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Crusader

The Neck Pickup Sweet Spot

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The Neck Pickup Sweet Spot

Several weeks after I bought my first Les Paul in 1977 I asked the shop owner why they don't make them with 24 frets and he said the neck pickup needs to be where the 24th fret would be to get the best sound. I thought he meant it has to be in that exact location so I was very skeptical. At another shop a few months later I heard a young salesman talking about the same issue and he said it was just distance from the bridge

I decided the only way to find the truth is to do my own experimenting and now I have done what I wanted to do all those years ago. I studied the Harmonic Series and compared pickups in different positions on three different guitars to arrive at my conclusions and I am convinced they are correct

Here are a few websites that cover the topic of the Harmonic Series and some of them touch on what I am talking about but I still haven’t found any that actually give a complete explanation

http://wapedia.mobi/en/Harmonic_series_(music)

http://www.physicsclassroom.com/Class/sound/U11L5b.cfm

http://www.gmarts.org/index.php?go=233

Most of my experimenting was on this guitar which I routered to get a pickup on the second octave where the 24th fret would be (I will call this position A) Before that I could only get it where the 26th fret would be (I will call this position :D

00beforeafter-1.jpg

First I moved a middle pickup in stages to position B which is 42mm and it was only slightly warmer each time. In other words position B just sounded like a warm middle pickup

Then I moved it 10mm further and noticed a significant change in tone as well as a steep increase in warmth. Finally another 7mm at position A the sound had completely changed to a clean rounded tone which seemed to cover the whole fretboard

To me this proves there is a sweet spot but the location does not have to be exact

01GraduallyWarmer.jpg

Next I installed a modified PAF which has adjusting screws on both coils to get a back to back comparison of position A & B

00ModPAF1-1.jpg

Coil A went from the open string to the 19th fret and was especially sweet at the 12th fret

(Above the 19th fret sounded the same as the bridge pickup)

Coil B went from about the 4th fret to the 21st and sounded nicer at the 14th fret

(Above the 21st fret sounded the same as the bridge pickup)

Although Coil B had this rounded tone it was not as nice as Coil A except at the highest frets. This diagram depicts the sound quality of each coil

02RoundedTone.jpg

So these simple tests indicate what I was told 33 years ago is quite true but what is so significant about the second octave? It is also the antinode of the second harmonic of the open string which would have a lot to do with warmth but what about the "clean" sound?

03SecondHantinodeOrange.jpg

When I played a 5th fret harmonic tuning up with Coil A there was no sound from the amp and I thought it had blown a fuse. I have always known the neck pickup is not the best for harmonics and I have heard people talk about cancellation but did not expect this

04CancellationProof.jpg

After studying the Harmonic Series for each fret I found there is always a node on or near the second octave so they would be cancelled or very faint

At the open string the fourth harmonic is cancelled

When you play the 1st fret the fourth harmonic is still virtually cancelled

When you play the 2nd and 3rd frets the fourth and third harmonics are both very faint

At the 4th fret the third harmonic is virtually cancelled

At the 5th fret the third harmonic is fully cancelled

05Cancel12345.jpg

At the 12th fret the second harmonic is cancelled then it goes back to the third then fourth harmonic at the 19th fret

So this means the distance from 19th fret to pickup is quarter of 19th fret to bridge. It has the same relationship to the pickup as the open string

06Cancel121719.jpg

Obviously a pickup in any position will cancel overtones (along with every harmonic above it that has a node at that point) but at the second octave it cancels the lowest-order harmonics possible so you get the most cancellations. If you remove all the overtones you end up with just the Fundamental which is known as a "Pure Tone" http://www.wordiq.com/definition/Pure_tone

I found where you get the best sound (see diagram 2) is also where the most cancellations are but it also depends on which harmonics are cancelled

At the 12th fret every second harmonic is cancelled

A A E A C# E G A B C# D E F# G G# A

This means you never hear the octaves of the fundamental so it is closest to a Pure Tone and sounds the best

