Pickup Position

[Crusader]

Please forgive me people for one last post...

I lied !

Frequencies that directly relate to the position of frets are all re-inforced at the second octave node, according to my knowledge of physics and mathematics

I think that would be true ONLY if the frets were positioned to play the (transposed-down) overtones of the fundamental of the open string...

Take the A string. Unfretted, its fundamental is 110 Hz. This produces an overtone C# of 550 Hz. Transpose this down to be in the same octave: the C# right above A110 should be 137.5 Hz...To get 137.5 Hz on a 110 Hz string, you will need to scoot the fourth fret back towards the nut (because the equal-tempered 3rd is sharp). Now the 4th fret position is "harmonically in tune" with the open string. NOW maybe the open string 2nd octave harmonic will come into play, because when you fret at the 4th fret, you aren't disturbing the harmonic nodes of the open string.

But when you fret the 4th fret on a normal guitar, you introduce a whole new set of overtones that are harmonically out-of-tune with the fundamental of the open string, because the guitar is tempered.

Perhaps a little off-topic, but it might be beneficial

The comment I made was a while ago but its not off-topic at all. This is the sort of disscussion I was hoping for when I started the thread. Its good to hear from someone who knows about the harmonic series and the tempered system. I was waiting for someone to pick me on that one

My answers to this are:

* Firstly, I don't think sound waves in the vibrating string are very "fussy" - I'm sure wavelengths from one side of a fret will blend with ones of similar length from the other. (ie:) when you pinch a harmonic, you don't have to have your finger right on the spot to get it. There is an area of about 1/2 an inch 'grace' (so to speak) and I anticipate the same for the example you have given, and on top of that there is compensation at the nut to consider!

* The harmonic series theoretically goes on up to infinity, so you will inevitably find a wavelength that goes into both sides even if it is way up in the series with a very small wavelength. (Just for the record on my guitar I calculated the 1/2 wavelength that will go into both sides at the 4th fret to be an impossible 0.000001252899814mm!!!)

* There are also other wavelengths that come into play. Just one millimetre either side of the 4th fret are nodal points from the harmonic series with much more user-friendly wavelengths of ~ 6.5mm and ~ 26mm - which is not EXACTLY what I was saying but;

The main point I'm saying is when playing a fretted note, the vibrations will transfer from one side of the fret to the other so its not like you have a shorter string. For example two of the guitars I made are exactly the same except one is 27 3/4" and the other 24 3/4" The longer one has a much deeper tone when playing the same note - and it must have a lot to do with the extra 3 inches of string

This is very "general" though and not entirely related to the idea about the 2nd octave node but it plays a part

2.25AM I've got to go

[Geo]

You bring up some interesting points... I'll attempt to answer them.

* Firstly, I don't think sound waves in the vibrating string are very "fussy" - I'm sure wavelengths from one side of a fret will blend with ones of similar length from the other. (ie:) when you pinch a harmonic, you don't have to have your finger right on the spot to get it. There is an area of about 1/2 an inch 'grace' (so to speak) and I anticipate the same for the example you have given, and on top of that there is compensation at the nut to consider!

I think they appear not to be fussy. The actual node of a harmonic is non-negotiable, and always falls at the same place for a given open string length. I think the muting/damping of your finger is insignificant enough within a 1/2" margin of the node that it doesn't significantly impede the ringing of the harmonic. If the damping mattered within that margin, you could never play harmonics with chubby fingers; you would need a knife-edge or something.

* The harmonic series theoretically goes on up to infinity, so you will inevitably find a wavelength that goes into both sides even if it is way up in the series with a very small wavelength. (Just for the record on my guitar I calculated the 1/2 wavelength that will go into both sides at the 4th fret to be an impossible 0.000001252899814mm!!!)

The problem with that is that the higher you go in the harmonic series, the weaker and less significant the harmonics become. I doubt that any harmonic above the first 20 or so has much of an audible effect on a note within the guitar's range. And remember, most of us can't hear beyond ~20,000 Hz anyway. So yes, technically you can derive any frequency from any other frequency, but it's only the lower partials that have an effect on music. (This is just my opinion.)

The main point I'm saying is when playing a fretted note, the vibrations will transfer from one side of the fret to the other so its not like you have a shorter string. For example two of the guitars I made are exactly the same except one is 27 3/4" and the other 24 3/4" The longer one has a much deeper tone when playing the same note - and it must have a lot to do with the extra 3 inches of string

I don't doubt that vibrations can pass through the string even when your finger holds it down. But I think it still comes down to the equal-tempered fret positions being out of tune with the same positions based on transposed-down overtones.

