliptically (if not round), but when you start to analyse the magnetic field from the magnets' pole pieces - you see that the magnetic field very quickly ends up with a uniform gradient up into / through the strings - so if the string moves on a constant magnetic potential line, vertical (normal) to the magnetic lines of force, then you will see that the strings do no 'work' - hence they will not produce an electrical signal via this lateral motion.

Be aware that the magnetic field stength / potential is not linear with distance from the magnet's centre and so the linear motion of the string will produce a non-linear voltage, and this accounts for the strong even harmonics (or that 'warm' sound), that can be accentuated by single-ended amplification without feedback - but that is another story!

Cheers, Malcolm

[Mike Sulzer]

Hi Mike

I used to think that the pickup picked up on vertical and horizontal motion relative to the strings but my experiments showed that relative horizontal motion gave very little output compared to the vertical relative motion - and that is why I wrote what vertical relative motion gets translated into electrical signal.


I agree that the horizontal motion of the string results in very little output. That is OK, but let us look at what happens when a string vibrates. Ideally, in the simple situation a physicist would analyze as a first attempt, if you started a string vibrating in the horizontal plane, it would continue to do so. That is, there would be no vertical motion. But you are not really going to achieve this simple situation in practice. There are asymmetries, both mechanical (how the string is supported), and magnetic. So one expects that the vertical and horizontal get coupled. So if the h and v vibrations are different in some way, as caused here by the B field, then this difference is audible when the h affects the v (which the pickup senses). String pull (the warbling sound) is something that occurs at a slow rate, much slower than the frequency of the string. So to explain it, we have to look for a frequency difference. This is provided by the differences of the vibration properties in h and v when B is present. This is a "seat of the pants" explanation; the details of how it works are probably quite complicated, and not so easy to analyze.

[Joe Gwinn]

I think the when the string moves vertically in the vertically-directed B field, the average tension on the string is altered as the force due to the field varies, thus changing the frequency. Horizontal motion, that is parallel to the field, does not result in a change in the force from the B field. With a blade pickup this would be strictly true. With magnet and especially slug poles, there is also a variation in magnetic field with horizontal motion.

With both motions present at once, the situation is nasty, resulting in a coupling of the two modes. I do not know the details, but this seems reasonable.The classic extreme example and demonstration is the Wilburforce Pendulum.

http://www.ap.stmarys.ca/demos/content/osc_and_waves/wilberforce_pendulum/wilberforce_pendulum.html

[David Schwab]

Hey Malcolm, nice for you to join us here!

Bill Bartolini had an interesting take on the up/down vs. side-to-side string motion. He showed that if you have a tall vertical pattern over your pole (such as from round rod magnets), the string's side-to-side motion will be picked up because the lines of flux are more vertical, so the sideways motion cuts through them.

He then designed the wide planar pole tips to produce a low field with more horizontal lines of flux to capture the up-and-down motion of the string, as he felt that was more akin to an acoustic guitar's soundboard motion, as they produce little sound from the sideways motion.

From his two patents:

Basically, the tone of a plucked or a struck string instrument is judged by the richness and complexity of the acoustic output in the "attack" or beginning portion of a note. In acoustic string instruments, the bridge structure constrains the motion of the soundboard such that those components of string motion which are perpendicular to the, plane of the soundboard are well amplified, while those components ofthe string motion which are parallel to the plane of the soundboard are not. The path described by any arbitrarily small segment of a smoothly released, plucked string is a precessing elliptical orbit of decreasing radius which rotates about the quiescent position ofthestring. Accordingly, the asymmetrical amplification of string motion provided by the bridge of an acoustic instrument yields a rich, full and complex tone of continuously varying, harmonic content.

The prior art variable reluctance pickup systems are characterized by separate pole tip and/or pole pieces for each string. Each pole tip and/or pole piece provides a distinct magnetic field region around the quiescent position of each string. The distinct magnetic field regions of prior pickup systems render them relatively insensitive to the plane of vibration of the particular string.

