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Post by antigua on Feb 26, 2018 13:29:53 GMT -5
I was going back over the Jungmann thesis research.spa.aalto.fi/publications/theses/jungmann_mst.pdf and noticed something I might not have appreciated enough the first time, on page 76 of the PDF (68 of the scanned pages):  There are some parts of the thesis that are at odds with what I've gathered from other sources, but everything stated above is correct, as far as I know. Based on the above, when the guitar string moves around, it's cutting through a magnetic field that is exponentially stronger, the closer it gets to the pole piece. Because the field strength is exponential, and not linear, the resulting wave form output ends up being more triangular in one half of the wave cycle, because the voltage becomes disproportionately stronger as it reached the peak of the cycle, and then weaker as it exits. Triangular waves make for odd harmonics, which would manifest as an increase in treble content. Therefore, it seems that a pickup that is closer to the strings should generate more treble, but particularly so right after the string is plucked, when the guitar string traverses the greatest distance through the exponential / non-linear magnetic field, maximizing the triangular wave effect, therefore maximizing the production of odd harmonics, and a sense of treble. Or as Jungmann states "a higher vibration amplitude will cause a hogher non-linear distortion". The wave form should also become more or less triangular as the string movement modulates from being more perpendicular, or more parallel to the face of the pole piece, giving rise to the sense that harmonic amplitude, or treble, comes and goes as the string rings out. In addition to the production of the distorted, triangular half-cycle, the overall induced voltage is increased along with the degree of non linear distortion. So if the pickup is farther away form the strings, or when the string's vibration becomes smaller, the output voltage becomes proportionately closer to the velocity, but when the strings are close to the pickup, the larger string movements produce a disproportionate amount of voltage relative to string velocity. Since the string moves the most immediately after being plucked, the "string pluck" or "pick attack" output of a pickup set close to the strings would be disproportionately higher than a pickup set further from the strings. In tests I've done in other threads with string plucks at various heights, which are documented in another thread guitarnuts2.proboards.com/thread/7998/tonal-effect-pickup-height , and there did appear to be a stronger harmonic representation in the transient, as well as a transient that is of a greater amplitude than the decay, especially when the pickup was set close with AlNiCo 5 pole pieces. ~~~ One thing that confuses me though is that it's often said that, in the context of a humbucker, the weaker AlNiCo 2 magnet sounds "soft", a slightly stronger AlNiCo 5 magnet sounds "tighter", while a much stronger ceramic magnet sounds "brittle". There's enough observational evidence out there to suggest that the adjectives relate to something real, and are not imagined, and these adjectives correlate with differences in transient amplitude as well as treble content, same as described above. But the above only deals with magnetic field strength in relation to distance. My question is, does a stronger magnet in a humbucker increase the flux density at the tops of the screws, and if so, is there a practical equivalence between that increase in flux density, and a decrease in distance between the screws and the guitar strings? It seems to me that because magnetic material are somewhat dynamic systems, with varying coercivities and permeability, that as humbucker screws, with a high permeability, are presented with a stronger magnet underneath, more of their magnetic domains would line up "straight", increasing the flux density out the top of the screws, increasing the degree of above described "distortion", whereas a weaker magnet in the humbucker would can more of the magnetic domains within the steel screw to point in directions other than "straight", decreasing the flux density at the top of the screw, therefore decreasing the above described distortion. I'm not sure this view is correct, but this is my current understanding. |
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Post by ms on Feb 26, 2018 14:46:14 GMT -5
Well, everything he says is not right, but I think a lot of it is. For example, on the wrong side, we know from MacDonald's paper that the string permeability does not matter when using ferromagnetic strings. Or you should just know that because that is what is expected when working with open magnetic circuits. But in any case, we expect the flux through the coil to change a nonlinear way with string vibration, and so harmonics are generated. Exactly what happens is complicated, and even MacDonald did not solve the exact case.
He does correctly show an asymmetrical waveform. Such a waveform is dominated by even harmonics, not odd, and his spectrum does correctly show larger 2nd harmonic than 3rd. It is not correct call this a triangle wave. A true triangle wave is symmetrical, and therefore has only odd harmonics.
I think that using a stronger magnet in a humbucker just proportionally increases the field everywhere. This should not increase the treble. I think what happens is that the output level increases, and this increases the distortion in the amp, and that gives more treble.
