  In this paper we consider the (weighted) spectral measure $\mu_n$ of a
$n\times n$ random matrix, distributed according to a classical Gaussian,
Laguerre or Jacobi ensemble, and show a moderate deviation principle for the
standardised signed measure $\sqrt{n/a_n}(\mu_n -\sigma)$. The centering
measure $\sigma$ is the weak limit of the empirical eigenvalue distribution and
the rate function is given in terms of the $L^2$-norm of the density with
respect to $\sigma$. The proof involves the tridiagonal representations of the
ensembles which provide us with a sequence of independent random variables and
a link to orthogonal polynomials.
