ABSTRACT
In this chapter, the author explains more systematic and formal presentation of set theory, after which the learners will be better prepared to succeed in our studies of atonal music. The concept of pitch class implies the property of octave equivalence: in set theory the authors do not distinguish between octave-related pitches with the same name. Intervals in the realm of pitch classes (which the author refers to as pitch-class space) are of a different nature than intervals in the realm of pitches (or pitch space). In pitch space, intervals are directional (ascending or descending), and an interval and its inversion are not the same. In pitch-class space, on the other hand, intervals may be ordered (if the author takes into account the distance between two pitch-classes considered in a particular order) or unordered. More relevant in pitch-class set theory is the concept of unordered pitch-class interval (also called interval class).
