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Post by antigua on Jan 2, 2017 13:55:12 GMT -5
I came across another technical guitar resource "THE SCIENCE OF ELECTRIC GUITARS AND GUITAR ELECTRONICS " by Jarmo Lähdevaara guitarscience.net/papers/guibook.pdf , this one is a few hundred pages of decent information, and a ton of math. It's not comprehensive despite the high page count, some concepts are only lightly covered, but I have yet to see a technical guitar resource that covers everything thoroughly. One interesting portion that is briefly mentioned on the 189th page of the PDF, or page 177 according to the content: The assertion is that, for the same same reason that plucking the string with a needle produce more harmonics than a soft finger tip, a very thin pickup will see a more harmonics than a wide pickup. Unfortunately it's just left at that. There doesn't appear to be an explanation as to how or why the pickup "creates the same effect on its behalf". My questions are: 1) is it true that a thin pickup will see a higher ratio of harmonics to fundamental? 2) if so, what would be the highest frequency perceivable my a Strat pickup, casting a near uniform magnetic field upwards from a 0.186" diameter magnet? My thinking is that a thin pickup would sense more high frequency harmonics, because it's all about magnetic delta, and if you have a wide pickup with wide magnetic and coils, then those tinier harmonic movements will increasing "blur" into one another, where as a narrow aperture will retain a clear perspective on the magnetic delta of the fundamental and harmonic string movement alike. If my thinking is true, though, I don't think that would be too closely related to the reason why a needle plectrum produces more harmonics than a finger tip. Thoughts?
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Post by JohnH on Jan 2, 2017 14:20:28 GMT -5
Donald Tillman went into this, in his studies on pickup placement and width: www.till.com/articles/PickupResponse/index.htmlFollowing some maths, his conclusion is that for each string there is a comb-filter effect due to where the pickup is along the string, and a high frequency roll-off determined by its equivalent 'sensing width'. In that piece, there is a graph showing a -6db per octave rolloff for a low E string with a -3db point at 1820hz. That's based on his belief that a single coil has a sensing width of about 1". I have the theory from that paper in the current GuitarFreak, and it comes into play if the 'full response' or 'envelope' options are engaged. But I suspect his 'sensing widths' are a bit wide and I use less, though it is a variable that can be changed for each pickup.
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Post by wgen on Jan 2, 2017 17:07:30 GMT -5
I really don't want to muddy up things, but also some other considerations closely related to these are those regarding string tension. I don't know if this had been covered before, and I haven't any serious information to provide, but somewhere in the Talkbass forum I found the speculation that more tension might equal more harmonics produced because of the firmer string movement, while lower tension = more fundamentals, because of the greater string movement. But, there is also who points out to strings flexibility, not just tension. More flexibility would equal more highs overall, for these people. This could be another matter of discussion, especially as far as string gauges/material are concerned (ie flatwound strings have usually, not always, more tension than roundwounds, but flats are also much less flexible than roundwounds, and so on...) I don't really know if there is any hint of authenticity in these informations. Edit: I found one of those threads where these kind of informations were discussed. I'm linking it here just as a reference of what I was wondering myself, I know that here there are just some opinions from players, but still, I was asking myself if someone knows some more, some real facts at the base of this subject. www.talkbass.com/threads/harmonics-a-function-of-gauge-tension-or-string-type.1096815/Also, two doubts come to mind..: 1) What if more tension goes hand in hand with less flexibility, in a string? ie in many cases, flats have more tension than roundwounds, but their tone almost always seems to produce less harmonics than those, not more. Now, this would disprove the speculations at the beginning of this post. Could this be because flats are also much less flexible than rounds, perhaps...? 2) more harmonics = brighter treble? ...This is what really bugs me, because I was wondering if, more harmonics equal more definition and highs than just fundamentals alone, yes, but couldn't it be that harmonics are especially located in the higher mids area, let's say, from 1 Khz onwards, and not particularly in that glassy treble presence around 4 Khz, which is located at the far limits of guitar speakers frequency response, instead...? In this case more harmonics wouldn't necessarily translate into brighter treble, I guess.....Hope that was clear enough.
