Abelian covers of
C
P
1
\mathbb {CP}^{1}
, with fixed Galois group
A
A
, are classified, as a first step, by a discrete set of parameters. Any such cover
X
X
, of genus
g
≥
1
g\geq 1
, say, carries a finite set of
A
A
-invariant divisors of degree
g
−
1
g-1
on
X
X
that produce nonzero theta constants on
X
X
. We show how to define a quotient involving a power of the theta constant on
X
X
that is associated with such a divisor
Δ
\Delta
, some polynomial in the branching values, and a fixed determinant on
X
X
that does not depend on
Δ
\Delta
, such that the quotient is constant on the moduli space of
A
A
-covers with the given discrete parameters. This generalizes the classical formula of Thomae, as well as all of its known extensions by various authors.