The tonal effect of pickup height

[antigua]

I'm having another go at measuring frequency response in relation to pickup height, using a coil to excite string movement. The first time I tried this I was using a two dimensional FFT analysis that was harder to make sense of, and the last time I used a three dimensional FFT (frequency by amplitude by time) I was doing strums instead of coil excitation, which adds a random element that makes the results hard to interpret, and that test showed nothing conclusive, so this test combines the better coil excitation and the better three dimensional FFT spectrogram of Adobe Audition.





The exciter was placed over the 5th fret of the G string. The exciter is set to a square wave of 98Hz, half the frequency of the open G string, which results in a pull / release / pull / release cycle. I also found that a square wave function pulls harder than a sign wave. 

The guitar in this test is an HH Tele type, as seen below:



This test is neck only, because the bridge pickup somehow came disconnected when I lowered it way down. 

The neck pickup is in parallel mode via the Seymour Duncan Triple Shot mounting ring. 

This screen shot shows the raw recording: noise sample, then neck pickup 6mm, 4mm 2mm distances:


You can see the expected, that as the output gets louder as the pickup is raised closer to the string. The harmonic content stops at precisely 1.38kHz, because this is a steady state excitation. With the plucking tests it's typical to see a lot of harmonic content as high as the pickup will reveal, which is up to 6kHz with the PAF clone in parallel, using a very short cable.

Here is the same thing, but with all the heights normalized:



The big thing to see here is that the when the neck pickup is closer to the string, the higher (steady state) harmonics definitely pick up.  This matches the conclusion I reached with the previous test "There seems to be a trend of pickups pulling in more harmonic movement / voltage when they're closer to the string.", but this time the FFT analysis is much easier to make sense of visually.  It can be seen that the 5th harmonic, in particular, really comes out when the neck pickup is especially close to the string. 








Here is a second test, this time the neck pickup is still selected, but the neck pickup is static at 6mm from the G string, and the bridge pickup is raised closer to the strings with each sample, showing how the proximity of the bridge pickup to the string effects the tone response of the neck pickup:



In this case there is not a linear relationship between proximity and amplitude, but there are harmonic difference none the less, here's the same thing normalized:



An interesting thing happens; as the bridge pickup is raised, the harmonic content over the neck increases upwards as the bridge pickup is raised closer to the string. Something similar was observed in the first experiment, and also with an experiment that involved placing a powerful magnet over the ends of the strings; my theory was that by adding "pull" at the end of the string, energy is drawn away from the lower harmonics and concentrated into the higher ones. Maybe the pulling makes the string stiffer, and by doing so promotes higher harmonics. What is seen above seems to suggest as much. Notice that the third harmonic, the one which the neck pickup is most blind to naturally, and the 4th harmonic, diminish in output as the higher harmonics gradually gain more relative amplitude.

The tentative conclusion is that having the pickups closer encourages 5th and 6th harmonics, while bringing down the 3rd and 4th over the neck. The particular frequencies effected would depend on the note being played, but it would lead to a slight "scooping", adding treble emphasis while bringing down mids. One thing that is clear is that the pickup interferes with the strings, and it can broadly be said that the stronger the magnetic pull of the pickup, the more "unnaturally" the string will vibrate.

I've personally never noticed a relationship between sustain and magnetic strength, but this lends credibility to the idea that less string pull would result in a longer sustain time, though I think the higher output that is achieve by a stronger magnetic field would hold the signal voltage above the noise floor for a longer period of time, so it might be a wash between actual sustain, and the longevity of an acceptable S/N ratio.

I'm going to fix the bridge pickup and do this test again, from the perspective of the bridge pickup. 

[newey]

Great stuff, antigua!

It has always amazed me how many folks never adjust the height of their pickups. I've often advised players to try doing so, before spending big bucks on some designer pickups to improve their sound. I know doing so makes a big difference anecdotally, but it's always nice to have some data.

I'm going to fix the bridge pickup and do this test again, from the perspective of the bridge pickup.

And, I hope, we will also see a N + B test as well? Given what you saw at the neck pickup while adjusting the bridge, it would seem that some fairly complex interactions are occurring, which would be evenmore complex where both pickups are active.

I also wonder whether your methods, on a Strat, could verify the anecdotal "wolf tones" from a too-close Strat single coil. IOW,how close is too close?

[ms]

This is very clear. Nice measurements!  I think the harmonics are a simple consequence of the variation of force on the string as a function of displacement from the rest position.  Without the magnetic pull the restoring force on the string varies smoothly with string displacement, the same for going towards or away from the pickup.  Add the magnetic force and it becomes a more complicated asymmetrical function of displacement.  Think of this function of displacement (and thus time since the string is moving) as non sinusoidal, and thus, composed, by Fourier analysis, of a set of sinusoids.  Thus you can think of the force from the magnet as driving the string at harmonics.

[wgen]

Aug 23, 2017 23:00:36 GMT -5 antigua said:

Maybe the pulling makes the string stiffer, and by doing so promotes higher harmonics. What is seen above seems to suggest as much. Notice that the third harmonic, the one which the neck pickup is most blind to naturally, and the 4th harmonic, diminish in output as the higher harmonics gradually gain more relative amplitude. 

Interesting...this is actually contradicting previous assumptions about string stiffness. Shouldn't stiff strings point out lower harmonics in respect to the higher ones?

[antigua]

Aug 24, 2017 7:09:48 GMT -5 ms said:

This is very clear. Nice measurements!  I think the harmonics are a simple consequence of the variation of force on the string as a function of displacement from the rest position.  Without the magnetic pull the restoring force on the string varies smoothly with string displacement, the same for going towards or away from the pickup.  Add the magnetic force and it becomes a more complicated asymmetrical function of displacement.  Think of this function of displacement (and thus time since the string is moving) as non sinusoidal, and thus, composed, by Fourier analysis, of a set of sinusoids.  Thus you can think of the force from the magnet as driving the string at harmonics.

