We introduce a new class of Sturm-Liouville operators with periodically modulated parameters. Their spectral properties depend on the monodromy matrix of the underlying periodic problem computed for the spectral parameter equal to 0. Under some assumptions, by studying the asymptotics of Christoffel functions and density of states, we are able to prove that the spectral density is a continuous function positive everywhere on the real line. This is a joint work with Bartosz Trojan (Wrocław University of Science and Technology).