RESULTS 151 greater Movement. Finally, Participants reported more Wandering when excerpts

were articulate, melodious, intense, and associated with more entrainment.

Because every musical metaphor could be characterized by a multitude of dif-ferent descriptors, ranging from emotions to acoustic and perceptual features, we decided to perform a multi regression with best subset selection to highlight a re-duced number of suitable descriptors. A regression with this subset of descriptors should reasonably fit the binomial value for each metaphor. More importantly, the addition of any other descriptors should not improve the fit by a large margin. While running the multi regression analysis, we extracted the Akaike Information Criterion (AIC) for every set of descriptors, starting with one only regressor to finishing with all the regressors in the model. Across all metaphor regressions, adding more than five regressors did not seem to improve the model by a large margin (Figure E.4).

In addition, we observed that the metaphors Force and Movement were associated with a better fit with the descriptors present in this study than Flow, Interior, and Wandering. Consequently, we looked for the best subset of five regressors to fit each metaphor. While most of the five regressors for each metaphor had a statistically significant impact, some regressors showed a greater weight, meaning that each vari-ation in this parameter resulted in a greater varivari-ation in the metaphor itself. To elaborate, we mainly report positive association between Force and Power, Arousal, and entrainment (Supplementary Material E.5.l). Movement was positively with entrainment. Flow was positively associated with Joyful activation, and negatively associated with entrainment. Interior was negatively associated with entrainment.

Finally, the weights associated with Wonder were negative for Tension and positive for entrainment.

A potential issue with using multiple regressors to describe metaphors lies in multicollinearities. Some of the descriptors might be strongly correlated and there-fore might explain the same part of the variance in our models. To explore that, we decided to compute the individual variance (R²), the variance inflation factors (VIF), and the correlation matrix. First, not all regressors explains the same amount of variance. Some might explain more of the variance of a certain model when taken individually. For example, the variance associated with the metaphor Force is bet-ter explained by Power (R² = 0.251), Arousal (R² = 0.282), and entrainment PC1 (R² = 0.191) than Wonder (R² = 0.005) despite all of these regressors being in the best subset (Supplementary Material E.5.m). Movement is best explained by entrainment PC1 (R² = 0.259). Second, not all regressors share the variance ex-plained. The variance inflation factor shows which regressor is linked with others,

Figure E.4 – Multi regression using best subset selection. A. Evolution of Akaike Information Criterion associated with models with increasing subset sizes. B. Weights associated with the best subset of regressors to estimate the binomial value of the metaphor Wandering. C. Weights associated with the best subset of regressors to estimate the binomial value of the metaphor Interior. D. Weights associated with the best subset of regressors to estimate the binomial value of the metaphor Flow. E. Weights associated with the best subset of regressors to estimate the binomial value of the metaphor Movement.

F. Weights associated with the best subset of regressors to estimate the binomial value of the metaphor Force. The faded bar represents the intercept present in every regression.

(.:p <0.1,∗:p <0.05,∗∗:p <0.01,∗ ∗ ∗:p <0.001)

