  We introduce a novel approach to scale-decomposition of the fluid kinetic
energy (or other quadratic integrals) into band-pass contributions from a
series of length-scales. Our decomposition is based on a multiscale
generalization of the ``Germano identity'' for smooth, graded filter kernels.
We employ this method to derive a budget equation that describes the transfers
of turbulent kinetic energy both in space and in scale. It is shown that the
inter-scale energy transfer is dominated by local triadic interactions,
assuming only the scaling properties expected in a turbulent inertial-range. We
derive rigorous upper bounds on the contributions of non-local triads,
extending the work of Eyink (2005) for low-pass filtering. We also propose a
physical explanation of the differing exponents for our rigorous upper bounds
and for the scaling predictions of Kraichnan (1966,1971). The faster decay
predicted by Kraichnan is argued to be the consequence of additional
cancellations in the signed contributions to transfer from non-local triads,
after averaging over space. This picture is supported by data from a $512^3$
pseudospectral simulation of Navier-Stokes turbulence with phase-shift
dealiasing.