At the open string every fourth harmonic is cancelled

A A E A C# E G A B C# D E F# G G# A

At the 5th fret every third harmonic is cancelled

D D A D F# A C D E F# G A B C C# D

You hear every octave of the fundamental so it is less of a Pure Tone and is probably why it does not sound as sweet as the open string or the 12th fret

So to sum it up in a brief explanation

"A pickup at the second octave cancels lower order harmonics leaving the fundamental of most notes on the fretboard as an almost pure tone"

I hope I haven’t gone overboard with this explanation but there are still other factors I have not mentioned

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I'm a little suspect of this theory I have to say...every fretted note will obviously change all the nodes along a string. All the harmonic nodes 'gather' at the ends of strings (so the nut or the fretted note and bridge end of a string).

So, for a natural harmonic you will find it easier to pluck them and they get closer together and have a more complex relationship with the "fundamental" mode of vibration.

So...a bridge pickup is always going to be near the end of the string and be harmonically "rich" regardless of note played. The neck pickup will become more rich the closer the string is stopped to it, so a note on the 22nd fret is going to be effectively very close to the neck pickup and the effective 'end of the string' (the note will so high however that the far higher overtones be heard far less than a lower note). An acoustic guitars string vibration is obviously at the very end of the string and potentially very rich in high order jangly harmonics.

I didn't look at your sources, except in additive synthesis perhaps, I've not hear the lowest node of vibration being termed as anything but the fundamental. It is perhaps a loaded term that implies it is "better" or "pure" and so necessarily desirable.

On one reading, you seem to have missed mentioning the most important thing, which is the "mix' of harmonics...the stuff that makes the more complex "tone" that people are looking towards.

At the neck pickup position, fairly much where ever it is, the 'fundamental' has a wide vibrational arch and so will appear to be the louder in the mix of overtones (exceptions being fretted note in the highest positions as mentioned but then the highest overtones of such frequencies tend to be attenuated by the ear). In fact, the 'fundamental' can swamp the overtones a fair bit and so give any neck pickup a smoother, more 'fundamental' sound.

So...the mix of harmonics is crucial, at the bridge end of course, the arch of the fundamental vibration is less being close to the fixed point and only fixed mode in the system, of the bridge. Therefore, the relative 'mix' of harmonics will be less fundamental and the harmonics more on a par...the whole lot will be less in output, pickups in the bridge are often compensated for this with more power to balance with the neck.

Also, there is not that much mention or an assumption about the sampling 'window' of a pickup. It is broader than you might thing, certainly broader than the physical poles of the device. An HB has a huge window sampling quite a bit of string, but even a single coil tends to sample points well beyond the individual nodes.

One might expect if this were true, that as you fret notes the tone would change radically. You show a series from an A string for instance, a note Bb will move everything up the space of a fret and with it condense the modes and shift them along...do you hear a radical change in tone and harmonic mix?

So...there are some concerns about the ideas and so the conclusions reached.

The 24 fret guitar thing has merit, especially in an HB guitar, the further away from the fixed bridge nodal point and from the bridge pickup position, the greater the difference and the higher the mix of fundamental.

But, as I say...I have quite a few reservations on this. There have been some in depth analysis done scientifically some where I have seen. And, I applaud that method of moving the pickup around to test your theories...the result is most likely that you have found a place where you prefer the neck pickup to be placed more than proven that there is a 'best' place to locate a neck pickup per se....but, happy to be convinced otherwise

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kudos for doing this, although clips would add a hell of a lot of validity to any claims of improved tone.

as you know, i am still very sceptical of this harmonic node stuff in relation to pickup placement. It does seem to me that a lot of effort has gone into trying to prove a guitar shop myth which does not really stand up to closer examination - although this is nicely done

you seem to be saying:

*an exact 24th fret location for the pickup is not that important

*neck pickups sound less like middle pickups the further they are away from the middle pickup

no arguments there!

