  We study the shapes of elastic membranes under the simultaneous exertion of
tensile and compressive forces when the translational symmetry along the
tension direction is broken. We predict a multitude of novel morphological
phases in various regimes of a 2-dimensional parameter space $(\epsilon,\nu)$
that defines the relevant mechanical and geometrical conditions. Theses
parameters are, respectively, the ratio between compression and tension, and
the wavelength contrast along the tension direction. In particular, our theory
associates the repetitive increase of pattern periodicity, recently observed on
wrinkled membranes floating on liquid and subject to capillary forces, to the
morphology in the regime ($\epsilon \ll 1,\nu \gg 1$) where tension is dominant
and the wavelength contrast is large.
