Harmonics in Music: Pan Flute, Filters & Distortion

[zabachi]

I made a pan flute that has 1 open end and 1 closed end, so when i blow into it, the fundamentral frequency I put actually generates harmonic freqeuncies of 2f,3f,4f... and this creates distortions? Is this correct? If so, why most musical intruments don't have any distortions and sound nice? Is it because they have harmonic filters? Or is this distortion very minute?

 

[maimonides]

There are at least three topics here:

In an amplifier you want the output signal to be as similar to the input as possible, (except for more amplitude). One way of testing the quality of an amplifier is putting in a pure sine wave and measuring the overtones it produces. (often called total harmonic distortion, THD).
(Amplifiers for electric guitars and basses are exempt from this, they are meant to add harmonics to the signal and contribute to the "sound". You´d better consider them part of the instrument)

Almost all musical instruments produce "sounds" (a fundamental and - sometimes a lot of - overtones/harmonics). This is one of the reasons you can distinguish the sounds of instruments at the same pitch and volume. (The other reason is "attack" the transient phase until a continuous tone is established.) A sine tone ("pure tone") by itself sounds awful.
So the existence of overtones is desired in music and not considered distortion. In some instruments the second harmonic has a higher amplitude than the fundamental.

A pan flute is a cylindrical resonator with one end open and one end closed. A resonator like this has no even harmonics, so the series is f₀, 3f₀, 5f₀ ... , which is part of what makes a panflute sound like a panflute.
(Actually, things are more complicated: The movement of the air column in the pipe will deflect the jet of air that is blowing over it. This deflection and the interaction of the air jet with the far edge of the pan pipe will not be totally linear, so a small amount of even harmonics will also be produced.)