Correction: The Nature and Perception of Fluctuations in Human Musical Rhythms

Hennig, Holger; Fleischmann, Ragnar; Fredebohm, Anneke; Hagmayer, York; Nagler, Jan; Witt, Annette; Theis, Fabian J.; Geisel, Theo

doi:10.1371/annotation/f0a4c12c-ebef-4b55-9beb-2ca30749965e

Cited by 2 publications

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References 38 publications

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“…In this section, we show that the temporal fluctuations in simple as well as in more complex music rhythms are generic in the sense that Gaussian 1/f β noise is produced, no matter if the task is accomplished with a finger, a hand, a stick, a foot, a combination of these or the voice [31]. The exponent β, however, depends on the individual and on the specific task.…”

Section: Long-range Correlations In Music Rhythmsmentioning

confidence: 84%

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Scale-free Fluctuations in in Bose-Einstein Condensates, Quantum Dots and Music Rhythms

Hennig¹

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Mesoscopic systems are prone to substantial fluctuations that typically can not be neglected or avoided. The understanding of the origin and the consequences of these fluctuations (e.g. for transport measurements) is thus a fundamental part of the theory of mesoscopic systems. We will encounter scale-free fluctuations in different kinds of complex nonlinear systems in this thesis, which consists of two main parts. The first part deals with Bose-Einstein condensates (BECs) in leaking optical lattices. Experimentalists have achieved an extraordinary level of control over BECs in optical traps in the past decade, which allows for the investigation of complex solid state phenomena and the emerging field of 'atomtronics' promises a new generation of nanoscale devices. It is therefore both of fundamental and technological importance to understand the dynamics and transport properties of BECs in optical lattices. We study the outgoing atomic flux of BECs loaded in a one dimensional optical lattice with leaking edges, using a mean field description provided by the discrete nonlinear Schrödinger equation with nonlinearity Λ. We find that for a nonlinearity larger than a threshold Λ > Λ b the dynamics evolves into a population of discrete breathers, preventing the atoms from reaching the leaking boundaries. We show that collisions of other lattice excitations with the outermost discrete breathers result in avalanches, i.e. jumps of size J in the outgoing atomic flux, which follow a scale-free distribution P(J) ∼ 1/J α characterizing systems at a phase transition. Our results are also relevant in a variety of other contexts, e.g. coupled nonlinear optical waveguides.In the second part, fractal fluctuations in two different complex systems are studied. Firstly, conductance fluctuations in mesoscopic systems (such as quantum dots) are considered, which are a sensitive probe of electron dynamics and chaotic phenomena. Using the standard map as a paradigmatic model, we show that classical transport through chaotic Hamiltonian systems in general produces fractal conductance curves. This might explain unexpected results of experiments in semiconductor quantum dots where a dependence of the fractal dimension on the coherence length was observed. Furthermore, we predict fractal fluctuations in the conductance of low-dimensional Hamiltonian systems with purely chaotic phase space.Secondly, we investigate temporal (fractal) fluctuations of human music rhythms compared with an exact pattern, e.g. given by a metronome. We show that the temporal fluctuations in simple as well as in more complex music rhythms are generic in the sense, that Gaussian 1/f β noise is produced, no matter whether the rhythmic task is accomplished with hands, feet, the voice or a combination of these. Professional audio editing software includes a so-called 'humanizing' feature, which adds deviations ξ n to a given audio sequence, where ξ n is white noise. We demonstrate that 1/f humanized music that we created is rated significantly better by listeners than co...

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Section: Long-range Correlations In Music Rhythmsmentioning

confidence: 84%

“…Finally, in Sec. 4.2 we are dealing with generic longrange correlations in human rhythmic drumming [31,32].…”

Section: Introductionmentioning

confidence: 99%