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Post by antigua on Jan 2, 2017 22:39:18 GMT -5
The PDF I linked to has a section on the effect of string stiffness. I don't think it says whether the proportion of fundamental to harmonics is more or less with respect to stiffness. Manfred Zollner's Physics of Electric Guitar echoes the same points, and neither talk about more or less harmonics with respect to tension, but say that more tension equals more deflection with higher frequencies, because the speed at which they propagate along the string increases with tension. I think the bigger cause of associating higher harmonic content with higher tension owes to differences in how you pluck a tight string versus a loose one. The way a string is plucked as a huge impact on the harmonic content that results.
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Post by antigua on Jan 3, 2017 3:05:05 GMT -5
Donald Tillman went into this, in his studies on pickup placement and width: www.till.com/articles/PickupResponse/index.htmlFollowing some maths, his conclusion is that for each string there is a comb-filter effect due to where the pickup is along the string, and a high frequency roll-off determined by its equivalent 'sensing width'. In that piece, there is a graph showing a -6db per octave rolloff for a low E string with a -3db point at 1820hz. That's based on his belief that a single coil has a sensing width of about 1". I have the theory from that paper in the current GuitarFreak, and it comes into play if the 'full response' or 'envelope' options are engaged. But I suspect his 'sensing widths' are a bit wide and I use less, though it is a variable that can be changed for each pickup. It appears that he does conclude that a narrower pickup does detect a higher amplitude of harmonic content, though the response is not as flat looking: This part concerns me a bit, though: "The effect of the pickup aperture on the response can be calculated by averaging the point response over the aperture length. This isn't completely accurate, the pickup sensitivity will be greater in the middle than at the ends, but this makes a fine first approximation."So, my math is not strong, but it sounds like he's assuming 100% amplitude within that full 1 inch width. If you take a strat pickup and hook it up to an amp by itself, then hold the pickup over a vibrating string, you can intuit the voltage output in relation to offset distance from the string. Two things about the reality of it that don't fit well with assuming a homogeneous sensor, 1) though it's true that there is audible sound within a one inch diameter, the output is much louder directly over the magnets. It sounds logarithmic, with a soft maximum, or a dulled point, directly above the magnet. 2) you will notice that the tone also changes with offset distance as well. The fundamental sounds more prominent the closer you get to the magnet. Of course, these things are to be expected, since the permanent magnetic field is not homogeneous, you can't expect a homogeneous result, but it looks to me like this is what Tillman does. In the PDF I linked to, Jarmo Lähdevaara did similar calculations, but assumed that the pickup was an "infinitesimal point", and I think that would actually be a better representation of a magnetic field than an averaged span, though it doesn't answer the original question. Incidentally, when I had the Strat pickup free, I tried holding it side ways to make a very wide pickup, but I couldn't really tell if the harmonic balance changed as a result. I don't read much into that, but it's worth nothing that having the full width of the pickup over one string didn't result in an extreme, except that it was especially loud.
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Post by stratotarts on Jan 3, 2017 6:55:12 GMT -5
Those calculations assume an open string. Play the chromatic scale ascending on a string. Does each note sound "different"? I think not very much. Yet according to this theory, completely different harmonic nodes are present over the fixed pickup. There is an obvious discrepancy between theory and practice here.
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Post by wgen on Jan 3, 2017 8:45:42 GMT -5
The PDF I linked to has a section on the effect of string stiffness. I don't think it says whether the proportion of fundamental to harmonics is more or less with respect to stiffness. Manfred Zollner's Physics of Electric Guitar echoes the same points, and neither talk about more or less harmonics with respect to tension, but say that more tension equals more deflection with higher frequencies, because the speed at which they propagate along the string increases with tension. I think the bigger cause of associating higher harmonic content with higher tension owes to differences in how you pluck a tight string versus a loose one. The way a string is plucked as a huge impact on the harmonic content that results. +1 on that!
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Post by JohnH on Jan 3, 2017 13:58:19 GMT -5
Those calculations assume an open string. Play the chromatic scale ascending on a string. Does each note sound "different"? I think not very much. Yet according to this theory, completely different harmonic nodes are present over the fixed pickup. There is an obvious discrepancy between theory and practice here. I actually think that the tone does change as you fret higher, and becomes a purer tone with more emphasis on the fundamental. I can think of three reasons: 1. The main reason would be because as the vibrating length gets shorter due to fretting, and the pickup is at a fixed distance from the bridge, it is becoming at a greater % of the vibrating part of the string and so getting relatively more fundamental. 2. The same effect is happening to the picking distance which, if you keep picking in one place, is getting nearer to the centre of the vibrating string as you fret higher. 3. There's possibly a third effect too due to bending stiffness of the strings which rends to limit the highest frequencies since the string resists bending so tightly. These frequencies represent a lower order of harmonics being curtailed if you fret higher.
