The distinctive quality of a musical note from either an Instrument or voice is more properly called the Timbre.
The Clarinet is said to be 'reedy'. An examination of the soundwaves produced by the two instruments would show the difference. There is a fundamental frequency (the note) whose height is the amplitude or volume. The shape of it however varies by instrument and depends on the number of extra frequencies the instrument produces (Harmonics) and the actual production method of the sound (single reed, double reed, plucked string, struck string, bowed string etc.).
Harmonic frequencies add or subtract from the fundamental and 'colour' the sound. A pure note is a Sine Wave of one frequency only and no instrument except a tuning fork and a Synthesiser can produce this. Flutes are close but still have overtones.