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In the quasistatic regime, generic modifications to gravity can give rise to novel scale dependence of the gravitational field equations. Crucially, the detectability of the new scale-dependent terms hinges upon the existence of an effective mass scale or length scale at which corrections to general relativity become relevant. Starting from only a few basic principles, we derive the general form of this scale dependence. Our method recovers results previously known in the specific case of Homdeski gravity, but also shows that they are valid more generally, beyond the regime of scalar field theories. We forecast the constraints that upcoming experiments will place on the existence of a new fundamental mass scale or length scale in cosmology. [ABSTRACT FROM AUTHOR]