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Post by ms on Jan 3, 2017 14:05:15 GMT -5
Those calculations assume an open string. Play the chromatic scale ascending on a string. Does each note sound "different"? I think not very much. Yet according to this theory, completely different harmonic nodes are present over the fixed pickup. There is an obvious discrepancy between theory and practice here. The relative level of harmonics is "filtered" by the pickup location and sampling width (or widths, in the case of a hum bucker pickup , which has two). The sound of the string does shift gradually as you run up the scale because the effective pickup location changes. But other things change, too, such as the ratio of length to stiffness. But there is no doubt that the difference in sound between the bridge and neck pickups changes as you fret higher, especially at the highest frets, because the changes in effective pickup location are different.
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Post by antigua on Jan 3, 2017 14:19:32 GMT -5
Suppose you have a Seymour Duncan Quarter Pound at one extreme, and at the other you have a Strat pickup with little tiny Neodymium pole pieces. All other things being equal, will there be a difference in harmonic content between the two pickups?
One reason this is an important(ish) question is because you have pickups like the Quarter Pound, and it's worth knowing exactly what their value proposition is, and you also have Strat pickups with various degrees of bevel around the pole pieces. I just got some pickups from China that feature a dramatic bevel, while some Strat pickups have none at all. What would happen if the AlNiCo pole piece was sharpened to a pencil point?
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Post by ms on Jan 3, 2017 14:59:57 GMT -5
Suppose you have a Seymour Duncan Quarter Pound at one extreme, and at the other you have a Strat pickup with little tiny Neodymium pole pieces. All other things being equal, will there be a difference in harmonic content between the two pickups? One reason this is an important(ish) question is because you have pickups like the Quarter Pound, and it's worth knowing exactly what their value proposition is, and you also have Strat pickups with various degrees of bevel around the pole pieces. I just got some pickups from China that feature a dramatic bevel, while some Strat pickups have none at all. What would happen if the AlNiCo pole piece was sharpened to a pencil point? The tests that I have done show that having two sampling regions with humbucker coil spacing, has a significant filtering effect on the wound strings, less noticeable on the plain strings. These higher harmonics are what one might call picking transients since they die out very quickly. You can both measure and hear the harmonic differences resulting from activating the second coil with the wound strings, most effect on the E. I doubt that the different narrower sampling widths that you mention when using different single coil pickups matter, but I have not done that test.
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Post by antigua on Jan 3, 2017 15:25:50 GMT -5
I suppose Tillman's math applies here, even if I believe that the effective width of a single coil is closer to 1/5th of a inch rather than one whole inch. The essence of it is that within the widow of the pickup, there is one complete cycle of vibration, so the magnetic delta of that harmonic is cancelling itself out. With a wider pickup window, it will see complete cancelling cycles of lower frequencies, where as a narrow window will not see this cancellation until a higher frequency is reached. It might be that the frequencies that are gained by a thinner pole piece, which would have to be physically very narrow, might be well beyond what the frequency range of the pickup's coil, let alone the amp and speaker. I think it's that high, you won't even hear it as a transient.
It would be a luxury to be able to say with certainty though, that at a certain point, pole piece width makes no audible difference, as far as movement parallel to the axis is concerned. It might come in useful when thinking about pickup design.
On the other hand, it is known that a narrower pole pieces will cause greater even harmonics, due to a greater magnetic displacement on the part of the strings "side to side" movement. Where as a "blade" pickup has no such magnetic delta, a sharp pole piece would be the opposite, and have the greatest delta. "They" say the amplitude of those even harmonics are very low, though, so I'm still not clear as to whether they make a distinct audible contribution. I have some Barden's in a Tele, and a lack of even harmonics is not apparent to my ears, though it might be coloring the tone in a way that I don't realize.
