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Guitars by their very nature are imperfect systems. Pick attack on notes, body materials and their flex, magnetic pull of the pickups on the strings and many more factors come into play. I think that it's admirable to consider this from a physics perspective, although the actuality is far too complex to model or condense unless you cut out these factors, thereby widening the gap between the real and the modelled. An instrument that it would be more practical to do this modelling on for "ideal" pickup placement would be a harp on the basis that the string lengths are set and the system doesn't have to take into account notes being fretted, bent, pinched, etc.

That's what makes guitars fun for me - they're fantastically varied in their voices and potential for sound depending on how you play them. Modelling such an organic instrument down to a set of rules is fundamentally flawed enough to fail or fall short. This is why Line6 amp modelling doesn't compare to real amps apart from in the most general of terms. The models hit 90% or whatever, but the rest is more and more complex, requiring exponentially more modelling power to emulate.

Oops....just noticed that Wez said this in like, two sentences. I do ramble....

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Putting theories aside, I don't know how you can't hear the difference between a pickup on the node compared to a 24 fretter (or an SG) to me it's not subjective. It doesn't matter what type of wood you use, type of strings, pickups, humbuckers or single coils. When a pickup is on the second octave node there is a distinctive sound (which you get all over the fretboard) And if you move it away from that point you get a similar sound but its not really "there"

To find the reasons why you get this sound you simply have to look into vibrations & soudwaves and its only High-School level physics. After I did a few simple calculations it was like a light switched on and I can 'see' whats happening in my mind, but where I fall down is my ability to put it into words. I suppose I'm assuming other guitar makers would take the same interest in the physics of sound as I did

Something to remember (I tried to say earlier) when I was first told about the neck pickup "sweet spot" I was also sceptical (because once you play fretted notes the node moves) But think about this, as you play further up the fretboard that 'creamy' sound gets better till the 12th fret then starts to fade, would you agree? So it actually helps the fretted notes more than the open string

What I'm saying in a nutshell is; Vibrations behind the fret re-inforce the vibrations on the pickup side, and the finger pressing on the string is not enough to stop those vibrations passing through (whereas a nut or bridge would stop them to a greater extent) The second octave node is a point where these vibrations are best picked up because its where most nodes/antinodes collide (There are three "octave nodes" in this area but the 2nd octave node captures the longer, stronger wavelengths)

I hope I can get around to drawing some graphs because illustrations speak a thousand words

By the way here's another little experiment I did, can you see what I was trying to do?

Picture2145.jpg

Edited by Crusader
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Putting theories aside, I don't know how you can't hear the difference between a pickup on the node compared to a 24 fretter (or an SG) to me it's not subjective. It doesn't matter what type of wood you use, type of strings, pickups, humbuckers or single coils. When a pickup is on the second octave node there is a distinctive sound (which you get all over the fretboard) And if you move it away from that point you get a similar sound but its not really "there"

The subjectivity is in what exactly is "there" though.

To find the reasons why you get this sound you simply have to look into vibrations & soudwaves and its only High-School level physics. After I did a few simple calculations it was like a light switched on and I can 'see' whats happening in my mind, but where I fall down is my ability to put it into words. I suppose I'm assuming other guitar makers would take the same interest in the physics of sound as I did

You are right that the physics is fundamentally highschool-level physics (although when you get to interference of multiple waves it makes life a lot easier if you use complex numbers, which here in the UK are A-level), the issue is the complexity of the system.

For example; stars have forces between them due to gravity. Simple highschool physics, right? Yet to model a galaxy full of these stars, you need some of the worlds most powerful supercomputers! The problem is the sheer amount that's going on.

Something to remember (I tried to say earlier) when I was first told about the neck pickup "sweet spot" I was also sceptical (because once you play fretted notes the node moves) But think about this, as you play further up the fretboard that 'creamy' sound gets better till the 12th fret then starts to fade, would you agree? So it actually helps the fretted notes more than the open string

What I'm saying in a nutshell is; Vibrations behind the fret re-inforce the vibrations on the pickup side, and the finger pressing on the string is not enough to stop those vibrations passing through (whereas a nut or bridge would stop them to a greater extent) The second octave node is a point where these vibrations are best picked up because its where most nodes/antinodes collide (There are three "octave nodes" in this area but the 2nd octave node captures the longer, stronger wavelengths)

I hope I can get around to drawing some graphs because illustrations speak a thousand words

What are you going to draw a graph of? You would need to quantify the 'creamy' sound you describe if you are going to plot anything, and I don't see how that's possible.