Now, could the clash of overtones from the total string length and overtones from the fretted string length contribute to tone? Absolutely (as long as the string behind your finger really does have an effect).

As to the longer-scaled guitar having a deeper tone, I think the freely vibrating string length may have more to do with the tone than the part behind your finger. Also string gauge really comes into play here... as well as pickups... oh dear.

not entirely related to the idea about the 2nd octave node

I would say it's all related, in a very confusing way.

Edited June 19, 2009 by Geo

[Prostheta]

Hey. It's almost related to this complex topic - did you know that Mars going to crash into the earth sometime? It'll happen somewhere around the 24th fret apparently.

Too much of this ignores simplistic physics behind the guise of complex-sounding theorems. Simple harmonic theory will get you through this. Till someone pipes up about having a Variax which can model a virtual 24th fret (ahem - 3/4 length) pickup depending on the note played.

We're not talking digital cleanliness - this is an organic and flawed instrument we're talking about. We can't even make them intonate perfectly. So you're bringing absolute math to the table? Sorry dude, but we're talking rough estimates here at best. Essentially, you're all looking for *THE SOLUTION* which cannot exist for the reasons stated several times through this thread - pickups observe a large cross-section of the string in the magnetic field, picking/fingering introduces nodes at weird points from the outset, physical interaction of the guitar medium.....

Stop mathematising and go spank yer plank FFS. You won't find an answer - you'll just come up with theory upon theory which will already have target holes in it. Someone *SHOW* me an instrument with a defined "perfect" sound based on a mathematical placement, and i'll bite my hat that no better (and better funded) minds over the last sixty years haven't thought of this already.

I wonder if there's some kind of "sweet spot" angle of looking at my wife's boss which will make her look less of a vacuous pig? Meh - perhaps not. Ye cannae change the laws of physics.

(this was meant to everyone, not to any specific individual....)

Edited June 19, 2009 by Prostheta

[Geo]

So...if I place my pickups where they have been for years, will it sound good enough?

Only if the total length of wire is harmonically related to your scale length.

Sorry, I couldn't resist.

[Prostheta]

I'm sure the alignment of the planets will have something to contribute, also. That and the amount of solar radiation the magnetic field of the pickups are preventing from getting into the system. I also find that my tinfoil hat increases mains hum.

[WezV]

I also find that my tinfoil hat increases mains hum.

a common problem - you have it on inside out!

[Prostheta]

Ahh. Parallel hat-ism.

Edited June 20, 2009 by Prostheta

[Crusader]

As to the longer-scaled guitar having a deeper tone, I think the freely vibrating string length may have more to do with the tone than the part behind your finger. Also string gauge really comes into play here... as well as pickups

This is typical of me, I forgot to mention that the longer scale guitar is tuned to D and the regular scale tuned to E. So the freely vibrating string I'm comparing is exactly the same length and pitch. The strings, tension, timber, pickups etc etc are all exactly the same

Edited June 21, 2009 by Crusader

[Crusader]

I know during this discussion that I’ve waffled-on with long boring posts but I’m just trying to find the best way to put my point across. I have delved into this deeper & deeper and every conclusion points towards nodes and antinodes having a great deal to do with the sound you get from pickup position

On the other hand the results I’ve been getting may be misleading. In any case the neck pickup loses its distinct sound as you move it away from the neck and I don’t believe its just because its getting closer to the bridge. Without going into great detail I think you start getting unwanted overtones

Another thing that hasn’t been clarified is how do you define “sweet spot” We might find that we have a different idea on what it means. People keep commenting that the magnetic field is too wide to detect a specific point on the string, but wouldn’t that just make the sweet spot wider? So, more like a “sweet area”

I think of it like tuning a radio. You turn the dial until you start getting a signal, then its good for a while. Then you turn the dial back to the centre of that good area, and that’s your sweet spot

If we could all agree with something like that then what are we arguing about? (Oh yeah those pesky nodes!)

cheers

[Geo]

I know during this discussion that I’ve waffled-on with long boring posts but I’m just trying to find the best way to put my point across. I have delved into this deeper & deeper and every conclusion points towards nodes and antinodes having a great deal to do with the sound you get from pickup position

I wouldn't discourage you from experimenting with this... I just imagine there's a lot more to it than the understanding that most guitar-types have. That's why I brought up the fact that fret placement is out-of-tune with the string's natural node points.

