René van Egmond & David Butler
Music Perception, Vol. 15, No. 1 (1997) pp. 1-29.
This is a music-theoretical study of the relationship of two-, three-, four-, five-, and six-member subsets of the major (pure minor), harmonic minor, and melodic (ascending minor reference collections, using pitch-class set analytic techniques. These three collections will be referred to as the diatonic sets. Several new terms are introduced to facilitate the application of pitch-class set theory to descriptions of tonal pitch relations and to retain characteristic intervallic relationships in tonal music typically not found in discussions of atonal pitch-class relations. The description comprises three parts. First, pitch sets are converted to pitch-class sets. Second, the pitch-class sets are categorized by transpositional types. Third, the relations of these transpositional types are described in terms of their key center and modal references to the three diatonic sets. Further, it is suggested that the probability of a specific key interpretation by a listener may depend on the scale-degree functions of the tones.