  For a projective hypersurface $Z$ with isolated singularities, we generalize
some well-known assertions in the nonsingular case due to Griffiths, Scherk,
Steenbrink, Varchenko, and others about the relations between the Steenbrink
spectrum, the Poincar\'e polynomial of the Jacobian ring, and the roots of
Bernstein-Sato polynomial for a defining polynomial $f$ up to sign forgetting
the multiplicities. We have to use the pole order spectrum and the alternating
sum of the Poincar\'e series of certain subquotients of the Koszul
cohomologies, and study the pole order spectral sequence. We show sufficient
conditions for vanishing or non-vanishing of the differential $d_1$ of the
spectral sequence, which are useful in many applications. We prove also
symmetries of the dimensions of the subquotients of Koszul cohomologies, which
are crucial for computing the roots of BS polynomials. We can deduce that the
roots of BS polynomial whose absolute values are larger than $n-1-n/d$ are
determined by the ``torsion part" of the Jacobian ring (modulo the roots of BS
polynomial for $Z$) if all the singularities of $Z$ are weighted homogeneous.
Here $d=\deg f$ and $n$ is the dimension of the ambient affine space.