For example, pickup systems with circular pole pieces provide a magnetic field having the form of a symmetrical sinusoidal shell and a string vibrating within such a magnetic field will generate approximately equal magnitude electrical signals for string vibrations both parallel and perpendicular to the string plane.

The pole pieces and the poletip faces provide a magnetic field region proximate each string which has a large magnitude magnetic flux gradient in a direction perpendicular to the string plane and a small magnitude magnetic flux gradient in a direction parallel to the string plane (parallel to the sound board).

http://sgd-lutherie.com/images/bart.jpg

[Mike Sulzer]

With a blade pickup this would be strictly true. With magnet and especially slug poles, there is also a variation in magnetic field with horizontal motion.

The classic extreme example and demonstration is the Wilburforce Pendulum.

http://www.ap.stmarys.ca/demos/content/osc_and_waves/wilberforce_pendulum/wilberforce_pendulum.html

Nice link! I had not seen that one.

Yes, there is some horizontal variation in B. It is smaller than the vertical, though; so I hope one can ignore it when looking for reasonable, simple, explanations!

[Mal88]

I used to think that the magnetic rods in pickups like the Strat and Tele would have created a series of ridges that would give signals a sense of 'ownership' between pole and string - but if you pull a string over a couple of the magnetic poles - do you hear a distinct drop and increase in level as the string transverses? I don't!

It therefore follows that the magnets in a single file form 'sheets of equivalent magnetic field strength' that sits like blankets on a matress - so you don't really feel the springs in the bed as you run your hand over the sheets - and that is equivalent to the strings moving in a plane a few mm over the magnetic poles, and the further you move away the more consistent these sheets become.

With Antennae, Hygens theory matches these comments! I did some finite element magnetic modelling and it shows that after about 2 mm there really is an almost flat magnetic field strength above the line of magnetic poles.

Interesting to note that the magnets lose a lot of their fields between each other in the strip, and it would also follow that because the magnets are separated, then the eddy current losses (in these highly conductive magnets) are isolated into the separate magnets and consequently these frequency dependent losses are somewhat limited - and that is good!!

[David Schwab]

I used to think that the magnetic rods in pickups like the Strat and Tele would have created a series of ridges that would give signals a sense of 'ownership' between pole and string - but if you pull a string over a couple of the magnetic poles - do you hear a distinct drop and increase in level as the string transverses? I don't!

You do to an extent. That's why a lot of people like blade poles, so they don't have drop outs when bending. You can see the profile of the rod magnets in the Bartolini patent picture above marked as "II".

It all depends on the size of the poles. You especially hear it with bass pickups.

[salvarsan]

A few years back, some of us created FEMM magnetic models for pickup magnet geometries.
Steve Kersting saved a few of them.

http://www.skguitar.com/SKGS/sk/Images/pickups/Pickup%20stuff/Magnetics.htm

-drh

[Mal88]

Yes, you are right, there is a discernable difference in level as the string is pulled laterally over the magnet poles! Now that is interesting because this implies that the level change is about 3 dB; which implies that the average effect on the magnetic field potential changes by as much as 1.414 times - but the magnetic modelling does not show that.

There is definitely a ripple in the magnetic field strength near the adjacent poles, so it could well follow that the energy transferred from the relative instanteanous movement of the string as it is laterally dragged over/between the poles, sits over a 'saucer' of the magnetic potential between the poles, and consequently vertical and horizontal movements are somewhat self-cancelling; thus causing the discernable drop in induced signal level.

My modelling to date shows that magnetic 'rails' would not suffer this 'ripple/fade' fate and that although magnetic rods look asthetically pleasing, rods/screws may be a rather poor engineering choice!

[David Schwab]

My modelling to date shows that magnetic 'rails' would not suffer this 'ripple/fade' fate and that although magnetic rods look asthetically pleasing, rods/screws may be a rather poor engineering choice!

We are used to the look of rod poles, but if pickups never had them we wouldn't care!

