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New sets of CMS underlying-event parameters (“tunes”) are presented for the pythia8 event generator. These tunes use the NNPDF3. 1 parton distribution functions (PDFs) at leading (LO), next-to-leading (NLO), or nextto-next-to-leading (NNLO) orders in perturbative quantum chromodynamics, and the strong coupling evolution at LO or NLO. Measurements of charged-particle multiplicity and transverse momentum densities at various hadron collision energies are fit simultaneously to determine the parameters of the tunes. Comparisons of the predictions of the new tunes are provided for observables sensitive to the event shapes at LEP, global underlying event, soft multiparton interactions, and double-parton scattering contributions. In addition, comparisons are made for observables measured in various specific processes, such as multijet, Drell–Yan, and top quarkantiquark pair production including jet …