Acoustical Foundations of Scales, Tempered Tuning, and Pitch Perception

date September 19, 2014
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Friday, September 19, 2014 4:00 p.m. ETC 4.150

Dr. James M. Gelb
Applied Research Laboratories
The University of Texas at Austin
http://www.arlut.utexas.edu

While seemingly disparate, the musical scales used throughout the world are in fact surprisingly universal. This talk touches on all aspects of this universality, from the perspectives of the acoustical properties of instruments (acoustics), the frequency resolution of the ear (signal processing), and the pattern-matching strategies of the brain (psychoacoustics). The lecture begins with an explanation of the distinction between, and the physical generation of, approximate pure tones (e.g., those produced by Helmholtz resonators and tuning forks) and complex tones (distributions of tones) produced by actual instruments. The science behind bowing and the reasons for the rich harmonic structure of the violin will be explored. The Helmholtz theory of consonance (pleasant-sounding intervals), as well as modern refinements of the theory that take critical bands in the ear into account, are discussed. This segues into an explanation of the non-uniform spacing of notes in the ubiquitous pentatonic and diatonic scales, which in turn leads to the topic of tempered tuning—the compromise between perfectly “just” intervals (frequency ratios of fundamentals involving small integers) and equal-tempered tuning used to freely support modulation (the switching between musical keys on the fly). Interesting aspects of tempered tuning (including the physical cause of the Wolf interval) are singled out for discussion, so as to avoid getting lost in the myriad of historical tuning schemes. The lecture concludes with an investigation of a pattern-matching model to explain pitch perception, drawing from results of a recent experiment conducted at ARL.