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A technical explanation of how guitar/bass strings work


dc2009
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Attached are a very small part of the notes for my maths exam a week on thursday, they include a nice analysis on how guitar strings work the way the do. The section can be read on it's own, and is very short (think it's 3.3) but the stuff before is decent background reading if you need it to rejig your maths brain.

Personally I find it very comforting to know that we understand how these things work, and can exploit them to make lovely sounding guitars and basses.
Just uploaded it for anyone who is interested.
So please enjoy,
Dan

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[quote name='dc2009' post='1248750' date='May 28 2011, 10:52 PM']Attached are a very small part of the notes for my maths exam a week on thursday, they include a nice analysis on how guitar strings work the way the do. The section can be read on it's own, and is very short (think it's 3.3) but the stuff before is decent background reading if you need it to rejig your maths brain.

Personally I find it very comforting to know that we understand how these things work, and can exploit them to make lovely sounding guitars and basses.
Just uploaded it for anyone who is interested.
So please enjoy,
Dan[/quote]
Thanks for that. Cocktail with Tom Cruise is about to start so I'll finish reading it later. Ta.

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Laplace and Fourier. Not good bedfellows on a Saturday night.

Love the negligible elasticity and horizontal displacement. They've not seen my playing then.

I'm going for Dusk 'til Dawn myself.

Edited by TimR
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[quote name='TimR' post='1248761' date='May 28 2011, 11:06 PM']Laplace and Fourier. Not good bedfellows on a Saturday night.

Love the negligible elasticity and horizontal displacement. They've not seen my playing then.[/quote]

Probably not good bedfellows since they're deceased :)

And +1 for the comment on your playing, gave me a right chuckle, though I fear mine is the same.

Edited by dc2009
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good ol' PDEs. Have spent the whole of my day revising part of my Vibrations module (mechanical engineering).

Thought I'd add something more visual to contribute. The impage below shows all the vibrations that are happening at once on a string, which occur with decreasing magnitude. The higher frequencies also decay faster, which is why a note will have an 'attack', this is the first instant before the highest mode shapes dissapear.



The circle on the images at a node (non-moving) point is the same effect as lightly touching the string, and it's in this way that you get the harmonic when playing.

p.s. I can go into the equations if you want, but I don't think any of us want that :)

Edited by ZMech
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[quote name='ZMech' post='1248928' date='May 29 2011, 09:34 AM']3rd year Bristol for me. Don't worry, you probably don't have it as bad as me, 7 exams with 5 left, the last one being on June 16th. Fun times...[/quote]
Lol 2nd year here, I do finish on the 10th June, but I have all 8 of my exams to do between Tuesday and then, fml.

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I covered a lot of DSP 20 years ago at Uni. when it was in its infancy. All a bit hazy now and the technology is much further advanced now. Analysing waveforms with a first generation Soundblaster card with very basic Windows 3.1 software was about as advanced as it was then.

Don't forget that this is a massive oversimplification of what is going on. All those waveforms (and a load of others due to resonant vibrations and damping in the wood etc.) are superimposed on top of each other and that's when the string is in the sustain phase. During the attack there are very strong transients which are shown as components at ALL frequencies.

It's a mathematical model of perfect string vibration. Good on paper but get into the physics lab and try to recreate the tone of a bass by summing sinewaves of different frequencies and you'll end up with something that sounds more like synthesiser (or at best a clarinet) than a bass.

When you put your finger on the "node" you're forcing the string to create a node because there isn't actually one there. This then allows the higher overtones to come through while the lower ones are effectively stopped. That's why it's called "false harmonics".

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