  We construct tame differential calculi coming from toral actions on a class
of C*-algebras. Relying on the existence of a unique Levi-Civita connection on
such a calculi, we prove a version of the Bianchi identity. A Gauss-Bonnet
theorem for the noncommutative 2-torus in this tame calculus set-up
corresponding to conformal deformations of the canonical bilinear metric is
formulated and proved for a class of conformally deformed metrics.
