Take the tour ×  I understand that when you pluck a guitar
string, then a bunch of harmonic frequencies are produced rather
than just the frequency of the desired note.  If this is true,
why does C2 sound so different from C1? I mean, C2 is a harmonic
of C1, and should therefore be heard when C1 is played. Why are
all these harmonics produced on top of the targeted note in the
first place?  Also, what happens if you don't pluck at the
center of a string?  share|improve this question Somewhat
related question here on Math.SE. –  Nick Kidman Jul 1 '12 at
22:08 add comment  3 Answers  up vote 6 down vote accepted
Let's look at frequency instead of notes. Let's say the string
has a natural frequency of $100 Hz$ and that harmonics are
present when you pluck it. Then, the frequency content of the
sound will be of the form:  $a_1 \cdot 100 Hz + a_2 \cdot 200 Hz
+ a_3 \cdot 300 Hz + ... $  Now, let's say you fret this string
halfway such that the natural frequency becomes $200 Hz$. When
plucked, the frequency conten