Left panels: distribution of velocity gradients along the filaments (determined in sections of 0.014 pc) shown in form of a violin plot. The outer (or violin) shape represents all possible velocity gradients, with broadening indicating how common they are, meaning that the broadest part represents the mode average. The black thin bar indicates all datapoints in the violin interior, while its thicker part corresponds to the quartiles of the distribution, with the white dot indicating the mean value of all velocity gradients along the respective filament. The distribution is shown for the molecules CH₃OCHO, CH₃OCH₃, CH₃OH and ¹³CH₃OH. Right panel: velocity variation along the filaments. The gray areas indicate subsections along the filaments, labeled with roman numbers. The position of the dense cores are indicatedby vertical, black dashed lines. Regions where the line emission is below 4σ are plotted with dashed lines.