I have a hard time visualizing what you're saying. Are you saying that if you magnetically pull on the string, it takes more of a shape of a check, as in this: ✓ , and that by having the string irregularly divided, you promote the higher harmonics that fit more evenly into the irregular and uneven halves? Would this be similar to what a pinch harmonic accomplishes; dividing the string into smaller oscillating halves? Am I close?

Aug 24, 2017 7:24:18 GMT -5 wgen said:

Aug 23, 2017 23:00:36 GMT -5 antigua said:

Maybe the pulling makes the string stiffer, and by doing so promotes higher harmonics. What is seen above seems to suggest as much. Notice that the third harmonic, the one which the neck pickup is most blind to naturally, and the 4th harmonic, diminish in output as the higher harmonics gradually gain more relative amplitude. 

Interesting...this is actually contradicting previous assumptions about string stiffness. Shouldn't stiff strings point out lower harmonics in respect to the higher ones?

 
Come to think of it, I suppose if it really were making the string stiffer, the pitch should increase as the pickup is brought closer, but even with the FFT resolution set to the highest value offered, I see no change in pitch:

[antigua]

Aug 24, 2017 5:23:05 GMT -5 newey said:

Great stuff, antigua!

It has always amazed me how many folks never adjust the height of their pickups. I've often advised players to try doing so, before spending big bucks on some designer pickups to improve their sound. I know doing so makes a big difference anecdotally, but it's always nice to have some data.

I'm going to fix the bridge pickup and do this test again, from the perspective of the bridge pickup.

And, I hope, we will also see a N + B test as well? Given what you saw at the neck pickup while adjusting the bridge, it would seem that some fairly complex interactions are occurring, which would be evenmore complex where both pickups are active.

I also wonder whether your methods, on a Strat, could verify the anecdotal "wolf tones" from a too-close Strat single coil. IOW,how close is too close?

Since the wiring scheme itself has no bearing on the magnetic pull (as far as anyone knows), the B+N would be the combined signals of what the neck and bridge pickups would produce individually. So for example, if as I suspect based on the earlier test, that the bridge pickup behaves the same way as the neck, but with an even more pronounced higher harmonic effect, due to the pull occurring as a smaller division of the string, then raising both the neck and the bridge would result in higher harmonic amplitudes all around, at least up to 1.38kHz. I can give it a try though, just to see for sure. 

The next test will be with a Strat because I had to order a new Triple Shot ring for the HH. The little ribbon cable that connects the solder board to the plastic ring broke (again). It's not the best design, because when you stuff the pickup and cables into the pickup hole, it puts torsion on the ribbon cable, causing the outer sides of the ribbon cable to shear away. When I get the new one, I'm going to put a glop of epoxy over the ends of that cable. 

The Strat test will definitely induce wolf tones, and that will be interesting to see in this context. Wolf tones are more well understood because they're so easy to observe compared the to subtle differences of pickup height otherwise. In the case of wolf tones, it is because you're irregularly dividing and deform the string to such an extent that it supports a second frequency that is slightly varied from the fundamental frequency, leading to "beating". To my ear, that second tone is a slightly lower frequency than that of the fundamental and its harmonics.  It will be interesting to see what it looks like in the spectrograph. 

[wgen]

Aug 24, 2017 11:26:25 GMT -5 antigua said:

Aug 24, 2017 7:24:18 GMT -5 wgen said:

Interesting...this is actually contradicting previous assumptions about string stiffness. Shouldn't stiff strings point out lower harmonics in respect to the higher ones?

 
Come to think of it, I suppose if it really were making the string stiffer, the pitch should increase as the pickup is brought closer, but even with the FFT resolution set to the highest value offered, I see no change in pitch:

Thank you, yes there isn't any increase in pitch.
I was now thinking about a particular type of bass string, the Taperwound strings (not to be confused with Tapewound string, which is a completely different animal).
Taperwound are made so that the small section, a few centimeters usually, which sits on the bridge saddle, has an exposed core, or a much thinner section of the string wrap.
This is made, usually just for the low B of 5 string basses, to achieve better definition and better treble response from those low fundamentals. I suppose that it means more higher harmonics from this type of string.
I've used One of these sets, and the feeling is that, when you pick, the string is less stiff and more free to vibrate, because of the smaller surface of the string at the bridge saddle. The higher movement at the pick attack should be making for more higher harmonics, much similar to the flexible bracelet situation of an example we talked about in the past.
I also searched for the tension measurements from D'addarios as well as GHS strings, and the string tension, the actual stiffness, is exactly the same between regular strings and taperwound strings.
So I was thinking that maybe, the effect of a pickup CLOSE to the string is kinda like a regular string, while a pickup FAR from the string could be similar to the taperwound string, where the string is free to vibrate.
But then, your analysis is showing the opposite thing: when the string is less free to vibrate, it has higher harmonics presence than when the pickup is far from the string.
Mmm...I don't know.

[ms]

Aug 24, 2017 11:26:25 GMT -5 antigua said:

Aug 24, 2017 7:09:48 GMT -5 ms said:

I have a hard time visualizing what you're saying. Are you saying that if you magnetically pull on the string, it takes more of a shape of a check, as in this: ✓ , and that by having the string irregularly divided, you promote the higher harmonics that fit more evenly into the irregular and uneven halves? Would this be similar to what a pinch harmonic accomplishes; dividing the string into smaller oscillating halves? Am I close?

Think of mounting a tiny tiny accelerometer on the string over the pickup.  Acceleration is proportional to force.  In the absences of the magnet you see the acceleration changing in time with the fundamental frequency and some harmonics.  Now turn on the magnet.  It pulls harder the closer you get to the string, and so you have a modified asymmetrical acceleration waveform, thus more harmonics.  If you take the acceleration and integrate in time once you have velocity.  This is kind of like a first order low pass filter: it reduces the relative importance of higher harmonics, but they are still there.   The pickup sees the string velocity, and so it must see the added harmonics.

It is not so simple to solve this more complicated problem exactly.

