What's the physics behind harmonics?

[AmazingGracePlayer]

I'm sure everyone's heard of and knows of harmonics, does anyone know the physics theory/concept/law behind harmonics?

[lemur821]

Yes.

Harmonics

[superjesus]

a harmonic is achieved by forcing the string to vibrate with a fixed number of "wavelenghts" from nut to saddle. This is called a standing wave

by placing your fretting finger over a "harmonic," you are playing on a node of the standing wave. for all intents and purposes, the node is not moving.

For example, playing the 12th fret harmonic causes the string to vibrate in 2 places, the length of string from the nut to the 12 fret and the length from the 12th fret to the saddle. The node is at the 12 fret.

Playing the 7th fret harmonic causes 3 standing wave vibrations, from the nut to the 7th fret, 7th fret to 19th fret and 19th fret to saddle. the nodes are at the 7th and 19th frets.

PLaying at the 5th fret harmonic causes 4 standing waves, from the nut to 5th fret, 5th fret to 12th fret, 12th fret to 24th fret, and 24th fret to saddle.

you can ideally play an open string harmonic note anywhere that will divide the string into a positive number of equal parts. However, getting past about 7 or 8 standing waves becomes inaudible (at least for me).

now capoing at any given fret changes the overall length and fundamental pitch of the string. you get a whole new set of harmonics (ala portrait of tracy) by doing this.

as for the physics....the concept of harmonics isnt taught in great detail to high school through sophomore college physics students. It is really first covered in detail Quantum Mechanics w.r.t. particle behavior in quantum wells.

[vindy500]

in new zealand high schools standing waves was taught alot in physics.

[Jazz Ad]

Lambda1 is a string played normally.
Lambda2 to Lambda4 are harmonics. To get it you stop the string on one of the nodes.

[lemur821]

To add to this, whenever you pluck a string it vibrates at many different frequencies. The basic one is called the fundamental, and it's just the pitch of the string (so on the A string this is 55 Hz). The others are all integer (2, 3, 4, 5...) multiples of this, so the next is an octave above, the next is an octave and a fifth, the next is two octaves, and so on.

Each overtone, as they are called, vibrates in segments. The fundamental has just one: the whole string. The next up divides the string as if it were two strings of half the real string's length, not moving at all right over the twelfth fret. The next up vibrates in three segments, and so on.

[AmazingGracePlayer]

Ohhhh I see... Need to take some time to absorb all those info.