  A common criterion in the design of finite Hilbert space frames is minimal
coherence, as this leads to error reduction in various signal processing
applications. Frames that achieve minimal coherence relative to all unit-norm
frames are called Grassmannian frames, a class which includes the well-known
equiangular tight frames. However, the notion of "coherence minimization"
varies according to the constraints of the ambient optimization problem, so
there are other types of "minimally coherent" frames one can speak of. In
addition to Grassmannian frames, we consider the class of frames which minimize
coherence over the space of frames which are both unit-norm and tight, which we
call 1-Grassmannian frames. We observe that these two types of frames coincide
in many settings, but not all; accordingly, we investigate some of the
differences between the resulting theories. For example, one noteworthy
advantage enjoyed by 1-Grassmannian frames is that their optimality properties
are preserved under the Naimark complement.