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this is quite interesting and has been speculated by many along the years. but the one thing i have to ask myself is what about the guitars that don't have the pickup where the 24th fret would be but behind it. my ibanez is 24 frets and the pickups is butted right against it. my brian moore. same scale length but 22 frets has the neck pickup in the same position butted right against the 24th fret or at least where it would be. however this is a very informative bit of info none the less

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Great work and nice of you to share. However a topic like this will probably only end up in one single conclusion. There might be a perfect placement, or a "sweetspot", but it will be very individual. You have done your homework and found the sweetspot that is right for you, but for me that might be (problably is) completely wrong. A sound with strong fundamentals and few overtones might be the ideal thing for one player while the other want a tone full of low order harmonics with less fundamentals (relatively) in the mix. Anyhow you seem to have found your sweetspot.

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This is all very basic stuff you presented. The stuff about harmonics and such is true, but only to an extent. A steel string under tension will exhibit a nonlinear harmonic spectrum as compared to an "ideal" massless string with no internal stiffness or modulus of elasticity. So while it is true to an extent, your strings different frequencies won't be exact multiples of the string length. Thus the idea of compensation. You are never going to get a pure sine wave out of a guitar. In fact, you won't really get all that close, because your picking technique is just as important as your pickup placement for your harmonic spectrum. The origin of initial displacement in your differential equation is going to introduce and in turn dampen all kinds of harmonics.

Again, thanks for the time and effort, as I always love getting into the physics of these things (that's what I spent 6 years studying, so I should). Unfortunately, there are a ton of variables. The short and long is that you found something that works for you and you shared it with us, so thanks again.

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I found where you get the best sound (see diagram 2) is also where the most cancellations are but it also depends on which harmonics are cancelled

At the 12th fret every second harmonic is cancelled

A A E A C# E G A B C# D E F# G G# A

This means you never hear the octaves of the fundamental so it is closest to a Pure Tone and sounds the best

At the open string every fourth harmonic is cancelled

A A E A C# E G A B C# D E F# G G# A

At the 5th fret every third harmonic is cancelled

D D A D F# A C D E F# G A B C C# D

You hear every octave of the fundamental so it is less of a Pure Tone and is probably why it does not sound as sweet as the open string or the 12th fret

So to sum it up in a brief explanation

"A pickup at the second octave cancels lower order harmonics leaving the fundamental of most notes on the fretboard as an almost pure tone"

I hope I haven’t gone overboard with this explanation but there are still other factors I have not mentioned

It looks like you're going about it systematically. I recall in your other thread (a year ago maybe) that people brought up how the nodes shift for every fretted note. It looks like you're taking this into consideration, which makes your theory far more valid in my mind.

Other things to consider... harmonics of open string even when it's fretted, string ringing along its ENTIRE length (behind nut and bridge), equal tempered frets being out of tune with open string harmonic nodes, etc., etc., etc.

I say, dive into the dirty details! :D

I would have to disagree with the other replies--I DO think there's something to this, and I don't think it comes down to "the 2nd octave is a sweet spot and it's all subjective".

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I don't think it comes down to "the 2nd octave is a sweet spot and it's all subjective".

Well, unless there is one general all including "best tone" that everyone agrees on, this is all going to be highly subjective. You can put sciense to it and say "if I put the pickup under the 27'th fret I will get a sound that is 60% fundamental, 10% first harmonic, 30% second harmonic" and so on. But at the end of the day it will be your subjectiv opinion if that placement is good or bad sounding.

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I don't think it comes down to "the 2nd octave is a sweet spot and it's all subjective".

Well, unless there is one general all including "best tone" that everyone agrees on, this is all going to be highly subjective.

I agree... I am more interested in the science behind it than finding a subjective sweet spot. Maybe it's just me, but I find the harmonic series and its relationship to tuning and temperament fascinating.

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Donald Tillman's java applet is a great tool: here.FF

Yes that came up during my research on this and is a good guide towards what I am talking about

Geo thankyou for your positive response. When I posted this up I cut lots out to keep it short so there are lots of factors left to explain, or should I say theories to put forward?

