The ambition in what follows is to begin a consideration of the lessons that might be learnt from a reassessment of 20th Century avant-gardist practice within the domain of musical composition. The goal here will not be an evaluation of the compositional outputs of this period but, rather, some reflections on the place and role of teaching within and amongst the musicians themselves; remembering that many of them gained a considerable reputation as teachers: Schoenberg, Messiaen, Stockhausen and Cage being the preeminent examples