Speakers are named first.
2:15-2:40 Tom Morley, Georgia Tech
morley@math.gatech.edu
Infinitely Ascending Tones
In this talk we give several constructions of infinitely ascending tones, using ideas from Fourier analysis and fractals.
2:45-3:10 James Peterson, Mathematical Sciences, Clemson University
and
Linda Dzuris, Performing Arts, Clemson University
Constraining Cognitive Models with Emotionally Labeled Musical Data
A simple cognitive model is presented that is based on mediated interactions between cortex and the limbic system. Musical data that has been carefully designed to capture primitive emotional labelings in neutral and distinct affective modalities is used as training data to constrain the cognitive model's output to have desired emotional labels. The cognitive model can then be used to generate novel musical streams which can be interpreted as primitive compositional elements. The implications of the autonomous generation of such elements is then placed within the context of a theory of musical composition.
3:15-3:40 Barbra Gregory, UNC Chapel Hill and Catawba Valley Community College
Entropy and Complexity in Music
We examine the concepts of complexity and entropy and their application to musical structures and explore the difficulty of obtaining a conclusive measure of entropy for a musical system. A set of tools is applied to examples from modern composers, classical Western music, and traditional tribal customs. Ergodic theory techniques are used to find the entropy of musical performance structures left up to chance or choice. Techniques set forth by Lempel and Ziv, Pressing, and Lerdahl and Jackendoff to explore the complexity of rhythms are studied and applied. Finally, we consider the complexity of linguistic structure on a series of notes, first by counting the patterns that are allowed within that structure and then by defining a new measure of complexity inspired by the work of Pressing.
3:45-4:10 Sam Kaplan, UNC Asheville
The Geometry of Post-tonal Music Theory
In the early twentieth century, Schoenberg and his contemporaries developed a music theory based on tone classes rather than harmonic structure. The new theory, called post-tonal music theory, includes a short list of tranformations which preserve melodic intervals. These transformations correspond geometrically to rotations and flips of a dodecagon. The natural expansion of this notion for a melody is to rigid transformations of a n-dimensional toral lattice.