How do you intend to prove that this effect is due to the reasons you describe and not some other factor?

By the way here's another little experiment I did, can you see what I was trying to do?

You were trying to calculate something approximately-but-not-quite the scale length from something approximately-but-not-quite the distance from the nut to this magical node :D ?

Or perhaps working what scale length your guitar would need to have its node directly over one of the neck pickup coils?

Ultimately, I think Prostheta summed it up nicely:

I think that it's admirable to consider this from a physics perspective, although the actuality is far too complex to model or condense unless you cut out these factors, thereby widening the gap between the real and the modelled.
Edited by Ben
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Ok, here are two tests to show that frequencies from the 'dead string length' dont affect the 'active' length.

To show that no new frequencies are added, take a string stopped from vibrating at a point between fret positions. The string length when fretted is the same as before, but the total length is no longer mathematically related to the fretted length, so the frequencies on this new string length will not be harmonically related to the fretted note. This would be heard as a new set of frequencies out of tune with the normal fretted note.

You talk about the 'perfect spot' where the sounds add together or cancel out in an opera house. These are exactly the nodes we have discussed earlier. If what you say about vibrations from the dead string is true, then these nodes must move along the string. This is easily tested, as the nodes are where you touch the string to get a particular pinch harmonic. So if you capo at a fret behind where you are fretting (like in your test above) the place you touch for a pinch harmonic must move significantly (by a few frets difference. Its probably best to test this with a pinch harmonic over the fretboard, so you can judge exactly where you are touching easier. Obviously, make sure you are playing the same harmonic.

If neither of these occur then the dead length has no effect relating to pickup position. Id be really interested if people could consistantly produce either result.

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You talk about the 'perfect spot' where the sounds add together or cancel out in an opera house. These are exactly the nodes we have discussed earlier. If what you say about vibrations from the dead string is true, then these nodes must move along the string.

Its a weak analogy anyway, the multiple source points, full frequency range, reflection, cancellation and absorption (and probably other things only an acoustic architect understands) all play a part in sound acoustics, You may as well be comparing a skipping rope to the oceans currents.......

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You talk about the 'perfect spot' where the sounds add together or cancel out in an opera house. These are exactly the nodes we have discussed earlier. If what you say about vibrations from the dead string is true, then these nodes must move along the string.

Its a weak analogy anyway, the multiple source points, full frequency range, reflection, cancellation and absorption (and probably other things only an acoustic architect understands) all play a part in sound acoustics, You may as well be comparing a skipping rope to the oceans currents.......

I dunno, i think it works as an analogy for standing waves, he wasnt bringing any complexities into it.

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Good to hear your input guys. I hope I will clarify what I'm saying a bit

First of all I'm pretty sure you'll find when you divide a string into two, there will always be wavelengths that will go into both parts. When I talk about vibrations from behind the fret I'm not talking about the sound, just the vibrations. And I'm suggesting these vibrations enhance the upper harmonics of the note being played. The first fret a little bit, the second a little bit more...and so on untill the 12th fret where its not just upper harmonics but where the wavelengths are the same as the note being played. (This is why I believe when playing on the neck pickup I find the sound gets better as you approach the 12th fret, then fades as you reach the 22nd fret)

The problem of course is when you fret a note you also press the string onto the fret behind the one you want. So how does this affect the vibrations? This is where I'm not sure but I'd say the string partially vibrates transversely and partly longitudinally

Now what I've found mathematically, the corresponding wavelengths on the pickup side always land on the 2nd octave node in antinodes, nodes or halfway between (I was previously saying nodes or antinodes) But consider this; in relation to the open string the 2nd octave node is not on a node or an antinode, its halfway between. Its on the antinode of the first harmonic, an octave higher

When I did the experiment of clamping a cappo tightly on the second fret, I was trying to simulate the nut to have the effect of making the scale shorter. I have to admit it was hard to tell the difference at first but after a few comparisons with it on and off I was convinced. I had effectively put the pickup on the 2nd octave and therefore it had a nicer tone

And this is what I did with the double bridge experiment;

The second bridge was positioned so the neck pickup was on the 2nd octave node of the "secondary scale"

The strings went lightly over the 1st bridge to simulate a fret

I was trying to see if the pickup would "see" the secondary scale but play the note of the first scale

And yes it did work, I got that creamy neck pickup sound...but with a kind of out-of-phase sound. Which is exactly what I'd say was happening

Of course the other thing I did was drop the first bridge and played to the longer scale and yes that distinctive neck pickup sound was totally there. It was really funny how well it played with the intonation being out so much!

