Motivated by recent developments in the computation of periods for string
compactifications with $c=9$, we develop a complementary method which also
produces a convenient basis for related calculations. The models are realized
as Calabi--Yau hypersurfaces in weighted projective spaces of dimension four or
as Landau-Ginzburg vacua. The calculation reproduces known results and also
allows a treatment of Landau--Ginzburg orbifolds with more than five fields.