Hindemith? Well, possibly. Stravinsky? Certainly not! Brahms? No, this was written over quite a number of years up to 1948 and not published until 1967. Here is the cover of the current edition:
Yes, that's correct, the author of this very conservative guide to musical composition is Arnold Schoenberg, one of the main proponents of modernism in music. The one who invented 12-tone music; the one who destroyed, apparently for all time, tonality; the one whose music, it is claimed, can empty any concert hall, the teacher of those icons of modernism Alban Berg and Anton Webern.
Yet decades after he developed 12-tone technique in the 1920s, he was teaching at UCLA where he wrote this textbook for young students of composition. He taught there through part of the 1930s and the 1940s. Among his students were both John Cage and Lou Harrison. (He used to play tennis with George Gershwin!) On one occasion Schoenberg said, "My music is not modern, it is merely badly played."
Does no-one see the astonishing contradiction here? This is like the abstract expressionist painter Mark Rothko insisting that his students study traditional drawing working with still lifes and human models. Instead, according to Wikipedia:
In 1936, Rothko began writing a book, never completed, about similarities in the art of children and the work of modern painters. According to Rothko, the work of modernists, influenced by primitive art, could be compared to that of children in that "child art transforms itself into primitivism, which is only the child producing a mimicry of himself." In this manuscript, he observed that "the fact that one usually begins with drawing is already academic. We start with color." Rothko was using fields of color in his aquarelles and city scenes."The fact that one usually begins with drawing is already academic." But Schoenberg, rather than regarding the study of tonal music as "academic", i.e. of interest only to historians, made it not only the foundation of his teaching of composition, but the only approach, based on his published texts at least. Atonal music is not even mentioned in this book, nor in Structural Functions of Harmony.
Why is it that the only one of the major figures in musical modernism to spend a significant amount of time teaching composition, taught according to the principles of tonal harmony? I don't want to make too much of this because obviously, as he taught the methods of 12-tone composition privately to Berg, Webern and others, he did not ignore his own method in his teaching. But none of his published works on theory deal with 12-tone composition.
I doubt I can resolve this contradiction; certainly not in a blog post. But I think there is a paradox here and I think the reason for it might be quite interesting. Let's listen to a little Schoenberg to end. This is the Violin Concerto, op. 36, written in 1936, soon after he began teaching at UCLA:
Perhaps in Schoenberg's music we can hear the tension between traditional musical structures and, as he saw it, the historical demands of modernism. And perhaps we could go even further and see these tensions as reflecting the tensions between the "progressivism" of certain 20th century political movements and the terrible struggle between them and the more traditional societies that resisted them. There is a kind of eerie authenticity in Schoenberg's music that is worth pondering...
UPDATE: Replaced the original clip with one of the complete concerto played by Louis Krasner who did the premiere in 1939.