Musical improvisation, much like spontaneous speech, reveals intricate facets of the improviser's state of mind and emotional character. However, the specific musical components that reveal such individuality remain largely unexplored. Within the framework of brain's statistical learning and predictive processing, this study examined the temporal dynamics of uncertainty and surprise (prediction error) in a piece of musical improvisation. This study employed the HBSL model to analyze a corpus of 456 Jazz improvisations, spanning 1905 to 2009, from 78 distinct Jazz musicians. The results indicated distinctive temporal patterns of surprise and uncertainty, especially in pitch and pitch-rhythm sequences, revealing era-specific features from the early 20th to the 21st centuries. Conversely, rhythm sequences exhibited a consistent degree of uncertainty across eras. Further, the acoustic properties remain unchanged across different periods. These findings highlight the importance of how temporal dynamics of surprise and uncertainty in improvisational music change over periods, profoundly influencing the distinctive methodologies artists adopt for improvisation in each era. Further, it is suggested that the development of improvisational music can be attributed to the brain's adaptive statistical learning mechanisms, which constantly refine internal models to mirror the cultural and emotional nuances of their respective epochs. This study unravels the evolutionary trajectory of improvisational music and highlights the nuanced shifts artists employ to resonate with the cultural and emotional landscapes of their times.