I'm convinced that blades are a better way to go.

[Mal88]

As your political combatants keep saying - "Lipstick"!!!

[Mal88]

Excellent work there! I did the same totally unaware that this had been worked on, and Steve had gone the one step further with the plot across the tops of the pickups (which I alluded to but never seriously followed up)!

Remember that this is a 'slice' of the magnetic field right through the centre of the magnetic structure and it appears bigger on the 'sides' - but - if you took several 'slices' (parallel to this one and normal to the strings) I believe that the overall magnetic field is 'fatter/wider' in the middle, but you are not seeing this in this case (because you are rignt in the centre); and like Bragg diffraction, the fatter/wider field intensity will considerably cancel these magnetic intensity ripples seen on this plane.

[salvarsan]

The other thing we noticed is that a pickup has a magnetic aperture
with a width and strength, a quality factor perhaps.
P90's and PAF's have a wide aperture, Fender SC types are more focussed.
Dual blade pickups have the best-focussed field of any of them.

The other thing the simulations let us do is estimate how much steel to put
in the magnet path if using rare earth magnets.

BTW, do _not_ believe anything FEMM has to say about Alnico 8.
It lists permeability as ~6 when it should be closer to 1.1.

-drh

[Mal88]

Yes I agree with the wider sensitive pickup area for the PAF and I measured that against the standard Strats. But the Strats do have a fairly consistent pickup width that is somewhat wider than the poles.

Remember that the FEMM analysis is an infinitely thin slice of 2D right along the centre axis and that is rather like a 'null' point - so you will get 'misleading' results if you don't think beyond the null situation. Case in point when you model a bar or cylinder magnet - you will see that the vast majority of the graduating magnetic potential is close to the side surfaces (because the magnetic lines oppose each other and there is nowhere else to go).

Unfortunately I have not been able to get my hands on a working P90, but I have seen the structure of the magnets / poles and that is a real worry. I have heard people say they are noisy, and the reasoning is there because the magnetic field is everywhere but via the strings - and that is why they are noisy!

The difference between the PAF and the Strat is that the PAF has a slightly improved magnetic circuit - but it really has a very long way to go to get it to be anywhere towards 'good'. It (PAF) really is not a hum bucker as the second coil does not 'buck hum' it merely partially closes some of the magnetic circuit nearer the strings. If this was really to buck hum, then it would have a very much smaller third winding under the mounting plate to cancel far-field excitations - but it can't - because the magnetic is so leaky and the common magnet is ill positioned (and there is virtually nil magnetic shielding)!

[David Schwab]

The difference between the PAF and the Strat is that the PAF has a slightly improved magnetic circuit - but it really has a very long way to go to get it to be anywhere towards 'good'. It (PAF) really is not a hum bucker as the second coil does not 'buck hum' it merely partially closes some of the magnetic circuit nearer the strings. If this was really to buck hum, then it would have a very much smaller third winding under the mounting plate to cancel far-field excitations - but it can't - because the magnetic is so leaky and the common magnet is ill positioned (and there is virtually nil magnetic shielding)!

Yeah, but for the hum they intended on bucking, the 60 (120) cycle stuff, the humbucker works, as the magnets are not needed to pick up hum, or buck it. It's the out-of-phase coils that do the trick. It doesn't mater which coil is bucking the hum... they both pickup the strings and the nose. The magnets are only needed to pick up the string's vibrations. Audio inductors are often wound as humbuckers and have no magnets at all.

The higher frequency electrostatic noise slips in between the coils as it were, so you need good shielding for that... something guitar humbuckers generally never have, unless they are covered.

Some of the newer stacked pickup designs are interesting as they use the top coil only to pick up the strings, and the bottom coil to induce noise into the system. The bottom coil is often wound less and has higher inductance due to more metal included.

See patent #7166793 by Kevin Beller with Duncan. It's similar to the Kinman and DiMarzio designs, but has a few twists.

