1 Introduction

Heinrich Schenker's arguments in support of his concept of the Ursatz include discussions of the role of the harmonic series as the basis of musical structure. Since, although these discussions are couched in mystical rather than physical terms, they impinge heavily on matters of fact, it is rather subversive of Schenker's argument that they contain substantial inaccuracies. He also supports his thesis of the construction of great music by generous quotations from the composers in whom he is interested. However, these same composers wrote works which seem, not only at first sight, to be in contradiction to Schenker's ideas. The procedure by which these samples are selected is therefore a question which arises, but to which Schenker does not give a satisfactory answer.

The work of Helmholtz, who first proposed the theory of consonance which contradicts Schenker's view of the primacy of the harmonic series, has been largely confirmed (in some aspects refined and corrected) by twentieth century psycho-acousticians. Schenker's argument is therefore in need of review, and possible correction in so far as his views of consonance are part of it.

The second doubtful aspect of Schenker's argument, his method of choosing his examples, is clearly an important determinant of the range of applicability of the concepts which the examples support. Thus, the lack of both well defined criteria for choice and a description of a randomising process by which to select from the works which meet such criteria suggests that one can have no confidence that Schenker's argument for his method supports its applicability beyond the works exemplified.