In regard to this being subjective. While I was experimenting I liked Coil B so much I have re-wired my pickups so I have it as a permanent option. It has a funky sound which is good for lots of the music I like to play while Coil A is simply outclassed by the pickup in full humbucking mode for other styles of music

But the issue here is this. Around the second octave node there is a small area where you get a completely different sound to anywhere else between the bridge and the neck. I believe you would have to put the pickup at the 12th fret to improve on this type of sound and to my knowledge it is called "Clarinet Tone"

In regard to the "sampling window" of a pickup I can assure you without a word of a lie that a single coil on the second octave will not produce the 5th fret harmonic. If you want to try this you may have to adjust the bridge saddle because it seems most manufacturers place the pickup slightly off the node. In any case even a Humbucker will be rather faint

...A steel string under tension will exhibit a nonlinear harmonic spectrum as compared to an "ideal" massless string with no internal stiffness...So while it is true to an extent, your strings different frequencies won't be exact multiples of the string length. Thus the idea of compensation

I wasn't going to go into it that deep but seeing as you brought it up. Tell me if I'm wrong

First here's something to try

Play an open string harmonic on the 6th string. You can actually put your finger back on and it will keep sounding out. You will see the nodal area does not vibrate and to me it appears to be about 8mm (As soon as you touch the area where it is vibrating you dampen the string) As you go up the Harmonic Series there are more and more of these nodal points introduced so the section of string that actually vibrates becomes less and the pitch becomes higher. They become slightly out of tune with the Fundamental so wouldn’t canceling them result in a "cleaner" sound?

PLEASE NOTE The numbers I have chosen in this diagram are just to give you the idea. They are not out of a science lab

11TrueHarmonics.jpg

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I'm still trying to get my head around Tillmans app and what I am seeing there, interesting stuff but I'd have to investigate more, perhaps ask some questions regarding this. As Tillman has done much of this work it seems, you didn't think to contact him with your own questions to try and 'disprove' you idea (which along with a methodical approach, is the scientific approach to ensure as objective conclusion)...

Playing with it there seems very little change in the frequency spectrum with moving the neck pickup position or fretting notes...hmmm...which leads me to think that perhaps I am misunderstanding something, or misinterpreting what the applet is showing me.

I notice that in your diagrams recently produced show a nodal point of 8mm...how did you derive at this figure?

I don't recall which coil was "coil B"...I have had splits on my LP you decades and my new guitar and like the "inner coil" but not because it is necessarily "sweet", I just like that sound. More important, and where position matters a lot, is the the combination of coils...this can be demonstrated in Tillmans other applet...and this is where some real 'magic' can be had. I almost always play in the combined pickup combinations to get the kind of sound I generally require. I play very clean as a rule so I need some complexity, I also use a lot of harmonics and require the neck pickup for the "body" and the high end of the bridge pickup for harmonics...but just generally, you get moe flexibility with combining multiple pickups, so this is perhaps where there might be a "sweet' spot, at least to my ears and on a particular guitar.

But, as Till man suggests, there are other factors at least as important...the window size, the resonances of the guitar, the qualities of the pickups...so many variables that effect things and likely more important in total than the asspect that you have been working on for a long time.

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But, as Tillman suggests, there are other factors at least as important...the window size, the resonances of the guitar, the qualities of the pickups...so many variables that effect things and likely more important in total than the aspect that you have been working on for a long time.

I agree. A different pickup might yield different results. Some pickups have all kinds of harmonics, and others don't.

And another thing to consider is the neck material and the neck profile. Those things also affect the resonance of a guitar.

And the bridge. And a bunch of other things... :D

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Of course there are many factors which affect the final sound but I am specifically talking about how it is affected by the position of the pickup. Take any guitar regardless if it's bright or warm and you will only get this "type" of sound with a pickup in the area I am talking about. Now that I have the neck pickup of the white guitar on the second octave it has the same sound character as the Les Paul although it is a lot brighter due to the timber, especially the maple neck

I also found Tillmans demonstration applet a bit confusing at first. I don't think its totally accurate and I'm sure he points that out. For example He says that it shows sub-harmonics even though guitar strings are not capable of supporting them. On his other page he says something about the fourth harmonic being cancelled by the neck pickup

http://www.till.com/articles/PickupResponse/index.html

And this website says the same thing with a diagram similar to this one

http://www.gmarts.org/index.php?go=233

Harmonic4alone.jpg

(Quoting the webpage)

"Now consider the 4th harmonic which has nodes at the 5th fret, the 12th fret and the neck pickup - there is no 4th harmonic vibration over the neck pickup. This strong difference in harmonic levels plays a major part in the unique character, or timbre of this pickup.

