Figure 1.
Movement components in fast repetitive bowing patterns.
The grey arrows indicate the main degrees of freedom of the bowing arm when performing FRBPs. The trajectory of the bow (clockwise circular bowing pattern (CW) in this example) is indicated by the colored loop. The color indicates the bowing direction (radial movement component; blue = down bow, red = up bow). The green arrow shows the bow inclination (angular movement component), whose main function is selecting the string.
Figure 2.
Simplified coordination model.
Panels A–C show the relation between bow inclination, bow velocity and bow force vs. time in three different situations. The grey areas indicate the angular area or the time intervals in which the bow traverses from one string to another (string crossings). The bowing direction is indicated by the color of the curves (blue = down bow, red = up bow), and bow changes are marked with an x. The bow-force subpanels show the bow force exerted on both strings, which are distinguished by the line style (solid and dashed, respectively). The respective panels show: (A) Basis case with zero phase difference ( = 0,
= 0.5), (B) a phase lead of bow inclination with respect to bow velocity (
= 30°) at the same value of
(in the figure shown as a phase lag of bow velocity, relative to the unshifted grey line), and (C) same phase lead at a large normalized string-crossing range (
= 0.9). Panel C includes annotations indicating the features extracted for analysis (see “Materials and Methods: Feature extraction”). Panel D shows the situations in panels A–C as points in the 2D coordination space
vs.
. The grey area represents the combinations of
and
at which bow changes take place within the string-crossing area.
Figure 3.
Musical notation of the three bowing patterns (CW = clockwise, ACW = anti-clockwise, Fo8 = figure-of-eight) used in the experimental conditions.
Table 1.
Condition overview.
Figure 4.
Distributions of main coordination parameters across all dynamic level and tempo conditions by all participants (N = 436).
The panels show (A) relative phase (), and (B) normalized range (
). The three bowing patterns are distinguished by their grey shade (see legend).
Figure 5.
Overview of the individual coordination strategies of all participants in the basic conditions (clockwise circular pattern, performed forte at moderate to fast tempo).
Each individual participant is represented by an ellipse showing the average (center) and one multivariate standard deviation (i.e., 68% of the data falls within the ellipse). Skill level is indicated by color (see legend). The grey area represents the combinations of and
at which bow changes take place within the string-crossing area.
Figure 6.
Coordination patterns of the four clockwise-pattern conditions in the dynamic-level block.
The plots represent the grand average across all participants of bow velocity versus bow inclination. The grey areas indicate the string-crossing areas, and the center of the string crossings are indicated by the vertical dashed lines. The thick solid lines show the grand average curves per condition (blue = down bow, red = up bow), and the thin lines indicate the individual averages. The columns (panels A/B and C/D) represent the two string combinations (E-A and A–D, respectively), and the rows (panels A/C and B/D) represent dynamic level (forte and piano, respectively).
Figure 7.
Comparisons between conditions in the dynamic-level block.
The plots give an overview of how the individual participants adapted the main coordination parameters between selected clockwise-pattern conditions in the 2D coordination space. Skill level is indicated by color (see legend). The dark grey arrow shows the average across all participants. The panels show (A) change from forte to piano (at the E-A string combination), and (B) the change from string combination E-A to A–D (at forte dynamic level).
Figure 8.
Example of range constraints in an individual (professional) participant.
Bow inclination versus time (normalized with respect to cycle duration) per individual cycle (thin lines) and averaged across cycles (thick colored line). The grey areas indicate the averaged string-crossing areas as a function of time. Bowing direction is indicated by the color of the curve (blue = down bow, red = up bow).
Figure 9.
Coordination patterns of all twelve conditions in the tempo block.
The columns (panels A–D, E–H, I–L) represent the bowing patterns (CW, ACW and Fo8, respectively). The rows (panels A/E/I, B/F/J, etc.) represent tempo (58, 72, 92 and 112 bpm, respectively). For a detailed explanation of the graphs, see Figure 6.
Figure 10.
Comparisons between conditions in the tempo block.
The panels show the adaptation of the coordination parameters from the slowest to the fastest tempo in (A) pattern CW, (B) pattern ACW, and (C) pattern Fo8. For a detailed explanation of the graphs, see Figure 7.