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Post by antigua on Feb 26, 2018 17:31:59 GMT -5
Well, everything he says is not right, but I think a lot of it is. For example, on the wrong side, we know from MacDonald's paper that the string permeability does not matter when using ferromagnetic strings. Or you should just know that because that is what is expected when working with open magnetic circuits. I've google this issue, and this is what I've found "With the introduction of an air gap the B-H loop of a magnetic circuit gets "sheared" (slanted), hence the value of its slope proportional to the effective permeability is reduced. The amount of “shearing” is proportional to the length of the air gap - the larger the air gap the lower the slope." From this description, I don't see the permeability not mattering, just that the permeability is "reduced". I know the McDonald equation showed that so long as it was well above 1, it didn't make much difference, but I can't relate that math to a plain English explanation, like the quote above. He does correctly show an asymmetrical waveform. Such a waveform is dominated by even harmonics, not odd, and his spectrum does correctly show larger 2nd harmonic than 3rd. It is not correct call this a triangle wave. A true triangle wave is symmetrical, and therefore has only odd harmonics. I'm the one who said odd harmonics, based on ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Triangle_wave.html "Like a square wave, the triangle wave contains only odd harmonics, demonstrating odd symmetry", so if you end up with a wave form that is triangular, my reasoning is that it would be producing odd harmonics. Since it's not a perfect triangle, maybe there is even harmonic content as well, but it appears that the overall trend is triangular. Regardless of whether they're even or odd though, any added harmonics should essentially mean greater treble content, and it seems that we get more distortion and more harmonics the more the guitar string is positioned to exploit the non-linearity of the magnetic field. Even supposing all this is true, I don't know if the contribution of harmonic amplitude is even audible, or if this is just academic, but there are apparently tonal differences associated with having the string and the pickup closer together, that I think go beyond string pulll intermodulation effects, and the main reason I don't credit the voltage output, or the amp, is because I have volume boost pedals which also push the amp, and I don't feel that they exhibit the qualities being discussed. |
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Post by antigua on Feb 27, 2018 2:06:42 GMT -5
I just did an experiment where I compared the magnetic strength at a distance of several AlNiCo pole pieces, using a little rig I made, which makes use of the probe hall effect sensor I bought last week. This allows for carefully controlled distance and orientation from the sensor:  Here's the data in Gauss, and then the percentage of field strength, relative to the strength at 0mm distance: AlNiCo 5, full strength
0mm: 1018
5mm: 236 (23%)
10mm: 69 (7%)
AlNiCo 5, partially degaussed
0mm: 710
5mm: 159 (22%)
10mm: 46 (6%)
AlNiCo 2, full strength
0mm: 668
5mm: 152 (22%)
10mm: 46 (7%)
AlNiCo 3, full strength
0mm: 566
5mm: 134 (23%)
10mm: 39 (7%)
AlNiCo 4, full strength
0mm: 787
5mm: 184 (23%)
10mm: 55 (7%)
And here's how it looks in graph form:  From the percentages and the graph, it can be seen that the rate of flux drop with distance is proportionately the same, no matter the field strength, at any given distance, the slope is steep the stronger the magnetic field, whether it be due to a weaker AlNiCo 2 pole piece, or an AlNiCo 5 pole piece that has been partly degaussed. The slope is also steeper the closer you get to the face of the magnet, therefore there is an equivalence between strength and distance. What is lacking in one can be made up for with the other. This means that a pickup with stronger AlNiCo 5 pole pieces, set further from the strings, will perform more or less the same as a pickup with AlNiCo 2 pole pieces which is set closer to the strings. The AlNiCo 2 pole piece measures 668G at 0mm, the fully charged AlNiCo 5 pole piece measures 668G if it's set to about 2mm distance from the sensor. The AlNiCo 2 pole pieces measures 159G at 5mm, the AlNiCo 5 measures the same at about 7mm. The AlNiCo 2 measures 46G at 10mm, the AlNiCo 5 measures 46G at 12.5mm. So for these distances, AlNiCo 5 shows a similar field strength to AlNiCo 2 when its 2mm further from the sensor. |
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Post by ms on Feb 27, 2018 7:05:37 GMT -5
Well, everything he says is not right, but I think a lot of it is. For example, on the wrong side, we know from MacDonald's paper that the string permeability does not matter when using ferromagnetic strings. Or you should just know that because that is what is expected when working with open magnetic circuits. I've google this issue, and this is what I've found "With the introduction of an air gap the B-H loop of a magnetic circuit gets "sheared" (slanted), hence the value of its slope proportional to the effective permeability is reduced. The amount of “shearing” is proportional to the length of the air gap - the larger the air gap the lower the slope." From this description, I don't see the permeability not mattering, just that the permeability is "reduced". I know the McDonald equation showed that so long as it was well above 1, it didn't make much difference, but I can't relate that math to a plain English explanation, like the quote above. He does correctly show an asymmetrical waveform. Such a waveform is dominated by even harmonics, not odd, and his spectrum does correctly show larger 2nd harmonic than 3rd. It is not correct call this a triangle wave. A true triangle wave is symmetrical, and therefore has only odd harmonics. I'm the one who said odd harmonics, based on ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Triangle_wave.html "Like a square wave, the triangle wave contains only odd harmonics, demonstrating odd symmetry", so if you end up with a wave form that is triangular, my reasoning is that it would be producing odd harmonics. Since it's not a perfect triangle, maybe there is even harmonic content as well, but it appears that the overall trend is triangular. Regardless of whether they're even or odd though, any added harmonics should essentially mean greater treble content, and it seems that we get more distortion and more harmonics the more the guitar string is positioned to exploit the non-linearity of the magnetic field. Even supposing all this is true, I don't know if the contribution of harmonic amplitude is even audible, or if this is just academic, but there are apparently tonal differences associated with having the string and the pickup closer together, that I think go beyond string pulll intermodulation effects, and the main reason I don't credit the voltage output, or the amp, is because I have volume boost pedals which also push the amp, and I don't feel that they exhibit the qualities being discussed. The magnetic circuit of a guitar is not well described by a gap, but rather by a large region of free space. It is certainly true that a gap reduces the effective permeability in, for example, a transformer, while maintaining the proportional relationship between material permeability and effective permeability, but that is not the case with guitar pickups. The lack of even harmonics is a result of symmetry, and does not apply to asymmetrical circuits that happen to look something like a particular symmetric circuit. I agree that the addition of all harmonics gives a greater treble content. I was puzzled why you seemed to be restricting it to odd harmonics. I think the addition of harmonics, even at low levels is audible, is audible. The ear-brain identifies different sounds by harmonic differences as well as by time domain (transient) effects. |
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Post by ms on Feb 27, 2018 7:16:34 GMT -5
I This means that a pickup with stronger AlNiCo 5 pole pieces, set further from the strings, will perform more or less the same as a pickup with AlNiCo 2 pole pieces which is set closer to the strings. I think the relative harmonic content is a function of the distance of the string from the pole piece, not its strength. This is because the relative change in field strength, that is, its non-linear component, is responsible for harmonic generation, Raising the pickup to give more treble makes sense, at least up to a point, |
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Post by antigua on Feb 27, 2018 12:35:27 GMT -5
The magnetic circuit of a guitar is not well described by a gap, but rather by a large region of free space. It is certainly true that a gap reduces the effective permeability in, for example, a transformer, while maintaining the proportional relationship between material permeability and effective permeability, but that is not the case with guitar pickups. The lack of even harmonics is a result of symmetry, and does not apply to asymmetrical circuits that happen to look something like a particular symmetric circuit. I agree that the addition of all harmonics gives a greater treble content. I was puzzled why you seemed to be restricting it to odd harmonics. I think the addition of harmonics, even at low levels is audible, is audible. The ear-brain identifies different sounds by harmonic differences as well as by time domain (transient) effects. Thanks for clarifying some of these things. I found an "effective permeability calculator" along with the equation it uses www.encyclopedia-magnetica.com/doku.php/effective_magnetic_permeability  according to the calculator, if you set the core length to "1", the air gap to "10", then if the value for relative permeability is below 1, the value of the effective permeability drops almost proportionately to the relative permeability, but if you set the relative permeability to any value above 1, you can set the value to 100, or 10000, and the "effective permeability" barely changes at all, it just gets increasing closer to 0.1, which is also the ratio of core length to air length, 1 and 10. Is the saying that, if the permeability of the guitar string is above 1, that the permeability is now effectively defined by air gap? What does this say about the permeability of the pole piece? It did appear in testing that the permeability of AlNiCo was so low, and steel so high, that a pickup with steel cores produced more voltage on account of the steel pole pieces, though the permeability of both steel and AlNiCo are above 1. |
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Post by antigua on Feb 27, 2018 12:42:36 GMT -5
I This means that a pickup with stronger AlNiCo 5 pole pieces, set further from the strings, will perform more or less the same as a pickup with AlNiCo 2 pole pieces which is set closer to the strings. I think the relative harmonic content is a function of the distance of the string from the pole piece, not its strength. This is because the relative change in field strength, that is, its non-linear component, is responsible for harmonic generation, Raising the pickup to give more treble makes sense, at least up to a point, But looking at the data points collected, the strongly charged AlNiCo 5 has a steeper slope approaching the face of the magnet. The weak magnets will have a steep slope also (though not seen at this low resolution), but closer to the face of the pole piece. It appears to me that AlNiCo 5 therefore does at a distance, what the weaker/weakened AlNiCos do with closer proximity. |
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Post by reTrEaD on Feb 27, 2018 14:43:14 GMT -5
Is it the steepness of the slope or the change in slope within the string excursion that causes the distortion?
