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Pickup Placement, measurements of specific basses
- Thread starter tdvt
- Start date
My MN4 P measures, from the center of 12th fret to center of top pu-- 11 1/8 inches.
13 1/4" to the center of bridge side pu.
f!
13 1/4" to the center of bridge side pu.
f!
That is interesting. In so many other TB threads, it is clearly stated that the P and MM sweet spots overlap. This diagram makes it appear that you could place them side by side and retain the sweet spots for each pickup. Would be great to get this confirmed as I was planning to take on exactly this project and was planning to reverse the P to accommodate the MM pickup in it's sweet spot location.
Sweet Spots and their relationship to open string nodes is really a bit of a red herring, especially once we start talking about +/-1/4". Every time you fret/stop a string, the nodes move in relation to the stopped position - for any given pickup position there will be notes that have nodes over the poles, meaning that harmonic will be weak. Different placement will make this happen for different notes, but it is unavoidable. Likewise, the pickup will effectively move in and out of the various 'sweet spots' as you play up and down the fingerboard. It is probably sufficient to accept that anywhere between 2" and 5" from the bridge gives a reasonable compromise.
If you want to have quantitative tools to get a sense of the frequency response of a particular pickup location or combination of pickups (per string as string tuning is a defining value as well) you can visit the guitar articles section of this page:
Don Tillman -- Articles
Reading the two pickup articles first will help the response demo tool make more sense. It ends up being a bit more comprehensible than you might think prior to studying the math.
Otto
@SteveCS is absolutely right. The fact that we play on fretted instruments, most of the time using the frets, means that attempts to calculate the optimum placement for pickups would only theoretically render a benefit a small portion of the time. And without doing the same kind of calculations to determine the adverse effects of "incorrect" pickup placement, and applying ALL of those calculations to both open strings and fretted positions, there is literally no way of knowing what the "best" pickup location is going to be -- or even if there is a "best" pickup location. I don't believe there is, at least not one that is driven by harmonic nodes.
I just read Tillman material you linked. Everything he wrote was based on open strings. The closest thing to accounting for fretted notes was to superimpose a red bar representing the frequency range of an instrument fretboard over his comb filter diagrams -- but those diagrams were based on open string frequencies.
I just read Tillman material you linked. Everything he wrote was based on open strings. The closest thing to accounting for fretted notes was to superimpose a red bar representing the frequency range of an instrument fretboard over his comb filter diagrams -- but those diagrams were based on open string frequencies.
Actually, the Tillman calculations are for a fretless bass. His continuous frequency scale is conceptually produced by sliding your finger down a string towards the bridge. You can't get the intermediate frequencies on a fretted bass but the frequencies corresponding to the locations of the frets will have the response as shown in his graphs. The situation is exceedingly complex. You cannot solve his equations for X where X is the perfect spot to put your pickup. The response of a Precision bass or a Musicman bass with their iconic pickups in their respective "sweet spots" is not something that you can calculate and get numerical results that can be shown to be "ideal" according to some criteria. Even though the situation is too complex to describe by a single number or a short sentence, people claim to be able to listen to recordings and tell that a Musicman or Precision was used to make the recording. Some of that ability to recognize the bass that was used undoubtedly comes from the response of the pickups themselves but it is possible that people can also recognize the frequency response that results from the pickup placement. It is not a constant thing that is the same from note to note but the way it varies from note to note is consistent from bass to bass of the same design.
Thanks for the insight, I wasn't trying to snub fretless players in making my point the way I made it.
I agree with most of your points, but you said something interesting at the end that I'm not so sure about. You are correct, of course, playing in different places on the neck will result in different pickup responses, and those specific differences will be consistent among basses of the same design. The thing is, we don't really hear it when we're playing. We don't hear the variation, we just hear the tone of the bass. For those who love P's, a P sounds like a P no matter where on the neck one is playing.