The guitar is a mathematical mess. Think about the tone of a sine-wave synth across its whole range and how homogenous the tone color is compared to the guitar. Every fret on every string seems to have a slightly different timbre, and certain areas (e.g. the E and B strings on the first few frets, or the low strings on the high frets) have very unique timbres. Surely the clash of open-string harmonics with fretted harmonics in a given fretted note could contribute to the unique "timbre areas" of the fretboard.

In any case the neck pickup loses its distinct sound as you move it away from the neck and I don’t believe its just because its getting closer to the bridge.

I think it's all the same thing man!

Without going into great detail I think you start getting unwanted overtones

Could you elaborate?

Edited June 21, 2009 by Geo

[Crusader]

Without going into great detail I think you start getting unwanted overtones

Could you elaborate?

How well does a pickup work? If the string passes across evenly (in the case of an antinode) would it sound different to when it passes over on an angle? (somwhere between an antinode and a node)

I imagine you would get a smoother response from antinodes

[Crusader]

I think a person is more inclined to accept your opinion if you guys are less insulting

Of course I realise other people have tried to figure out the 'sweet spot' mystery but I have the point of view that if someone figured it out with big budgets they wouldn't just go out and tell everybody. Either that or they missed something because I found what I was looking for and it would take a lot to convince me I'm wrong

First of all I can hear the difference and its not just because the pickup is further from the bridge. There's something else going on and there's got to be a scientific reason for it. I believe its all to do with overtones. The pickup may observe a large cross-section of the string but its very small compared to listening to an accoustic instrument where you just hear the whole lot all at once

They say some people can hear overtones and some can't. That's just a part of the imperfect world we live in. Take my eyesight for example. I can't read a steet sign at ten paces but I can see in the dark when everyone else says its just pitch-black

DISCLAIMER: A lot of what I'm saying here is my own opinion

To continue with what I was saying in the previous post

I believe a pickup can detect unecessary overtones and the best way to avoid that for the neck pickup is to have it at the 2nd octave node. The reason I put forward is best represented by playing at the 12th fret where the fundamental is at its antinode and every harmonic is either a node or antinode

The antinodes do the work and nodes do nothing (as far as I know) so it's a perfect combination. The string passes through the magnetic field with even, parralel vibrations which provide a cleaner signal. I'm sure anyone would agree that you get the sweetest sound at the 12th fret. My main point being that antinodes over the pickup are good and it’s a bonus if your overtones have them too

Talking about it in general

The further the pickup is from the bridge, the closer it is to the antinode (centre) of the open string. When playing up the fretboard you move the antinode of the fundamental closer to the pickup. It reaches perfection at the 12th fret, then passes it as you play up to the 22nd fret

Overtones at the second octave

When playing the open string every second overtone has a node or antinode occuring over the second octave. When playing a fretted note the string still vibrates in its full length, so some of those overtones are still there. The string behind the fret adds tone and sustain - a bit like when you play a high note on the thicker strings compared to playing the same note on the first string

Obviously fretted notes have their own harmonic series. Many of the overtones have antinodes over the 2nd octave and they just happen to have the same wavelengths as the ones left from the open string! When you have the pickup set back as with a 24 fret guitar you separate this “marriage” between the two harmonic series. You may still have antinodes over the pickup which both have in common but its all hit-and-miss

There's too much to put it all in a nutshell so I'm working on a step by step way of explaining it which I may post up later on

I’ve worked everything out based on the harmonic series but I believe what I’m saying will still work on evenly spaced frets. Also - people say the pickups field is too wide to focus on such a small area of the string but I don't think it destroys what I’m saying altogether. If you had a moveable pickup like on this guitar there would be a gradual change in tone as you move it along

Edited June 24, 2009 by Crusader

[psw]

Well...

I have been away for a bit and come back to see this discussion is still going. Unfortunately, and at the risk of sounding insulting, i think there are a lot of things that are not being taken into account in the search for a definitive answer where there simply may not be one.

That said, perhaps I misunderstand what the question is. As I understand it you are trying to ascertain if there is a sweet spot and why (if there is) this may be. There seems to be an assumption that there is in fact a sweet spot for the placement of a neck pickup.

