We have used the ratio of column densities derived independently from the 850-μm continuum James Clerk Maxwell Telescope Plane Survey and the ¹³CO/C¹⁸O (J = 3 → 2) Heterodyne Inner Milky Way Plane Survey to produce maps of the dense-gas mass fraction (DGMF) in two slices of the Galactic plane centred at ℓ = 30° and 40°. The observed DGMF is a metric for the instantaneous clump formation efficiency (CFE) in the molecular gas. We split the two fields into velocity components corresponding to the spiral arms that cross them, and a two-dimensional power-spectrum analysis of the spiral-arm DGMF maps reveals a break in slope at the approximate size scale of molecular clouds. We interpret this as the characteristic scale of the amplitude of variations in the CFE and a constraint on the dominant mechanism regulating the CFE and, hence, the star formation efficiency in CO-traced clouds.