CHAPTER 21 DIRECTIONAL PITCH SPACES

摘要

Certainly some reactions to music are direct consequences of the listeners' musical experience and culture. However, we might all agree that, regardless of their degree of musical sophistication, all who listen to music have an innate feel for proximity (distance between consecutive notes, or what note is expected to follow the other), and direction (whether the melody is ascending or descending). In Izmirli (2000), I had looked into the mathematics of the idea of pitch spaces where proximity was the distinguishing characteristic. In this chapter, I will discuss directional pitch spaces, where one is interested not in the distance between the pitches, but in whether a pitch is higher than, lower than, or the same as another pitch. The resulting idea of contour classes are used as sequences in fugues, as leitmotifs in operas, and as changes of mode from major to minor in variations.