  We derive generalized TKNN-equations via bundle representations of the
noncommutative torus with rational deformation parameter, the bundle coming
from spectral projections in the torus algebra. These equations relate Chern
numbers of dual bundles which we interpret as Hall conductances for Dirac-like
Hamiltonians describing magnetic Bloch electrons in a strong magnetic field. We
also present their generalizations for irrational values of the deformation
parameter.
