Daniel Harrison

Some Group Properties of Triple Counterpoint and Their Influence on Compositions by J. S. Bach

Invertible counterpoints in tonal music are a special and unique class of thematic repetition. Like unvaried reprises, recapitulations, and transpositional sequences, invertible counterpoints reuse thematic material in different parts of a musical form. Unlike these other procedures, which preserve interrelationships among the several melodic lines, invertible counterpoint alters these interrelationships so that the melodic components are rearranged with respect to each other upon repetition. For this reason invertible counterpoint can be a more subtle and covert means of thematic repetition than the other procedures mentioned above, and therefore can become a powerful way to unify musical structure. In the hands of J. S. Bach, who recognized new and unexplored possibilities for invertible counterpoints, it is used so often and with such imagination that the formal economies of his compositions are often extraordinarily simple in relation to the beautifully complex sound of the music. In the pages following, I will examine both the general properties of triply invertible counterpoints (triple counterpoint) and the use of this compositional technique in some of Bachs music. The reader might well ask why a study of Bachs use of double counterpoint is not prerequisite. The answer lies in the different abstract structure of these two types of invertible counterpoint and the effect these differences have on compositional procedure.

Max Reger's Motivic Technique: Harmonic Innovations at the Borders of Atonality

The long-standing and continuing controversy swirling about Max Regers harmonic technique has befogged a feature of his compositional design equally unusual, provocative, and important. That the motivic structure of Regers music has been lost in this storm is not only unfortunate, but also ironic; for it is perhaps the most reliable compass, the best guide out of the incomprehension that seems to trap most listeners in his works. When we consider that Regers admiration (adoration?) of the music of two great masters of motivic organization, Bach and Brahms, is the essence of the received musicological opinion,I and that the debt to these two composers is thought by some to be so great that it crushed any stylistic expression of his own, then the value of examining the motivic techniques that Reger took from them--particularly from Brahmsappreciates dramatically. I thus intend in this study to explore this heretofore lost aspect of Max Regers compositional style, using three representative works: the Intermezzo, op. 45/5, the Larghetto, op. 143/1, from Triiume am Kamin, and the first 18 bars of the Introduktion, Variationen, und Fuge iiber ein Originalthema, op. 73.