Algorithmically-generated Corpora that use Serial Compositional Principles Can Contribute to the Modeling of Sequential Pitch Structure in Non-tonal Music

Abstract

We investigate whether pitch sequences in non-tonal music can be modeled by an information-theoretic approach using algorithmically-generated melodic sequences, made according to 12-tone serial principles, as the training corpus. This is potentially useful, because symbolic corpora of non-tonal music are not readily available. A non-tonal corpus of serially-composed melodies was constructed algorithmically using classic principles of 12-tone music, including prime, inversion, retrograde and retrograde inversion transforms. A similar algorithm generated a tonal melodic corpus of tonal transformations, in each case based on a novel tonal melody and expressed in alternating major keys. A cognitive model of auditory expectation (IDyOM) was used first to analyze the sequential pitch structure of the corpora, in some cases with pre-training on established tonal folk-song corpora (Essen, Schaffrath, 1995). The two algorithmic corpora can be distinguished in terms of their information content, and they were quite different from random corpora and from the folk-song corpus. We then demonstrate that the algorithmic serial corpora can assist modeling of canonical non-tonal compositions by Webern and Schoenberg, and also non-tonal segments of improvisations by skilled musicians. Separately, we developed the process of algorithmic melody composition into a software system (the Serial Collaborator) capable of generating multi-stranded serial keyboard music. Corpora of such keyboard compositions based either on the non-tonal or the tonal melodic corpora were generated and assessed for their information-theoretic modeling properties.