Physical representation of tension caused by harmonic progression

Abstract

Studies have shown that language is an essential tool for forming complicated concepts. The syntactical similarities between music and language have led some researchers to focus on perception of music in order to further understand the form, syntax, and development of language. A key component of music is tonality. Theories regarding the perception of musical tonality have been formulated based on acoustics [1], culture [2, 3], physiology [4, 5], and psychology'. Lerdahl proposed a model which formally quantifies the terms tension and relaxation commonly used to describe the element of tonality in music. His harmonic tension model articulates the perception of harmonic progression in music. In an attempt to tangibly explain the concepts of tension and relaxation, a physical representation of Lerdahl's harmonic tension model is presented. The physical representation is created by mapping tension caused by harmonic progression onto the surface tension of a visco-elastic sphere. The level of distortion on the sphere surface is made to correspond to the amount of tension in the music. Additionally, the elastic property of the sphere reflects the relaxation or resolution phases in tonal music which normally follow periods of high tension. Two demonstration systems were developed based on the physical representation of harmonic tension as an evaluation of the concept's effectiveness. The first system is a simulation of the visco-elastic sphere written using the Netlogo 3D Preview program. In this system, the surface tension of the simulated sphere is manipulated according to the harmonic tension of Pachelbel's Canon in D and Rimsky-Korsakov's The Flight of the Bumblebee. The simulated sphere provides users with visual feedback on the tension/relaxation phases of the music. The second system is an interactive tool for intuitively learning the harmonic tension model using the sphere representation.

(cont.) This interactive system consists of a visco-elastic sphere simulation controlled by an approximated spherical input device. The only difference between this simulation and the first system's is that the second system's input is controlled by the user. Using simulation and audio output, users explore different tension values and observe the associated chord progressions. The interactive system was found not to be as intuitive a learning tool as expected because highly dissonant chord progressions with different tension values are indistinguishable by hearing alone. The question of how sensitive humans are to tension/dissonance and the factors that affect that sensitivity certainly warrants more attention. The physical model of Lerdahl's harmonic tension model presented explores tangible means for grasping the relation between harmonic progression and tonality. The simulated model provides visual feedback of the tension/relaxation patterns in music thus enhancing ones listening experience.