I have to point out that I haven't got everything completely worked-out, but I know enough about physics and experience with the guitar to be sure there is something here

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Good to hear your input guys. I hope I will clarify what I'm saying a bit

First of all I'm pretty sure you'll find when you divide a string into two, there will always be wavelengths that will go into both parts. When I talk about vibrations from behind the fret I'm not talking about the sound, just the vibrations. And I'm suggesting these vibrations enhance the upper harmonics of the note being played. The first fret a little bit, the second a little bit more...and so on untill the 12th fret where its not just upper harmonics but where the wavelengths are the same as the note being played. (This is why I believe when playing on the neck pickup I find the sound gets better as you approach the 12th fret, then fades as you reach the 22nd fret)

The problem of course is when you fret a note you also press the string onto the fret behind the one you want. So how does this affect the vibrations? This is where I'm not sure but I'd say the string partially vibrates transversely and partly longitudinally

Now what I've found mathematically, the corresponding wavelengths on the pickup side always land on the 2nd octave node in antinodes, nodes or halfway between (I was previously saying nodes or antinodes) But consider this; in relation to the open string the 2nd octave node is not on a node or an antinode, its halfway between. Its on the antinode of the first harmonic, an octave higher

When I did the experiment of clamping a cappo tightly on the second fret, I was trying to simulate the nut to have the effect of making the scale shorter. I have to admit it was hard to tell the difference at first but after a few comparisons with it on and off I was convinced. I had effectively put the pickup on the 2nd octave and therefore it had a nicer tone

And this is what I did with the double bridge experiment;

The second bridge was positioned so the neck pickup was on the 2nd octave node of the "secondary scale"

The strings went lightly over the 1st bridge to simulate a fret

I was trying to see if the pickup would "see" the secondary scale but play the note of the first scale

And yes it did work, I got that creamy neck pickup sound...but with a kind of out-of-phase sound. Which is exactly what I'd say was happening

Of course the other thing I did was drop the first bridge and played to the longer scale and yes that distinctive neck pickup sound was totally there. It was really funny how well it played with the intonation being out so much!

I have to point out that I haven't got everything completely worked-out, but I know enough about physics and experience with the guitar to be sure there is something here

I dont really get what you are saying here, the vibrations ARE the sound. If the two effects i described above cannot be seen, then there is no physical way the vibrations from the two strings are interfering. Any other effects would be constant over the string, and so would not produce a 'special' pickup position (they would affect a pickup anywhere equally).

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So, Crusader, what you're saying is, that if you play a note on the 12th fret with "open string to the nut" behind it, it would sound differently than if you played the same note but capo'd?

Move the capo around (behind your fretted note), and the sound changes?

Interesting...

I still don't understand how you would capture a specific node, if the "node" moves around as you fret...

Not just that, a pickup doesn't just capture the vibration directly above it. The field is much too wide to try to zero on a single, specific point.

But hey, what ever keeps you occupied...

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…Any other effects would be constant over the string, and so would not produce a 'special' pickup position (they would affect a pickup anywhere equally)

Wasn’t sure what you were saying before but good point. When I talk about the string behind the fret re-inforcing the sound, yes it would affect the sound everywhere. Its just one factor in the whole theory I’m putting forward

The 1st fret on my guitar is very close to 1/18 of the scale. That means the remaining string is 17/18 of the scale. These 1/18th partials are half-wavelengths and I believe their vibrations re-inforce each other. The main point is these wavelengths have nodes or antinodes over the 2nd octave node.

So, Crusader, what you're saying is, that if you play a note on the 12th fret with "open string to the nut" behind it, it would sound differently than if you played the same note but capo'd?

Move the capo around (behind your fretted note), and the sound changes?

When I did the experiment with the cappo I put it on very tightly, a lot more than you usually would. I was trying to simulate the angle of the headstock in order to create a shorter scale, which shifted the 2nd octave node over the pickup

I still don't understand how you would capture a specific node, if the "node" moves around as you fret...

