ABSTRACT
This chapter begins by examining several types of post-tonal symmetrical structures, including equal divisions of the octave, symmetrical motivic cells, and spatial symmetry around an axis. It presents study of pitch centricity generated by scales, in particular by three types of symmetrical collections: the whole-tone, the octatonic, and the hexatonic scales. The highly symmetrical nature of the octatonic scale complicates the issue of pitch centricity in octatonic music. Each of the five remaining interval cycles divides the octave into equal segments both in pitch and in pitch-class spaces. All of these equal divisions are non-diatonic and symmetrical. Symmetrical motivic cells are some of the basic building blocks in Bartok’s music. Bartok’s symmetrical cells, moreover, display a property common to most symmetrical sets. Imitation of various types is very common in the music of Bartok. Imitation is the successive statement of the same thematic material in two or more voices.
