QUOTE(Andromeda_Aiken @ Jun 2 2008, 02:27 PM)

Why? What's the physics behind it?
the acoustics of string harmonics are quite similar to those of a brass instrument. a string has many modes of vibration, the simplest being the fundamental, where the string is stationary at either end (where its fixed) and moving most in the middle. By placing your finger in the middle of the string you can force it to play a harmonic, or overtone, where it vibrates in two equal halves, with three stationary points, one at each end, and the middle. (In a brass instrument it is the air column that it divided into sections, but the overtones are pretty much the same)
The harmonic series progresses as you place your finger dividing the string into smaller sections, 1/2 a string will sound an octave above open, 1/3 a string will sound a perfect 12th and have 4 stationary points, 1/4 2 octaves with 5 stationary points, 1/5 2 octaves and a major 3rd with six stationary points etc. All of these harmonics sound at varying degrees when you play a note, playing a harmonic causes only that harmonic and its multiples to sound, so they have a "thinner" sound than ordinary notes.
Some reasons behind why the notes start to sound fuzzy -
when the wavelength becomes a very small percentage of the string, the antinodes (the stationary points on the string) become unstable, as the very small length of string your finger is seperating is a very high overtone, and probably very close in ratio to others. Fir example, if you divide a string into 20 parts, the length os very similar to 19 or 21 parts so these can sound as well, causing a distortion of sound.
When the vibrating length is very small the width of the sting comes into play, it cannot be considered a 1-dimensional line, and takes on the properties of a vibrating bar, which has much more complicated acoustics and will not produce clear overtones.
If you are not using high quality strings they may be of non-uniform density or diameter, a harmonic cannot sound unless all vibrating parts of the string have a roughly equal acoustic characteristic.
I'm not entirely sure why the quality of the instrument makes a difference, though it obviously does! can anyone explain?