Is it possible to accurately describe the tone of magnets and/or pickups?

[Mike Sulzer]

In reference to the bolded statement: Impedance measurements characterize the pickup-cable resonance, and this is without doubt the most important factor in determining the tone of the pickup. They can even describe the deviations from the two pole resonance of a simple linear circuit, that is, the more subtle effects introduced by the frequency dependent losses due to eddy currents.

I have not been able to get access to the full text of the paper you cite, but the abstract indicates that it presents an analysis using the law of magnetic induction and calculates in detail that the response is nonlinear. The well known causes of this nonlinearity are the nonlinear part of the variation of the flux through the coil resulting from the change in distance of the string, the frequency doubling resulting from string motion parallel to the face of the pole piece, and the variation of the strength of the permanent field with distance from the magnet. I do not see any indication that hysteresis enters into this. The "minor loops" that you describe are extremely close to straight lines, and so I do not see how you get an effect from them.

Certainly materials such as you describe with low conductivity and permeability make a pickup with a higher resonance frequency and Q, and I think this would be very similar to using neo magnets with no additional pole piece. Neos are of course available in a vast range of sizes and shapes, and so the field strength variations and spatial variations due to magnet shape are easily produced. However, you seem to be describing changes other than those I mentioned, and I do not see what they can be.

I agree with the later statement (Post #117) that impedance measurements are poor predictors of pickup tone. A magnetic pickup and the ferromagnetic strings of a musical instrument in which it installed can be accurately modeled as a magnetic circuit with a flux that varies in response to string vibration. This formalism was used, for example, by Lemarquand in “Calculation Method of Permanent-Magnet Pickups for Electric Guitars,” (IEEE Transactions of Magnetics, Vol. 43, No 9, pp. 3573-3578, 2007) to describe the harmonics that are produced by the string as it moves in the asymmetric field generated by the poles of single coil pickup. The flux variations in the permanent magnets that are part of a magnetic circuit are described by minor hysteresis loops that are centered along recoil permeability lines. (See, for example, pages 483-484, Introduction to Magnetic Materials, 2nd Ed., B.D. Cullity and C.D. Graham, Wiley, Hoboken, 2009). The area of a minor hysteresis loop is much smaller than the area of the major loop that describes the magnetization (and demagnetization) of a material but the nonlinear relationship between B and H around a minor loop generates harmonics. These harmonics vary significantly with the small scale structural properties of a material and contribute significantly to the tonal differences that are observed in samples of the same alloy from different vendors.

Impedance and other parameters that have been put forth to explain alloy-dependent tonal variations cannot explain the fact that I can significantly alter the tone of a pickup by attaching components to it that do not affect its impedance or alter the spatial distribution/strength of the magnetic field at the strings. The recoil permeabilities of my insulator-bound alnico powder materials (see US Patent #8,853,517) are near unity and their eddy current losses are much lower than bulk samples of the materials from which they are made. They are, however, quite effective in changing the tone of a pickup in both magnetized and unmagnetized conditions.

[Antigua]

The area of a minor hysteresis loop is much smaller than the area of the major loop that describes the magnetization (and demagnetization) of a material but the nonlinear relationship between B and H around a minor loop generates harmonics. These harmonics vary significantly with the small scale structural properties of a material and contribute significantly to the tonal differences that are observed in samples of the same alloy from different vendors.

These are just assertions. I'm not sure how those small hysteresis loops are supposed to produce harmonics, and even if they do, how loud are they? Could you even hear them? If everything were audible, you'd probably hear the sound of magnetic domains re-orienting too, but in the end, only the most prominent string movements manifest in something that we hear.

Impedance and other parameters that have been put forth to explain alloy-dependent tonal variations cannot explain the fact that I can significantly alter the tone of a pickup by attaching components to it that do not affect its impedance or alter the spatial distribution/strength of the magnetic field at the strings. The recoil permeabilities of my insulator-bound alnico powder materials (see US Patent #8,853,517) are near unity and their eddy current losses are much lower than bulk samples of the materials from which they are made. They are, however, quite effective in changing the tone of a pickup in both magnetized and unmagnetized conditions.

Mike is correct in stating (Post #119) that the reluctance of the magnetic circuit that is formed by the pickup and strings is dominated by large air gaps but incorrect in stating that the small gaps in the circuit do not affect tone. I can hear the effect of the small gaps that are created when I glue two pieces of material together to form a composite pole piece (see US Patent # 8,415,551) and sometimes use the surface quality of the mating surfaces to adjust tone.