And ultimately, that's why I don't find any credibility in arguments for precise pickup placement. It's not just that it's impossible to account for playing on the neck, it's also that IMO it wouldn't make a difference even if it was possible. I don't think 1/4" difference in a P pickup placement would even be noticeable. Certainly, there are a lot of variables in the sound that would make a much more significant impact -- brand and type of strings, brand and design of pickup, etc. Sweet spots are a myth IMO.
Not that there aren't reasons to put pickups in a common location. On my 3-pickup J bass, the bridge pickup is in the standard (non-70's) location. Why? Because it seems as good a place as any, and Warmoth's equipment was already set up to route a pickup hole there, so it didn't cost anything extra.
I agree with most of your points, but you said something interesting at the end that I'm not so sure about. You are correct, of course, playing in different places on the neck will result in different pickup responses, and those specific differences will be consistent among basses of the same design. The thing is, we don't really hear it when we're playing. We don't hear the variation, we just hear the tone of the bass. For those who love P's, a P sounds like a P no matter where on the neck one is playing.
And ultimately, that's why I don't find any credibility in arguments for precise pickup placement. It's not just that it's impossible to account for playing on the neck, it's also that IMO it wouldn't make a difference even if it was possible. I don't think 1/4" difference in a P pickup placement would even be noticeable. Certainly, there are a lot of variables in the sound that would make a much more significant impact -- brand and type of strings, brand and design of pickup, etc. Sweet spots are a myth IMO.
Not that there aren't reasons to put pickups in a common location. On my 3-pickup J bass, the bridge pickup is in the standard (non-70's) location. Why? Because it seems as good a place as any, and Warmoth's equipment was already set up to route a pickup hole there, so it didn't cost anything extra.
Hmm. Nice posts. I can't believe that "Sweet spots are a myth." One's gotta put them somewhere and Leo's designs are a suitable beginning point (perhaps not mathematically mappable, but perhaps earhole detectable-- per instrument confinements, etc.)/fnord!
It's just my opinion. I think the "sweet spot" is the result of marketing as much as anything else.
You are correct, pickups have to go somewhere. And Leo's designs are not a bad starting point -- but then which of Leo's pickup placements represent the "sweet spot"? He put different pickups in different places on different basses. One might infer that there are different sweet spots for different pickups, but then any argument for a mathematical sweet spot goes out the window, at least as far as Leo is concerned.
You are correct, pickups have to go somewhere. And Leo's designs are not a bad starting point -- but then which of Leo's pickup placements represent the "sweet spot"? He put different pickups in different places on different basses. One might infer that there are different sweet spots for different pickups, but then any argument for a mathematical sweet spot goes out the window, at least as far as Leo is concerned.
I don't have a strong opinion on whether or not a sweet spot exists in physics but in the real world it does exist in the minds of people I might have to please so I give the notion at least a tip o'the hat. There is some mathematical basis for the belief as Tillman demonstrates and you certainly do get different sounds from pickups in different locations so the math does play out in practice. I for one do hear a difference in tone as I move up and down the neck and I believe that almost everyone does. Clearly either the harmonic nulls or just the balance change from fundamental to harmonics or both come into play as you move up and down the neck. If you are going to buy a bass with a Precision pickup, or have one built, or route one into an existing bass and your goal is to sound as much like a Precision as possible then why risk money on a potential disappointment? Put the pickup EXACTLY where Leo put it!!
It would be fun to build an experimental bass with a big swimming pool route for the pickups so that you swap various ones in and out and move them around willy-nilly, making recordings, and seeing if anyone really could hear the difference, or more exactly how small a difference people really could hear in pickup placement. I hope that I am still about 6 years from retirement and I won't have the time to do this before then and may not have the money to do this after so don't count on me. But I'd love to see the results and listen to the recordings to see what I could and could not hear if someone else wants to take this on.
