Bridging the Tonal/Atonal Dichotomy: Some Principles of Pitch Organization Across the Border

The present paper analyzes Webern's atonal music and argues that the same resources of the diatonic set are utilized by both tonal and some atonal music.

An analysis of the first movement from Webern's _Variations for Piano_ Op. 27 shows that all the pc-sets in the movement are, with few "exceptions," subsets of diatonic sets. For example, all the triadic motives in the first seven bars, the Tn/TnI types of which are 3-5 and 3-8, are such instances. Those set classes can be derived from the 12-tone row and its P, R, I, and IR forms only when those row forms are carefully combined in specific ways. In other words, the probabilities of the formations of those set classes are significantly low. Therefore, it may well be the case that the formations are not accidental, but Webern observed some unknown principles of atonal pitch organization that allowed him to deliberately use the subsets.

Browne (1981) suggests that, while listening to tonal music, we constantly try to find which diatonic set we are currently in when it modulates. Furthermore, Butler and Brown (1981) and Butler (1989) observe that even a single triad consisting of a tritone and an extra note such as 3-5 and 3-8 can be sufficient for us to find our position in a specific diatonic set. Therefore, since 3-5s and 3-8s are ubiquitous in Webern's Op. 27, we may constantly be able to find particular diatonic sets while listening to the piece. In fact, the analysis demonstrates that the arrangements of those subsets closely coordinate with the formations of the melodic contours and the phrase structures.

These findings suggest that both tonal and some atonal music utilize the same resources of the diatonic set and our listening to both of them is controlled by the same principles.