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Post by stratotarts on Jan 3, 2017 20:56:19 GMT -5
Those calculations assume an open string. Play the chromatic scale ascending on a string. Does each note sound "different"? I think not very much. Yet according to this theory, completely different harmonic nodes are present over the fixed pickup. There is an obvious discrepancy between theory and practice here. I actually think that the tone does change as you fret higher, and becomes a purer tone with more emphasis on the fundamental. I can think of three reasons: 1. The main reason would be because as the vibrating length gets shorter due to fretting, and the pickup is at a fixed distance from the bridge, it is becoming at a greater % of the vibrating part of the string and so getting relatively more fundamental. 2. The same effect is happening to the picking distance which, if you keep picking in one place, is getting nearer to the centre of the vibrating string as you fret higher. 3. There's possibly a third effect too due to bending stiffness of the strings which rends to limit the highest frequencies since the string resists bending so tightly. These frequencies represent a lower order of harmonics being curtailed if you fret higher. Actually, I got entangled in my point. I realize that the tone changes as you go up. What I meant is that it seems to do it fairly proportionally, without huge peaks and valleys. I'm wondering why those aren't clearly audible if the harmonic nodes are positioned over the pickup aperture. The audible effect is a smooth, linear change of tone in proportion to the increase in fret. As a rough analogy, the human vocal tract modulates the harmonics in different ways which sound like vowel expressions. That is what I'd expect to hear from filtering different harmonics. Kind of like a vocorder. On a related note, one would expect the effect to be stronger with a single pickup because the nodes overlap and "fill each other in". But I've never noticed any difference like that between single and both pickups engaged.
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Post by antigua on Jan 3, 2017 23:05:02 GMT -5
Are you asking why, for example, the middle pickup of a Strat doesn't sound like the neck pickup when you play the high frets, since at that point it will be at the quarter mark of the string, as if you had a half sized Strat playing an open note? I've wondered that myself, and my best guess is that if you had a half-sized Strat, the neck pickup would sound like a middle pickup. I think the "voicing" associated with the pickup position is retained up the fret board by counteracting forces; the harmonic makeup is changing, but the overall pitch is simultaneously increasing.
One way to test this might be to detune the strings and see if the middle pickup sounds more like a neck pickup in turn.
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Post by reTrEaD on Jan 3, 2017 23:49:11 GMT -5
I realize that the tone changes as you go up. What I meant is that it seems to do it fairly proportionally, without huge peaks and valleys. I'm wondering why those aren't clearly audible if the harmonic nodes are positioned over the pickup aperture. While you can find positions on the string relative to the endpoint that are a node for more than one harmonic, you will not find one that is a node for ALL harmonics. The exact midpoint is a truly interesting case. While it's true that it's a node for all EVEN harmonics, it's also an antinode for all ODD harmonics.
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Post by JohnH on Jan 4, 2017 0:09:53 GMT -5
I think what happens is that the fundamental dominates and doesn't have a null point, and the 2nd harmonic usually doesn't either. The others get more or less filtered by the comb effect, but usually are not fully nulled, and they all roll around under a steady declining gradient with frequency and the ear/brain tends to merge them together as a general impression of tonality. I think you can hear particular harmonics in a very clean controlled audio test, but generally not so much in musical practice.
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Post by wgen on Jan 4, 2017 8:40:41 GMT -5
Please excuse me for the real dumb question, but...Should a humbucker be considered a large sensing pickup or a narrow type one, maybe because of the two bobbins which are both sensing fundamentals and harmonics? Generally speaking, how should the sensing part of pickups be considered when you have more than just one "sensing unit" involved, each other wired in series or in parallel...? Hope that was clear.... For example, if I have a Jazz Bass with two single coils typically wired in parallel both on, should I consider the sensing of the vibrating string from the perspective of a wider sensing area or a narrower one, if compared with a split single Precision Bass pickup alone? I hope that this makes sense, I admit that I might have distorted everything on this subject...Please excuse me in that case.