In any case, distortion is an artifact. Any harmonics added because of that aren't actually occurring in the motion of the string at that location. Seems that might less desirable than accurately representing the actual harmonic content?
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Post by ms on Feb 27, 2018 14:57:21 GMT -5
The magnetic circuit of a guitar is not well described by a gap, but rather by a large region of free space. It is certainly true that a gap reduces the effective permeability in, for example, a transformer, while maintaining the proportional relationship between material permeability and effective permeability, but that is not the case with guitar pickups. The lack of even harmonics is a result of symmetry, and does not apply to asymmetrical circuits that happen to look something like a particular symmetric circuit. I agree that the addition of all harmonics gives a greater treble content. I was puzzled why you seemed to be restricting it to odd harmonics. I think the addition of harmonics, even at low levels is audible, is audible. The ear-brain identifies different sounds by harmonic differences as well as by time domain (transient) effects. Thanks for clarifying some of these things. I found an "effective permeability calculator" along with the equation it uses www.encyclopedia-magnetica.com/doku.php/effective_magnetic_permeability according to the calculator, if you set the core length to "1", the air gap to "10", then if the value for relative permeability is below 1, the value of the effective permeability drops almost proportionately to the relative permeability, but if you set the relative permeability to any value above 1, you can set the value to 100, or 10000, and the "effective permeability" barely changes at all, it just gets increasing closer to 0.1, which is also the ratio of core length to air length, 1 and 10. Is the saying that, if the permeability of the guitar string is above 1, that the permeability is now effectively defined by air gap? What does this say about the permeability of the pole piece? It did appear in testing that the permeability of AlNiCo was so low, and steel so high, that a pickup with steel cores produced more voltage on account of the steel pole pieces, though the permeability of both steel and AlNiCo are above 1. "The equation is valid only for a simple magnetic circuit, made out of bulk material, for relative permeability if lcore >> lgap" The pickup geometry is not covered by this. |
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Post by ms on Feb 27, 2018 15:01:33 GMT -5
I think the relative harmonic content is a function of the distance of the string from the pole piece, not its strength. This is because the relative change in field strength, that is, its non-linear component, is responsible for harmonic generation, Raising the pickup to give more treble makes sense, at least up to a point, But looking at the data points collected, the strongly charged AlNiCo 5 has a steeper slope approaching the face of the magnet. The weak magnets will have a steep slope also (though not seen at this low resolution), but closer to the face of the pole piece. It appears to me that AlNiCo 5 therefore does at a distance, what the weaker/weakened AlNiCos do with closer proximity. When you change the strength of the magnet, the strengths of the fundamental and harmonics change by the same percentages, and so the distortion level does not change. |
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Post by antigua on Feb 27, 2018 15:16:37 GMT -5
But looking at the data points collected, the strongly charged AlNiCo 5 has a steeper slope approaching the face of the magnet. The weak magnets will have a steep slope also (though not seen at this low resolution), but closer to the face of the pole piece. It appears to me that AlNiCo 5 therefore does at a distance, what the weaker/weakened AlNiCos do with closer proximity. When you change the strength of the magnet, the strengths of the fundamental and harmonics change by the same percentages, and so the distortion level does not change. The non-linearity of the magnetic field produces harmonics though, it's not about proportional amplification. The rapid increase and rapid decrease of flux density as the string moves nearer and further from the pole piece induces harmonics all by itself, as the wave form takes on that more triangular shape, as shown in figure 3.24 of the screen shot. The top part of the cycle is like a triangle wave, with associated harmonics, and the bottom half of the cycle is more like a sine wave, lacking those harmonics. The distortion comes from the fact that the magnetic strength is a curve and not a line, and the greater the curve, the greater the distortion. It appears that increases strength also gives a greater curve, for a given distance. I think this bears out in observation also, it this weren't true, degaussing a magnet would not change the tone whatsoever, it would merely make the pickup more quiet, but there is a fairly large amount of discussion out there relating to variance in tone with respect to magnetic strength. |
