Structural Scaling in Bach's Cello Suite No. 3

Brothers, Harlan J.

doi:10.1142/s0218348x0700337x

Cited by 7 publications

(1 citation statement)

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“…Rather, human behaviors, like many other natural processes, reveal fractal, power-law scaling (Brown & Liebovitch, 2010;West & Deering, 1995), including heart beats (Goldberger et al, 2002), posture (Blaszczyk & Klonowski 2001), gait (Hausdorff, Peng, Ladin, Wei & Goldberger, 1995), reaction time (Holden, 2002), speech (Kello, Anderson, Holden, & Van Orden, 2008), visual search (Aks, Zelinsky & Sprott, 2002), memory retrieval (Rhodes & Turvey, 2007), music (Brothers, 2007), and self-esteem (Delignières, Fortes, & Ninot, 2004). Like geometric fractals, these processes display self-similar, scale-invariant structure such that small-scale variation reveals the same pattern as large-scale variation (Mandelbrot, 1983).…”

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The complexities of keeping the beat: dynamical structure in the nested behaviors of finger tapping

Coey

Hassebrock

Kloos

et al. 2015

Atten Percept Psychophys

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Recent research on fractal scaling in simple human behaviors (e.g., reaction time tasks) has demonstrated that different aspects of the performance (e.g., key presses and key releases) all reveal pink noise signals but yet are uncorrelated with one another in time. These studies have suggested that the independence of these signals might be due to the functional independence of these different sub-actions, given the task constraints. The current experiments investigated whether under a different set of constraints (e.g., finger tapping with and without a metronome) nested sub-actions might show interrelated dynamics, and whether manipulations affecting the fractal scaling of one also might have consequences for the scaling of others. Experiment 1 revealed that the inter-tap intervals and key-press durations of participants' tapping behavior were dynamically related to one another and that the fractal scaling of both changed in the switch from selfpaced to metronome-paced tapping. Consistent with past research, the inter-tap intervals changed toward an antipersistent, blue noise pattern of variation, but the keypress durations became even more persistent. Experiment 2 revealed that this pattern of results could be altered by asking participants to attempt to hold the key down for the entire length of the metronome tone. Specifically, the key-press duration of participants in the Bhold^group became less persistent in the switch across task conditions. Collectively, the results of these experiments suggest that fractal scaling reliably reflects the functional relationships of the processes underlying task performance. Keywords Fractal scaling . Long-range correlation . Finger tappingThere is growing appreciation within the fields of psychology and cognitive science that human behavior is inherently complex. Although there is not yet a consensus scientific definition (Delignières & Marmelat, 2012;Gell-Mann, 1995; Goldberger, Peng, & Lipsitz, 2002;Kelty-Stephen & Dixon, 2012;Kloos & Van Orden, 2010;Mainzer, 2005), Bcomplexity^here is intended to mean not only that behavior involves Ba lot of parts^(neurons, muscles, and bones within an actor, the behavior of other actors, the perpetually changing state of the environment) but also that these parts are interdependently coupled via nonlinear and sometimes nonobvious interactions. Understanding such complexity is no easy task, especially given that even the simplest of behaviors can reveal a surprising degree of complexity.Consider the task of rhythmically tapping one's finger. Although this is a relatively common and easily performed human behavior, scientific investigation has found that this simple act is supported and influenced by a range of complex, interdependent processes. Indeed, a vast literature on Bsensorimotor synchronization^has shown that the ability of humans to time their actions to other events depends on a host of neural

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