## 2 Results
### Training Performances  
Participants performed two training tasks: (1) Scales, and (2) Arpeggios. For each layout, participants completed three training performances of the scale, and three of the arpeggios. The accuracy of performances in the two training tasks, averaged across participants, are summarized in Figures 2 and 3 as a function of the independent variables detailed in Section 1.3. The 95% confidence intervals were obtained with 100,000 bootstrap samples, calculated and plotted in MATLAB. The generalized linear mixed effects models used to estimate the effects' sizes and significances of _Adjacency_, _Shear_, _LayoutNo_, and _PerfNo_ are summarized in Tables 1 and 2. The significant coefficient for _Shear_ (1.14) indicates that sheared layouts worsen performance accuracy in the scale training task: they multiply inaccuracy by 1.14 (increase it by 14%). Looking at \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Fixed Effect** & **Estimate** & **Factor** & \(p\)**-Value** \\ \hline (_Intercept_) & 3.48 & 32.61 & \textless{}0.001 *** \\ _Adjacency_ & \(-\)0.06 & 0.94 & 0.263 \\ _Shear_ & 0.13 & 1.14 & 0.026 * \\ _LayoutNo_ & \(-\)0.37 & 0.69 & 0.001 *** \\ _PerfNo_ & \(-\)0.27 & 0.77 & \textless{}0.001 *** \\ _LayoutNo:PerfNo_ & 0.12 & 1.13 & 0.003 ** \\ \hline Log Likelihood & \(-\)727.67 & & \\ Num. obs. & 208 & & \\ Num. groups: ID & 24 & & \\ Var: ID (Intercept) & 0.04 & & \\ Var: Residual & 0.17 & & \\ \(r^{2}\) & 0.44 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Generalized linear mixed effects model for the scale training task. Figure 2: Inaccuracies, averaged across participants, for the scale training task. The higher the line, the more accurate the average performance. The bootstrapped confidence intervals cover a 95% range. Adjacent layouts have solid lines, nonadjacent have dashed lines. Sheared layouts have orange lines, unsheared have blue lines. The first performance is coded 0, the second is coded 1,...; the first layout is coded 0, the second is coded 1. Figure 2, it is apparent that this effect is arising mainly in the non-adjacent layouts--the accuracies for \(A^{\prime}S\) (dashed orange) are lower than the accuracies for \(A^{\prime}S^{\prime}\) (dashed blue). Note that the interaction between _Adjacency_ and _Shear_ was not tested for the reasons explained in Section 2.1. The significant coefficients for _LayoutNo_ (0.69), _PerfNo_ (0.77), and their interaction _LayoutNo:PerfNo_ (1.13), indicate that accuracy in the scale training task improves over successive layouts and performances, but less so when either is high. In Figure 2, the positive gradient of the lines in the first layout block (0/0, 1/0, 2/0) appear greater than those of the second (0/1, 1/1, 2/1) and third (0/2, 1/2, 2/2) blocks; the inaccuracy measured at the beginning of each layout block (performance 0) also appears to increase across layout blocks 0-2, but less so with performances 1 and 2 (the middles and ends of each layout block). The significant coefficient for _Adjacency_ (0.65) indicates that adjacent layouts strongly improve performance accuracy in the arpeggio training task: they multiply inaccuracy by 0.65 (decrease it by 35%). This is visible in Figure 3 where the dashed lines in the second layout block are lower than an imaginary line connecting the first and third blocks. The significant coefficient for _Shear_ (1.08) indicates that sheared layouts slightly worsen accuracy in the arpeggio training task: they multiply inaccuracy by 1.08 (increase it by 8%). Looking at Figure 3,