  The purpose of this paper is to investigate the duality between large scale
and small scale. It is done by creating a connection between C*-algebras and
scale structures. In the commutative case we consider C*-subalgebras of
$C^b(X)$, the C*-algebra of bounded complex-valued functions on $X$. Namely,
each C*-subalgebra $\mathscr{C}$ of $C^b(X)$ induces both a small scale
structure on $X$ and a large scale structure on $X$. The small scale structure
induced on $X$ corresponds (or is analogous) to the restriction of $C^b(h(X))$
to $X$, where $h(X)$ is the Higson compactification. The large scale structure
induced on $X$ is a generalization of the $C_0$-coarse structure of N.Wright.
Conversely, each small scale structure on $X$ induces a C*-subalgebra of
$C^b(X)$ and each large scale structure on $X$ induces a C*-subalgebra of
$C^b(X)$. To accomplish the full correspondence between scale structures on $X$
and C*-subalgebras of $C^b(X)$ we need to enhance the scale structures to what
we call hybrid structures. In the noncommutative case we consider
C*-subalgebras of bounded operators $B(l_2(X))$.
