Thermodynamics and Harmony.

Columbia College, Columbia WI

Investigators

Abstract

Physics is the "art" of discovering and understanding the patterns of nature; seeking connections and using them to look further. Establishing direct connection between the patterns of nature and those of harmony in music is a tantalizing avenue of research. This project seeks to unify basic research in thermodynamics and statistical mechanics with music and composition. The research builds upon the PI’s recently published work on how harmony, informed by mathematical physics, can generate new insights in both. The ultimate goal is to derive a general music theory driven by nature itself, instead of the harmonic style of 18th century European composers. Students at the PI’s institution will get opportunities to use their artistic expertise, in the context of physics, to help develop innovative pedagogical tools that show how music is the voice of mathematics. The project will study the synergy between physics and music in three different ways: 1) In music, harmony studies ways in which an octave (frequencies ranging from f to 2f) can be divided and ordered into patterns of pitch in time. These patterns in pitch are connected to the patterns of order that emerge during phase transitions in 2-D physical systems, obtained by minimizing a “musical free energy” as a function of pitch. Extending this work to 3-D will allow established patterns in harmony to give insight into cosmology of the early universe. 2) Investigate extensions on symbolic dynamic scales like those obtained from the Thue-Morse sequence, to other symbolic dynamic sequences such as Fibonacci, Feigenbaum, etc. The PI will construct a 3-D version of the Euler Tonnetz to interpret the geometry of their harmony, and thereby link harmony to these dynamical systems. 3) Perform a detailed investigation of the role of beat overtones in harmony, and to use them in an innovative technological way by developing the first dynamic, chorus harmonizer. This is a new electronic effect that has the potential to impact the sonic landscape of live and recorded music. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.