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Post by ms on Jan 4, 2017 11:30:51 GMT -5
I actually think that the tone does change as you fret higher, and becomes a purer tone with more emphasis on the fundamental. I can think of three reasons: 1. The main reason would be because as the vibrating length gets shorter due to fretting, and the pickup is at a fixed distance from the bridge, it is becoming at a greater % of the vibrating part of the string and so getting relatively more fundamental. 2. The same effect is happening to the picking distance which, if you keep picking in one place, is getting nearer to the centre of the vibrating string as you fret higher. 3. There's possibly a third effect too due to bending stiffness of the strings which rends to limit the highest frequencies since the string resists bending so tightly. These frequencies represent a lower order of harmonics being curtailed if you fret higher. Actually, I got entangled in my point. I realize that the tone changes as you go up. What I meant is that it seems to do it fairly proportionally, without huge peaks and valleys. I'm wondering why those aren't clearly audible if the harmonic nodes are positioned over the pickup aperture. The audible effect is a smooth, linear change of tone in proportion to the increase in fret. As a rough analogy, the human vocal tract modulates the harmonics in different ways which sound like vowel expressions. That is what I'd expect to hear from filtering different harmonics. Kind of like a vocorder. On a related note, one would expect the effect to be stronger with a single pickup because the nodes overlap and "fill each other in". But I've never noticed any difference like that between single and both pickups engaged. I think the sound of neck and bridge pickups together is mostly explained by a significant reduction in certain harmonics that have opposite polarity over the two pickups and are not too different in amplitude.
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Post by antigua on Jan 4, 2017 12:55:40 GMT -5
Please excuse me for the real dumb question, but...Should a humbucker be considered a large sensing pickup or a narrow type one, maybe because of the two bobbins which are both sensing fundamentals and harmonics? Generally speaking, how should the sensing part of pickups be considered when you have more than just one "sensing unit" involved, each other wired in series or in parallel...? Hope that was clear.... For example, if I have a Jazz Bass with two single coils typically wired in parallel both on, should I consider the sensing of the vibrating string from the perspective of a wider sensing area or a narrower one, if compared with a split single Precision Bass pickup alone? I hope that this makes sense, I admit that I might have distorted everything on this subject...Please excuse me in that case. The pickups only see what is directly above them, and in the case of the Jazz Bass the coils are a few inches apart. Parallel more has a distinct sound for two different reasons, one is the resonant peak goes up quite a lot, the other is comb filtering, where one pickup sees the positive change in a give frequency while the other pickup sees a negative change, and the amplitude of the two are close enough that it audibly cancels, even if it doesn't perfectly cancel. The case of a humbucker, where the two coils are side by side is more convoluted, because you still have that two coil comb filtering, but it's only effecting very high pitched frequencies since the separation width is so narrow. At the same time, the intensity of "change" is a magnitude higher directly over the slugs and screws, so getting back to the Tillman assertion, I don't think you can assume that a humbucker sees a homogeneous 2.5" area of string, and then integrate all of the perpendicular string movement within that area. Again, my math is not strong, but it appeared to me that this mathematical modelling correctly accounted for the amplitude based on how the guitar string intersects the magnetic field of a guitar pickup www.physics.princeton.edu/~mcdonald/examples/guitar.pdf Maybe someone who's great at math could combine the two models together to create one super model.
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Post by wgen on Jan 5, 2017 5:27:01 GMT -5
Thank you again, I think I reached that now. For what is worth, the split Precision style ceramic pickup I have in my Yamaha BB bass has the most bassy and full tone (and also "muddy", I should say) I've ever heard from a Precision type of pickup, both alnico or "steel-over-ceramic magnet" types. And its geometry is noticeably wider than any Precision bass replacement by a good amount, so I think that the Tillman theory you pointed out before is evident here. Now, what I find MUCH interesting in all of this, is that frequency response from your instrument is influenced not just because of the inherent frequency response of the pickups alone when they are loaded, but also because of how the pickups "read" the harmonics. From the Figure 10 and 11 here above, it seems to me that we are not talking about slight differences here. If I understood correctly, if, for example, I had a Strat and I were in the classical situation where I wanted that growly PAF tone at the bridge, but without going for a HSS pickguard, this thread should suggest that I definitely wouldn't find that exact tone if I only chose a single coil bridge pickup with the same resonant peak of that humbucker. It wouldn't be the same thing as installing a real PAF there, I mean, because of the different harmonics sensing. Now, I don't know how that angled bridge single coil translates as far as harmonics sensing, but I guess that's still different from a full size humbucker, because of the lack of comb filtering and narrow geometry of the single coil, isn't it?
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Post by stratotarts on Jan 5, 2017 6:12:57 GMT -5
I think it's a case where Occam's Razor applies... a typical humbucker has a notably lower Q and loaded resonant frequency than a typical single coil. It's amply sufficient to explain the difference. It's also easy to demonstrate, unlike the aperture phenomenon which is a perfectly plausible theory with almost no experimental validation. What we need to know, is the magnitude of the effect. There are too many physical variables feeding into it to trust math alone.