A way to prove this is to play this harmonic by damping an open string above the 5th fret (making sure not to pluck the harmonic at its nodes over the 12th fret or neck pickup). You will hear almost nothing from the neck pickup, but a strong note if you switch to the middle or bridge pickups"

When I first heard about this issue of the neck pickup I was immediately skeptical and replied "But when you play up the fretboard it all changes" The shop owner commented that everybody says that and went back to reading his book. He knew I didn't have any money after buying the Les Paul so he wasn't trying to sell me anything, he just wanted me to bugger-off out of his shop

Like me, most people don't have a problem with the pickup being in the best pozi for the open string. Its when you play up the fretboard that is not understood. Those websites I referred to speak of the sound I am talking about and say it is due to the fourth harmonic being cancelled and I have just gone the step further to show how there are still harmonics cancelled or nearly cancelled all the way up the fretboard

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Yes, there are nodal points everywhere for every note on every string. The nodal points, however, shrink as the number of them increases. Additionally, your pick placement plays an equal role in determining your tone. So as soon as someone with a different pick technique and placement comes along, your sweet spot is no longer so sweet. In fact, the mathematics dictate that you could straight up swap your picking and pickup locations and get the same frequency response out of your string. It's something called reciprocity and is really quite neat. Every time you pick a string, there are lots of harmonics that you are not producing because you are picking on a nodal point for those harmonics. Thus your pickup is not doing all the work. That is why one pickup sounds so different when an open string (just for simplicity) is picked above the 12th fret and right next to the bridge. That is the entire secret behind getting acoustic guitars to sound so radically differnt from one player to the next.

You are right in that harmonics are always cancelled by pickup position, but the same is true of picking. One could just as easily leave the pickup in the same place and experiment with where to pick the strings and claim they have found their sweet spot.

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...The nodal points, however, shrink as the number of them increases...

Point taken. It is an area of physics I am not 100% on

The other factor you were speaking about I understand is to do with Fourier's Theorem. "...standing wave patterns which have a node at the pluck point will not be excited"

Obviously you get a different sound depending on where you strum or pick but this is introducing other factors and I am only talking about the position of the pickup. You can get a warmish sound from your bridge pickup by strumming over the 12th fret. But the resulting sound will be a combination of the two. Likewise you can strum close to the bridge while using the Neck pickup but you will still have the Neck pickup character in the sound, it doesn't completely change

Anyway I logged on just now to give an update on my white guitar with the pickup on the node. It is a brand new Dimazio PAF wired up to swap between coils and to go full humbucker. The primary coil (Coil A) is right on the second octave node and the 5th fret harmonic is cancelled on every string

The secondary coil (Coil B ) is louder than Coil A. It is usually the other way round and it must be due to the missing harmonics. My Les Paul has the pickup 1.5mm closer to the bridge and did not completely cancel the 5th fret harmonic when I had the modified PAF in it. I also suspect it is causing "wolf notes"

Just something that people might find interesting

Edited by Crusader

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your pick placement plays an equal role in determining your tone. So as soon as someone with a different pick technique and placement comes along, your sweet spot is no longer so sweet.

Yeah, and I take advantage of this a lot. I can totally change how I sound just by changing the angle of the pick and/or where I am strumming on the strings, in terms of the distance from the bridge. It's not quite a one size fits all kind of thing...

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One reason I have an interest in this and perhaps observe some of these things from a different way is because such aspects have always been of importance and observable from the sustainer project....consider this...

bluetele6.jpg

As on my guitar here, the driver is as far away from the source pickup at the bridge and drives the string electromagnetically.

The phase of a string where it is sourced and where it is driven is of concern of course and there is a lot to the ideas.

Further though, if you reverse the drive signal, it will dampen the fundamental and drive the next strongest harmonic (although there may well be more to that also)...

