  We study a collection of stability conditions (in the sense of Schmitt) for
complexes of sheaves over a smooth complex projective variety indexed by a
positive rational parameter. We show that the Harder-Narasimhan filtration of a
complex for small values of this parameter encodes the Harder-Narasimhan
filtrations of the cohomology sheaves of this complex. Finally we relate a
stratification into locally closed subschemes of a parameter space for
complexes associated to these stability parameters with the stratification by
Harder-Narasimhan types.