[frankfalbo]

It always helps me to magnify the phenomenon in my mind. Lets say we're looking at a solid 6" diameter steel rod. Hit that with a hammer and you'll hear high frequencies. Trade it for a 6" diameter rubber and the pitch will drop. Of course there is an entirely different occurrence in a long, thin string soft enough to vibrate in an ellipse, and being under tension rather than static. But sometimes it helps to overlay the two to see how a stiff string can produce high harmonics at the expense of fundamental. 

Aside from all that, anecdotally I can say that on Angus' main SG's, there was one with an extremely degaussed neck pickup, and that was part of matching the "magic" sound of the bridge pickup on that particular guitar, which comports with your findings that changing pickup height/pull of one pickup can have an impact on the other(s) 

[antigua]

Aug 24, 2017 13:06:51 GMT -5 ms said:

Aug 24, 2017 11:26:25 GMT -5 antigua said:

I have a hard time visualizing what you're saying. Are you saying that if you magnetically pull on the string, it takes more of a shape of a check, as in this: ✓ , and that by having the string irregularly divided, you promote the higher harmonics that fit more evenly into the irregular and uneven halves? Would this be similar to what a pinch harmonic accomplishes; dividing the string into smaller oscillating halves? Am I close?

Think of mounting a tiny tiny accelerometer on the string over the pickup.  Acceleration is proportional to force.  In the absences of the magnet you see the acceleration changing in time with the fundamental frequency and some harmonics.  Now turn on the magnet.  It pulls harder the closer you get to the string, and so you have a modified asymmetrical acceleration waveform, thus more harmonics.  If you take the acceleration and integrate in time once you have velocity.  This is kind of like a first order low pass filter: it reduces the relative importance of higher harmonics, but they are still there.   The pickup sees the string velocity, and so it must see the added harmonics.

It is not so simple to solve this more complicated problem exactly.

Thanks, that makes it much more clear. You're saying that the string becomes even less of an ideal sin wave (or less natural in movement), and produces more of a pointed wave form due to the unnatural acceleration and deceleration, that in turn manifests as higher harmonics? That's an interesting notion. Would is also slow the velocity at which the string moves away? Would the wave become more "saw tooth", specifically, as a result of lopsided acceleration / deceleration?

One issue I see with this though, is that I believe the increase in higher harmonic content should be rather uniform and predictable, but to some extent these harmonic increases are not perfectly predictable. For example, if what you're saying is accurate, I think you should see an increase in 3rd harmonic also, but I see suppression, it actually gets even lower in amplitude with added proximity. 

I'll try overlapping the actual waves, and we can seen if anything intuitive can be seen there.

How do you think the matter of irregular velocity relates to wolf tones, if at all?

Aug 24, 2017 13:30:04 GMT -5 frankfalbo said:

It always helps me to magnify the phenomenon in my mind. Lets say we're looking at a solid 6" diameter steel rod. Hit that with a hammer and you'll hear high frequencies. Trade it for a 6" diameter rubber and the pitch will drop. Of course there is an entirely different occurrence in a long, thin string soft enough to vibrate in an ellipse, and being under tension rather than static. But sometimes it helps to overlay the two to see how a stiff string can produce high harmonics at the expense of fundamental. 

Aside from all that, anecdotally I can say that on Angus' main SG's, there was one with an extremely degaussed neck pickup, and that was part of matching the "magic" sound of the bridge pickup on that particular guitar, which comports with your findings that changing pickup height/pull of one pickup can have an impact on the other(s) 

I think it might partly explain the appeal of single pickup guitars, also.

I think guitarists often go to some unusual lengths to achieve an outcome that can be had more easily through other means. For example, removing the cover of a humbucker for a higher Q factor, instead of changing the load on the circuit with some simple value changes. Or swapping pickups to achieve fine EQ variations that the guitar cable, amp, or other post processing is more responsible for setting. If the log gauss magnet really did the trick, I'd think lowering the pickup would have worked as well, but might not have been given consideration due to the aesthetic consequence. 

It all comes down to knowledge. There are a lot of companies out there who would rather suggest that guitarists spend more money to solve their perceived problem, rather than offer information on how to fix the issue for little or no cost. That's capitalism.

[ms]

Aug 24, 2017 14:40:44 GMT -5 antigua said:

Aug 24, 2017 13:06:51 GMT -5 ms said:

Thanks, that makes it much more clear. You're saying that the string becomes even less of an ideal sin wave (or less natural in movement), and produces more of a pointed wave form due to the unnatural acceleration and deceleration, that in turn manifests as higher harmonics? That's an interesting notion. Would is also slow the velocity at which the string moves away? Would the wave become more "saw tooth", specifically, as a result of lopsided acceleration / deceleration?

One issue I see with this though, is that I believe the increase in higher harmonic content should be rather uniform and predictable, but to some extent these harmonic increases are not perfectly predictable. For example, if what you're saying is accurate, I think you should see an increase in 3rd harmonic also, but I see suppression, it actually gets even lower in amplitude with added proximity. 

I'll try overlapping the actual waves, and we can seen if anything intuitive can be seen there.

How do you think the matter of irregular velocity relates to wolf tones, if at all?

All I can say is that harmonics are produced.  Solving for the details mathematically would be difficult.  It is possible that some of the harmonics generated by the magnet could be out of phase with those already present.

[antigua]

I'm having trouble with the Strat / AlNiCo 5 pole piece testing. It's very obvious with the stronger, more pointed AlNiCo 5 that the pickup interferes with the stead state vibration of the string. You can hear the string generate more or less amplitude, and see it physically see it change how it moves as the magnet is moved closer or further from the string. So it really goes to show the extent to which the pickup interacts with the string, though that's obvious to anyone who has experienced wolf tone problems with a Strat. Anyway, it's really messing up my experiment because the pickup modifies the steady state vibration, transposing a second variable over the one I'm trying to observe. With the humbuckers, it might be the case that the more widely dispersed magnetic pull didn't cause as such dramatic interference. Another issue with this is that the stead state doesn't induce higher harmonics, or allow the decay to be observed, which is an argument for trying to get a constant string pluck working, which has been very difficult to do in the past.