What you find is that as you shorten the string by fretting, different notes will produce different notes in the harmonic series derived from that note...indicating that things change as you fret the string...

...

PAF HB's will often be intentionally wound with one coil louder than the other. At the very least the qualities of a slug coil and screw coil are generally different because of the inductance and resonances that are different between coils. I suppose a test would be to reverse the pickup and see if the better sounding coil is the louder one or the one in the position designated as "sweet"...

...

I think you have a hypothesis but for really getting any conclusive data to make a theory from it and not simply set out to prove mojo with still more...you'd need to plug your test guitar into an oscilloscope and spectrum analyzer (you can get free software versions) and put the time in to really learn to understand what you are seeing there.

The drawings of waves is all very well, but they are not accurate, only to illustrate a point, in the end they are not "real" but made up.

I found that the tillman thing to be surprising in that there were things about the wave form I expected to change as the string was shortened in much the same way as things changed when the pickup was moved, yet there seemed to be something 'not quite right' going on there either. As you say, and I didn't read it all, it too may not be accurate but demonstrate the principle from theories of vibrational movement of a string. Obviously a real string is very complex.

...

(Quoting the webpage)

"Now consider the 4th harmonic which has nodes at the 5th fret, the 12th fret and the neck pickup - there is no 4th harmonic vibration over the neck pickup. This strong difference in harmonic levels plays a major part in the unique character, or timbre of this pickup.

A way to prove this is to play this harmonic by damping an open string above the 5th fret (making sure not to pluck the harmonic at its nodes over the 12th fret or neck pickup). You will hear almost nothing from the neck pickup, but a strong note if you switch to the middle or bridge pickups"

Yes, but one can surely see that this applies only to the open string, shorten the string (by fretting another note) and everything moves to the right while the pickup remains stationary. At the 12th fret it will hit the next node to the left as it moves up perhaps. Therefore, the notes played in the 5th-7th fret area may well have the opposite qualities to the open string...no?

Similarly, and it was pointed out years ago on this forum to me by someone, if you fret the very highest frets of a guitar, you are up real close to the neck pickup and it will be offering up similar qualities as the bridge pickup situated always near the end point of the string down by the bridge. So, you see, as you fret surely everything changes? If so, there can't really be a particular "sweet spot" except in relation to the length of a string which is ever changing.

This, as before, is still the thing to be answered, no amount of making up of hypothetical harmonic lines of open strings is really going to be convincing, neither will physically moving a pickup around a string on a real guitar. What needs to be done is to set out to disprove the theory as hard as you can to see if it holds up...and so find some surprising results that perhaps we haven't seen. So, you quote tillman about the 4th harmonic not being sounded, and this is "sweeter" to you...ok, does that still hold true for any fretted note, at what stage is this no longer true? These are the kinds of test that really show rigor and will be convincing of the theory, not just the stuff that supports and idea that you believe to be so.

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When I got up this morning it occured to me that my guitar is in need of a new set of strings. Old ones that have been taken off and put back on again have flat spots which cause buzzing and may be what I percieved as "wolf notes"

As for cancellation of the fourth Harmonic it does not only affect the open string. When you play the 5th fret the third Harmonic is cancelled and when you play the 12th fret the second is cancelled, yet they are all the fourth Harmonic of the open string

07CancelO512.jpg

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Not quite following that...but you know, may well be confused and it's after midnight. These simple divisions of open, 5th and 12th frets can be a bit deceptive.

However, on the fifth, all these wave forms move along and condense to smaller wave forms...so some nodes somewhere for instance, at some fret is going to to cancel that isn't going to be on a different fret...is that not so?

Not explaining it too well...but if you condense the 4 wave purple "open" wave from the 5th fret, surely the pickup will be more in line with the middle of the wave, not the nodal point...and so forth for other waves...so quite different than the open string...yet we don't hear 'radical' changes in tone as other factors are likely to be more influential perhaps.

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With all due respect... it seems that the point of the OP is getting lost here. Where the string is plucked is obviously a huge factor in the final tone, as are all other aspects of playing technique, guitar and pickup construction, and amp technology. But I don't think we're talking about the final tone yet.