[SK66]

Remember that this is a 'slice' of the magnetic field right through the centre of the magnetic structure and it appears bigger on the 'sides' - but - if you took several 'slices' (parallel to this one and normal to the strings) I believe that the overall magnetic field is 'fatter/wider' in the middle,.
Yes, the pickup's aperature is a bit "wider" in the middle. Also note that some of that extra strength from the end poles is cast off into useless space (off the end of the pickup).
The one thing that I find interesting is that magnet "strength" doesn't seem to be a huge factor in a pickups "volume"....

[Mal88]

Yes I believe that you are right in that the magnet strength is not a major factor in sensitivity (but don't tell the musos)! The sensitivity is really locked up in the incremental change in overall inductance caused by the relative movement of the string. Just as dV = L di/dt, so also dV = R dL/dt (where R is the magnetic potential (or flux) of the field where the movement of the string is taking place). Plus / minus signs neglected for simplicity in these equations.

The magnetic flux is not linear with distance from the magnetic centre so if the pickup is slightly closer then it will be far more sensitive to string movement than if the magnet was proportionally weaker or stronger.

[Mike Sulzer]

Yes I believe that you are right in that the magnet strength is not a major factor in sensitivity (but don't tell the musos)!

I do not agree. If the magnet has zero strength you get no output from the pickup because the there is no changing flux through the coil from the vibrating string. A weak magnet weakly magnetizes the string and gives a small output, and a strong magnet gives more. That is an observed fact. Of course, you cannot make the magnet too strong or you affect the vibration of the string.

[Mal88]

Right Mike! Look at the equation again - if there is no magnetic strength then there will be no output. The output is proportional to the change in magnetic field. If the field is twice as strong, then the change for the same relative movement wil be 6.02 dB louder (agreed), but move the string to 0.7071 times the current distance position and the magnetic field will be double the potential and also be 6.02 dB louder. (compre') Alternatively use a more effective magnetic circuit - (most manufacturers neglect the inefficiency of the distant end pole and leave it floating in the breeze).

[David Schwab]

I do not agree. If the magnet has zero strength you get no output from the pickup because the there is no changing flux through the coil from the vibrating string. A weak magnet weakly magnetizes the string and gives a small output, and a strong magnet gives more. That is an observed fact. Of course, you cannot make the magnet too strong or you affect the vibration of the string.

Right, but getting past using a weak magnet, if you take a fully charged alnico V, and a fully charged Ceramic 8, the ceramic is quite a bit stronger, but the pickup will not be louder by the same degree, if at all. It might be brighter though.

Also the shape of the pole piece makes a difference... alnico rods will pull the strings a lot more than a blade charged by even a strong neo magnet. I'm working with N42 grade neo bar magnets which are spec'd at: Pull Force: 22.40 lbs; Surface Field: 4480 Gauss; Brmax: 13,200 Gauss; and I have no string pulling problems when used in the context of a pickup. I would also imagine my cores are quite saturated by the magnets, but that's another subject.

Interestingly I get a lot more low end with the neos than with a C8 in the same pickup.

[Mike Sulzer]

Right Mike! Look at the equation again - if there is no magnetic strength then there will be no output. The output is proportional to the change in magnetic field. If the field is twice as strong, then the change for the same relative movement wil be 6.02 dB louder (agreed), but move the string to 0.7071 times the current distance position and the magnetic field will be double the potential and also be 6.02 dB louder. (compre') Alternatively use a more effective magnetic circuit - (most manufacturers neglect the inefficiency of the distant end pole and leave it floating in the breeze).

This is how I see the B field vs. distance thing: If you weaken the field, you can move the pickup closer to the string without getting string pull. Then you actually get more output from the pickup because: 1. The magnetic field at the string is the same in the two situations. 2. The change in magnetic flux through the coil when the string vibrates is greater because the magnetized string is closer to the pickup. There are limits as to how close you can go, of course.

I do not see where the .707 factor comes from. Far away, the field is like a dipole, varying with inverse distance cubed. Close up it hardly varies at all. In between is complicated.