Not just that, a pickup doesn't just capture the vibration directly above it. The field is much too wide to try to zero on a single, specific point

The 2nd octave node of a fretted note being played shifts up the fretboard but thats not what I'm talking about. The only 2nd octave node that has any importance is that of the open string. What I'm saying is the vibrations from the string partial behind a fretted note have wavelengths that have a node or antinode over the 2nd octave of the scale

And I think the wider magnetic field would be beneficial

Well I got around to setting out the main point of my theory here. I only did calculations up to the 12th fret but I hope it clears a few things up although I know there would still be questions

Nodecalculations80pc.jpg

Nodesbypaint.jpg

Edited by Crusader
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Something just occured to me that could need more clarification. When I did my experiment on the white guitar with the cappo

If I play a fretted note, the nodes are going to be in the same place with or without the cappo on. And this is where I believe the string behind the fret must be having an effect

When the cappo is on, the frequencies of the string length behind the fret are related to those nodes/antinodes (which occur over the pickup) and will give them support

When the cappo is off, the string behind the fret is unrelated and will not re-inforce those frequencies (It is related to the frequencies which have nodes over the 24th fret)

Edited by Crusader
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So to clarify;

In a single sentence, am I right that your theory is that this 'sweet spot' at the 24th fret is because there is an unusually high concentration at that point of nodes and antinodes of the fundamental frequencies of all the frets?

edit: also, wxMaxima lets you plot things easily. Its pretty simple to learn and free. (also here's the link for platforms other than windows)

Edited by Ben
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Something just occured to me that could need more clarification. When I did my experiment on the white guitar with the cappo

If I play a fretted note, the nodes are going to be in the same place with or without the cappo on. And this is where I believe the string behind the fret must be having an effect

When the cappo is on, the frequencies of the string length behind the fret are related to those nodes/antinodes (which occur over the pickup) and will give them support

When the cappo is off, the string behind the fret is unrelated and will not re-inforce those frequencies (It is related to the frequencies which have nodes over the 24th fret)

If the nodes dont change then there would be nothing special about the 24th fret position, this "reinforcement" of frequencies would have to happen everywhere on the string.

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If the nodes dont change then there would be nothing special about the 24th fret position, this "reinforcement" of frequencies would have to happen everywhere on the string

I may need to clarify what I've said

When you play a fretted note, the new string length will have its own set of harmonic series. The wavelengths that are reinforced are the ones which both sides have in common

So when I put the cappo on really tightly, the string behind the fret is reinforcing a different wavelength which has different positions for nodes and antinodes, but they were always there

Also, different wavelengths have different lengths but no matter which fret you play on, (as shown in the diagram I put up) there will be a wavelength that both sides have in common and they have a node or an antinode at the 24th fret

So to clarify;

In a single sentence, am I right that your theory is that this 'sweet spot' at the 24th fret is because there is an unusually high concentration at that point of nodes and antinodes of the fundamental frequencies of all the frets?

Yes but I may have said "frequencies" when what I mean is 'wavelengths' or 'half-wavelengths'

Everyone seems to agree that the pickup on the 2nd octave node works for the open string but not for fretted notes. What I'm showing is there are always nodes or antinodes over that point that relate to the note you are playing

Btw thanks for that link, I'll have a look at it

In the past few days I've kept researching this 2nd octave node thing and found some surprising outcomes. But when you look at it a different way its quite obvious

First of all when playing the open string, if you take the 1st octave (12th fret) every harmonic has a node or an antinode over that point. Think about it, if you divide the string by an odd number you get an antinode over the 12th fret and if you divide it by an even number you get a node. And a string will only vibrate in whole numbers (so to speak) At the 2nd octave every harmonic has an node, antinode or half-way between node and antinode. So if you have a wavelength that is half way, then at double the frequency you get an antinode. When playing a fretted note, the "theory" I'm suggesting requires a wavelength that both sides have in common, so the rules for the open string will apply. Or in other words the fret is on a node

Now here's the killer. What if you use a slide? and you're half way between frets? Does the tone suddenly sound crap? Of course not...

Theoretically (mathematically) there is always a wavelength that both sides have in common. For example take 12mm of a 628.65mm scale (24 3/4")

12 divided by 628.65 = 80/4191 (btw I've got a scientific calculator which converts decimals to fractions)

This means the whole string is vibrating in 4191 half-wavelengths. The 12mm takes up 80 of them and the remaining string has 4111

The half-wavelengths are .15mm long so how many fit into 1/4 of the scale?

