In this paper we propose a new graph convolutional block, called MusGConv, specifically designed for the efficient processing of musical score data and motivated by general perceptual principles. We evaluate our approach on four different musical understanding problems, such as monophonic voice separation, harmonic analysis, cadence detection, and composer identification which, in abstract terms, translate to different graph learning problems, namely, node classification, link prediction, and graph classification. Our experiments demonstrate that MusGConv improves the performance on three of the aforementioned tasks while being conceptually very simple and efficient.