...that the first four harmonics of a string form a major chord? (root-perfect 5th-octave-maj3rd) Is there some kind of theory related to this, or is it just a coincidence?
i'm no expert on the physics of string vibration, but on any vibrating string there are overtones going on as well as the original note. every note can be found within the overtone series of every other note, it's just that octaves, fifths and 3rds tend to be among the stronger overtones. (hence they sound strongly together and make for good chords).

here's how to show this: play fret 9 on the G string (E) with all other strings muted except the low E. play that note and quickly release. the low E string will still be vibrating sympathetically with the fretted E. now do the same only play fret 4 on the G string (B, the fifth of E). The E string will now vibrate simpathetically with that note. listen closely, and you will hear that the harmonic that is ringing on the E string is in fact, the note B that you just played! this is because B is a strong note in the overtone series for E: it's the fifth. Lastly, play 6th fret on the D string, (G#), the third of E. Again, the E string will ring, and as a G#. You can do this with all the other notes of the chromatic scale and you will get an overtone, but the major chord tones are the strongest. Basically, therefore, major chords sound "strong" or "consonant" because the notes within them vibrate against each other well, and the vibrations are weaker in other types of chords, like minor, diminished, augmented, etc.
^ Kind of what Dan said, it's all physics stuff with over tones, pinching at the node points and how the waves line up... I've forgotten most of the physics though, so I can't explain it very well.
Fundamental - Root - open string.
1st overtone - octave - 12 fret harmonic
2nd overtone - 12th (fifth) - 7th fret harmonic
3rd overtone - Octave - 5th fret harmonic
4th overtone - 3rd - 4th/9th fret harmonic.

When you hit an open string and let it ring long enough, all of those play simultaneously on one string. This is also why major triads sound really good.
Thas Crasy. How does one string effect another string? Is it the work of the devil?
yeah becuase on guitar u have over tones. when you play an open string, not just the open string is being played. When u hit the open string, u get certian spots on the guitar string called nodes. these nodes are the points on the guitar where the waves and vibration cancel out each other and at that spot, the string is not vibrating as much. The node is the point where a nat. harmonic is. So like each node of the vibrating open string makes up the major scale (over tones)
meow :3
it's like a tuning fork. you can hit one tuning fork, and then if another one is around, you can hear both tuning forks.
Quote by mikeman
Thas Crasy. How does one string effect another string? Is it the work of the devil?

hehe it's really cool, but i have no clue how it works
The only correction I'd make to what Dan said is that it's not just on strings. Every pitch generating sound rings in overtones (arguably unpitched sound does... but since it's unpitched, I'm not sure how I'd confirm that).

When a pitch is sounded it reflects off of different surfaces, this is easiest to understand on a vibrating string (oddly enough). When a string vibrates it generates a wave at some point along its length, normally that fundamental vibration normalizes to the midpoint of the string.

It's good to visualize ripples in water expanding outward here, that's the wave, if you were to draw a line straight across the expanding ripple, with the center of the line at the center of the ripple, that would be the string, and the part of the wave travelling along that line would be the wave as it travles along the string.

A vibrating string generally needs to be anchored to two points, on a guitar that's the bridge and the nut. When the wave on the string reaches these endpoints, it reflects back in on itself, and the reflections collide and reflect off of each other at the mid point. The reflection is the same wave, but only half as long (and generally speaking about half as strong).

But it continues, this second reflection starts moving back to its end point, at the same time another first reflection is generated, and they collide half way between the mid point and the anchor. This second reflection is 1/4th of the length of the original wave.

And it continues again, but at this point gets a little more complicated. Those reflections continue to divide evenly, however, they also divide at about 1/4th (or 3/4ths, depending on how you look at it) their length as they come into contact with new original waves being generated.

The effect is that, roughly, a vibrating pitch, especially a string, rings at increments of its original pitch. Namely a string ringing at 100hz will also ring more softly at 200, 300, 400, 500, 600, 700, ... hz. These are the overtones of any pitched sound. Harmonics are simply isolated overtones.

Why do those make a chord? For every doubling of a pitch, you reach the octave of that pitch, such that 100hz doubled to 200hz is one octave higher, and 400hz is an octave higher than that. While playing with sound, Pythagoras noted that the more pure a division of the string was, the more consonant it was, such that the division 2:1 was the most consonant (the octave), followed by 3:2 (the 5th). To see how that works out compared to the overtones, take 100hz as our fundamental, and multiply by 3:2 -- 300:200. Where 200hz is the octave, 300hz is the fifth (notice that it's also the third overtone). The next in the series is 400hz, 4:1 (or 2:1:2:1...) a double octave. And then next, 5:4, for 500hz, the major third. (continuing you get 6:4, which reduces to 2:3..), and so on.
Quote by les_kris
Corwinoid is God
I'm not even God-like... I've officially usurped the Almighty's throne.
Click here to worship me.

Member #3 of the Corwinoid Fan Club
^No wonder powerchords sound so solid. Where would the harmonic for a major 3rd be? I confused myself.
^ or 9th, or 16th, or somewhere up near the bridge.
Quote by les_kris
Corwinoid is God
I'm not even God-like... I've officially usurped the Almighty's throne.
Click here to worship me.

Member #3 of the Corwinoid Fan Club