ABSTRACT
This chapter examines the harmonic and melodic potential of trichords, tetrachords, pentachords, and hexachords, and demonstrates their usefulness in jazz improvisation and composition. One of the most remarkable facts about atonal music theory is its reductive power and the ability to represent a vast array of harmonic and melodic structures using a relatively small number of abstract set classes. The triadic category of trichords features two set classes: (036) and (037). The most complex category of trichords is the semitonal category. The label semitonal indicates that these set classes include ic1 in their pitch structure. A pitch-class (pc)-set complex offers a harmonic reinterpretation of set classes and demonstrates how a single set class can participate in a number of different harmonic settings. The ability to identify set classes aurally and hear intervals in their original and inverted form is central in developing one's atonal improvisatory skills.
