Dense gas mass fraction as a function of volume density threshold n(H₂)cm^-3. The y-axis shows the sum of ¹³CO pixels from the GRS cube with H₂CO-derived density above the value shown on the x-axis divided by the total. Both values are computed over the velocity range 40 km s^-1<v_LSR< 75 km s^-1. The solid line represents the fraction of ¹³CO emitting voxels above the mean measured H₂CO density as described in Sect. 3.3. The blue shaded region shows the extent of plausible model fits at each density: effectively, this is the ~ 1σ error region. The vertical line at n = 10⁴cm^-3 indicates the approximate completeness limit. The horizontal line shows the fraction of ¹³CO flux in pixels that had corresponding detections at > 2σ in both the H₂CO1₁₀ − 1₁₁ and 2₁₁ − 2₁₂ lines: it represents the upper limit of what could have been detected if, e.g., all H₂CO detections were toward regions with n> 10⁴cm^-3. The failure to converge to a fraction f → f_max indicates that there are some real detections of low-density gas.