Simultaneous consonance is a salient perceptual phenomenon corresponding to the perceived pleasantness of simultaneously sounding musical tones. Various competing theories of consonance have been proposed over the centuries, but recently a consensus has developed that simultaneous consonance is primarily driven by harmonicity perception. Here we question this view, substantiating our argument by critically reviewing historic consonance research from a broad variety of disciplines, reanalyzing consonance perception data from 4 previous behavioral studies representing more than 500 participants, and modeling three Western musical corpora representing more than 100,000 compositions. We conclude that simultaneous consonance is a composite phenomenon that derives in large part from three phenomena: interference, periodicity/harmonicity, and cultural familiarity. We formalize this conclusion with a computational model that predicts a musical chord's simultaneous consonance from these three features, and release this model in an open-source R package, incon, alongside 15 other computational models also evaluated in this paper. We hope that this package will facilitate further psychological and musicological research into simultaneous consonance.