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Post by ms on Jan 5, 2017 6:23:54 GMT -5
I think it's a case where Occam's Razor applies... a typical humbucker has a notably lower Q and loaded resonant frequency than a typical single coil. It's amply sufficient to explain the difference. It's also easy to demonstrate, unlike the aperture phenomenon which is a perfectly plausible theory with almost no experimental validation. What we need to know, is the magnitude of the effect. There are too many physical variables feeding into it to trust math alone. Of course most of the difference is the result of different frequency response in the pickup circuit. But the effects of the two regions of sampling in a humbucker are both measurable and audible in a consistent way. After all, bridge and neck pickups do sound grossly different because they sample the string in different locations and thus have different ratios of harmonics. Considering closer spacing is just an extension of this to more subtle effects.
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Post by stratotarts on Jan 5, 2017 11:02:42 GMT -5
I think it's a case where Occam's Razor applies... a typical humbucker has a notably lower Q and loaded resonant frequency than a typical single coil. It's amply sufficient to explain the difference. It's also easy to demonstrate, unlike the aperture phenomenon which is a perfectly plausible theory with almost no experimental validation. What we need to know, is the magnitude of the effect. There are too many physical variables feeding into it to trust math alone. Of course most of the difference is the result of different frequency response in the pickup circuit. But the effects of the two regions of sampling in a humbucker are both measurable and audible in a consistent way. After all, bridge and neck pickups do sound grossly different because they sample the string in different locations and thus have different ratios of harmonics. Considering closer spacing is just an extension of this to more subtle effects. Yes, but subtlety can extend to imperceptibility. I've taken an unmounted pickup and held it over the strings, moved it up and down the strings. I think if you try this, you will not be able to detect a difference of one inch.
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Post by wgen on Jan 5, 2017 11:21:05 GMT -5
Thank you! So, you are basically saying that from your experience something has to be missing with that Tillman theory...? I don't know, but if I look at Figure 10 and 11 in the page one of this thread, I think I can see a lot of difference in dBs for the harmonics from around 1 Khz and above...also, the wider sensing area has some more evident notches that the narrower one doesn't seem to have....Am I reading those two figures wrong? Maybe, the approximation of a 100% homogeneous sampling region, which Antigua said before, has an importance in this context...?
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Post by ms on Jan 5, 2017 12:40:08 GMT -5
Of course most of the difference is the result of different frequency response in the pickup circuit. But the effects of the two regions of sampling in a humbucker are both measurable and audible in a consistent way. After all, bridge and neck pickups do sound grossly different because they sample the string in different locations and thus have different ratios of harmonics. Considering closer spacing is just an extension of this to more subtle effects. Yes, but subtlety can extend to imperceptibility. I've taken an unmounted pickup and held it over the strings, moved it up and down the strings. I think if you try this, you will not be able to detect a difference of one inch. But that is the wrong test. What matters is what happens when you have two sampling windows both present at the same time with the responses adding. Then you have a kind of funny low pass filter that takes out some of the picking transients. You can hear this on the low E because the string makes these harmonics and they lie within the bandpass of the system. You cannot hear it on the high E because those harmonics lie outside the bandpass of the system (primarily the guitar speaker, which falls like a ton of bricks near 5 KHz), and the sting has fewer of the harmonics to start with.
