Summer K. Rankin
Center for Complex Systems and Brain Sciences,
Florida Atlantic University,
Boca Raton, FL,
rankin@ccs.fau.edu

Edward W. Large
Location: Center for Complex Systems and Brain Sciences,
Florida Atlantic University,
Boca Raton, FL,
large@ccs.fau.edu

Philip W. Fink
Location: Institue of Food, Nutrition, and Human Health,
Massey University,
Palmerston North, New Zealand,
P.Fink@massey.ac.nz

Popular version of paper 1aMU5.
Presented at 11:00 a.m. on Monday, November 10, 2008 in Plum A & B, Doral Resort Miami
156th Meeting of the Acoustical Society of America, Miami, FL

A piece of music is never performed exactly the way it is written. Musicians add their own expression by changing tempo: speeding up or slowing down -- sometimes by a little, sometimes by a lot. When listening to music, we follow changes in tempo without even realizing it, often tapping our feet or clapping along with the beat. Our study found that people are very good at tapping the beat of musical performances, so good, in fact, that they even predict the changes in tempo. How can they foresee the musical future?

An analysis of musical performances found that tempo changes exhibit a particular type of regularity, called fractal structure. Fractal structure is something that is found in many physical and biological processes. Fractal structure describes the complex geometric shapes of coastlines and mountain ranges so well that mathematical descriptions of fractal structures are used to create computer-generated landscapes to make them appear more natural. One important property of fractally structured time series,  such as musical performances, is that past changes are extraordinarily useful in making predictions -- even very far into the future. In other words, performers shape their performances according to a general principle of nature, and people pick up on this temporal structure easily and naturally to predict what is going to happen in the future.