The large deviation multifractal spectrum is a function of central importance in multifractal analysis. It allows a ne description of the distribution of the singularities of a function over a given domain. The 2-microlocal spectrum, on the other hand, provides an extremely precise picture of the regularity of a distribution at a point. These two spectra display a number of similarities: their de nitions use the same kind of ingredients; both functions are semi-continuous; the Legendre transform of the two spectra yields a function of independent interest: the 2-microlocal frontier in 2-microlocal analysis, and the "\tau " function in multifractal analysis. This paper investigates further these similarities by providing a common framework for the de nition and study of the spectra. As an application, we obtain slightly generalized versions of the 2-microlocal and weak multifractal formalisms (with simpler proofs), as well as results on the inverse problems for both spectra.