It is now apparent that the two principal models of turbulence (the 'beta' and 'lognormal' models) are the extremes of a continuous family of (stable, attractive, hence 'universal') multifractals characterized by Levy indices alpha = 0 and 2, respectively. Using a technique called 'double trace moment analysis', and turbulent velocity data, alpha of about 1.3 +/-0.1 is empirically obtained. As has long been suspected, turbulence really is 'in between' the Beta and lognormal models. This describes the entire hierarchy of singularities of the Navier-Stokes equations.