For the record, i think there are preferential pickup placement points for different pickups and players and types of play. But I don't think that this can be explained simply or "scientifically" by just nodes and antinodes and such. Some of the reasons have been given such as the obvious moving of all these nodes as the strings length is shortened by fretting.

Other reasons however have not been fully explored, a vibrating string for instance does not only vibrate at the fundamental frequency but a very complex accumulation of overlapping, reinforcing and cancelling nodes and anti nodes related to the harmonic series. The amount and amplitude of these harmonic waves behind a note a greatly affected by the construction and materials used in the guitar, the type, magnetism and width of the sensing device (pickup) as well as its placement and the way the guitar is played.

For a given player then, I believe there ma be a preferential (sweet spot) for the neck pickup. Certainly further towards the centre of a strings vibration gives a more fundamental heavy smoother sound. So, if this is the sound that one is after, for play from the lower frets to the mid board, further from the bridge is an advantage....and could be taken to be a general rule.

I don't think a universal sweet spot exists though or that it is that important given all the other factors and the ability to compensate for a lot of these things with the pre-amplification if desired.

...

For the way I play in recent times and with my particular telecaster, I use the neck pickup alot and in combination with the bridge pickup. In fact I have always had a bit of a preference for the combined pickup selection even when I played a les paul. Part of the reason is that I like the smoother tone but I still want to be able to get the harmonics that the bridge pickup senses.

I use an SCn tele chrome covered pickup which has a narrower field than even a strat...but I have used others and the quality of this pickup has had more of an effect on this tone in the same place than the positioning. But then, I am also using a fairly clean tone these days and doing a lot of chord work or leads in the lower register (below the 12th fret) and this gives a good bright and true sound to this kind of play for me. I believe that if I moved this pickup a cm either way it would have perhaps a slightly different tone, but still a usable and good sound for this purpose.

Ironically I guess...looking at the guitar right now...it has 21 frets but the fretboard extends to where the 22nd would be...and the pickup is far enough from that that I dare say on this guitar I could have 23-24 frets and have the pickup placed exactly where it is now or extremely close.

Now...HB pickups will warm things up a lot more and a neck HB will even out the response to a warm fundamental heavy sound as it will be more consistent in reading fundamental modes of vibration over the many secondary harmonic modes. However, the guitar itself makes a huge difference to this...my les paul will also have a very smooth neck tone largely as a result of it's rock solid construction...where as my tele is an extremely bright harmonically rich guitar...even if I were to put a neck HB on it, it would still have an enormous amount of harmonic content in it regardless and this matters far more IMO than the placement of the pickup.

...

Anyway...I don't no if this is of any use or value to your thesis.

I'd be very careful about comparisons with acoustic guitars...they are likely even more complex again. You are not just hearing the string but the manner that the top is vibrated by them and this involves so many different factors...even though many do relate to the solid body as well in the nature of a strings vibration, we do sense and amplify the strings directly in this case by enlarge.

But I am not entirely sure what it is that you are seeking, verification that there is a "sweet spot" (which seems to be largely disputed here) and if so (since you feel that you can hear one) why that would be. What I think you can hear is your own preference for pickup placement and I would not dispute that, as I explained, I can hear it too...for me...but this is more to do with the type of play and expectations that I have over some mystical "best" location theory.

But...you know...my considered opinion of course. I am sure that a lot of work went into some of this by those modeling guys who allow you to simulate locating virtual pickups anywhere along the strings length...perhaps there is some material there.

pete

[Crusader]

Other reasons however have not been fully explored, a vibrating string for instance does not only vibrate at the fundamental frequency but a very complex accumulation of overlapping, reinforcing and cancelling nodes and anti nodes related to the harmonic series

Well actually I have explored this quite extensively but I don't think I've been very good at explaining things. I started this thread talking about sweet spots in general. I know for myself that with two single coils (bridge and middle) if you move the middle more than ¼ of an inch in either direction you start to lose that quacky sound. Surely that indicates a sweet spot for the middle pickup. But ever since the first reply the topic has been about the neck pickup sweet spot

To give you some idea of how far I have explored the overtones, I have an Excel worksheet showing the ½ wavelengths of the first 128 harmonics up to the 20th fret. I have it set up for different pickup positions and also Gibson fret spacings

If you want to critisise me because I'm only using maths, I don’t see what else is involved. When you move a pickup on a guitar nothing else changes. The timber, strings and pickup all remain the same. Wavelengths follow a very mathematical order. The results show, for any note you play, there is an abundance of overtones that have nodes or antinodes over the second octave node, which is what you would want to get "the neck pickup sound" (Which of course is not suitable for all types of music)

I've tried various ways of explaining what I can see so I hope that clears it up a bit. By the way I would say the neck pickup would be 19 1/8" from the nut on a Telecaster

[psw]

To give you some idea of how far I have explored the overtones, I have an Excel worksheet showing the ½ wavelengths of the first 128 harmonics up to the 20th fret. I have it set up for different pickup positions and also Gibson fret spacings

Well...I am not doubting that you have explored it a lot. I am also perhaps not completely understanding or indeed not taking everything into account at all.