Without knowing what you're talking about, I still do know that claiming you can alter the tone does not mean you actually alter the tone. You're mixing objective claims and subjective outcomes. Not only should an outcome be quantifiable, but the quantity itself should be known, again, to figure out whether or not we might actually hear it.

That is the reason that trial and error is the only effective way to optimize the tone of a pickup. Possum’s technical explanations (Post #115, for example) are less than accurate but the multiyear trial and error optimization of his PAF pickups appears to have yielded some pretty good results. (See review of Stephen’s Design PAF at https://www.guitarplayer.com/gear/fi...reviewed-video).

The reason why trial and error is necessary is because ultimately it's an aesthetic decision. No musician is ever going to say "I hate the sound, but he mathematical formula says this is the sound I must use." It's the same reason you use a swatch to choose a color of paint instead of a calculator.

[Mike Sulzer]

"...incorrect in stating that the small gaps in the circuit do not affect tone."

Obviously there are certain cases in which contact matters. For example, if you space the magnet from the pole piece, the latter is less magnetized, and that certainly has an effect. But that is nothing like what Possum was saying.

[Tone Cam]

Its not possible to describe the tonality of any alnico magnets. Why? Because no two alnico manufacturers use the same formulas. So you think alnico 2 is warmer, less trebly? Nope. I have different company A2 magnets that are super bright and really high gauss readings when hot charged. Its the same for all the alnicos, A4 from one company won't sound like A4 from another company.

I don't understand why it is not possible to accurately describe the tone of materials from different vendors. If you take a scale with ‘super bright’ on one end and 'really dark' on the other, add additional variables that talk about the smoothness or harshness of the high frequencies, the overall harmonic density (‘fat’ or ‘thin’), the relative magnitude of other frequency bands and the overall loss (sharp vs dull tone??) I think that you would have a description that could be used to accurately differentiate the Super Bright Al2 material from Al2 samples that were cast at other foundries.

I agree with the later statement (Post #117) that impedance measurements are poor predictors of pickup tone. A magnetic pickup and the ferromagnetic strings of a musical instrument in which it installed can be accurately modeled as a magnetic circuit with a flux that varies in response to string vibration. This formalism was used, for example, by Lemarquand in “Calculation Method of Permanent-Magnet Pickups for Electric Guitars,” (IEEE Transactions of Magnetics, Vol. 43, No 9, pp. 3573-3578, 2007) to describe the harmonics that are produced by the string as it moves in the asymmetric field generated by the poles of single coil pickup. The flux variations in the permanent magnets that are part of a magnetic circuit are described by minor hysteresis loops that are centered along recoil permeability lines. (See, for example, pages 483-484, Introduction to Magnetic Materials, 2nd Ed., B.D. Cullity and C.D. Graham, Wiley, Hoboken, 2009). The area of a minor hysteresis loop is much smaller than the area of the major loop that describes the magnetization (and demagnetization) of a material but the nonlinear relationship between B and H around a minor loop generates harmonics. These harmonics vary significantly with the small scale structural properties of a material and contribute significantly to the tonal differences that are observed in samples of the same alloy from different vendors.

Impedance and other parameters that have been put forth to explain alloy-dependent tonal variations cannot explain the fact that I can significantly alter the tone of a pickup by attaching components to it that do not affect its impedance or alter the spatial distribution/strength of the magnetic field at the strings. The recoil permeabilities of my insulator-bound alnico powder materials (see US Patent #8,853,517) are near unity and their eddy current losses are much lower than bulk samples of the materials from which they are made. They are, however, quite effective in changing the tone of a pickup in both magnetized and unmagnetized conditions.

Mike is correct in stating (Post #119) that the reluctance of the magnetic circuit that is formed by the pickup and strings is dominated by large air gaps but incorrect in stating that the small gaps in the circuit do not affect tone. I can hear the effect of the small gaps that are created when I glue two pieces of material together to form a composite pole piece (see US Patent # 8,415,551) and sometimes use the surface quality of the mating surfaces to adjust tone. The output tone of a pickup is a very sensitive meter that responds to small parameter variations that have little/no effect in other applications. That is the reason that trial and error is the only effective way to optimize the tone of a pickup. Possum’s technical explanations (Post #115, for example) are less than accurate but the multiyear trial and error optimization of his PAF pickups appears to have yielded some pretty good results. (See review of Stephen’s Design PAF at https://www.guitarplayer.com/gear/fi...reviewed-video).

[Antigua]

Its not possible to describe the tonality of any alnico magnets. Why? Because no two alnico manufacturers use the same formulas. So you think alnico 2 is warmer, less trebly? Nope. I have different company A2 magnets that are super bright and really high gauss readings when hot charged. Its the same for all the alnicos, A4 from one company won't sound like A4 from another company.