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Post by antigua on Feb 27, 2018 15:20:52 GMT -5
"The equation is valid only for a simple magnetic circuit, made out of bulk material, for relative permeability if lcore >> lgap" The pickup geometry is not covered by this. That's a good point, but that still puts us back to where we started. Suppose the permeability of the guitar string is not especially relevant, well if the guitar string had no permeability at all, that would be relevant, so the question is, where does it cross the threshold from being relevant to not relevant? McDonald said any value greater than one, so even though steel has a permeability of several thousand, does this mean it could be just 2 µ and work just as well? |
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Post by ms on Feb 27, 2018 17:31:17 GMT -5
"The equation is valid only for a simple magnetic circuit, made out of bulk material, for relative permeability if lcore >> lgap" The pickup geometry is not covered by this. That's a good point, but that still puts us back to where we started. Suppose the permeability of the guitar string is not especially relevant, well if the guitar string had no permeability at all, that would be relevant, so the question is, where does it cross the threshold from being relevant to not relevant? McDonald said any value greater than one, so even though steel has a permeability of several thousand, does this mean it could be just 2 µ and work just as well? Steel is not several thousand. More like several hundred. (mu - 1)/(mu+ 1) is 1/3 for u = 2, 9/11 for u = 10, and 99/101for mu = 100. |
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Post by antigua on Feb 27, 2018 22:02:37 GMT -5
I've performed the same test as with the ALNiCo pole pieces, though this time with bar magnets, with a steel pole piece intermediary:  Here is the data: BAR MAGNET & STEEL POLE PIECE
AlNiCo 8 bar, full strength 0mm: 383 3mm: 184 6mm: 94 9mm: 62 AlNiCo 5 bar, full strength 0mm: 200 3mm: 91 6mm: 47 9mm: 30 AlNiCo 4 bar, full strength 0mm: 150 3mm: 71 6mm: 37 9mm: 23 AlNiCo 3 bar, full strength 0mm: 138 3mm: 66 6mm: 34 9mm: 22 AlNiCo 2 bar, full strength 0mm: 137 3mm: 65 6mm: 34 9mm: 22 Put into a graph: BAR MAGNET & STEEL POLE PIECE If you look at the green and red lines, suppose you shift the green line (A8) all the way to the left, it would nearly overlap the red line (A5). This again shows an equivalence between field strength versus proximity. If amplitude distortion = harmonics, and harmonics = treble, then this shows that a stronger magnet in a humbucker will result in more treble, as will a closer proximity to the strings. |
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Post by antigua on Feb 27, 2018 23:09:14 GMT -5
Here is a redo of the AlNiCo pole pieces, this time with four distances instead of three: ALNICO POLE PIECEAlNiCo 5, full strength 0mm: 1171 3mm: 432 6mm: 181 9mm: 92 AlNiCo 5, partially degaussed 0mm: 415 3mm: 153 6mm: 61 9mm: 31 AlNiCo 4, full strength 0mm: 774 3mm: 313 6mm: 129 9mm: 66 AlNiCo 3, full strength 0mm: 557 3mm: 223 6mm: 91 9mm: 46 AlNiCo 2, full strength 0mm: 644 3mm: 249 6mm: 106 9mm: 54 ALNICO POLE PIECE |
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Post by ms on Feb 28, 2018 10:41:37 GMT -5
The equivalence of field strength and distance is as accurate as the approximation that field strength increases exponentially as you approach the pole piece. (Yes, you did use that word to describe it, but it is an approximation.) web.pa.msu.edu/people/stump/EM/chap9/9ex1.pdf shows a plot of the field of a rod magnet along the axis. It falls off linearly near the end of the magnet, and as 1/(r^3) far away. It does have an approximately exponential shape in between, and in this region what you are saying is a good approximation. |
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Post by antigua on Feb 28, 2018 13:57:18 GMT -5
The equivalence of field strength and distance is as accurate as the approximation that field strength increases exponentially as you approach the pole piece. (Yes, you did use that word to describe it, but it is an approximation.) web.pa.msu.edu/people/stump/EM/chap9/9ex1.pdf shows a plot of the field of a rod magnet along the axis. It falls off linearly near the end of the magnet, and as 1/(r^3) far away. It does have an approximately exponential shape in between, and in this region what you are saying is a good approximation. Thanks for that link. I was saying exponential mostly just to mean, "not linear". Someone in a phsyics forum thread says "If you were to start next to one pole of a bar magnet and move away in any direction, measuring the magnetic force as you go, you'd find that it starts out looking like 1/r^2 and then gradually transitions to 1/r^3.
