# Influence of Piano Key Vibration Level on Players' Perception and Performance in Piano Playing
## 3 Results
### Influence of Piano Key Vibration Levels on Musical Performance  
To analyze the MIDI-based performance data, a custom data structure was used. The structure groups notes played at the same time (\(\pm 40\) ms) into clusters, removes accidentally played wrong notes, and assigns if the note was played by the left or right hand. Key velocity \(v\), a measure of a keystroke's excitation strength, was directly extracted from the MIDI messages. For the calculation of the inter-onset interval \(\tau\)--the time interval between two subsequent note onsets--only notes played by the left hand were considered. The tempo of each trial was normalized. To compare trials by the distribution of key velocity \(v\) (analogously for inter-onset interval \(\tau\)) histogram intersection was used. Histogram intersection was introduced by [PERSON] [PERSON] and [PERSON] (1988) to identify objects by color similarity in computer vision. Histogram intersection is defined as [PERSON] and [PERSON] (1988)  
\[H_{1}(v)\cap H_{2}(v)=\sum_{i=1}^{n}\min\left(h_{1i}(v),h_{2i}(v)\right), \tag{1}\]  
where \(H_{1}\) and \(H_{2}\) represent two trials by normalized discrete distributions of key velocity \(v\) with \(n\) bins \(h_{1i}\), \(h_{2i}\). Equation (1) measures the overlap of two histograms in the range \([0,1]\). The number '1' corresponds with perfect overlap; '0' means no overlap. In contrast to an evaluation based on mean values only, histogram intersection also identifies differences in the distributions' shape or offset. To judge significance, two tests were demanded to reject the null hypothesis: non-parametric Friedman analysis of variance with a 95% confidence level in combination with pairwise Wilcoxon signed-rank tests with Bonferroni correction. We used non-parametric tests, because the evaluated quantities do not necessarily follow a normal distribution and because of the sample size. Two approaches were used to compare the distributions of key velocity \(v\) and inter-onset interval \(\tau\) by histogram intersection. The distribution of both parameters was calculated for each trial and was analyzed for each participant separately. The first approach considered if the pianists adapted their playing to the vibration levels (e.g., if a pianist perceived an overemphasis of bass notes and therefore played the bass notes with less finger force than before). This force adaption manifests in the shape of the distribution of key velocity \(v\). An increase in the \"amount of adaption\" was expected with increasing vibration levels. The \"amount of adaption\" for key velocity \(v\) was measured as follows. Let \(H_{P_{k},V,i}(v)\) denote the normalized histograms describing the distribution of key velocity \(v\) for trial \(i\in\{1,\ldots,9\}\), vibration level \(V_{\ell}\) with \(\ell\in\{0,1,2,3\}\), and pianist \(P_{k}\) with \(k\in\{1,\ldots,11\}\). Then the \"amount of adaption\" \(A_{P_{k},V_{n}}\) of pianist \(P_{k}\) to vibration levels \(V_{n}\) with \(n\in\{1,2,3\}\) was estimated as the histogram difference relative to \(V_{0}\) condition \(H_{P_{k},V_{0},i}(v)\cap H_{P_{k},V_{n},i}(v)\) for all combinations of trials \(i,j\in\{1,\ldots,9\}\) and key velocity \(v\). For the inter-onset interval \(\tau\) the same procedure was conducted. Figure 3 shows the \"amount of adaption\" of the pianist's playing to the feedback levels for both performance parameters. The differences in Figure 3 are not significant. There is no general tendency that the participants adapt their playing to the key vibration level. Nonetheless, by analyzing the  
influence of the vibration levels per participant individually, three participants showed significant differences for key velocity \(v\) and three for inter-onset interval \(\tau\).