One interesting thing, with the neck pickup in particular, is that getting the magnet closer to the string would sometimes decrease the amplitude of the steady state, as in it pulled so hard that damped the overall amplitude in a rather obvious way. The neck and bridge would cause intermdoluation effects when raised and lowered, but not so readily sap the string of overall vibration.  I strongly suspect, and I think it follows logically, that the AlNiCo 5 neck pickup has the capacity to shorted the duration of string vibration, to a greater degree than does the middle or bridge. 

Aug 25, 2017 7:09:56 GMT -5 ms said:

Aug 24, 2017 14:40:44 GMT -5 antigua said:

Thanks, that makes it much more clear. You're saying that the string becomes even less of an ideal sin wave (or less natural in movement), and produces more of a pointed wave form due to the unnatural acceleration and deceleration, that in turn manifests as higher harmonics? That's an interesting notion. Would is also slow the velocity at which the string moves away? Would the wave become more "saw tooth", specifically, as a result of lopsided acceleration / deceleration?

One issue I see with this though, is that I believe the increase in higher harmonic content should be rather uniform and predictable, but to some extent these harmonic increases are not perfectly predictable. For example, if what you're saying is accurate, I think you should see an increase in 3rd harmonic also, but I see suppression, it actually gets even lower in amplitude with added proximity. 

I'll try overlapping the actual waves, and we can seen if anything intuitive can be seen there.

How do you think the matter of irregular velocity relates to wolf tones, if at all?

All I can say is that harmonics are produced.  Solving for the details mathematically would be difficult.  It is possible that some of the harmonics generated by the magnet could be out of phase with those already present.

Here is an overlapping of the wave form from the humbucker neck near / far, from a couple days ago. The softer curve is "far", the more contoured curve is "near". The various contours suggest that the string was supplying harmonic movement within the magnetic field. There might also be the effect of an accelerated descent and decelerated ascent, but the complexity of the wave form suggest there is more to it than just that. Both effects could be present at the same time.

My gut instinct is that any effect caused by added acceleration/deceleration velocity would be very subtle, though. The string is moving very fast, I don't think the added pull increases the velocity by a significant amount.  One way to test for it might be to muffle the string with cloth, in order to discourage
physical harmonics, so that only the rapid movement of the string would manifest a harmonic amplitude.

The Strat test is still in limbo while I work out the steady state interference issue, but the odd thing about the middle pickup, that seemed rather consistent, was that it showed no increased harmonics as the pickup came closer to the string. That's not to say nothing changed, but that this test wasn't able to demonstrate that change, whatever it is. The low ceiling of steady state harmonics might obscure interesting things that happen when higher harmonics are induced in the system by a guitar pick. In order to make the steady state more reliable, I was thinking of placing the exciter coil over the center of the string, over the 12th fret, but I suspect that will depress harmonics even more. Trying to revisit a "constant pluck" test seems like a better bet. 

[antigua]

Strat Neck Pickup, D string

Here is my first practical test using the second plucker device shown here guitarnuts2.proboards.com/thread/8001/string-plucking-mechanism-consistent-testing 

This setup tests the neck pickup height variance of a Strat with AlNiCo 5 pole pieces, as seen here with the pickup at its highest possible setting before the string would make contact with the magnet upon release:



As seen, the D string is being plucked, and the other two pickups are set very low, so that their impact on the string is not removed, but is at a practical minimum.

The wave form below starts with the pickup lowered to the pick guard, tested twice, then the pickup is moved slightly closer to the strings. So there are a total of ten height adjustments, with two plucks per height setting, for twenty plucks total, each is fifteen seconds. The distances are not equal, because as the pickup gets closer to the string, the differences become more pronounced, so I started with two screw turns per increment, but towards the end I was only adjusting the screws by half a turn.

If you right click on the image below, there should be in option to view the image in a new tab so that you can see the whole thing in full size. 

I appears that the overall amplitude variation undergoes a "back and forth" type pattern, with more amplitude on one side of the cycle than the other, and that this "back and forth" pattern become more rapid as the string and pickup come closer together, until they're so close that the waveform is fairly symmetrical throughout. Then once the pickup and string are really close, it become less symmetrical again. 



Here is the waveform with each increment normalized:



It appears that the closer pickup settings do decrease the overall amplitude over time, with respect to the amplitude of the transient, but it's very slight and only prominent at all when the pickup, which has powerful AlNiCo 5 pole pieces, is very close to the D string.


Here is a view that highlights the harmonic content. Again, it's best to view this in full size i.imgur.com/9NZRmh2.jpg



As can be seen, the transient and initial decay are full of higher harmonics, extending beyond with the pickup would normally deliver to the amplifier, but within about four seconds they die off, with only lower harmonics remaining below 1kHz, which is well below the resonant cut off of most guitar pickups.

Which the pickup set low, the harmonics show a consistent amplitude throughout, meaning the string vibration is consistent and undisturbed. As the pickup gets closer to the string, the fundamental (lowest line) increase and decrease in periodic intervals. The interval becomes shorter as the pickup gets closer to the string. When the pickup is really close to the string, the first harmonic above the interval starts to do the same.

Also with the pickup set low, third and fourth harmonics are really low, while the fifth and sixth harmonics are fairly strong, but as the pickup gets closer to the strings, the third and fourth are present in the transient, while the fifth and six decay more quickly. 

In general, with the pickup set low, the strings are undisturbed, but as the pickup is raised, most of the difference is in the amplitude of the fundamental over time, and then once the pickup and the string are very close, more harmonics are present in the transient, many of the harmonic amplitudes vary rapidly, and the overall decay is more rapid. 

I'll try this test with the B string to see how it compares.

[antigua]

Strat Neck Pickup, B string

Here is the same test with the B string, though I realized while doing this that I can't get that pole piece as close to the string, because it's recessed in the pickup compared to the D and G pole pieces. 

Here is low to high again:



This shows a similar pattern of the lopsided cycles becoming more rapid as the string comes nearer to the pole piece.

Here they  are normalized:



This seems to also show that there is a bit less "sustain" when the pole piece is closer to the strings. 

