Pitch Organization and Compositional Techniques in Carter's Dialogues

The main purpose of this paper is analyzing pitch-class organization and compositional techniques in "Dialogues", a piece composed by Elliott Carter. Written in 2003, the piece has been composed for piano and chamber orchestra. In the first part, the authors have studied the ways in which the composer has represented his harmonic language, as well as the manners that he has pursued in order to organize pitch-classes: Utilizing some sets having unique properties, such as sets )“chords” in his own word rather than “sets”( which are two all-interval tetrachords, (0146) and (0137) with Forte names of 4-Z15 and 4-Z29 and all-trichord hexachord )012478(, with Forte name of 6-Z17. Another kind of sets have been presented which have a significant role through the piece, and those are aggregates. These four sets (as the composer himself named them "key chords") have a structural role in the harmony of the piece. Except the sets mentioned above, there are some sets which have a graphical phenomenon: symmetry on the circle diagram. We can summarize the utilization of symmetric sets in two ways. First, using a symmetric set as a superset of one of the key chords. In this way, we can separately consider the importance of the superset on the one hand, and its key chord subset on the other. Second, we can find one of the key chord subsets as the subset of the symmetric superset. There is a priority of using symmetry over using key chords or their subsets in the second way. It also has been asserted that the above sets interactively have been combined together and the ways Carter has used these sets in the piece have been reviewed and classified all together. We can follow some of his used procedures in the piece such as adding or removing pitch-classes and consequently augmenting or diminishing intervals, key chords transformations, key chords as subsets as well as utilizing invariance between all-trichord hexachords.
In the second part, some other techniques have been presented which demonstrate how Carter makes use of them as compositional possibilities in the piece. Using key chords in the shape of vertical blocks as well as melodies are the most common ways in which Carter combines key chords together. In addition, we can follow three employed methods the composer has exerted aggregates. First, which is similar to serial music, the pitch-classes have been used without repetition to form an aggregate. In the second, we find repeated pitch-classes. In the third, some sets present incomplete aggregates lacking one or two pitch-classes (semi-aggregates). It may be logical to consider the third way as a combination of the first and the second categories. The third method is also most typically found in sets composed in vertical or horizontal structures. Both combinations are other techniques that provide new combinations which can lead to larger sets such as Key chords, subsets, or even aggregates. It has been tried in almost every part of this paper to simplify the complexity of the piece with the analytical examples taken from the "Dialogues" score.