At the heart of many musical genres is the highly valued concept of improvisation; usually understood as shorter or longer periods of time where the musicians play what comes into their minds, creating music in the moment. Spontaneous improvisation is seen as a hallmark of musical creativity and as such taken to be highly meaningful and pleasurable. In fact, it could be argued that improvisational elements can be found in all kinds of music making (Brattico & Tervaniemi, 2006). While the importance of improvisation varies across genres, there is at least a touch of improvisation when a string quartet plays Joseph Haydn where notes and note values are fixed, but the phrasing is determined by the musicians, or even when DJs mix tracks into each other. Similarly, when composing a piece of music, which is often described as the opposite process of improvisation, improvisation still plays a significant role when composers try out various alternatives, though this process is free of improvisation’s usual temporal constraints.