Here is the spectrogram:



This shows a similar increase in periodic amplitude drops that are harmonic specific. The same overall trends that were seen with the D string appear with the B string.  

[antigua]

Strat neck pickup selected, raising the bridge pickup, and then the middle pickup



Here I have the neck pickup selected and set low to the pick guard, and with each pluck, the bridge pickup is raised closer to the string:



Having the bridge pickup closer to the string causes, and increases, periodic pulsing in the fundamental and second harmonic, while the first harmonic is fairly stable, and seems to even increase in amplitude. The other harmonic proportions seem relatively unaffected. 

Here the bridge pickup is set up about half way, and the middle pickup is raised one step per pluck:



The same things happens as above, but the pulsing becomes even more frequent, and the harmonic proportions change slightly. The fourth harmonic also picks up overall amplitude. The fifth becomes more brief, and the sixth is unchanged. 

With the strong second harmonic and the weaker fundamental of the final plucks (furthest to the right), the second harmonic is more prominent, compared to the first pluck. It comes across as a more rapid drop off in low end. The harmonics of the final plucks, which show a lot of pulsing, have a more pronounced metallic, ringing sound to them.   

I'm not exactly sure what causes the pulsing in the fundamental and other harmonics, but my suspicion is that as the magnetic pull causes asymmetrical damping along the length of the string, movement energy transfers from side to side, or at the very least moves around, and this pulsing increases with frequency as the amount of asymmetry becomes more extreme. 

The next test will evaluate what is seen from the bridge as the neck and middle pickups are varied in height.

[antigua]

Strat bridge pickup selected, raising the bridge pickup


Raising the bridge pickup, while receiving signal from the bridge pickup, shows less apparent differences, aside from overall amplitude, as the pickup comes closer to the moving string.




Here is a normalized version showing the spectrograph: 



It looks like there is a little more pulsing in the fundamental and second harmonic, there's an increase in second harmonic amplitude, and the fifth and 7th harmonics hang on a little longer as the pickup becomes closer, but overall the differences seem very slight.  




Strat bridge pickup selected, raising the neck pickup, and then the middle pickup

This shows the difference made, from the perspective of the bridge, as the neck pickup is raised:




The 4th and 5th harmonics become stronger with decreased distance between the neck pickup and strings, but most other harmonics have about the same amplitude, and as was seen when raising the bridge pickup, the seventh harmonic sustains longer. Also as seen above, it looks as though the pulsing in the fundamental and second harmonic increase in frequency as the pickup comes closer to the string, but with increasing frequency, to the point that the lines appear solid again. 

Here is a close up on the fundamental and lower harmonics:



You can see that even though the fundamental look increasingly solid, if you look close, there is actually very fine, rapid pulsing. 

This higher res view also shows other frequencies in between the harmonics. It turns out I should have damped the other guitar strings, as that is simply the other strings ringing out very quietly. 

As I was setting the neck pickup as close as it would go, "wolf tones" or "Stratitus" could also be heard. The higher spectral resolution shows what that looks like. Looking to the left, all the harmonics start out as clean straight lines, but as the pickup comes nearer to the string, they all split into two or three lines. In each case, the second line is a few hertz below the primary fundamental or harmonic. You can even see one of the other guitar strings producing a wolf tone at about the 2/3rd's mark, at 164Hz (the first harmonic of the low E string)






This shows the difference made, from the perspective of the bridge, as the middle pickup is raised:



Yet again, the 7th hamronic appears to become stronger, and the fundamental, and lower harmonics show more rapid pulsing as the middle pickup becomes closer to the strings. There doesn't appear to be to much "wolf tone" separation, maybe just a tiny bit, as the pole piece comes closer to the strings. It can be seen that the neck pickup more readily induces wolf tones than does the neck or middle pickups. 

[antigua]

Humbucker in Les Paul, Neck Pickup, D string






I've attached the plucker v2 to a Les Paul with Tone Rider AlNiCo IV Classic PAF replica, so this pickup has a slightly weaker pull than a humbucker equipped  AlNiCo 5 or ceramic. 

This test is the same format as above, the pickup is moved closer and closer to the strings with each pluck, starting from flush with the plastic ring, then raised to the point where the string rattles against the tops of the screw. Note that it's around the 2/3rd's  mark the pickup is as close as you could get it without having the string hit the pickup when fretting at the 22nd fret, so the plucks beyond that point represent a proximity between the string and pickup that would only exist if you have the pickup set lower, and were fretting higher up the neck, thereby bring the string and pickup into close proximity.



What can be seen, in addition to have the overall increase in amplitude, is that the asymmetry of the cycles modulates more rapid as the pickup is moved closer to the string, so if you're using an amp or pedal that creates asymmetrical clipping, the amount of fuzz you hear would increase and decrease over time, along with the asymmetry of cycles. When the pickup is set low, that asymmetrical modulation is slower, and when the pickup is closer to the string, it modulates more rapidly, creating a more lively chorus-like effect. 

Here is the same file, but with all plucks normalized:



First observation, when the pickup is at its lowest, sustain appears to be improved slightly, because the initial plucks have a higher amplitude at the end of the 15 second windows, but as you get closer to the string, the benefit disappears quickly, and since the amplitude is so low when the pickup is set that low, any benefit to sustain is probably outweighed by the low signal to high noise ratio. 

Similar to the Strat test above, the change in cycle asymmetry (the wavy appearance of the wave form) becomes more rapid as the pickup becomes closer, until the wave form almost looks smooth, and then becomes more jagged again. Coinciding with the more rapid asymmetry of the cycle, looking at the spectrogram, you can see that individual harmonics pulsate more rapidly as the pickups is moved closer to the string. At the far left, all the harmonics are even and smooth, but as you get to the right, nearly all harmonics, except the first harmonic above the fundamental, show pulsating. Listening to the plucks through headphones, when the pulsing tends to be wider, it can be heard as a "louder / quieter" and a "wah wah" oscillation, but as the pulse becomes more narrow, the pulsing becomes harder to hear, so the very furthest and very nearest plucks actually sound more alike than the plucks in the middle height settings, where the pulses are rather wide. The "louder / quieter" aspect comes from the literal fact that that there is less overall amplitude when two or more pulses hit their "off" cycle at the same time, while a "wah wah" sound is also present, that coincides with some harmonics entering the "off" cycle of their pulse, while some harmonics enter the "on" cycle, which leads to a fluttering of harmonics that varies over time. 