" www.physicsforums.com/threads/is-1-r-3-descriptive-of-magnetic-force-drop-off.326451/One thing that I don't see addressed is how the coercive force factors into the field strength with respect to distance. If the magnet has a lower coercive force, it means that the magnet domains are more reluctant to line up straight, which is why they say AlNiCo magnets need to be about four times longer than they are wide in order to get the most strength out of them, they need more "runway" in a sense, where as this is not true with ceramic or neodymium, which have a high coercive force, and do not need to be long relative to width in order to achieve a full strength. So if you have an AlNiCo bar, and it's lines of flux are tending to stray internally, I'd think you'd reach the "1/r^3" rate of drop off, closer to the magnet. |
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Post by ms on Feb 28, 2018 14:17:55 GMT -5
The equivalence of field strength and distance is as accurate as the approximation that field strength increases exponentially as you approach the pole piece. (Yes, you did use that word to describe it, but it is an approximation.) web.pa.msu.edu/people/stump/EM/chap9/9ex1.pdf shows a plot of the field of a rod magnet along the axis. It falls off linearly near the end of the magnet, and as 1/(r^3) far away. It does have an approximately exponential shape in between, and in this region what you are saying is a good approximation. Thanks for that link. I was saying exponential mostly just to mean, "not linear". Someone in a phsyics forum thread says "If you were to start next to one pole of a bar magnet and move away in any direction, measuring the magnetic force as you go, you'd find that it starts out looking like 1/r^2 and then gradually transitions to 1/r^3.
" www.physicsforums.com/threads/is-1-r-3-descriptive-of-magnetic-force-drop-off.326451/One thing that I don't see addressed is how the coercive force factors into the field strength with respect to distance. If the magnet has a lower coercive force, it means that the magnet domains are more reluctant to line up straight, which is why they say AlNiCo magnets need to be about four times longer than they are wide in order to get the most strength out of them, they need more "runway" in a sense, where as this is not true with ceramic or neodymium, which have a high coercive force, and do not need to be long relative to width in order to achieve a full strength. So if you have an AlNiCo bar, and it's lines of flux are tending to stray internally, I'd think you'd reach the "1/r^3" rate of drop off, closer to the magnet. That is for the case where you use an approximation using two magnetic monopoles. When you get close to a face of a magnet it is just 1/r. The field as a function of distance of an alnico or neo rod magnet will be somewhat different for the reason you state, but I think it is a small difference. I think the domains in alnico have preferred direction in most manufacturing processes. (but I do not know a lot about this.) Thus they tend to line up in the direction of the majority or opposed to it. Those opposed will tend reduce the total field without affecting the directional properties. |
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Post by antigua on Feb 28, 2018 15:09:23 GMT -5
Regarding the harmonic content, I was thinking odd harmonics due to a triangular looking wave, but looking at page 6 of www.physics.princeton.edu/~mcdonald/examples/guitar.pdf , McDonald says "The right figure is the total induced voltage (almost entirely due to the y vibration of the string), which contains frequency components at all harmonics of the fundamental, with exponentially decreasing strength as a function of the harmonic number."and it shows a exponential decrease for each successive harmonic, with a slight boost to even harmonics, due to the movement which is perpendicular to the axis. I also see based McDonalds equations, in the screen shot below, that there is no increase or decrease in the degree of distortion (greater harmonics relative to the fundamental) with respect to magnetic strength, as the B 0 term is always the first term of the overall equation, not to be seen anywhere else, outside of where the harmonic amplitudes would be distinguished from the fundamental. According to this math, there would be no tonal change in relation to magnetic strength, not counting the effects of the string pull and inter-modulations that arise from that. If that's true, which I'm guessing it is, that puts be back to square one, because there does seem to be a tonal change with magnetic strength that goes beyond mere amplitude. I suppose it could be chalked up to string pull effects, where differences are clearly observed, regardless of whether the pickup's magnet is causing the string pull, or the magnet of another pickup.  |
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Post by antigua on Feb 28, 2018 16:17:15 GMT -5
I think one flaw, or shortcoming, of both the McDonald and Jungmann descriptions is that they don't account for distortions caused by the magnetic attraction between the string and the magnet. Their models assume that the string's vibration is uniform, no matter the value B0 . Their models account for the fact that the flux density is higher near the pole piece, which is a source of distortion, but it doesn't account for the fact that with a stronger B field, the the string will increasingly accelerate as it approaches the pickup, and increasingly decelerate as it is pulled away from the pickup. I would assume that this increased acceleration / deceleration would introduce yet another distortion effect, and it would be proportional to B0. It might be that that the added acceleration in one direction, and deceleration in the other, is very small, too small to generate a distortion.
