Ronaldo Vigo, Ph.D. -- vigo@ohio.edu
Asst. Professor of Mathematical & Computational Cognitive Science
Director, Center for the Advancement of Cognitive Science
Mikayla Barcus - mikaylabarcus@gmail.com
Yu Zhang
- kb016011@ohio.edu
318 Porter Hall
Ohio University, Athens OH 45701
Popular version of paper 3aPP8
Presented Wednesday morning, October 24, 2012
164th ASA Meeting, Kansas City, Missouri
As far back as the time of the ancient Pythagoreans, researchers have suspected that certain acoustic regularities or patterns in sequences of sounds may account for differences in the way people judge their appeal. But the precise quantitative relationship between the nature of an acoustic pattern and what makes the pattern appealing has remained an open problem. Symmetry, a property that plays an important role in the physical sciences, may hold the key to this mystery. Roughly speaking, symmetries are balanced arrangements among the parts of an object. Their occurrence in a wide variety of physical phenomena has shaped many important theories such as the theories of electromagnetism, relativity, and quantum mechanics. In spite of the important role that symmetry has played in the physical sciences, not many researchers are familiar with the fact that symmetry also has played an important role in explaining the workings of the human mind. For example, Vigo (2009, 2011a, 2011b, 2012) developed a mathematical theory of human conceptual behavior named Categorical Invariance Theory or CIT that is grounded on a general notion of symmetry called an invariant.
The theory explains and predicts how people classify objects in their environment by extracting abstract symmetrical patterns (referred to as invariants) from the relationships between the objects that comprise a set of objects. Using this theory and a novel experiment, Vigo and his doctoral students Mikayla Barcus and Yu Zhang were able to predict with great accuracy people's judgments as to what is a good musical pattern. The basic idea was that acoustic structures (i.e., relationship between sets of sounds) that have many invariants are judged to be more appealing. They also discovered that there seems to be a tradeoff between the degree of invariance (i.e., proportion of invariants) inherent to a sequence of sounds and its complexity. The described tradeoff between degree of complexity and invariance may explain why the music of classical music composers like Bach, Beethoven, and Mozart, whose musical motives are highly invariant, place a greater musical challenge to people's ears. Although the high invariance content of its musical motives makes this kind of music extremely appealing, its complexity (in terms of processing difficulty) can be quite overwhelming to untrained ears. Of course, this does not prevent a person without any musical training or aptitude from detecting and acknowledging the greater degree of order and complexity expressed by it. Consequently, music from these great composers remains greatly respected and admired by most, lending support to a common acknowledgement among musicians: "I know that Bach's music is the greatest, but I like listening to The Beatles more."
These findings may potentially impact the music industry. In particular, they may potentially help music producers to predict whether or not a newly written musical motif, melody, or song will be a commercial success, or whether or not a composer should write a motif, melody, or song in a certain style to achieve a desired effect. In particular, using the mathematical models in Vigo's categorical invariance theory, producers will be able to objectively rank musical melodies and songs in terms of their degree of invariance and complexity and use these values to predict degrees of musical appeal.