  Frames for $\R^n$ can be thought of as redundant or linearly dependent
coordinate systems, and have important applications in such areas as signal
processing, data compression, and sampling theory. The word "frame" has a
different meaning in the context of differential geometry and topology. A
moving frame for the tangent bundle of a smooth manifold is a basis for the
tangent space at each point which varies smoothly over the manifold. It is well
known that the only spheres with a moving basis for their tangent bundle are
$S^1$, $S^3$, and $S^7$. On the other hand, after combining the two separate
meanings of the word "frame", we show that the $n$-dimensional sphere, $S^n$,
has a moving finite unit tight frame for its tangent bundle if and only if $n$
is odd. We give a procedure for creating vector fields on $S^{2n-1}$ for all
$n\in\N$, and we characterize exactly when sets of such vector fields form a
moving finite unit tight frame.
