A theory based on existing science.

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A theory based on existing science.

Postby Navron » 17 Dec 2013 23:57

As a guitar player, I'll occasionally enjoy picking the guitar at the 12th fret, especially when I'm playing old-school game themes like Tetris or Mario. Picking at the 12th fret seemed to give it a more hollow chiptune sound like the original tunes.

Now, after learning more about digital music, I wonder if the reason it sounds like a chiptune, is because of the nature of digital waveforms, most notably the square wave.

A square wave contains the fundamental frequency in addition to every odd number harmonic with an amplitude ratio of 1/n (n = harmonic #). A sawtooth contains all harmonics with the same amplitude ratio.

Getting back to the guitar. My theory is that by picking at the 12th fret, you're reducing approx. half the harmonics that you would normally hear if you were picking at the normal location near the end of the string, effectively mimicking the same relationship between a saw and square waveform, ultimately creating your own guitar version of a square wave.

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Re: A theory based on existing science.

Postby Fimbulin » 18 Dec 2013 07:58

I wish I had time to study this out. I do believe you are partly correct. The guitar body does not change size so it still resonates mostly the same. The string size is halved, and therefore sounds an octave higher. You don't have any of the lower frequencies. Pitches aside, I'd betcha that the overtones that are non-existent at the 12th fret could be what makes the "saw" sound more "square". If the body of the guitar changed size with the string, then you would start hearing different overtones and perhaps have a constant tone.

It would be an interesting study for sure.
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Re: A theory based on existing science.

Postby CitricAcid » 18 Dec 2013 08:26

You could record yourself picking the guitar at the normal position and at the 12th fret, take an FFT of each signal, and compare the harmonic content. That would be one way to check your theory.

And I presume you mean that you are plucking the string with the pick at the 12th fret location and not just fretting the 12th fret. Playing sul tasto, as it were. (Do guitarists use such terms or is that just for bowed string instruments?)
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Re: A theory based on existing science.

Postby S.P.P » 19 Dec 2013 06:42

CitricAcid wrote:Playing sul tasto, as it were. (Do guitarists use such terms or is that just for bowed string instruments?)

Never heard that one used for guitar, but I guess it's a perfectly relevant term.

On topic: The only thing I can think, is that if you're picking further up the neck, the string will inherently vibrate faster, owing to the fact that the distance from the pick to the bridge is shorter. Because of this, the string will not vibrate slowly enough to get the lower harmonics you would normally get. It might be so that if you pick hard enough and hold the note, the body of the sound will warble in and out as the lower end of the string vibrates. If this is the case, then it supports your theory, as that's exactly happens with PWM square waves (unless I'm mistaken .. I hope I'm not!).

Not sure what good that is, but it seems to back up the saw/square theory you've got going on. :3
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Re: A theory based on existing science.

Postby ChocolateChicken » 22 Dec 2013 23:43

I think it more has to do with the type of guitar amp and distortion that is being used. The effect of distortion will affect the waveform of a string and essentially make it into more of a square wave-type shape, which also explains why it sorta sounds like chiptunes as well. The more distortion that is added, the more this chiptune/square wave effect will become noticeable. As for picking at the 12th fret, I think all this does is give the string a shorter decay on the input signal.

Note: If you add enough distortion to a plain saw wave, you will notice it sounds more like a square wave, and it will even lose its harmonics until it has only the odd harmonics, just like a square. Try it and see for yourself!
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Re: A theory based on existing science.

Postby ph00tbag » 30 Dec 2013 17:44

When a string vibrates, it's wavelength is always twice the length of the string, because the the fundamental is basically the whole string moving up and down, forming half a sine wave. See? The string also vibrates at all other harmonics of that fundamental.

When you pick a guitar, you excite the string at all harmonics that vibrate that part of the string, relative to their amplitude at that part of the string. If the harmonic is at a node at that part of the string, that is to say if the harmonic has no amplitude at that part of the string when the string vibrates, then that harmonic will not vibrate.

Now, look at all of these little sines vibrating. That's what the first eight harmonics of a vibrating string look like. Now see all of those sines that are at zero when you hit π/2? You can check the list of functions on the left to see that all of those sines are even harmonics. So following from the second paragraph, second sentence, if you pluck the string halfway across its length, then those harmonics will not sound, and the string will be vibrating like this.

A square wave is the sum of all of a pitch's odd harmonics, as you've observed. Since plucking the string at its center mutes all of the even harmonics, it follows that the resulting waveform will be a square.

Playing stringed instruments at different parts of the string is a popular way to change the instrument's character. Playing near the bridge will dampen the fundamental, while bringing out the highest harmonics, making the sound thin and tinny. You can selectively dampen other harmonics by targeting other parts of the string as well. Experiment! Stringed instruments are really versatile instruments because of this quality.

(Note, in the second graph, I've also included functions for triangle and square waves if you want to see what the summed harmonics look like.)

This is a mathematical proof of your theory, but if you want to prove it scientifically, just record yourself playing notes on different parts of your string, then look at the waveform in audacity. For the part where you play the middle of the string, the waveform will look significantly more square-like than other parts. Note that it won't look exactly like a square wave, though, because the body and interior of the guitar shape the wave form just as much as the string does.
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