This harmonic fluttering also becomes more prominent when the signal clips. Since the clipping reacts to the sum voltage of all the harmonics combined, a pulsing that occurs at, say, the 3rd harmonic might not be audible with a clean signal, but under gain, that harmonic might cause voltage clipping that induces new harmonics that are much more audible than the 3rd harmonics alone. 

As for harmonic balance, in the first test of the thread, where I'd used an exciter to move the string, it looked as though there was an increase in higher harmonics, but I believe now, after having tested a bit with plucking the string, that this was an artifact of actively exciting a guitar string. I don't see any such trend when plucking the strings. There is fairly little variance in the harmonic content. In fact, the only trend I can see that reliably spans the samples is that the 12th harmonic goes from nonexistent to slightly existent. 


The pickup reads about 250 gauss over the slugs and screws, where as the Strat pickup measured over 1000 gauss over the pole tops, so even with the humbucker extremely close to the string, no "wolf tone" is heard, or seen in the spectrograph:




In conclusion, it appears that the most significant effect of the height on the neck humbucker with a weaker magnet is the rate at which harmonics amplitudes modulate over time, with the rate tending to increase as the pickup comes closer to the string. 

[antigua]

Humbucker in Les Paul, Bridge Pickup, D string

This screen show below shows the waveform of the Tonerider AlNiCo IV Classic bridge pickup being selected, and the open D string being plucked mechanically, and having the pickup moved closer to the strings with each pluck. The effective maximum height is about 2/3rd's in, with the remaining 1/3rd having the pickup so high that fretting the 22nd fret would cause the string to hit the pickup. The mechanical plucking is placed right in between the pickup, and the string is pulled back about 2mm when released. 



The only thing of note is that appears that the attack appears to be proportionately larger than the decay, but only when the pickup is very close to the strings.

This screen shot shows all the plucks normalized. It can be seen more clearly how the decay is more rapid when the pickup is very close. This might be a problem when playing notes higher up the fret board, especially when playing clean, and you don't have any feedback or saturation helping to sustain the note.  



The spectrogram doesn't show anything too dramatic. The only thing that is consistent end to end is that the 2nd harmonics dies out rather quickly when the pickup is farther from the strings, but gets gradually stronger as the pickup is moved closer to the string, although interestingly it always seems to show a burst of energy, followed by a relatively low amplitude decay. Most all of the other harmonics have a more gradual drop off.

It's not surprising that the effect of pickup height it subtle for a bridge pickup, that also features rather weak magnets. The magnetic damping effects will be weaker at the ends of the string due to the increased rigidity at the ends. It's the same reason that, if you use your own fingers, it's harder to pull on the guitar string towards the ends, than it is towards the middle of the string. 

[antigua]

In order to get some further clarity on what sort of magnetic pull results in more rapid modulation, I performed some tests using a neodymium near the guitar string. The modulation I'm speaking of is where the signal amplitude alternates between favoring the positive and negative sides of the wave cycle. The more rapid modulation is seen as lots of ripples in the waveform, where as a slower modulation shows up as longer, wavy curves.

The testing confirms that it is the magnetic pull of the pickup, that is responsible for the modulation seen in the waveform as the pickup was set closer to the strings. It confirms that stronger magnetic pull, almost regardless of how it is applied, results in more rapid modulation. Or, stated more generally, increased asymmetry results in more rapid modulation. This can even be seen with the naked eye. If you pluck a string, especially the larger wound string, you can see that the way the string moves changes over time, aside from simply vibrating less and less. And, if you hold a powerful magnet near the string as it decays, you can see that "change" increase in its frequency. This testing goes to show that the physical movement pattern and the the modulation seen in the waveform are one and the same.

The modulation pattern changes; there are times where they amplitude is move positive, more negative, or the amplitude is higher or lower overall, but there generally is a pattern, and it repeats periodically. A question to ask is why does some pattern of string movement result in more positive amplitude, more negative, or more or less overall? I think the answer to that is implied in Faraday's Law; the more quickly the flux changes, the greater the voltage spike. Imagine the string moving in a triangular motion; if the base of the triangle is closer to the pickup, then the string might be moving fast, but it's distance from the pickup isn't changing as quickly , thus you get low voltage. But if the tip of the triangle is pointing down at the pickup, then the string is still moving at the same speed, but moving towards and away from the pickup very rapidly, so you get a higher voltage when the string is moving in that pattern. It should even be possible to figure out what sort of string movements result in which types of cycles, so that you could guess, with some accuracy, how the string was moving, just by looking at the wave form.

So the string moves back and forth in different patterns of movement, resulting in increasing and decreasing voltages on particular sides of the cycles, and that pattern modulates more quickly when the string is asymmetrically "damped" by a magnet. It seems that energy must be moving from one side of the guitar string to the other, the "damping" must essentially have pushed the energy to the other side of the string, only to have it return like a pendulum, and the more imbalanced the two sides of the string are, the more quickly that energy bounces back and forth. But, if the frequency increases the stronger the magnet is, and it behaves like a pendulum, I don't believe the magnet is actually "damping" the string at all, rather, it's stiffening half string, resulting in an oscillating mass-spring-damper system across the length of the string.

A more complicated aspect to this is why particular harmonics show different type degrees of pulsing with different degrees of magnetic damping. Except in the case of the fundamental, it could even be the case that side-to-side movement, movement which passes across the center of the pole piece, produces a harmonic that periodically cancels out an actual physical harmonic of the guitar string, resulting in pulsing. 




So, here are the different tests I carried out with an externally applied neodymium....

