Schoenberg credited his students with helping him learn the principles of harmony practiced by Mozart, Beethoven, Wagner, and Brahms. What they had learned together, Schoenberg codified in his book Harmonielehre (1911), which he hoped would supersede all previous textbooks. In his youth, Schoenberg had escaped the experience of studying assigned texts. Later, he had explored several texts and criticized them on the basis of his practical knowledge of the musical classics and his experience as a composer whose practice was constantly changing to incorporate more of the tradition he loved and to seek its unexploited possibilities. His students resembled him enough to join in this complex process of learning. Each student helped in some way. Those who later became famous, e.g., Berg and Webern, found distinctive possibilities of extending or transforming the tradition, so that by the time they died their works and theoretical utterances were beginning to be incorporated in the best teaching of younger musicians. The idea of learning from students, though not widely prevalent by 1959 or even 1979, was no longer a shocking paradox.

Is the idea of learning from students familiar in other traditions? Is it applicable in the interactions of diverse cultural traditions?

From reports about how music is studied throughout the world and throughout history, it seems that students rarely contribute to their teachers' learning. Students may be more or less submissive. The best students must take initiative about learning, not merely parrot what they are taught. But first they must obey a teacher; either they defer any question of that authority until they have mastered the tradition, or, in their questioning, they risk all hope of mastery. Good teachers continue their own studies and their learning of old and new ramifications of their tradition. Many teachers testify that their teaching contributes to their own internal processes of clarification, but usually no student's fresh insight is expected to make such a contribution. For example, when Beethoven postponed any rebellious impulses, to study under Neefe, Haydn, Albrechtsberger, Salieri, and others, none of those teachers learned from Beethoven, as far as we know. When Beethoven taught Czerny, he incidentally gained something, but not from Czerny's own thinking. When Ives chafed under Parker's instruction, attaining a degree of traditional mastery, Parker learned nothing of Ives's arranging thought, and when Ives taught Kirkpatrick how to play the Concord Sonata, Ives learned nothing from Kirkpatrick's deep knowledge of Mozart, Josquin, or Stephen Foster. Probably Ali Akhbar Khan learned nothing from Ravi Shankar, but perhaps Shankar, living in a confused world where Schoenberg looms largely, does learn from some of his students.

Many more teachers and students participate in math and modern sciences than in any one tradition of music. Textbooks are far more efficient, constantly revised to be more so. Vast wastes and frustrations in schools are outweighed by evident collective statistical advances. The image of a student submitting for more than a year to an individual teacher -- a guru -- is faded, though not entirely lost in relation to the most advanced scientific studies. Through years of scientific progress, a student submits to impersonal public truth, in order to be equipped to ask or even understand the questions that occupy the leaders of the discipline. So far, attempts to apply scientific methods to the teaching of music or musicology have been mostly inept and discouraging. When we think of studying music, even in the most crowded and swiftly changing cities of Europe and America, we think immediately of a single student stumbling in performance, submitting to one teacher's correction, and expecting to pursue that relationship for many years. A student wanting to learn to compose seeks a teacher who will accept him/her as an unusual individual and criticize his/her efforts for more than one year. Our cities do have classes for music instruction in schools of many levels and special emphases. The music education enterprise is bigger than the more traditional "professional" teacher-student enterprise but is not integrated with it as well as the math and science enterprises. Most prospective musicologists scorn "music ed." They seek a faculty of several teachers who are internationally known scholars but rely on a chairman or thesis adviser as if he or she were a neighborhood piano teacher.

Whereas the learning of math and science spreads throughout the world, delayed but little troubled by cultural boundaries, the learning of music is deeply affected by the question of how the world's many musical traditions are related to each other. Does teaching European music in America or Australia or Japan do more harm than good? Is teaching Indonesian music in America more than a tolerable specialization?

In the practice and theory of the visual arts, 19th-century efforts to ape the sciences are largely discredited. Students learn a little in classes, but they learn from the start that many great painters flunked their classes and taught themselves. The traditional crafts of painting are hardly defended by schools where individual creativity is glorified. Some teachers of painting must hope to learn from their students, though there is no instance of such learning so famous as that of Schoenberg. Since Schoenberg's innovations and Cage's challenges, traditional musical crafts are somewhat similarly endangered in the 20th century, but not so desperately as those of painting. Cross-cultural learning seems to be easier in painting than in music, and the history of art, detached from its practice and involved in the market of dealers, collectors, and state-supported museums, expands more nearly like a science than do musicology and ethnomusicology. If art history teachers ever learn from their students, it must be only at the most advanced levels, as in the sciences. Musicology and ethnomusicology teachers, most of whom spend part of their time teaching appreciation or performance to beginners, may have more opportunities to learn from students in more ways.