Hyper-Frequency Network Topology Changes During Choral Singing.

Viktor Müller,Ulman Lindenberger,Julia A. M. Delius

doi:10.3389/fphys.2019.00207

Abstract

Choral singing requires the coordination of physiological subsystems within and across individuals. Previously, we suggested that the choir functions as a superordinate system that imposes boundary conditions on the dynamic features of the individual singers and found reliable differences in the network topography by analyzing within- and cross-frequency couplings (WFC and CFC, respectively). Here, we further refine our analyses to investigate hyper-frequency network (HFN) topology structures (i.e., the layout or arrangement of connections) using a graph-theoretical approach. In a sample of eleven singers and one conductor engaged in choral singing (aged between 23 and 56 years, and including five men and seven women), we calculated phase coupling (WFC and CFC) between respiratory, cardiac, and vocalizing subsystems across ten frequencies of interest. All these couplings were used for construction of HFN with nodes being a combination of frequency components and subsystems across choir participants. With regard to the network topology measures, we found that clustering coefficients (CCs) as well as local and global efficiency were highest and characteristic path lengths, correspondingly, were shortest when the choir sang a canon in parts as compared to singing it in unison. Furthermore, these metrics revealed a significant relationship to individual heart rate, as an indicator of arousal, and to an index of heart rate variability indicated by the LF/HF ratio (low and high frequency, respectively), and reflecting the balance between sympathetic and parasympathetic activity. In addition, we found that the CC and local efficiency for groups singing the same canon part were higher than for groups of singers constructed randomly post hoc, indicating stronger neighbor–neighbor connections in the former. We conclude that network topology dynamics are a crucial determinant of group behavior and may represent a potent biomarker for social interaction.

Highlights

In 1619, Johannes Kepler noted, “A collection of individual notes does not in itself form a melody; the melody comes only when we produce a particular arrangement of the individual notes
In- and out-strengths showed significant differences between conditions and were generally significantly highest during canon singing with eyes open, and lowest when singing the canon in unison, as indicated by Scheffé post hoc tests
Separate analyses of within-frequency coupling (WFC) and cross-frequency coupling (CFC) strengths showed such a relationship only for the CFC strengths but not for the WFC strengths, which were highest during canon in unison (Cun) and lowest during Cec

Summary

Introduction

In 1619, Johannes Kepler noted, “A collection of individual notes does not in itself form a melody; the melody comes only when we produce a particular arrangement of the individual notes. In our previous work (Müller et al, 2018a), we suggested that a choir functions as a superorganism or a superordinate system that imposes boundary conditions on its constituents (Wheeler, 1926; Emerson, 1939; Detrain and Deneubourg, 2006). Superordinate systems enclose all other systems in a given time and space, and are characterized through multilevel dynamics as well as upward and downward causation (Noble, 2012). Such superordinate systems are “true emergents, in which whole organisms function as the interacting determining parts” We wanted to examine whether canon groups, as particular constituents of the superordinate system, exhibit the same or a similar network topology as the superordinate system (i.e., the choir) itself and how this topology changes under different choral conditions

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