By appealing to the resonant frequency distribution, we can rationalize the nonmonotonic trend in ensemble linewidth W with increasing volume fraction that we observe for all the disordered dispersions in Figures . At low η, nanoparticles are too far apart to optically couple, and they each resonate around the same frequency (i.e., small dev[ω res,i ]). At large η, nanoparticles couple strongly to one another, but there is small variance in the local density around each particle due to steric hinderance. Because their local environments are similar, all particles resonate around the same frequency (again, small dev[ω res,i ]). The quantity dev[ω res,i ] is large only at intermediate η, where the dispersion is dense enough for particles to couple significantly but not too dense as to suppress the heterogeneity of local environments. The balance of these competing effects is what causes the ensemble linewidth W to be nonmonotonic with respect to η.