Algebraic Mozart by Tree Synthesis

Thus far, we have been automatizing the time-span analysis of Jackendoff and Lehrdahl’s Generative Theory of Tonal Music (GTTM). We have also introduced the distance between two time-span trees and verified by an experiment that the distance was properly supported by the psychological similarity. In this paper, we synthesize a new piece of music using the algebraic operations on timespan trees, with this notion of distance. For this process, we need an operation to retain a certain number of pitch events as well as reduction, then we employ join operation on two input pieces of music. But, the result of the join operation is not obvious as two or more pitch events may occupy the same position on a score in a conflicting way. Therefore, in this research, we distinguish the tree representation from actual music written on a score and define join and meet in the domain of the tree representation in the algebraic manner. Then, to demonstrate the validity of our approach, we compose artificial variations of K.265/300e by Wolfgang Amadeus Mozart by a morphing technique using join and meet. We examine the results with human intuitive similarity and show that algebraic operations such as join and meet suffices to produce viable Mozartoid variations.