I've tested both the magnetic and electrical properties of a few dozen AlNiCo 2 magnets that came with pickups sourced from all over the place, I've never seen much variation. There is room for creativity in the production of AlNiCo, but they also adhere to specs that ensure that they will not be exceedingly different, either. Otherwise it must be said that the magnets are poorly made. For example, AlNiCo 2 should not have "really high gauss" like that of AlNiCo 5, and if it does, there is something wrong with that magnetic alloy, and it should be sent back for a refund.

Alnico is mostly IRON.

It's not as simple as the composition, the structure of the alloy plays a big role. That's why electrical steel has a permeability that's many times higher than that of AlNiCo, even though both are primary composed of iron.

And iron sucks up treble, so the more massive a magnet is, the less brightish it will be. Some TTop magnets were super thin and short, those things are really shrill.

To say this is an oversimplification would be an understatement. All of these same effects manifest in inductors and transfomers, where they are categorized as wanted or unwanted inductance, core losses and capacitance, and so while there might be limited resources with respect to pickups specifically, reading up on inductor and transformer design reveals nearly all there is to know about the electrical side of pickups, too. Treble is lost to inductance, capacitance and conductivity, due to eddy currents. The fact that iron is involved is almost incidental, for example, you mention a pickup with a thin AlNiCo magnet was shrill, in your subjective estimation, but were you to add a few thousand more turns of wire, or put a high value capacitor across that pickup, these factors could also reduce the treble content to such an extent that it could not be described as "shrill". You mention a large magnet subtracting from the highs, but as an example, testing shows that a Filter'tron's treble attenuation is caused, almost exclusively, by the twelve fillister screws. But of course Filter'trons tend to be bright pickups none the less, and that owes to its very low inductance.

[Antigua]

there is some truth to what he is saying - you can't fool my ears......

Yeah there is some truth, but then you have the remainder, which is not truth.

[jack briggs]

The fact that the metal parts are in contact is irrelevant because the overall magnetic circuit is dominated by the huge air gap, and thus it is a wide open circuit without any possibility of interpretation similar to a transformer or other closed magnetic circuit. Your idea that an ally containing a significant amount iron must act like iron is just plain silly. You do not know metallurgy from witchcraft. I also think you are mentioning measurements that you have never made. I know you can fool some guitarists with this kind of talk, but you cannot fool everyone.

there is some truth to what he is saying - you can't fool my ears......

[Mike Sulzer]

The fact that the metal parts are in contact is irrelevant because the overall magnetic circuit is dominated by the huge air gap, and thus it is a wide open circuit without any possibility of interpretation similar to a transformer or other closed magnetic circuit. Your idea that an ally containing a significant amount iron must act like iron is just plain silly. You do not know metallurgy from witchcraft. I also think you are mentioning measurements that you have never made. I know you can fool some guitarists with this kind of talk, but you cannot fool everyone.

You're forgetting that all the metal parts including the magnet are all directly in contact with eachother. Alnico and "alni" are somewhere around 75% or more IRON. The steels used in pickups are largely iron with some carbon content. In a humbucker or P90 those magnets are large chunks of iron. So the metallurgy of the magnets is a big piece of the magnetic circuit and its formula has a very noticeable effect, electrically on the sound of the coils. Proof of this is if you swap in a ceramic magnet that has no iron content, just hook up your LCR meter and watch those Henries drop like a rock when ceramic magnets are used because ceramic is nonconductive, non-metallic. All the metal parts including the baseplate are electrically connected and losses are from the entire magnetic circuit parts. This is why if you change a single part, a slug, or a screw, to say something with high carbon it changes the sound of the pickup. But as I said in my reply, no two factories make the same kinds of alnico, there isn't a universal recipe being used. So, if you have two radically different alnico magnets, each one is going to make the pickup sound different, and each magnet could be called "alnico 2" but have completely different tone signatures. A really brittle sounding magnet will far outshadow the metallurgy in the ferrous parts. This is where the "fun" is. Change a single part, change the sound. In vintage PAF's there are 4 different alloys (magnet included). Play with those and now you have a design tool ;-)

[Helmholtz]

I would ignore the inductance readings and use AC resistance readings at 1khz. I always found this much more useful than Henries. I seem to remember than putting a base plate on a Tele bridge raised the AC resistance while henries went down, so inductance is less intuitive for pickup designers. In pickups, everything affects everything else, just like in guitar amplifiers where everything affects the whole.

Well you talked about Henries, not AC resistance. The differencies in AC resistance caused by different alnicos are even lower than for inductance.