Do you have an example of how a more efficient magnetic circuit can help?

[salvarsan]

Do you have an example of how a more efficient magnetic circuit can help? Reluctantly, variably, no.

-drh

[David Schwab]

2. The change in magnetic flux through the coil when the string vibrates is greater because the magnetized string is closer to the pickup.

You know Mike, the whole magnetized string thing is greatly exaggerated in my opinion. Yes, the strings become magnetized, but they are very poor magnets on their own, and a brand new set you put on is not as magnetized as set that's been on there a while, yet they sound just fine.

Many years ago I tried removing the magnet from the pickup after the strings were magnetized, and you get very little output without the main magnet. That would lead one to believe the string's own magnetic field plays very little in the overall output of the pickup.

A pickup is a variable reluctance sensor. As the strings move over the pickup, the reluctance of the flux path through the coil changes, as well as the flux linkage through the coil. The coil always has a magnetic field around it because of the permanent magnets. The motion of the string varies the magnetic reluctance in the circuit created by the permanent magnet.

The fact that the strings might be magnetized is of less interest than the main magnet in the circuit. This is why different magnet types will sound different in the same pickup with the same strings. When the pickup is closer to the strings, so is the magnet and coils. You have greater lines of flux to disturb as well, especially in a humbucker where the field is pretty compact over the pickup.

[Mike Sulzer]

You know Mike, the whole magnetized string thing is greatly exaggerated in my opinion. Yes, the strings become magnetized, but they are very poor magnets on their own, and a brand new set you put on is not as magnetized as set that's been on there a while, yet they sound just fine.

Many years ago I tried removing the magnet from the pickup after the strings were magnetized, and you get very little output without the main magnet. That would lead one to believe the string's own magnetic field plays very little in the overall output of the pickup.

A pickup is a variable reluctance sensor. As the strings move over the pickup, the reluctance of the flux path through the coil changes, as well as the flux linkage through the coil. The coil always has a magnetic field around it because of the permanent magnets. The motion of the string varies the magnetic reluctance in the circuit created by the permanent magnet.

The fact that the strings might be magnetized is of less interest than the main magnet in the circuit. This is why different magnet types will sound different in the same pickup with the same strings. When the pickup is closer to the strings, so is the magnet and coils. You have greater lines of flux to disturb as well, especially in a humbucker where the field is pretty compact over the pickup.


Variable reluctance is an analysis method; it is convenient to use for some magnetic problems. However, it adds nothing to the fundamentals of magnetism. Maxwell's equations have that function, with Faraday's law of induction (part of Maxwell's equations) most important for pickups. You do not need the method of variable reluctance to understand how a pickup works. To use the VR method, you must be very familiar with how it works, and how it relates to the fundamentals of magnetism. Understanding the operation of a pickup directly through the law of induction allows one to get a better feel for how observed behavior relates to the basic physics.

When it becomes becomes magnetized, the string does not become a permanent magnet, at least not significantly so. It remains so only while in the field of the pickup's magnet. Please do not think that I am saying that it does.

This temporary magnetization is the only way in which the vibrating string can produce a changing magnetic field resulting in a changing flux through the coil, inducing a voltage. If the string does not become magnetized, there is no induced voltage.

Yet your third paragraph seems to imply that there is some other way that the string could influence the reluctance of the magnetic circuit, other than responding to the applied field by becoming magnetized. Ferromagnetism is the process in which the microscopic magnetic domains in some materials tend to line up when a B field is applied. This lining up is magnetization. If the alignment of the domains does not take place, there is no effect.

The final paragraph of your post confuses two different things. As far as the permanent magnetic field is concerned, it is only the field at the string that matters, because by definition of this field, the magnetization of the string is determined by the field at that location. However, the permanent magnet can have two other effects. It is part of the entire magnetic circuit, and if it has a permeability significantly greater than unity, it can have an effect on the changing flux through the coil due to the vibrating magnetized string. Also, its electrical conductivity can modify the pickup response through the flow of eddy currents. This pretty much sums up what the magnet can do.