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Post by ms on Mar 2, 2018 10:00:47 GMT -5
I think one flaw, or shortcoming, of both the McDonald and Jungmann descriptions is that they don't account for distortions caused by the magnetic attraction between the string and the magnet. Their models assume that the string's vibration is uniform, no matter the value B 0 . Their models account for the fact that the flux density is higher near the pole piece, which is a source of distortion, but it doesn't account for the fact that with a stronger B field, the the string will increasingly accelerate as it approaches the pickup, and increasingly decelerate as it is pulled away from the pickup. I would assume that this increased acceleration / deceleration would introduce yet another distortion effect, and it would be proportional to B 0. It might be that that the added acceleration in one direction, and deceleration in the other, is very small, too small to generate a distortion. MacDonald assumes that the magnetic field caused by the pole piece is constant with distance from the guitar: "At all times the string is immersed in a uniform magnetic field B0 that is perpendicular to the face of the guitar." The variation of flux with string vibration is a result of the magnetization (constant in time, but varying in space) of the string moving with respect to the coil and pole piece. The spatial variation of the permanent field should be considered, too, and this would increase the non-linearity since both increase towards the pickup. It is not clear to me what Jungmann assumes from the quote in the first post of this discussion. |
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Post by antigua on Mar 2, 2018 15:48:30 GMT -5
I think one flaw, or shortcoming, of both the McDonald and Jungmann descriptions is that they don't account for distortions caused by the magnetic attraction between the string and the magnet. Their models assume that the string's vibration is uniform, no matter the value B 0 . Their models account for the fact that the flux density is higher near the pole piece, which is a source of distortion, but it doesn't account for the fact that with a stronger B field, the the string will increasingly accelerate as it approaches the pickup, and increasingly decelerate as it is pulled away from the pickup. I would assume that this increased acceleration / deceleration would introduce yet another distortion effect, and it would be proportional to B 0. It might be that that the added acceleration in one direction, and deceleration in the other, is very small, too small to generate a distortion. MacDonald assumes that the magnetic field caused by the pole piece is constant with distance from the guitar: "At all times the string is immersed in a uniform magnetic field B0 that is perpendicular to the face of the guitar." The variation of flux with string vibration is a result of the magnetization (constant in time, but varying in space) of the string moving with respect to the coil and pole piece. The spatial variation of the permanent field should be considered, too, and this would increase the non-linearity since both increase towards the pickup. It is not clear to me what Jungmann assumes from the quote in the first post of this discussion. What I'm getting at is that the phenomena of, for example, wolf tones, doesn't manifest in their models because that deal with how the movement of the string changes as a consequence of B. Their models seem to show that the harmonic content will change very little in relation to either B or distance, save for the issues concerning perpendicular string movement. A "rail" style pickup should have no harmonic reception due to perpendicular movement, so based on their models, the string will sound the same anywhere and everywhere, with the only change being in the amplitude. Another test I want to conduct is how much pulling force exists between a 0.46 low steel string and an AlNiCo 5 pole piece at various distances. |
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Post by ms on Mar 2, 2018 17:10:09 GMT -5
A "rail" style pickup should have no harmonic reception due to perpendicular movement, so based on their models, the string will sound the same anywhere and everywhere, with the only change being in the amplitude. But movement parallel to the face of the guitar still causes harmonics. |
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Post by antigua on Mar 2, 2018 18:15:44 GMT -5
A "rail" style pickup should have no harmonic reception due to perpendicular movement, so based on their models, the string will sound the same anywhere and everywhere, with the only change being in the amplitude. But movement parallel to the face of the guitar still causes harmonics. I'm not saying it doesn't, but according to their model's, once you hit that 1/r^3 gradient, the amplitude of those harmonics is homogeneous everywhere, most especially in the case of a rail pickup (as opposed to pole pieces / screws / slugs), where the perpendicular string movement has no symmetrical flux change. The harmonic amplitude would differ if the gradient transitioned between 1/r^3 and 1/r^2, I supposed the more linear-ish gradient near the magnetic face would mean less harmonics. Maybe if I go back and measure the Gauss strength at every millimeter, a transition between the two would reveal itself, but it might be a little difficult achieve that precision. |
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Post by antigua on Mar 3, 2018 4:18:45 GMT -5
There's lot of talk about string pull with various pickups and their various magnetic pole pieces. I'm curious to find out exactly how much pull there is.
The amount of string pull I measured between the wound strings and an AlNiCo 5 pole piece measuring 125mT (1250G) flux density at the face was about 0.1 newton (10g) at 1mm distance and 0.2N at a hair's distance. Beyond 1mm is lower than 0.1N, which, sadly, is the minimum resolution of my digital force gauge. It looks like I'd need to get a hold of something with higher precision in order to find values for greater distances or weaker magnets.