OP, correct me...

The only factors in the OP's entirely theoretical point are:

1) harmonic nodes and anti-nodes along a theoretical vibrating string that has no harmonic bias from pick position

2) placement of pickup along the length of the string, and portion of string length over which the pickup senses

Of course all other factors are important, but perhaps they should build on each other.

Carry on. :D

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Very interesting subject. Its making me wonder is I'm going to flounder the pickup placement on my first build.

Should I be worried?

Anyways after reading this I remembered seeing this video on youtube. Most of this is fluff but there is some slow mo footage of guitar strings in action that might relate to this.

http://www.youtube.com/watch?v=bhBBo_0LtVY...feature=related

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With all due respect... it seems that the point of the OP is getting lost here. Where the string is plucked is obviously a huge factor in the final tone, as are all other aspects of playing technique, guitar and pickup construction, and amp technology. But I don't think we're talking about the final tone yet.

OP, correct me...

The only factors in the OP's entirely theoretical point are:

1) harmonic nodes and anti-nodes along a theoretical vibrating string that has no harmonic bias from pick position

2) placement of pickup along the length of the string, and portion of string length over which the pickup senses

Of course all other factors are important, but perhaps they should build on each other.

Carry on. :D

I see your point, but a guitar string is not an ideal string. The simplest representation of it requires a differential equation that requires an initial condition, such as pick placement, string displacement, etc. Any other representation is entirely too simplistic. In physics, we have a joke referred to as the "spherical cow" which pokes fun at our habit of simplifying problems as much as possible in order to make the math nice. Using a purely ideal string is much like modeling a cow as a sphere. Pick placement is not merely a technique or some "other" factor. Pickup placement and an analysis of the spectral output simply cannot be looked at independently of where the string is plucked (or struck, which is a totally different initial condition). I'm not trying to be argumentative, I just think that a lot of the people who talk about strings vibrating simply don't know (usually because it gets very mathematical) about the interdependence between the two.

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I think though for this discussion, though I agree that things are more complex than they seem in some areas, that things like pickup qualities or picking style is a little outside of what the OP is getting at. The assumption is of course, that all things being equal, for example being picked in the same way, the placement of the neck pickup has a "sweet spot" that relates to the harmonic series in the strings vibrational mode.

I do believe that there are far too many variables, different pickups with unknown qualites for instance being used on the test rig....but there are a few concerns...

But, what I am having trouble getting my head around is how these diagrams relate to fretting on any string. To me it looks as if even fretted on the 5th fret, the '4 wave harmonic' is going to condense up and be somewhat opposite to the open string. This is pretty much as I would expect, that when a note is fretted, the string length changes and so then all the harmonics must move along with it...however, the neck pickup, where ever it is positioned is stationary, therefore, it would seem obvious that as soon as you start fretting notes, the relative position of the pickup in relation to the string length and all the harmonics must move. It was brought up last time this conjecture was put forward but I don't see a convincing explanation of why it wouldn't do what seems obvious as the string shortens with fretting.

One of the problems is that it is a hypothesis that is put forward and a lot of drawings (that themselves are not really real world) that appear designed to support the conjecture...however these kind of obvious 'challenges' to the notion are not really "tested" and shown not to matter.

I believe that there is perhaps a preferential kind of positioning but it relates to other factors such as the distance between pickups and pickup types for instance.

One thing is that an HB format has a very wide 'window' and sampling a fair bit of string, it may well be that things cancel out if the node is exactly centered between two coils (though it isn't proven as such)...but with such a wide aperture, any deviation from centre could have quite dramatic results with this line of thinking as the string is shortened by fretting.

...

An interesting thing is the way a pickup does sense a string and whether such things could be designed to pickup up more complex vibrations than it does in it's current format, making it more sensitive to picking technique and revealing more of the complexity, much as acoustic instruments typically do.

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Very interesting subject. Its making me wonder is I'm going to flounder the pickup placement on my first build.

Should I be worried?

no! if your guitar sounds awfull its very unlikely that the exact pickup placement is to blame :D

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