Potential effect of the CMB on the ﹩{L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }﹩ ratio, a proxy for the dense gas fraction, for a select sample of parameters. The effect is negligible for most parameters, with the greatest effect seen when HCN is least affected and contrary to the data. Different temperatures, densities, and indeed galaxy integrated measurements will affect this plot, but it is hard to find a realistic set of conditions that could lead to observations overestimating the dense gas fraction. The excess of HCN in the high luminosity galaxies may indeed be due to a real excess of dense gas.