  We obtain bounds for the spectrum and for the total width of the spectral
gaps for Jacobi matrices on $\ell^2(\Z)$ of the form $(H\psi)_n=
a_{n-1}\psi_{n-1}+b_n\psi_n+a_n\psi_{n+1}$, where $a_n=a_{n+q}$ and
$b_n=b_{n+q}$ are periodic sequences of real numbers. The results are based on
a study of the quasimomentum $k(z)$ corresponding to $H$. We consider $k(z)$ as
a conformal mapping in the complex plane. We obtain the trace identities which
connect integrals of the Lyapunov exponent over the gaps with the normalised
traces of powers of $H$.