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Post by ms on Mar 3, 2018 7:15:25 GMT -5
But movement parallel to the face of the guitar still causes harmonics. I'm not saying it doesn't, but according to their model's, once you hit that 1/r^3 gradient, the amplitude of those harmonics is homogeneous everywhere, No, it is not. It is an exponentially falling field that has the property that you are describing, not 1/(r^^3). (This can be understood from their Taylor series expansions, should I attempt an explanation?) But in any case, even if the steady field is constant with distance from the pickup, the relative harmonic levels fall off with distance from the pickup. Eq. 13 of MacDonald shows this. h is the distance from the pickup, y is the string vibration in the direction perpendicular to the face of the guitar. As h gets larger, y becomes relatively less important in those terms that generate the harmonics. So, even neglecting string pull, there is a change in tone with the distance of the string from the pickup. (The main problem with MacDonald is that he assumes that the steady magnetic field is spatially constant. I think a full solution would change his results some, but the distortion he describes would still be present.) |
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Post by antigua on Mar 3, 2018 13:00:15 GMT -5
I'm not saying it doesn't, but according to their model's, once you hit that 1/r^3 gradient, the amplitude of those harmonics is homogeneous everywhere, No, it is not. It is an exponentially falling field that has the property that you are describing, not 1/(r^^3). (This can be understood from their Taylor series expansions, should I attempt an explanation?) But in any case, even if the steady field is constant with distance from the pickup, the relative harmonic levels fall off with distance from the pickup. Eq. 13 of MacDonald shows this. h is the distance from the pickup, y is the string vibration in the direction perpendicular to the face of the guitar. As h gets larger, y becomes relatively less important in those terms that generate the harmonics. So, even neglecting string pull, there is a change in tone with the distance of the string from the pickup. (The main problem with MacDonald is that he assumes that the steady magnetic field is spatially constant. I think a full solution would change his results some, but the distortion he describes would still be present.) You're right, it's clear to see in the equation now that you mention it. It's only B 0 that doesn't seem to matter according to McDonald's limited model. In this thread guitarnuts2.proboards.com/thread/7998/tonal-effect-pickup-height , I had looked at harmonic amplitudes by raising both the neck and the bridge pickup, but with just the neck pickup selected, and there were increases in harmonic amplitudes when either pickup was raised, though the increase was not in near-evenly spaced steps, as is the case with the magnetic distortions, so it seems that both factors must me contributing to added harmonics with closer proximity, with string pull effects adding an uneven, textured timbre of harmonics, while the magnetic distortion adds a much more linear distribution of harmonics:  That V(f) scale appears to depict dBV, because its volts, and it's logarithmic, but I'm not sure what drop in dBV is being shown with each successive harmonic, according to this model. Assuming that proximity adds some portion of harmonics, and string pull adds some portion of harmonics, then there would be a difference between the effect of pickup height versus the effect of higher flux density at the pole tops, with proximity dictating one source of harmonics, and a higher flux density dictating the other source. It's still not clear which of the two is a more dominant effect. Assuming both were roughly equal in their practical effects, the end result would probably be a sense of increased treble response in either case. |
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Post by antigua on Mar 5, 2018 23:53:30 GMT -5
I appears that if there is a difference, it might require a finer lens to see, so here is a high precision version of the strength versus distance test. I attached the probe and the AlNiCo pole pieces to the fingers of a Mitutoyo digital caliper, so the distance is accurate to within 0.01mm:  The question at hand is whether the degree of non linearity diverges between the magnets, or with distance. It looks to me like there is a distinct region of near linearity between 0mm and 2mm, while a harder curve seems to emerge at 3mm and beyond. One thing that sticks out, especially with high resolution, is that the degaussed AlNiCo 5 pole piece tracks rather precisely with the lower AlNiCo grades. Despite the somewhat different Br and Hc values between AlNiCo 5 and 2/3/4, the magnetic drop at distance, and by extension the magnetic field's shape, are essentially identical. For reference, here are the raw numbers:
AlNiCo 5, full strength
1191
830
564
394
286
215
166
131
105
86
71
AlNiCo 5, half strength
697
490
330
230
166
124
95
75
60
49
41
AlNiCo 4, full strength
730
508
351
248
182
138
108
86
70
58
48
AlNiCo 3, full strength
510
356
246
175
128
97
76
60
49
40
34
AlNiCo 2, full strength
641
451
309
218
158
118
91
72
58
47
39
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