[David Schwab]

Mike, pickups work by variable reluctance. If the string isn't moving, you wont get any current. Yes soft magnetic metals become temporarily magnetized around permanent magnets.

But don't take my word for it...

If you look up "variable reluctance sensor" in Wikipedia you get (emphasis added):

A variable reluctance sensor (VRS) is used to measure position and speed of moving metal components. This sensor consists of a permanent magnet, a ferromagnetic pole piece, a pickup coil, and a rotating toothed wheel.
As the wheel rotates, the reluctance of the flux path through the coil changes, and the flux linkage through the coil changes, which results in a change in voltage that is measured by an external circuit.

Wheel... string.. it doesn't matter. Hammond organs worked on the same principal. What matters is you are disturbing the lines of flux.

If you look up "magnetic reluctance" you see:

Applications

...
Variable reluctance (magnetic) pickups

Let see what they have for "Variable reluctance (magnetic) pickup"

The vibration of the nearby soft-magnetic strings modulates the magnetic flux linking the coil, thereby inducing an alternating voltage through the coil of wire.

More generally, the pickup operation can be described using the concept of a magnetic circuit. In this description, the motion of the string varies the magnetic reluctance in the circuit created by the permanent magnet.

Lastly in Bill Bartolini's patent:

The invention relates to a variable reluctance pickup for steel string musical instruments in which the vibrating strings cause variations of reluctance in a magnetic circuit generating electrical signals which, upon electronic amplification, are suitable for driving acoustic speaker systems.

Description of the Prior Art
Generally, variable reluctance pickups for steel string musical instruments comprise an arrangement of magnets and magnetically susceptible materials which establish a magnetic circuit in combination with the playing strings. As the strings vibrate, the changes in their position affect the reluctance and magnetic flux of the magnetic circuit. A sensing coil is inductively linked to the magnetic circuit for converting the variations in magnetic flux into a corresponding electrical signal. The electrical signals from the sensing coils is amplified electronically and fed into an acoustic speaker system producing musical sounds.

Mike, your a smart guy. We all know that. But this is how you used to piss off people at MIMF. All these articles I quoted said the same thing I did in my post.

If you move the pickup too far from the string, the string will have less of an effect because its out of the useful range of the magnet. Thats common sense. Move a microphone too far from a singer and you get the same thing. A stronger magnet will allow the pickups to be farther from the strings, if that's what you wanted to do.

I certainly think Bill Bartolini knows about pickups, just as you know about RADAR. You need to be pedantic were it counts. I've always enjoyed your experiments with pickups, such as at Project Guitar, but have you actually made something that works well?

[Mike Sulzer]

Mike, pickups work by variable reluctance.

I did not say it was wrong to look at it that way. Let's look at reluctance. Suppose you have a magnetic field caused by some currents somewhere. Where do the field lines go? You can say they tend to go where the reluctance is low. What has low reluctance? Ferromagnetic materials.

But now the key question is why do ferromagnetic materials tend to make the field lines go through them? Because the magnetic domains tend to line up in a way that reinforces the field. This process is magnetization.

So when I said two posts ago that the permanent field magnetizes the string, and the vibrating string then results in a varying flux through the coil, this does not differ from the idea that a pickup is a variable reluctance sensor. So when you replied two posts ago that this magnetization was not how it works, but rather it is variable reluctance, I tried to explain to you that the two ways of looking at it are really the same thing. I also tried to explain to you that if you do not understand this, you would have some incorrect ideas about how it works. Apparently I did not succeed in communicating these ideas. I hope that this attempt is more successful.

[David Schwab]

Well that's the way the internet often is... so sorry about the confusion.

However, this was the statement:

Variable reluctance is an analysis method; it is convenient to use for some magnetic problems. However, it adds nothing to the fundamentals of magnetism.

So I said, it's also how pickups work, so it's not just "an analysis method".