It would be fun to build an experimental bass with a big swimming pool route for the pickups so that you swap various ones in and out and move them around willy-nilly, making recordings, and seeing if anyone really could hear the difference, or more exactly how small a difference people really could hear in pickup placement. I hope that I am still about 6 years from retirement and I won't have the time to do this before then and may not have the money to do this after so don't count on me. But I'd love to see the results and listen to the recordings to see what I could and could not hear if someone else wants to take this on.
There are some discussion in 'Luthier's Corner' about this subject. This one, for example:
The Science of Pickup Positioning?
It is helpful to remember that we are ultimately interested in the output signal, but also that it is the product of two frequency-dependent functions: the string vibration velocity and the pickup response.
The pickup response alone (for a given vibrating length or corresponding frequency) is as described in Tillman's analysis and is dictated for all notes on a string by the scale length, open tuning and pickup position. However, that basically describes only the low end roll off and the sequence of comb-filter nulls.
The other component is the spectrum of the string vibration, which as noted will change for every note along the fingerboard and also be influenced by how and where the string is plucked.
So, beyond understanding the extent of low end roll off and the tonal influence of the comb filter nulls, the point is well-taken that there really is no magic pickup placement, just differences that will lend different tonal characteristics as the location varies.
Otto
The pickup response alone (for a given vibrating length or corresponding frequency) is as described in Tillman's analysis and is dictated for all notes on a string by the scale length, open tuning and pickup position. However, that basically describes only the low end roll off and the sequence of comb-filter nulls.
The other component is the spectrum of the string vibration, which as noted will change for every note along the fingerboard and also be influenced by how and where the string is plucked.
So, beyond understanding the extent of low end roll off and the tonal influence of the comb filter nulls, the point is well-taken that there really is no magic pickup placement, just differences that will lend different tonal characteristics as the location varies.
Otto
Something that Tillman wrote kinda stuck in the back of my mind since I read it, and it just now popped to the front. He said that one of the assumptions he makes in doing his equations is that a pickup senses the string at only one point.
One of the reasons the mathematical/harmonic reasoning for pickup placement never made sense to me (besides the open string vs. frets thing) is that for a bass with one pickup, the math predicts null spots -- but we never hear them. I'm not one to argue against math or physics, but I do question assumptions. Given that Tillman's analysis is based on the assumption that a pickup senses a string at only one point, I have come to the conclusion that the magnetic aperture on a typical pickup is wide enough to render the math irrelevant.
To put it another way, I have no doubt that the null points exist, but they're effectively masked by the non-null part of string vibrations that occur within the entire length of the string being sensed by the pickup, even if that length is only a fraction of an inch.
One of the reasons the mathematical/harmonic reasoning for pickup placement never made sense to me (besides the open string vs. frets thing) is that for a bass with one pickup, the math predicts null spots -- but we never hear them. I'm not one to argue against math or physics, but I do question assumptions. Given that Tillman's analysis is based on the assumption that a pickup senses a string at only one point, I have come to the conclusion that the magnetic aperture on a typical pickup is wide enough to render the math irrelevant.
To put it another way, I have no doubt that the null points exist, but they're effectively masked by the non-null part of string vibrations that occur within the entire length of the string being sensed by the pickup, even if that length is only a fraction of an inch.
Tillman does two different analyses. One does assume that the pickups sense the string at only one point and as a result the math does predict zero output at certain points. The sensing aperture of a pickup is larger than zero of course so this simplification cannot be precisely true. I don't think the nulls go away however. One reason I say that is that even though the zero motion null exists only at a single point, the amplitude of the motion in the region on both sides of that point is low. A true, zero output, null may not exist due to the non-zero sensing aperture of the pickup but there certainly would be a dip in the output at the place where the null is predicted simply because the average string motion amplitude is small and you should be able to hear that. There is a second reason that would tend to make the dips closer to true nulls. The motion of the string on either side of the null is going to be in opposite directions. So, while part of the string inside the sensing aperture of the pickup is moving closer to the pickup and increasing the total magnetic flux the pickup is sensing the other part of the string that the pickup is sensing is moving away from the pickup and decreasing the total flux the pickup is sensing. It is unlikely that these two effect cancel each other out exactly and produce a true null in spite of the finite sensing aperture but surely the output will be low, even lower than you would expect from the lower average string motion across the pickup aperture if you assumed that it were all in the same direction.
