  The periods of the three-form on a Calabi-Yau manifold are found as solutions
of the Picard-Fuchs equations; however, the toric varietal method leads to a
generalized hypergeometric system of equations which has more solutions than
just the periods. This same extended set of equations can be derived from
symmetry considerations. Semi-periods are solutions of this extended system.
They are obtained by integration of the three-form over chains; these chains
can be used to construct cycles which, when integrated over, give periods. In
simple examples we are able to obtain the complete set of solutions for the
extended system. We also conjecture that a certain modification of the method
will generate the full space of solutions in general.
