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Btw, a Strat neck pickup lines up proportionally with the neck pickup on a 22 fret PRS / Les Paul. I made sure it did before I switched from both of those to a humbucker Strat as my main guitar because that tone is important to me.
It’s simply that the pickup is further from the bridge on 22-fret guitars and so has a different mix of harmonics which slightly emphasises some of the lower ones.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
Most energy goes into the first harmonic (wavelength = 2L, one node above the 12th fret and no antinodes [not counting the obvious antinodes at the nut and bridge]) and that controls the note we perceive it to be playing.
But energy also goes into the second harmonic (wavelength L, one antinode and two nodes), the third harmonic (wavelength 2L/3, two antinodes and three nodes), etc etc.
The key is that the string is playing all these notes at once. Exactly what balance there is between all the harmonics is very hard to predict, and is a massive contributor towards the tone of the guitar. There's a whole branch of mathematics, Fourier analysis, which is to do with breaking the extremely complex sum of all these waves back down into their individual harmonics. Thankfully that doesn't come up on A level...
What you need to think about is which harmonics have large amplitudes above each pickup. Most importantly, the first harmonic has max amplitude in the middle of the string and goes to zero as you approach the bridge. So a bridge pickup sees much less energy from this harmonic, so comparatively it's getting more energy from the higher harmonics and less from the lower ones. In comparison, the (say) 10th harmonic will have a wavelength smaller than the distance between the bridge and the bridge pickup, so that pickup still gets the full influence of that harmonic.
Regardless of where you're fretting, this pattern remains true: you'll be setting up a new string length, and the first harmonic of that length won't have much amplitude above the bridge pickup but the higher ones will.
This also explains things like tapped and pinched harmonics - when you tap above the 12th fret you are effectively forbidding the first harmonic (as well as the third, fifth, etc) so all the energy has to go into the second, fourth, etc. A pinched harmonic forces there to be a node very close to the bridge, so you are preventing energy from entering all the lower harmonics and the lowest allowed mode will be the 10th (or something like that).