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1/f structure of temporal fluctuation in rhythm performance and rhythmic coordination
Title
1/f structure of temporal fluctuation in rhythm performance and rhythmic coordination.
Creator
Rankin, Summer K., Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
Abstract/Description
This dissertation investigated the nature of pulse in the tempo fluctuation of music performance and how people entrain with these performed musical rhythms. In Experiment 1, one skilled pianist performed four compositions with natural tempo fluctuation. The changes in tempo showed long-range correlation and fractal (1/f) scaling for all four performances. To determine whether the finding of 1/f structure would generalize to other pianists, musical styles, and performance practices, fractal...
Show moreThis dissertation investigated the nature of pulse in the tempo fluctuation of music performance and how people entrain with these performed musical rhythms. In Experiment 1, one skilled pianist performed four compositions with natural tempo fluctuation. The changes in tempo showed long-range correlation and fractal (1/f) scaling for all four performances. To determine whether the finding of 1/f structure would generalize to other pianists, musical styles, and performance practices, fractal analyses were conducted on a large database of piano performances in Experiment 3. Analyses revealed signicant long-range serial correlations in 96% of the performances. Analysis showed that the degree of fractal structure depended on piece, suggesting that there is something in the composition's musical structure which causes pianists' tempo fluctuations to have a similar degree of fractal structure. Thus, musical tempo fluctuations exhibit long-range correlations and fractal scaling. To examine how people entrain to these temporal fluctuations, a series of behavioral experiments were conducted where subjects were asked to tap the pulse (beat) to temporally fluctuating stimuli. The stimuli for Experiment 2 were musical performances from Experiment 1, with mechanical versions serving as controls. Subjects entrained to all stimuli at two metrical levels, and predicted the tempo fluctuations observed in Experiment 1. Fractal analyses showed that the fractal structure of the stimuli was reected in the inter-tap intervals, suggesting a possible relationship between fractal tempo scaling, pulse perception, and entrainment. Experiments 4-7 investigated the extent to which people use long-range correlation and fractal scaling to predict tempo fluctuations in fluctuating rhythmic sequences., Both natural and synthetic long-range correlations enabled prediction, as well as shuffled versions which contained no long-term fluctuations. Fractal structure of the stimuli was again in the inter-tap intervals, with persistence for the fractal stimuli, and antipersistence for the shuffled stimuli. 1/f temporal structure is suficient though not necessary for prediction of fluctuations in a stimulus with large temporal fluctuations.
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Date Issued
2010
PURL
http://purl.flvc.org/FAU/2705083
Subject Headings
Music, Psychological aspects, Emotions in music, Perceptual-motor learning, Computational neuroscience, Synchronization, Musical perception
Format
Document (PDF)
Numerical Investigation of Finite Kuramoto model with time dependent coupling strength
Title
Numerical Investigation of Finite Kuramoto model with time dependent coupling strength.
Creator
Khatiwada, Dharma Raj, Wille, Luc T., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
Synchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social and physical to biological and technological systems. The most successful approach to describe how synchrony emerges in these systems is given by the Kuramoto model. This model as it stands, however, assumes oscillators of fixed natural frequencies and a homogeneous all-to-all coupling strength. The Kuramoto model has been analytically discussed to address the...
Show moreSynchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social and physical to biological and technological systems. The most successful approach to describe how synchrony emerges in these systems is given by the Kuramoto model. This model as it stands, however, assumes oscillators of fixed natural frequencies and a homogeneous all-to-all coupling strength. The Kuramoto model has been analytically discussed to address the synchronization phenomena of coupled oscillators in the thermodynamic limit (N --> ∞). However, there needs to be a modi cation to address the inevitable in uence of external fields on the pattern of various real life synchronization phenomena which, in general; involves a finite number of oscillators. This research introduces a time dependent coupling strength K(t) which is from the modulation of external elds in the form of, for example, a periodic impulse, in the nite oscillators assembly. A sinusoidal function with some arbitrary values of amplitude and frequency is added to the fixed coupling strength as a perturbation of external elds. Temporal evolution of order parameter r(t) and phase θ(t), both of which measure the degree of synchronization of an assembly of oscillators simultaneously, are compared between uniform and time dependent cases. Graphical comparison are made using a 2 oscillator system, a building block of any finite oscillators case. Also, similar comparisons are performed for a system of 32 oscillators which are chosen randomly as a representative of a nite number of oscillators (2 < N < ∞). A temporal variation of the relative phase angle θ(t) = θ2(t) - θ1(t) in 2 and 32 oscillators systems using uniform and time dependent cases is also a part of this research. This work also introduces a time-dependent coupling strength in the form of a step function. The main objective of using such a function is to keep the synchronized behavior of the oscillators persistently. This behavior can be achieved with the perception that occasional boosting with higher coupling strength K(t) should be enough to sustain synchronous behavior of oscillators which, in general, are tuned with lower K(t).
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Date Issued
2018
PURL
http://purl.flvc.org/fau/fd/FA00013120
Subject Headings
Synchronization, Oscillations, Nonlinear oscillators--Mathematical models, Oscillator strengths, Frequency of oscillating systems
Format
Document (PDF)