Music offers a uniquely abstract way for the expression of human emotions and moods, wherein melodic harmony is achieved through a succinct blend of pitch, rhythm, tempo, texture, and other sonic qualities. The emerging field of “Robotic Musicianship” focuses on developing machine intelligence, in terms of algorithms and cognitive models, to capture the underlying principles of musical perception, composition, and performance. The capability of new-generation robots to manifest music in a human-like artistically expressive manner lies at the intersection of engineering, computers, music, and psychology; promising to offer new forms of creativity, sharing, and interpreting musical impulses. This manuscript explores how real-time collaborations between humans and machines might be achieved by the integration of technological and mathematical models from Synchronization and Learning, with precise configuration for the seamless generation of melody in tandem, towards the vision of human–robot symphonic orchestra. To explicitly capture the key ingredients of a good symphony—synchronization and anticipation—this work discusses a possible approach based on the joint strategy of: (i) Mapping— wherein mathematical models for oscillator coupling like Kuramoto could be used for establishing and maintaining synchronization, and (ii) Modelling—employing modern deep learning predictive models like Neural Network architectures to anticipate (or predict) future state changes in the sequence of music generation and pre-empt transitions in the coupled oscillator sequence. It is hoped that this discussion will foster new insights and research for better “real-time synchronized human computer collaborative interfaces and interactions”