Music is a powerful means for communicating emotions among individuals. Here we reveal that this continuous stream of affective information is commonly represented in the brains of different listeners and that particular musical attributes mediate this link. We examined participants' brain responses to two naturalistic musical pieces using functional Magnetic Resonance imaging (fMRI). Following scanning, as participants listened to the musical pieces for a second time, they continuously indicated their emotional experience on scales of valence and arousal. These continuous reports were used along with a detailed annotation of the musical features, to predict a novel index of Dynamic Common Activation (DCA) derived from ten large-scale data-driven functional networks. We found an association between the unfolding music-induced emotionality and the DCA modulation within a vast network of limbic regions. The limbic-DCA modulation further corresponded with continuous changes in two temporal musical features: beat-strength and tempo. Remarkably, this “collective limbic sensitivity” to temporal features was found to mediate the link between limbic-DCA and the reported emotionality. An additional association with the emotional experience was found in a left fronto-parietal network, but only among a sub-group of participants with a high level of musical experience (> 5 years). These findings may indicate two processing-levels underlying the unfolding of common music emotionality; (1) a widely shared core-affective process that is confined to a limbic network and mediated by temporal regularities in music and (2) an experience based process that is rooted in a left fronto-parietal network that may involve functioning of the ‘mirror-neuron system’.