Fig 1.
Theoretical versus actual phasing performance.
Left: How phasing would occur, in theory, if partners were uninfluenced by each other’s performance. The static part (blue) remains constant, while the moving part (green) steadily shifts its metrical position. Right: Actual performance of “Drumming” by Becker and Hartenberger. The “static” part actually varies along with the moving part during phasing. In other words, the drummer who intended to maintain the original tempo was unable to do so; instead, this drummer unintentionally increased and decreased their tempo along with the phasing drummer. (Figure reproduced with permission from Schutz [4]).
Fig 2.
Sample multidimensional recurrence plot (MdRP) produced for one phasing trial.
(A) How subsections were created from the MdRP to conduct region-based analysis. Each sample in the time series contains a vector of x- and y-coordinates of ψ. Recurrences or revisitations of the same multidimensional space (within a given tolerance) between the two time series (i.e., the same time series represented on the x-axis and y-axis) are plotted as points on the MdRP. (B) How participants’ taps were assigned to regions 1, 2, and 3 based on circular ψ values. As described in “Region-Based MdRQA,” synchronous taps were excluded from region-based MdRQA to effectively compare Successful and Unsuccessful Trials”.
Table 1.
Descriptive statistics for general MdRQA for successful, unsuccessful, and incomplete trials.
Table 2.
Linear mixed effect model results for general MdRQA with trial type, language experience, and tempo range as predictors of %REC, %DET, and MAXL.
Each MdRQA metric was predicted using a separate model. Marginal and conditional R2 for each model included below each model label. Effect sizes provided as standardized estimates (ß) for statistically significant predictors. As noted in the Model Specifications section, the use of deviation coding yields k-1 variables that test the difference between a given level of the categorical variable and the reference level. General MdRQA models used the incomplete trials, monolingual language experience, and middle tempi as reference categories; for more on mathematical interpretation of deviation-coded interaction terms, see Barr et al. (2013) [51].
Fig 3.
Effects of language experience (red: Multilingual; blue, monolingual) and tempo range on MdRQA metrics: %REC (Panel A, top), %DET (Panel B, middle), and MAXL (Panel C, bottom).
The metronome ranged from 80–140 bpm. In our linear mixed effects model, we binned tempo into the following categories: lower (80–90 bpm), middle (100–120 bpm), and upper (130–140 bpm). The violin plots depict the probability density of the binned tempo data at different %REC, %DET, and MAXL values. The mean value is indicated by a diamond near the center of each violin. Results of statistical analyses are located in Table 2.
Fig 4.
Effects of trial type (green: Successful; purple: Unsuccessful), tempo range, and region on MdRQA metrics: %REC (Panel A, top), %DET (Panel B, middle), and MAXL (Panel C, bottom).
The metronome ranged from 80–140 bpm. In our linear mixed effects model, we binned tempo into the following categories: lower (80–90 bpm), middle (100–120 bpm), and upper (130–140 bpm). The violin plots depict the probability density of the binned tempo data at different %REC, %DET, and MAXL values. The mean value is indicated by a diamond near the center of each violin. Results of statistical analyses are located in Table 4.
Fig 5.
Effects of language experience (red: Multilingual; blue: Monolingual), tempo range, and region on MdRQA metrics: %REC (Panel A, top), %DET (Panel B, middle), and MAXL (Panel C, bottom).
The metronome ranged from 80–140 bpm. In our linear mixed effects model, we binned tempo into the following categories: lower (80–90 bpm), middle (100–120 bpm), and upper (130–140 bpm). The violin plots depict the probability density of the binned tempo data at different %REC, %DET, and MAXL values. The mean value is indicated by a diamond near the center of each violin. Results of statistical analyses are located in Table 4.
Table 3.
Descriptive statistics for region-based MdRQA for successful and unsuccessful trials.
Table 4.
Linear mixed effect model results for region-based MdRQA with trial type, language experience, tempo range, and region as predictors of %REC, %DET, and MAXL.
Each MdRQA metric was predicted using a separate model. Marginal and conditional R2 for each model included below each model label. Effect sizes provided as standardized estimates (ß) for statistically significant predictors. As noted in the Model Specifications section, the use of deviation coding yields k-1 variables that test the difference between a given level of the categorical variable and the reference level. Region-based MdRQA models used the successful trials, monolingual language experience, middle tempi, and region 1 as reference categories; for more on mathematical interpretation of deviation-coded interaction terms, see Barr et al. (2013) [51].