628.65/4 divided by .15 = 1047.75

The number ends in .75 which is half-way between a node and an antinode. So if you double the frequency you will get an antinode over the 2nd octave node

No matter which length you try, you end up with a whole number or one that ends in .25 .50 or .75

Now I don't know if its physically possible for a string to vibrate in such small increments but the in any case the theory is there

Also btw I tried the experiment with the cappo on another of my guitars and had the same result. Its not a huge difference because its not really a nut and theres no fret exactly in the right place so it takes a bit to notice the change in tone. What it sounds like to me is when the cappo is on, the note "rings like a bell" When it is off there are unwanted overtones

I am convinced about this idea and what it means is you can have a 24 fret guitar and still get a true neck pickup sound just by putting a cappo on in the right place. The way to do it is measure from the bridge to the pickup pole piece then multiply by 4 Then measure from the bridge to the closest fret to that length and put a cappo on, really tightly close behind the fret. You may need to re-tune though. And if you don't hear a difference then try it over and over again. Then try it the next day, the next week...

One day I showed my new guitar to a friend of mine. He couldn't tell the difference between the neck pu and the bridge. But after I explained it he goes "Ah yea, I can hear it now" In other words you sometimes need to "train your ear" to notice differences in tone

Edited by Crusader
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If the nodes dont change then there would be nothing special about the 24th fret position, this "reinforcement" of frequencies would have to happen everywhere on the string

I may need to clarify what I've said

When you play a fretted note, the new string length will have its own set of harmonic series. The wavelengths that are reinforced are the ones which both sides have in common

So when I put the cappo on really tightly, the string behind the fret is reinforcing a different wavelength which has different positions for nodes and antinodes, but they were always there

Also, different wavelengths have different lengths but no matter which fret you play on, (as shown in the diagram I put up) there will be a wavelength that both sides have in common and they have a node or an antinode at the 24th fret

So to clarify;

In a single sentence, am I right that your theory is that this 'sweet spot' at the 24th fret is because there is an unusually high concentration at that point of nodes and antinodes of the fundamental frequencies of all the frets?

Yes but I may have said "frequencies" when what I mean is 'wavelengths' or 'half-wavelengths'

Everyone seems to agree that the pickup on the 2nd octave node works for the open string but not for fretted notes. What I'm showing is there are always nodes or antinodes over that point

Btw thanks for that link, I'll have a look at it

In the past few days I've kept researching this 2nd octave node thing and found some surprising outcomes. But when you look at it a different way its quite obvious

First of all when playing the open string, if you take the 1st octave (12th fret) every harmonic has a node or an antinode over that point. Think about it, if you divide the string by an odd number you get an antinode over the 12th fret and if you divide it by an even number you get a node. And a string will only vibrate in whole numbers (so to speak) At the 2nd octave every harmonic has an node, antinode or half-way between node and antinode. So if you have a wavelength that is half way, then at double the frequency you get an antinode. When playing a fretted note, the "theory" I'm suggesting requires a wavelength that both sides have in common, so the rules for the open string will apply. Or in other words the fret is on a node

Now here's the killer. What if you use a slide? and you're half way between frets? Does the tone suddenly sound crap? Of course not...

Theoretically (mathematically) there is always a wavelength that both sides have in common. For example take 12mm of a 628.65mm scale (24 3/4")

12 divided by 628.65 = 80/4191 (btw I've got a scientific calculator which converts decimals to fractions)

This means the whole string is vibrating in 4191 half-wavelengths. The 12mm takes up 80 of them and the remaining string has 4111

The half-wavelengths are .15mm long so how many fit into 1/4 of the scale?

628.65/4 divided by .15 = 1047.75

The number ends in .75 which is half-way between a node and an antinode. So if you double the frequency you will get an antinode over the 2nd octave node

No matter which length you try, you end up with a whole number or one that ends in .25 .50 or .75

Now I don't know if its physically possible for a string to vibrate in such small increments but the in any case the theory is there

Also btw I tried the experiment with the cappo on another of my guitars and had the same result. Its not a huge difference because its not really a nut and theres no fret exactly in the right place so it takes a bit to notice the change in tone. What it sounds like to me is when the cappo is on, the note "rings like a bell" When it is off there are unwanted overtones

I am convinced about this idea and what it means is you can have a 24 fret guitar and still get a true neck pickup sound just by putting a cappo on in the right place. The way to do it is measure from the bridge to the pickup pole piece then multiply by 4 Then measure from the bridge to the closest fret to that length and put a cappo on, really tightly close behind the fret. You may need to re-tune though. And if you don't hear a difference then try it over and over again. Then try it the next day, the next week...

