Figure 1.
Spectral power density (SPD) for respiration and HRV time series during rest and singing conditions.
a-c, SPD for respiration during rest (a), song singing (b) and canon singing (c); d-f, SPD for HRV during rest (d), song singing (e), and canon singing (f). Note that SPD was averaged across subjects and all respective conditions.
Figure 2.
Schematic presentation of phase synchronization analyses.
a, Complex Morlet wavelet transformation of signals from two subjects (S1 and S2) in the time-frequency domain. b, Time course of instantaneous phases from two subjects and their phase difference (S1 = violet curve; S2 = green curve; S1-S2 = red curve); at the right, the phase difference is depicted in form of the vectors in complex space, where the blue arrows reflect single phase angles and the red arrow represents the mean vector of the angular dispersions; its length displays the PSI measure. c, Coding of the phase difference (-π/4<S1-S2<0: blue stripes; 0<S1-S2<+π/4: red stripes; S1-S2<-π/4 or S1-S2 > +π/4: green stripes = non-synchronization). d, Pair-wise synchronization pattern of the whole choir (132 lines). Each line represents one pair of subjects. For each subject, 11 lines represent the coded phase difference between this subject and other choir participants. Note that these lines or phase differences coded with +1 (red), 0 (green) or -1 (blue) at each time point are used for calculation of the four synchronization measures (i.e., PCI, NCI, ACI, and ICI) as described in the Methods section.
Figure 3.
Phase synchronization patterns of the choir for respiration and HRV signals during rest and the five singing conditions.
a, Phase synchronization patterns for respiration; b, Phase synchronization patterns for HRV. Each diagram contains 132 lines displaying synchronization pattern of all possible participant pairs in the choir. Color coding and structure of the diagram are in accordance with Fig. 2. These diagrams display the phase synchronization at the frequency of 0.24 Hz.
Table 1.
ANOVA results (F and P values) for the three coupling measures (PSI, ACI, and ICI) of respiration and HRV.
Table 2.
ANOVA results (F and P values) for the three coupling measures (PSI, ACI, and ICI) at different frequencies and GC of respiration and HRV.
Figure 4.
Directed connectivity networks for respiration ICI and GC measures during different singing conditions.
a, song singing in unison. b, singing of the song in four parts. c, single canon entry sung in unison. d, canon singing with eyes open. e, canon singing with eyes closed. ICI-based networks are displayed on the left, and the GC-based networks are displayed on the right. The size of the circle representing choir participants depends on the number of both incoming and outgoing connections. The thickness of the links corresponds to the connection strength, and the arrow displays the direction of the causal influence. Note that the frequency of interest in the case of ICI corresponds to 0.24 Hz. (ICI = Integrative Coupling Index; GC = Granger Causality).
Figure 5.
Phase synchronization patterns, connectivity networks, and modularity effects during the different canon singing conditions.
a, Phase synchronization patterns for the three canon-singing conditions: canon singing with eyes open (left column), canon singing with eyes closed (middle column), and canon singing in unison (right column). b-c, The two rows of diagrams in the middle display undirected networks for ACI (b) and directed networks for ICI (c) measures. ACI and ICI were determined at the low frequency of 0.03 Hz. The colored areas display the partition of the networks into modules. d, diagrams reflecting the Z-P parameter space measures: within-module degree (Zi) and participation coefficient (Pi); for more details, see legends at the bottom. Note that the modularity effect during canon singing in unison was low and the partition into modules is therefore blurred.
Figure 6.
Phase synchronization patterns, connectivity networks, and modularity effects during the singing of the song in four parts and singing it in unison.
a, Phase synchronization patterns for the two song-singing conditions: singing of the song in parts (left column), and song singing in unison (right column). b-c, The two rows of diagrams in the middle display undirected networks for PSI (b) and ACI (c) measures. PSI and ACI were determined at the moderate frequency of 0.11 Hz. The colored areas display the partition of the networks into modules. d, Diagrams reflecting the Z-P parameter-space measures: within-module degree (Zi) and participation coefficient (Pi); for more details, see legends at the bottom. Note that the modularity effect during song singing in unison was low and the partition into modules is therefore blurred.