  We introduce and the study the space of homeomorphisms of the circle (up to
M\"obius transformations) which are in $\ell^2$ with respect to modular
coordinates called diamond shears along the edges of the Farey tessellation.
Diamond shears are related combinatorially to shear coordinates, and are also
closely related to the $\log \Lambda$-lengths of decorated Teichm\"uller space
introduced by Penner. We obtain sharp results comparing this new class to the
Weil-Petersson class and H\"older classes of circle homeomorphisms. We also
express the Weil-Petersson metric tensor and symplectic form in terms of
infinitesimal shears and diamond shears.
