Simplex plots afford barycentric mapping and visualisation of the ratio of three variables summed to a constant as positions in an equilateral triangle (2-simplex); for instance, time distribution in three-interval musical rhythms, elemental composition in chemistry, and evolutionary dynamics in game strategies. We propose a novel use of simplex plots to visualise the balance of autonomic variables and classification of autonomic states in baseline and music performing and listening.
Thirty-six RR interval series extracted from electrocardiographic traces were collected from a musical trio (pianist, violinist, cellist) and one listener (9 signals each) under two conditions: baseline (5 min) and during music performance (~10 min). Schubert's Trio Op. 100, Andante con moto was performed in nine sessions on five different days. Each series' very low (VLF), low (LF), and high (HF) frequency component power values, calculated in 30 sec windows (hop size 15 sec), were normalised (sum=1) and visualised in separate simplex plots. Spectral clustering was used to cluster data points for baseline and music conditions.
We correlated the accuracy between the clustered and true values with the performance index. Strong negative correlation was observed for the violinist (r = –0.80, p < .01, accuracy range: [0.64,0.94]) and pianist (r = –0.62, p = .073, [0.64,0.80]), suggesting adaptation of the cardiac response (reduction between baseline and performance) over the performances; weak and very weak correlation was obtained for the cellist (r = –0.23, p = .545, [0.50,0.61]) and listener (r = –0.13, p = .746, [0.50,0.74]), indicating low or no adaptation.
Using simplex plots, we represented VLF, LF and HF ratios and tracked changes in autonomic response over a series of music performances. This two-dimensional visualisation of three-dimensional data effectively shows differences between autonomic states and individuals' adaptation over time.