One day I showed my new guitar to a friend of mine. He couldn't tell the difference between the neck pu and the bridge. But after I explained it he goes "Ah yea, I can hear it now" In other words you sometimes need to "train your ear" to notice differences in tone

Frequencies and wavelengths are the same thing.

None of what you are saying here is really relevant. Either the effect you are hearing is due to a node, in which case moving the capo would move the location of certain pinch harmonics, or it is not due to a node, in which case the relative position of the pickup makes no difference (other than how it would without the capo).

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No, wavelengths and frequencies are not always the same. Remember I am talking about upper harmonics, not the fundamental. I was in error in an earlier post when I used the term "fundamental" and I did point that out

Think about how you tune from string to string at the 5th fret

On the 6th string the open string is E

At the 24th fret you have 1/4 of the string which is "E" (the second octave)

At the 12th fret you have 2/4 of the string which is "E" (the first octave)

At the 5th fret you have 3/4 of the string which is "A"

Each of these have a different fundamental wavelength but they all share the fundamental wavelength of the second octave E as an upper harmonic

(You could say 3 x E = A)

I don't know if that explains it well enough but I hope so,

cheers

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No, wavelengths and frequencies are not always the same. Remember I am talking about upper harmonics, not the fundamental. I was in error in an earlier post when I used the term "fundamental" and I did point that out

Think about how you tune from string to string at the 5th fret

On the 6th string the open string is E

At the 24th fret you have 1/4 of the string which is "E" (the second octave)

At the 12th fret you have 2/4 of the string which is "E" (the first octave)

At the 5th fret you have 3/4 of the string which is "A"

Each of these have a different fundamental wavelength but they all share the fundamental wavelength of the second octave E as an upper harmonic

(You could say 3 x E = A)

I don't know if that explains it well enough but I hope so,

cheers

Your post doesnt make any sense, they do correspond, for each and every harmonic. Whether it is the fundamental or a higher harmonic does not matter.

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Your post doesnt make any sense, they do correspond, for each and every harmonic. Whether it is the fundamental or a higher harmonic does not matter

When I said 'frequency' I was referring to 'pitch' On the E string the length from the bridge to the 24th fret is a half-wavelength which on its own gives you E. When you double that length you get E an octave lower. When you triple that length you get A and four times that length is E, the open string

I think what you are getting at is there are nodes all along the string, so the position of the pickup is not relevant. But if you move the pickup along to another node, you may get the same effect but only for one note. With the pickup on the second octave you capture the nodes and antinodes for every note you play. And as I said before, its not conclusive but I think it holds a lot of weight to my theory

Can't we just agree that this is bull and close this thread?

I was going to let this topic go ages ago but if people have questions I think its curtious to answer them, and if people accuse me of being full of bull I will endeavor to prove I'm not

I won't take offence to your remark though because I would also like to end this thread. I have to agree with Ben when he said earlier that there's too many factors involved and lets put it in the too-hard-basket

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Please forgive me people for one last post. I have come up with a better way to explain what I’m saying which I hope will answer massive propagator and the whole concept in general

It all hinges on what a college physics lecturer told me ten years ago (I should have mentioned this before but my mind has been too focused on other things)

He said something to the effect

"Due to the tension in a guitar string, pressing your finger on a fret is not enough to stop it vibrating in its natural harmonic series"

(I don't think the whole series would still be there, only that which can be supported by the string length behind the fret you're playing)

So what I’m saying is this

When you play a fretted note you create a new set of harmonic series which is superimposed over the other. The 2nd octave node is a point where both harmonic series are in sync

To hopefully clear things up for Massive Propagator (talking about pickups) as Prostheta said earlier on

...The magnetic field around the pickup is affected by anything within the field disturbing and deforming it, which is generally a small length of the string. :D

So the pickup doesn’t “hear” the whole string but that one small area and because there are less conflicting vibrations at that point, you get a cleaner tone

If anyone still has questions please send me a pm

cheers

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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. But the standard guitar fret positions are equal-tempered, all based on the same ratio.

To illustrate with an example: the interval of the major third is taken from the fourth overtone (not counting the fundamental). The "overtone" 3rd is significantly flatter (and more consonant) than the equal-tempered major third.

Say you base your whole guitar on the frequency A440. 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. (This is NOT an equal-tempered C#; it will only sound in tune with A and related notes.)

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.

Edited by Geo
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