  We show that every two-bridge knot $K$ of crossing number $N$ admits a
polynomial parametrization $x=T_3(t), y = T_b(t), z =C(t)$ where $T_k(t)$ are
the Chebyshev polynomials and $b+\deg C = 3N$. If $C (t)= T_c(t)$ is a
Chebyshev polynomial, we call such a knot a harmonic knot. We give the
classification of harmonic knots for $a \le 3.$ Most results are derived from
continued fractions and their matrix representations.