The middle pickup quack is by enlarge a cancelling effect with the pickup it is combined with and placement is crucial. I'd also say that the combined setting (B and N) is greatly affected by this relationship between pickups...I think I may have mentioned that earlier in the thread.

Perhaps if you have something that shows how the waves of any fretted note are particularly unique to a certain position I might understand where you are coming from with these concepts.

I guess the thing that is holding me back is that while you might find a great spot for an open string, but the time you are playing notes on the 7th fret say these relationships and "preferential" position of a pickup must surely have moved fairly dramatically. And I imagine by the same principle that a pickup perhaps not in the "sweet spot" for an open string may well fall into that area when playing around the 7th fret for example.

For any combination of pickups though...I think we are in some agreement that there are much better positions than others and in that there are "sweet spots" to produce those tones. It's kind of amazing that on a strat that fender got it so right...yet it was unintentional and he reportedly hated that quacky sound and the original strats were never wired to produce it with the old three way switches.

The tele has an interesting combined pickup sound as well...mine isn't typcial in that department because it has this huge bridge HB...it seems to just sound like the neck pickup with more harmonics for some reason. The out-of-phase version of these two pickups is unique though...sounds like a cocked wha and you can even get wha like effects just by playing things with this setting I have found lately. If interested some of these sounds are in the red like of my sig and a description somewhere in the tele thread of what settings are which (not intending to hijack the thread you understand).

It would be interesting if you could perhaps demo in this way audibly if you have a guitar that you think illustrates a superior pickup positioning of tone...

pete

[Geo]

Obviously fretted notes have their own harmonic series. Many of the overtones have antinodes over the 2nd octave and they just happen to have the same wavelengths as the ones left from the open string! When you have the pickup set back as with a 24 fret guitar you separate this “marriage” between the two harmonic series. You may still have antinodes over the pickup which both have in common but its all hit-and-miss

Just to state my response to this clearly (I'm not trying to offend you--I see that you've digested the response. Just for others' sake):

As I understand it, there is no marriage between the open-length harmonics and the fretted harmonics in a fretted string because equal-tempered fret placement is out of tune with the natural (transposed down) overtones of the open string.

[Crusader]

I really don't want this thread to go on to yet another page but a couple of comments

Pickup at the second octave

I've always known you get the sweetest sounds playing on and around the 12th fret (in comparison, the open string sounds quite ordinary) but it took me a while to cotton-on to this;

Having the pickup there isn't in the optimal place for the open string, its the best place for the 12th fret. You want the antinode of the fundamental over the pickup, not the second harmonic. So as you play up the fretboard the sound gets better. The seventh fret is about where is starts sounding really good

Nodes-and-such of the upper harmonics

I have to admit I've gone into this area more than neccessarry and I've overlooked the more simple things like what I just mentioned. However its been a very fascinating journey that perhaps the majority would find boring but a few may find quite interesting. I'd love to show people what I've found but it needs some explaining

Equal Tempered frets

I knew from the start that this is an issue but I'm sure it doesn't throw the whole idea out the window. I vaguely remember from college physics lessons that scientists sometimes develop "mathematical models" using simple numbers, then apply it to a real-world situation where they have no idea what numbers are actually involved, but it still works

Definition of "Sweet Spot"

This is something which should have been discussed at the start. It may turn out we're talking about different things or using a different "language" (if you know what I mean) For example I never heard the term 'sweet spot' before joining this forum. But after searching recently it came up again and again..."buy this guitar, pickup in the sweet spot" So now I can understand that people here are probably sick of hearing it

By the way

I actually saw a guitar recently that has the neck pickup further up the neck than usual. The twin neck Gibson SG. I always knew they only had 20 frets but it didn't twig that the pickup is hard against the end of the fretboard. The inner coil is under the second octave (And just to think, I've hear Stairway to Heaven a billion times!)