In his second analysis Tillman does consider the sensing aperture of the pickups and this also produces nulls. At any frequency where the wavelength of the string motion allows an integer number of waves to fit exactly across the sensing aperture there will be a null. These nulls occur for exactly the same reason I mentioned in the second reason above: parts of the string inside the aperture are moving towards the pickup and parts are moving away. For frequencies where the sensing aperture is a perfect integer multiple of the wavelength then these two motions will cancel out mathematically. Once again, in the real world they are unlikely to cancel perfectly but there will be output dips at these frequencies.
I think the real reason why these nulls are not as easy to hear as one might predict comes down to the human hearing system. These nulls never affect the fundamental so we always hear the fundamental at roughly the same volume. They can only suck out one or more of the harmonics. But it is well known that the ear/brain can derive the fundamental by "synthesizing" it from the harmonic series that is left if we artificially remove it, the missing fundamental effect. I don't know that it has been studied but I would imagine that in similar fashion the harmonics can be at least partially restored by the ear/brain when a harmonic is removed. In the thread that someone linked to a few messages above one individual claimed to be able to hear the result of moving a pickup by 1/8 inch. That is much more sensitive than I would have expected. Just because he claims he can do this does not mean that he really can in a double blind test that would prove it, but internet skepticism does not prove that he cannot either. Human visual astronomers have detected things that physics "proved" were both impossible to see and impossible to exist and so where ignored and ridiculed by the scientific community until spacecraft imaging proved that they were correct. On the other hand humans have also seen canals on Mars. So until someone does conduct a rigorous study of pickup locations we won't really be able to say what human listeners can and cannot hear or what fraction of them can hear a given effect at a given level.
If you are familiar with how magnetic sensing works you will know that it is rather peculiar that magnetic pickups have a pretty even frequency response (ignoring these nulls) over the range of a stringed instrument. The magnetic induction equation says that for equal motion an equal change in the B field should occur but as the frequency of the motion increases the rate of change increases and therefore the output should increase. In other words, all guitars (bass or otherwise) with magnetic pickups should need an equalization network like those used for magnetic phonograph pickups and automotive ABS electronics if they want to have an even frequency response. But they do not. There is something going on here with how strings vibrate that compensates for this naturally, at least that is the only conclusion I can reach. The physics of the bass guitar is more complex than it appears to be at a glance and so nothing can be taken for granted, everything ends up being somewhat surprising.
In his second analysis Tillman does consider the sensing aperture of the pickups and this also produces nulls. At any frequency where the wavelength of the string motion allows an integer number of waves to fit exactly across the sensing aperture there will be a null. These nulls occur for exactly the same reason I mentioned in the second reason above: parts of the string inside the aperture are moving towards the pickup and parts are moving away. For frequencies where the sensing aperture is a perfect integer multiple of the wavelength then these two motions will cancel out mathematically. Once again, in the real world they are unlikely to cancel perfectly but there will be output dips at these frequencies.
I think the real reason why these nulls are not as easy to hear as one might predict comes down to the human hearing system. These nulls never affect the fundamental so we always hear the fundamental at roughly the same volume. They can only suck out one or more of the harmonics. But it is well known that the ear/brain can derive the fundamental by "synthesizing" it from the harmonic series that is left if we artificially remove it, the missing fundamental effect. I don't know that it has been studied but I would imagine that in similar fashion the harmonics can be at least partially restored by the ear/brain when a harmonic is removed. In the thread that someone linked to a few messages above one individual claimed to be able to hear the result of moving a pickup by 1/8 inch. That is much more sensitive than I would have expected. Just because he claims he can do this does not mean that he really can in a double blind test that would prove it, but internet skepticism does not prove that he cannot either. Human visual astronomers have detected things that physics "proved" were both impossible to see and impossible to exist and so where ignored and ridiculed by the scientific community until spacecraft imaging proved that they were correct. On the other hand humans have also seen canals on Mars. So until someone does conduct a rigorous study of pickup locations we won't really be able to say what human listeners can and cannot hear or what fraction of them can hear a given effect at a given level.
