Knee flexion of saxophone players anticipates tonal context of music

Music performance requires high levels of motor control. Professional musicians use body movements not only to accomplish and help technical efficiency, but to shape expressive interpretation. Here, we recorded motion and audio data of twenty participants performing four musical fragments varying in the degree of technical difficulty to analyze how knee flexion is employed by expert saxophone players. Using a computational model of the auditory periphery, we extracted emergent acoustical properties of sound to inference critical cognitive patterns of music processing and relate them to motion data. Results showed that knee flexion is causally linked to tone expectations and correlated to rhythmical density, suggesting that this gesture is associated with expressive and facilitative purposes. Furthermore, when instructed to play immobile, participants tended to microflex (>1 Hz) more frequently compared to when playing expressively, possibly indicating a natural urge to move to the music. These results underline the robustness of body movement in musical performance, providing valuable insights for the understanding of communicative processes, and development of motor learning cues.

showing statistical differences between them using the Wilcoxon signed-rank test (with Bonferroni-Holm correction for multiple comparisons). The centre line of each boxplot represents the data median and the bounds of the box show the interquartile range. The whiskers represent the bottom 25% and top 25% of the data range-excluding outliers which are represented by a rounded point. b Spectral analysis (in logarithmic scale) comparing the different passages across conditions to determine the initial higher frequency threshold for knee motion data. The (vertical) dashed grey lines represent the second peak in frequency of the curves whereas the black line is the mean of all of them (the red lines are the standard deviation around this mean, 1.059 ± 0.326). c Granger causality (GC) results between averaged pitch expectation and knee curves on a time grid {0.05, 0.1, . . . , 1.5}. d GC analysis across participants (average values) and passages measuring in % the global significance level (p < 0.05) of causality between marginal curves. Confidence band relate to percentage values of the four passages. -All error bands were calculated at a 95% bootstrap confidence interval.
A cautionary note on measuring Granger causality between pitch expectation profiles and knee curves 19 As it has been previously reported, a suitable selection of the lag-length is crucial to avoid the so-called spurious causalities 1, 2 . 20 We used an approach that combines both local (0.1 s) and global (1.5 s) echoes to determine the optimal time-lag for Grangers' 21 causality (GC) analysis. The rationale is straightforward: the ratio that defines the global echo in relation to the local one 22 provides the reference lag, that is, λ global = lag/λ local . The optimality of this choice (EXP condition) is shown in Fig. S1c (GC 23 over averaged curves), where it can be observed that the joint p-value level across conditions reaches maximal significance at 24 time-lag 0.15 s. We could partially confirm this using the Akaike information criterion (AIC) and the Bayesian information 25 criterion (BIC), as these criteria tend, respectively, to overestimate and underestimate the lag-length 2 . Bellow 0.05 s lag, we 26 found GC analyses on mean curves were often biased due to substantial autocorrelation in the residuals (Portmanteau test) 27 while Granger's principle that "the effect does not precede the cause in time" did not hold. Therefore, in order to improve 28 AIC/BIC estimation we removed the 5 first onset-lags, and perform again the analyses: the average results for the four curves 29 evaluated for {6, . . . , 100} suggested an onset-lag of 10.5 (average of both criteria) which corresponds to a time-lag of 0.150 30 (calculated using the mean of all timings). This last step was performed taking logarithms and first differences in all mean 31 curves (otherwise the common procedure gives a time-lag equal to 0.157). 32 We further calculated the mean percentages of p-values < 0.05 across all subjects, which are also shown in Fig. S1d pooled   33 by condition. Comparing with the results in Fig. S1c (see also Tab. S1 for a detailed account on the p-values), it can be argued  S1c).
provides the sufficient information to claim that knee flexion is valuable to enhance expectation on prospective pitch. This 41 interpretation paves the way to explore non-linear relations between motion data and other musical parameters possibly using 42 nonlinear kernel/functional methods.

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Trend stationary was warranted in all mean curves (p < 0.01, Kwiatkowski-Phillips-Schmidt-Shin test) which allowed to 44 test GC under weak stationarity. Only for P4 we found signs of non-stationarity (p = 0.064). Curves were de-trended where 45 necessary in all of our analyses. GC tests were conducted using the grangertest function of the R-package lmtest. 46 We additionally report the GC results for both knees using a time-lag of 0.15. We found the following interactions for the

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Selection of the initial higher frequency threshold for knee flexion motion data 52 We normalized the sampling rate of all knee curves. Further, we performed the fast Fourier transform and derived the log 53 spectrum (log-PSD) up to 5 Hz (Fig. 1b). For each passage across conditions we calculated the averaged log-PSD's (6 curves 54 in total) and then estimated the second peak of these curves, as we observed the first one (mean=0.387 ± 0.084 Hz) was 55 clearly related to wide movements of the knee. The mean frequency for this second peak was 1.059 ± 0.326. This result is not 56 surprising, since the starting point defining the high-frequency activity of various slow phenomena, such as seismic waves 3 or 57 cognitive-related pupil activity 4 , is around 1 Hz. Accordingly, we used 1 Hz in our analyses.