Music is often studied as a cognitive domain alongside language. The emotional aspects of music have also been shown to be important, but views on their nature diverge. For instance, the specific emotions that music induces and how they relate to emotional expression are still under debate. Here we propose a mental and neural chronometry of the aesthetic experience of music initiated and mediated by external and internal contexts such as intentionality, background mood, attention, and expertise. The initial stages necessary for an aesthetic experience of music are feature analysis, integration across modalities, and cognitive processing on the basis of long-term knowledge. These stages are common to individuals belonging to the same musical culture. The initial emotional reactions to music include the startle reflex, core “liking,” and arousal. Subsequently, discrete emotions are perceived and induced. Presumably somatomotor processes synchronizing the body with the music also come into play here. The subsequent stages, in which cognitive, affective, and decisional processes intermingle, require controlled cross-modal neural processes to result in aesthetic emotions, aesthetic judgments, and conscious liking. These latter aesthetic stages often require attention, intentionality, and expertise for their full actualization.