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Post by antigua on Jan 5, 2017 13:20:16 GMT -5
Thank you again, I think I reached that now. For what is worth, the split Precision style ceramic pickup I have in my Yamaha BB bass has the most bassy and full tone (and also "muddy", I should say) I've ever heard from a Precision type of pickup, both alnico or "steel-over-ceramic magnet" types. And its geometry is noticeably wider than any Precision bass replacement by a good amount, so I think that the Tillman theory you pointed out before is evident here. Now, what I find MUCH interesting in all of this, is that frequency response from your instrument is influenced not just because of the inherent frequency response of the pickups alone when they are loaded, but also because of how the pickups "read" the harmonics. From the Figure 10 and 11 here above, it seems to me that we are not talking about slight differences here. If I understood correctly, if, for example, I had a Strat and I were in the classical situation where I wanted that growly PAF tone at the bridge, but without going for a HSS pickguard, this thread should suggest that I definitely wouldn't find that exact tone if I only chose a single coil bridge pickup with the same resonant peak of that humbucker. It wouldn't be the same thing as installing a real PAF there, I mean, because of the different harmonics sensing. Now, I don't know how that angled bridge single coil translates as far as harmonics sensing, but I guess that's still different from a full size humbucker, because of the lack of comb filtering and narrow geometry of the single coil, isn't it? There is an order of precedence with the filters that are at play; the RLC low pass resonant filtering of the pickup takes priority over any of that comb filtering. So if the loaded peak of your pickup is 4kHz, you can just cover up fig 10 and 11 beyond the 4kHz mark with your hand, because you're not going to hear anything into that range. As far as the width of your pickup and it sounding full and muddy, I'd definitely attribute that to resonance filtering, not comb filtering. When it comes to aperture with, any width can produce a very bright sound. On one extreme you have a split rail pickup, very thin aperture, very bright. On the other extreme you have "wide" Filter'tron featuring a high resonant peak, which is also very bright. Looking at figure 10 and 11, it's pretty clear that the wider aperture places more emphasis on bass frequencies below 1kHz, and has a flatter response with a steeper slope beyond 1kHz, which does jive with the perception that humbuckers put out more low end. I deleted a part of this comment regarding what happens beyond 5kHz, then I realized that most of that has little chance of being heard. The graphs depict the low E, so as you go into higher notes, those things just shift further out of audible range, but even below 5kHz, it's still clear to see that narrow apertures see more treble.
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Post by antigua on Jan 5, 2017 13:29:40 GMT -5
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Post by wgen on Jan 5, 2017 14:18:50 GMT -5
Thanks again, very helpful! Yes, I guess that before any conclusion I have to consider the resonant peak of my pickups first, where it is in the spectrum and the Q of the peak. Only then, I can consider the harmonics really involved...If the pickup considered has a peak around 2 Khz, and considered that the frequencies above are significantly cut off, for example, this would make any consideration about harmonics pretty pointless because, then, there would be just a minor difference in the harmonics sampled between different widths.
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Post by antigua on Jan 5, 2017 14:25:45 GMT -5
Yeah the comb filtering with respect to width looks to be flat up to about 1kHz for humbuckers and 2kHz for single coil widths, for the low E string, and then Tillman says "effect of pickup width scales with the pitch of the open string", so I'd guess that both quickly exceed 2kHz further up the fret board. I think the GuitarFreak dynamic spread sheet that JohnH made might incorporate this math guitarnuts2.proboards.com/thread/3627/guitarfreak-guitar-frequency-response-calculator , but I don't have spread sheet software installed at the moment.
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Post by JohnH on Jan 5, 2017 15:37:19 GMT -5
Yeah the comb filtering with respect to width looks to be flat up to about 1kHz for humbuckers and 2kHz for single coil widths, for the low E string, and then Tillman says "effect of pickup width scales with the pitch of the open string", so I'd guess that both quickly exceed 2kHz further up the fret board. I think the GuitarFreak dynamic spread sheet that JohnH made might incorporate this math guitarnuts2.proboards.com/thread/3627/guitarfreak-guitar-frequency-response-calculator , but I don't have spread sheet software installed at the moment. Yes indeed, and here is a "'fer instance": These graphs represent a Fat50 single coil in the bridge position of a Strat, plucking the open 2nd string at a distance of 110mm from the bridge. The theories represented are: - Electrical response based on a 6-part model derived from tests here (loaded case with approx. 10' cable and 200k load)
- Harmonic amplitudes of string vibration based on Jungmann
- Comb filtering due to pickup position based on Tillman
- Roll off of high harmonics due to pickup sensing width based on Tillman
The grey line is the pure electrical response, and is also incorporated in the other graphs The thick blue is an envelope under which the string harmonics lie, based on a 15mm sensing width (which is my guess of an appropriate value for a single coil, Tillman suggests 1" = 25mm) The pale blue line is also with 15mm width, but plotting just the individual harmonics, starting with the fundamental at 247hz, then 2x, 3x etc The red line is the same, with a 1mm sensing width, so demonstrating the effect on higher frequencies The green line is with 50mm width (ie, imagine a humbucker with the electrical properties of a Fat50) The width effects are really having just a small effect in the upper frequencies. You can also see the roll-off of bass, due to this being a bridge pickup picked at a position towards the bridge. Another effect is the apparent null at the 6th harmonic, which is due to picking position. A move of 15mm to 20mm either way fills this in.
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