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
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).