Tonal, Formal, and Proportional Design in Hindemith's Music

Abstract

In one of the appendices to his study of structure based on symmetry and golden section divisions in Debussy's mature music, Roy Howat discusses briefly what he calls proportional intrigue in other composers' music. Among these composers are Schubert, Schoenberg, Berg, Bart6k, Ravel, and Messiaen. In the case of Debussy, Howat believes he has sufficient evidence for his claims about the music, in Debussy's own statements, and in the intellectual and cultural context-although we must have at least some residual doubt-but with the other composers (Bartok excepted) it is more a matter of suggestion than clear evidence, of conjecture rather than certainty. The name of Paul Hindemith does not appear, an omission which is really rather surprising, given his well-known interest in medieval music theory and in Johann Kepler, as well as his scarcely concealed debt to the self-styled harmonicalist Hans Kayser, an Austrian neo-Pythagorean strongly influenced by Albert von Thimus and Jakob Bohme.2 At the end of the intro-