  We address the possibility of bounding the spectral index $n$ of primordial
density fluctuations, using both the cosmic microwave background (cmb)
anisotropy and data on galaxies and clusters. Each piece of galaxy and cluster
data is reduced to a value of $\sigma(R)$ (the linearly evolved {\em rms}
density contrast with top hat smoothing on scale $R$) which allows data on
different scales to be readily compared. As a preliminary application, we
normalise the spectrum using the ten degree variance of the COBE data, and then
compare the prediction with a limited sample of low energy data, for the MDM
model with various values of $n$, $\Omega_\nu$ and $h$. With $h=.5$, the data
constrain the spectral index to the range $0.7\lsim n \lsim 1.2$. If
gravitational waves contribute to the cmb anisotropy with relative strength
$R=6(1-n)$ (as in some models of inflation), the lower limit on $n$ is
increased to about $0.85$. The uncertainty in $h$ widens this band by about
$0.1$ at either end.