In all of these wave forms, the first string pluck has no magnet nearby, aside from the pickups that are already installed in the guitar, and then in each subsequent the magnet is moved to a position where its pull upon the string becomes more prominent. I'm suspending the magnet over the fret board, so it's opposite side of guitar's pickups, which are also magnetically attracting the guitar strings all the while.

In all of these wave forms, the G string is utilized, and is open, except for the third wave form below, where it's fretted at the sixth fret.



In this wave form, the neodymium is suspended above the 12th fret, and moved closer to the string. At some distances, the neo apparently has no effect, but once it passes a certain point, you can see the rate of modulation increase significantly. The spectrogram view shows that the rate of modulation coincides with pulsing of particular harmonics, most notably the second harmonic in this case. With the neo over the 12th fret, it's pulling at the center most anti node of the 2nd harmonic, along the length of the string.

Also, if you look at the spectrogram, far bottom right, you can even see where the neo induces a "wolf tone", evidences by two lines at the fundamental instead of one.






This next wave form has the neo removed, then, at a height of 10mm, above the 2nd fret, 4th fret.. up to the 12th fret. In this case, the magnet is as a fixed distance, but as the magnet is moved more towards the center of the string, it pulls the string more, as the string tension is lower the closer you get to the center of the string (imagine pulling back a bow and arrow anywhere other than at center). Again, it's seen that this rate modulation increases. 





This next wave form is the same test, but this time fretted at the 6th fret; no magnet, then over the 8th fret, the 10th, 12th and 14th, and the same trend is seen, simply showing that this effect doesn't require that a string be open / unfretted. 





This wave form is the same as the 2nd, but this time rather than position the neo above the string, it is placed to the side of the string, parallel to the fret board, at the same 10mm distance. First the magnet is removed, then parallel to the 2nd fret, 4th .. up to the 12th.

The rate of modulation increases again, but not quite as dramatically as when the magnet was above the string. Considering the only difference here is angle, the most likely reason the effect is more moderate than before is because the neo is not pulling on the string along common axis with the guitar pickups. Having the neo pull up while the pickups pull down probably increases the modulation effect, versus having the pickups pull down while the neo pulls sideways. 





In conclusion it's apparent that imposing magnetic damping upon the string increases the rate of modulation from positive to negative amplitude as the string movement decays. The magnetic damping introduces asymmetry in the way the string moves as the movement decays, because the magnet is pulling in a particular direction, and/or on a particular side of the string. And so, a higher degree of asymmetry, in general, appears to result in a more rapid modulation.   

[wgen]

Hello, I'm writing here because, even if what I'd like to ask isn't strictly about the tonal differences of different pickup heights, it is closely related to what is represented in Antigua's analysis about the "reading" of a passive pickup of the plucking, or picking of a guitar string. Please excuse me for my use of the English language, among other technical gaps I have.
Now, what I've understood from the analysis of Antigua is that the transient, the peak-to-peak signal of the pluck of a string exhibits strong fundamentals and lower harmonics, but also some higher harmonics, which are lost in the decay of the signal much sooner than the lower harmonics.
Somewhere in this forum I even read that someone could even say that the most, if not all, of the differences between different pickups are given in the very first transients, just a few milliseconds after the plucking of the strings. The decaying part of the signal would be much more similar for the different pickups tonal response.
The graphs which represent the pickup tonal response (the "envelope" I think to remember that's called...?) don't seem to capture the quality of the transients, because these graphs tend to "normalize" the pickup tonal response of the very first seconds of the signal, and especially the higher harmonics response is quite a bit sacrified, because as Antigua noticed, these higher harmonics decay in just a few milliseconds, differently from the lower harmonics, which decay in a few seconds, instead.

I was now thinking about the use of compressors and limiters, which are quite popular for bass as well as for guitar (ie the popular Boss CS-3 is much more of a limiter and not a smooth compressor, despite how it's called).
I don't understand how to think about this: does the signal maintain its properties after the compression, so that the transients maintain their "full bandwidth harmonics", from low to high registers, and the signal still become dull after a few ms of the decay?
Or does the signal become almost flat tonal-wise for the most part, so that, especially when using limiters, the transients don't exhibit that "more treble" quality at the transient, because the plucking of the strings is being squashed by the limiter?
I don't know if the doubt is clear...it has more to do with how the compression works perhaps, but I thought that this could be interesting, considering the behaviour of guitar pickups, especially when you're in the studio and you want to better understand how to properly use equalizers after compression, for example, to achieve an overall balanced timbre.
Thank you very much

[antigua]

May 30, 2018 4:51:27 GMT -5 wgen said:

Hello, I'm writing here because, even if what I'd like to ask isn't strictly about the tonal differences of different pickup heights, it is closely related to what is represented in Antigua's analysis about the "reading" of a passive pickup of the plucking, or picking of a guitar string. Please excuse me for my use of the English language, among other technical gaps I have.
Now, what I've understood from the analysis of Antigua is that the transient, the peak-to-peak signal of the pluck of a string exhibits strong fundamentals and lower harmonics, but also some higher harmonics, which are lost in the decay of the signal much sooner than the lower harmonics.
Somewhere in this forum I even read that someone could even say that the most, if not all, of the differences between different pickups are given in the very first transients, just a few milliseconds after the plucking of the strings. The decaying part of the signal would be much more similar for the different pickups tonal response.
The graphs which represent the pickup tonal response (the "envelope" I think to remember that's called...?) don't seem to capture the quality of the transients, because these graphs tend to "normalize" the pickup tonal response of the very first seconds of the signal, and especially the higher harmonics response is quite a bit sacrified, because as Antigua noticed, these higher harmonics decay in just a few milliseconds, differently from the lower harmonics, which decay in a few seconds, instead.

