Teachers and mentors in creative fields ranging from scientific research to the arts may shape their students' skills and views of the craft, and in turn the work they produce. How significant is this influence, how long does it last, and are there consequences for the variety and quality of students' inventive output? We study these questions in the context of Western music composition over four centuries. We find strong evidence of influence, document when it arises and persists, and evaluate its consequences. The results provide insight into the production of creative or intellectual output, specifically around questions of where ideas come from, why certain ideas get produced as opposed to others, and what the ramifications might be.