let me explain it with something i posted like a year ago or so:
When a string vibrates, it is not only an up and down
movement of the whole string, but it is full of
layered vibrations (overtones) which give the sound
a lot of texture and actually determine whether it is
a guitar sound, or a piano sound and so on.
If you have a string that is fixed between two points
(on a guitar for example) and you strum it,
the wavelength is of course limited by the two points
where the string is fixed, thus (along with the tension
and the diameter of the string) determining the tone.
Now lets dampen the string with a finger on the exact
middle (12th fret on a guitar). You will see (hear)
that the string does not stop ringing:
When the string is tuned to C for example, the sound
that you hear now is c (one octave higher). The ratio
between Root and harmonic is 1:2 because we divided
the string in two halves.
The string can only vibrate with a straight multiple
of the ground frequency because the endings of the
string are immovably fixed on both sides.
The next logical tone is therefore at a 1:3 ratio:
In the case of a C-string this tone is a G
You can do this over and over again until infinity.
but only the first few overtones are really important
for music. Actually, starting on a c-string, you get
the whole major-scale ut of it:
1/1 C - 1/2 c - 1/3 g - 1/4 c' - 1/5 e' - 1/6 g' - 1/7
b' - 1/8 c'' . . . . .
All those overtones are ringing at the same time when
striking a string, thus determining the "colour" of the
tone. If it was just one steady vibration like I
mentioned in the beginning, it would be nothing but a
plain sine wave (now you can imagine how a synthesizer
creates different sounds from one and the same
ground-frequency. It adds all those overtones to
create specific sounds)
As you can see it is always a mirror image - therefore
you can create the same overtones below the 12th fret
as you can above the 12th fret!
The method you use to create them, is either Natural
Harmonic or Artificial (Pinch) Harmonic. Putting the
finger on the string above the respective knot point is
referred to as "natural harmonic"
Doing it with the picking hand by slightly touching the
string with the thumb when picking is called
Artificial Harmonic.
Of course those harmonics are pretty high pitched, for
it's a pretty high vibration-ratio. That's what makes
the screaming sound.
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