Origins of 1/f noise in human music performance from short-range autocorrelations related to rhythmic structures.

Ian D Colley,Roger T Dean

doi:10.1371/journal.pone.0216088

Abstract

1/f fluctuations have been described in numerous physical and biological processes. This noise structure describes an inverse relationship between the intensity and frequency of events in a time series (for example reflected in power spectra), and is believed to indicate long-range dependence, whereby events at one time point influence events many observations later. 1/f has been identified in rhythmic behaviors, such as music, and is typically attributed to long-range correlations. However short-range dependence in musical performance is a well-established finding and past research has suggested that 1/f can arise from multiple continuing short-range processes. We tested this possibility using simulations and time-series modeling, complemented by traditional analyses using power spectra and detrended fluctuation analysis (as often adopted more recently). Our results show that 1/f-type fluctuations in musical contexts may be explained by short-range models involving multiple time lags, and the temporal ranges in which rhythmic hierarchies are expressed are apt to create these fluctuations through such short-range autocorrelations. We also analyzed gait, heartbeat, and resting-state EEG data, demonstrating the coexistence of multiple short-range processes and 1/f fluctuation in a variety of phenomena. This suggests that 1/f fluctuation might not indicate long-range correlations, and points to its likely origins in musical rhythm and related structures.

Highlights

We show that a parsimonious, SRD interpretation of 1/f in human rhythmic performance—which is consistent with the short-range models of movement timing in the sensorimotor synchronization literature [54,55,56, 58]—may be preferable to the more nebulous long-range dependence (LRD) interpretation
The moving average (MA) filters differed in their window size, q
1) ARIMA simulations of the hi-hat series did produce moderate-strong 1/f structures. 2) “Long-range” structures can result from a variety of short-range, ARIMA structures, and this is detectable by both PSD and detrended fluctuation analysis (DFA)

Summary

Introduction

1/f-type correlations have been identified in numerous physical and biological systems, often being described as ‘ubiquitous’ [1, 2]. In early preliminary work, one researcher made the case that 1/f could arise from certain short-range, autoregressive processes (SRD) when they occur over multiple time lags [19] In this interesting report, a series of simulations showed that by applying moving average filters of varying window sizes—where the window sizes represent different time lags—to a white noise signal, the resulting series will show very clear 1/f properties when analyzed using PSD plots. In what follows we describe the methods for each research question alongside the results, with a general Methods section following at the end

Results

Conclusions and discussion

Materials and methods