  We study natural variations of the G2 structure {\sigma}_0 \in {\Lambda}^3_+
existing on the unit tangent sphere bundle SM of any oriented Riemannian
4-manifold M. We find a circle of structures for which the induced metric is
the usual one, the so-called Sasaki metric, and prove how the original
structure has a preferred role in the theory. We deduce the equations of
calibration and cocalibration, as well as those of W3 pure type and
nearly-parallel type.