[Possum]

I would ignore the inductance readings and use AC resistance readings at 1khz. I always found this much more useful than Henries. I seem to remember than putting a base plate on a Tele bridge raised the AC resistance while henries went down, so inductance is less intuitive for pickup designers. In pickups, everything affects everything else, just like in guitar amplifiers where everything affects the whole.

[Helmholtz]

Proof of this is if you swap in a ceramic magnet that has no iron content, just hook up your LCR meter and watch those Henries drop like a rock when ceramic magnets are used because ceramic is nonconductive, non-metallic.

If you remove the alnico magnet of a humbucker, the inductivity drops around 6..8%. The PU's L difference between different alnico grades charged to similar Gauss values is 1..2%.
If Henries drop for more than 8% when exchanging a ceramic magnet for alnico, I suppose the ceramic was much stronger than the alnico. Strong magnets reduce the µ of the ferrous core parts causing an additional drop of L.

While the iron content of alnicos lies between 50% and 60%, their µ is only 5..8. Low carbon steel is 200...500, lower carbon (and other "impurities') content resulting in higher values.
The µ of ceramic magnets is close to 1.

[Possum]

In a humbucker the steel is high loss and inside the coil; therefore it has a much larger effect than the magnet, which is lower loss and outside the coil.

You're forgetting that all the metal parts including the magnet are all directly in contact with eachother. Alnico and "alni" are somewhere around 75% or more IRON. The steels used in pickups are largely iron with some carbon content. In a humbucker or P90 those magnets are large chunks of iron. So the metallurgy of the magnets is a big piece of the magnetic circuit and its formula has a very noticeable effect, electrically on the sound of the coils. Proof of this is if you swap in a ceramic magnet that has no iron content, just hook up your LCR meter and watch those Henries drop like a rock when ceramic magnets are used because ceramic is nonconductive, non-metallic. All the metal parts including the baseplate are electrically connected and losses are from the entire magnetic circuit parts. This is why if you change a single part, a slug, or a screw, to say something with high carbon it changes the sound of the pickup. But as I said in my reply, no two factories make the same kinds of alnico, there isn't a universal recipe being used. So, if you have two radically different alnico magnets, each one is going to make the pickup sound different, and each magnet could be called "alnico 2" but have completely different tone signatures. A really brittle sounding magnet will far outshadow the metallurgy in the ferrous parts. This is where the "fun" is. Change a single part, change the sound. In vintage PAF's there are 4 different alloys (magnet included). Play with those and now you have a design tool ;-)

[Mike Sulzer]

In a humbucker the steel is high loss and inside the coil; therefore it has a much larger effect than the magnet, which is lower loss and outside the coil.

Its not possible to describe the tonality of any alnico magnets. Why? Because no two alnico manufacturers use the same formulas. So you think alnico 2 is warmer, less trebly? Nope. I have different company A2 magnets that are super bright and really high gauss readings when hot charged. Its the same for all the alnicos, A4 from one company won't sound like A4 from another company. This is why its good to buy from many different manufacturers, you get so many different flavors. When I choose a magnet for a certain design, I try ALL my alnicos in that design and find one that sounds the best in that particular model. It also depends on physical dimensions. The older PAF/P90 magnets were all thick and 2/5" long. Mojo for example, sells all their bucker/P90 magnets in a shorter dimension than anyone else. Alnico is mostly IRON. And iron sucks up treble, so the more massive a magnet is, the less brightish it will be. Some TTop magnets were super thin and short, those things are really shrill. Keep a good stock of various company's products and use where it works.

[Possum]

Its not possible to describe the tonality of any alnico magnets. Why? Because no two alnico manufacturers use the same formulas. So you think alnico 2 is warmer, less trebly? Nope. I have different company A2 magnets that are super bright and really high gauss readings when hot charged. Its the same for all the alnicos, A4 from one company won't sound like A4 from another company. This is why its good to buy from many different manufacturers, you get so many different flavors. When I choose a magnet for a certain design, I try ALL my alnicos in that design and find one that sounds the best in that particular model. It also depends on physical dimensions. The older PAF/P90 magnets were all thick and 2/5" long. Mojo for example, sells all their bucker/P90 magnets in a shorter dimension than anyone else. Alnico is mostly IRON. And iron sucks up treble, so the more massive a magnet is, the less brightish it will be. Some TTop magnets were super thin and short, those things are really shrill. Keep a good stock of various company's products and use where it works.

[Helmholtz]

Helmholtz, any numbers for leaded steels like 12L14?

Sorry, no.
But I have 1215: 17.4


Edit:

Easy find with Google:
http://www.noblefix.com/pdfs/mechanical_properties.pdf
i.e. values for 1215 and 12L14 are the same.