If you are familiar with how magnetic sensing works you will know that it is rather peculiar that magnetic pickups have a pretty even frequency response (ignoring these nulls) over the range of a stringed instrument. The magnetic induction equation says that for equal motion an equal change in the B field should occur but as the frequency of the motion increases the rate of change increases and therefore the output should increase. In other words, all guitars (bass or otherwise) with magnetic pickups should need an equalization network like those used for magnetic phonograph pickups and automotive ABS electronics if they want to have an even frequency response. But they do not. There is something going on here with how strings vibrate that compensates for this naturally, at least that is the only conclusion I can reach. The physics of the bass guitar is more complex than it appears to be at a glance and so nothing can be taken for granted, everything ends up being somewhat surprising.
You can see from the avatar that my Wishbass has a J style pickup just over an inch from the bridge. Obviously, this gives a lot of low end roll off.
It was rather vexing when I got it, because it had a single coil J. Lack of bass, low output and hum were not a good combination! I've since swapped in a humbucking J and added stacked tone controls (both standard tone and Q-filter midrange cut). So, now I get essentially no hum and can shape the tone with the onboard controls plus about 12 dB of shelving from 400 to 100 Hz with a graphic eq to strengthen the low end.
The other aspect of the close bridge location is that the first null is much higher than usual, leaving very smooth frequency response throughout the low end and midrange. Having dealt with the hum and other issues, it really has become a delightful sounding instrument.
Otto
It was rather vexing when I got it, because it had a single coil J. Lack of bass, low output and hum were not a good combination! I've since swapped in a humbucking J and added stacked tone controls (both standard tone and Q-filter midrange cut). So, now I get essentially no hum and can shape the tone with the onboard controls plus about 12 dB of shelving from 400 to 100 Hz with a graphic eq to strengthen the low end.
The other aspect of the close bridge location is that the first null is much higher than usual, leaving very smooth frequency response throughout the low end and midrange. Having dealt with the hum and other issues, it really has become a delightful sounding instrument.
Otto
This is certainly true. Pickups with the same form factor have resonance peaks and frequency responses that can vary widely from manufacturer to manufacturer and from model to model. And I agree with you, trying to get an even frequency response from a pickup would require far more trouble than it's worth. (It makes me wonder, if it were possible and cost effective to do, would the result be that all such pickups sound the same? How boring would that be?) I just think that trying to find a precise sweet spot based on math and physics, all things considered, is as futile as trying to even out the freq response of a pickup -- far more trouble than it's really worth.
I believe that if any of it matters at all, then all of it matters a little. Everything from body/neck/fingerboard woods, to hardware, to pickup design and placement, it all matters. How it matters and how much it matters? Probably as many different opinions as bass players. Ultimately, the sound is determined by the physics of the interactions of all those things, but there's only so much we can calculate or measure. To our ears, there will alway be an element of magic/voodoo/mojo -- and that's a good thing.
As noted, the differential nature of the magnetic sensing of pickups produces a 6dB/octave increase in response.
You can see that on the low end of the response in Tillman's graphs.
However there is a compensating increase in magnitude of sensed string vibration (except for the nodes) at lower frequencies as the pickup moves farther from the bridge.
Those two factors cancel over much of the frequency range of interest for standard pickup positions.
Otto
You can see that on the low end of the response in Tillman's graphs.
However there is a compensating increase in magnitude of sensed string vibration (except for the nodes) at lower frequencies as the pickup moves farther from the bridge.
Those two factors cancel over much of the frequency range of interest for standard pickup positions.
Otto
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