Maybe you mean the "bode plots" which show the resonant peak. The transfer function of the pickup is the same, no matter if the signal is a transient or not, so the bode plots do also reflect the transient. According to one of the FFT analysis in the transients above 2kHz decay very fast, while those between 1kHz and 2kHz decay a little slower, and those under 1kHz last for a longer time. If the bode plot reveals that a pickup's resonant peak is around 2kHz, like a P-90 or a Seymour Duncan JB, then you never here the fast harmonics above 2kHz, only the longer harmonics below 2kHz. As a result, the pickup sounds punchy, because the initial attack will seem long by virtue of omission of quick decaying high harmonics. Conversely, a pickup with a high resonant peak reveals all of the quick decaying harmonics, making the attack sound sharp and glassy, rather than soft and punchy. Combining the transfer function indicated by the bode plot, along with the harmonic content of the guitar strings, paints a complete picture of the final sound that is heard.

May 30, 2018 4:51:27 GMT -5 wgen said:

I was now thinking about the use of compressors and limiters, which are quite popular for bass as well as for guitar (ie the popular Boss CS-3 is much more of a limiter and not a smooth compressor, despite how it's called).
I don't understand how to think about this: does the signal maintain its properties after the compression, so that the transients maintain their "full bandwidth harmonics", from low to high registers, and the signal still become dull after a few ms of the decay?
Or does the signal become almost flat tonal-wise for the most part, so that, especially when using limiters, the transients don't exhibit that "more treble" quality at the transient, because the plucking of the strings is being squashed by the limiter?
I don't know if the doubt is clear...it has more to do with how the compression works perhaps, but I thought that this could be interesting, considering the behaviour of guitar pickups, especially when you're in the studio and you want to better understand how to properly use equalizers after compression, for example, to achieve an overall balanced timbre.
Thank you very much

Compressors and limiters don't change the harmonics content at all (unless it's a multiband compressor, but that's something different). Compressors will take the existing content and make all of it louder or quieter, but won't filter the harmonics one way or another. Some people say pickups sound "compressed", a pickup can't compress, but since it's a "low pass filter", it can omit, and that omission of high harmonics sounds similar to compression because you hear only low, slow decaying harmonics, no high, quick decay harmonics. A real compression effect would increase the entire amplitude over a longer period of time, slowing the decay of all harmonics, not just high or low ones. So they're similar effects, but not exactly the same.

[wgen]

Thank you very much! You answered the question I had perfectly. I meant not the bode plot but the graph which fully comprehend also the picking effect, as well as the position of the pickup along the string (ie neck, middle or bridge, following the Tillman pickup demo), kinda like the most "complex" of the various graphs inside the Guitarfreak software... Don't know how to call that.
In these graphs you don't have a clear visual representation of the transient I would say, and the 4 khz, let's say, are down about 12-15 db in respect to 100hz to 1000hz, for example.
Anyway, you explained the pickup and the compression behaviour very precisely, thank you very much for all of your help.

[antigua]

I want to put this idea out there to see what others might have to say, I was watching a YouTube video of an eddy current break   , and one thing that struck me is how small the magnet is relative to the conductive wheel, and yet it still stops the wheel rather quickly.

Is it possible that the asymmetries that occur in relation to pickup height owes to "eddy current breaking" of the guitar string? Are there any assumptions about relative quantities and values that could be made in order to determine if "eddy current breaking" is at play between the guitar string and pickup? 

[newey]

Just so we're clear, I believe you mean "braking", not "breaking".

[stratotarts]

Any significant eddy current in a string would have to be longitudinally because the diameter is so small. Since we typically only ground the bridge end, there is no return path for the current, except through the other strings. Try measuring the voltage between the bridge and the nut end of the string, for a really cheap pickup!

[straylight]

So here's a thought, if we can consider a pickup as a magnetised string vibrating near a coil of wire, then is the string also the magnet and the pickup (cover) the wheel?

[ms]

Aug 12, 2018 9:20:35 GMT -5 stratotarts said:

Any significant eddy current in a string would have to be longitudinally because the diameter is so small. Since we typically only ground the bridge end, there is no return path for the current, except through the other strings. Try measuring the voltage between the bridge and the nut end of the string, for a really cheap pickup!

As shown in diagrams here: en.wikipedia.org/wiki/Eddy_current_brake,  the currents in the conducting surface near the magnet need to be circular, and so the small diameter of the string would be a factor even if the circuit were completed by connecting the ends of the string together.

[antigua]

Aug 21, 2018 1:57:49 GMT -5 straylight said:

So here's a thought, if we can consider a pickup as a magnetised string vibrating near a coil of wire, then is the string also the magnet and the pickup (cover) the wheel?

I'd say yes, the guitar string might not have a substantial diameter, but the pole pieces do. 

I've found that steel pole pickups produce a higher output, all other things being equal, on account of the lower magnetic reluctance path, but by that same virtue, any eddy current braking that exists, and it sounds like some must exist, would be higher with steel pole pieces. I doubt the braking / damping is audible, especially with human hearing being so much less sensitive to amplitude than to frequency.  

[straylight]

I wonder whether the effect of this is what guitarists tend to describe as compression, only in a negatively correlated sense in that a guitar with less damping will have the higher order harmonics ring longer and exhibit a bright "compressed" sustain and guitars with higher damping factors have a faster decay on harmonics with a darker and more "natural sounding" sustain.

I've got a few pickups on the bench at the moment with similar cutoff frequencies as measured with driver coil and bode plot methods, the difference between them being how they ring on long notes, some of them sounding more vowel like. More research needed.

[antigua]

Aug 21, 2018 14:00:37 GMT -5 straylight said:

I wonder whether the effect of this is what guitarists tend to describe as compression, only in a negatively correlated sense in that a guitar with less damping will have the higher order harmonics ring longer and exhibit a bright "compressed" sustain and guitars with higher damping factors have a faster decay on harmonics with a darker and more "natural sounding" sustain.

I've got a few pickups on the bench at the moment with similar cutoff frequencies as measured with driver coil and bode plot methods, the difference between them being how they ring on long notes, some of them sounding more vowel like. More research needed.

I'm highly certain, based on countless observations of "compressed" being described in relation to pickups with a low resonant peak, that the perceived compression is due to the omission of quick decaying higher harmonics.  In fact, if you turn down the tone knob to zero on any guitar so as to fake a pickup with a very low resonant peak, that same sense of compression will manifest itself.