E.4. DISCUSSION 153 with values approaching 1 when the regressor is independent of other regressors. In our data, some were characterizing the same variance. It is the case, for example, for Tenderness and Nostalgia in the Movement model, with very high VIF (respectively 22.08and22.19). Joyful activation and entrainment PC1 seemed to be sharing a part of the variance, with V IF = 3.48 and 4.45respectively. Third, to create the corre-lation matrix, we used permutations as a way to match participants. Since the two questionnaires were answered by two different groups of participants, permutations created artificially a multitude of pairs or responses representing a wider popula-tion. We rotated a thousand times the order of responses of our participants for each excerpt. After every rotation, we computed a Spearmann correlation between pairs of items. All the permutations resulted in a normal distribution of correlation from which we retained the mean. Correlation ranged from negative, r = −0.46, between the component for entrainment and the first perceptual component, to pos-itive, r= 0.5, between Power and entrainment (Table E.1). Groups of descriptors seem to be correlated together. Therefore, we performed a multidimensional scaling (MDS) in order to reduce dimensionality of our data and display graphically, in two dimensions, the correlation between the different ratings obtained. We later per-formed a k-mean clustering with city block method on the obtained MDS results in order to group items together. The resulting clustering showed a good trade-off be-tween model complexity and accuracy (Supplementary Material E.5.n). It displayed 6 clusters (Figure E.5). Going around the graph in a clockwise manner, the first cluster was associated with Wonder, as well as the first components for acoustic and perceptual features, respectively. The second cluster featured Tenderness, Peaceful-ness, and Flow. The third cluster consisted of Nostalgia, Interior, SadPeaceful-ness, and the lack of intensity and roughness. The fourth cluster featured Transcendence from the GEMS. The fifth cluster was associated with Power, Tension, Arousal, Move-ment, entrainment and articulation. Finally, the last cluster consisted of Wandering, Valence, and Joyful activation.

E.4 Discussion

This study aimed to test the links between musical emotions and metaphors and acoustical and perceptual features in the context of listening to classical music. In order to do so, we created two different surveys where participants had to listen to the same musical excerpts. One was focused around the musical metaphors while the others asked the participants about musical emotions. We collected the responses

Table E.1 – Correlation table between every item of every scale. Correlation was calcu-lated based on permutations of pairs of participants.

from 162 participants and proceeded to model the relationships between emotions and metaphors, as well as acoustic and perceptual features, using generalized linear mixed models. Finally, we explored the correlation between every item and displayed such relationships onto two dimensions using a multidimensional scaling approach.

When exploring the collected data, we came across two main findings: an accrued amount of zero compared to any other ratings and no difference in ratings between musicians and non-musicians, and almost no difference between participants with vivid imagination or not. The former can be explained by multiple reasons. The first one is associated with the way the scales are designed. While being continu-ous scales, both GEMS and GEMMES feel like categorical scales. Even if music is capable of eliciting mixed emotions (P. N. Juslin et al., 2011), participants tend to choose very few or even sometimes only one category to represent one musical piece.

The way both GEMMES and GEMS were created, by allowing rotation in the con-firmatory factorial analysis, is also showing a desire to maximize the discrimination between the different factors (Schaerlaeken et al., 2019; Zentner et al., 2008). The more discriminable the items in a scale, the more zeros we found in the participants

E.4. DISCUSSION 155

Figure E.5 – Multi-dimensional scaling based on the Spearmann correlations between every item of all scales and features. The six clusters are based on a clustering k-mean analysis

responses on the not relevant subscales. In contrary, valence and arousal are seen as dimensions and not categories (Russell, 1980), consequently, they invite the partici-pants to rate both independently. Furthermore, the presence of zeros in our dataset might reflect the ineffability of music in general. It has been argue that participants sometimes "lack the necessary vocabulary to provide accurate verbalizations of their emotional experience" (Zentner and Eerola (2010), p. 193)). People also tend to categorize their subjective experience rather than representing them in a more com-plex mixed feeling. The fact that people judge once their emotions might also bias them to one category. Actually, it has been shown that this integration process changes a lot the reported emotions compared to dynamic judgments for the same excerpts (Eliard, 2017). Furthermore, some subscales are used less frequently than others (e.g. Transcendence and Wonder), as they lead to more zeros in the data collected (Aljanaki, Wiering, & Veltkamp, 2016). This might be related to the fact that people are less used to represent these categories, or that these categories are

ill-defined, or that these categories are more rarely induced than others. The lack of difference between musicians and non-musicians as well as between high and low vivid imagination, can be explained by the fact that musical training is not required to perceive emotions in music (e.g., (P. N. Juslin, 1997b)). As for the metaphors, since they are culture-dependent (I. Cross, 2009; Zbikowski, 2008), the use of a population coming from one single culture (French-speaking Europeans) helped cre-ate an environment where musicians and non-musicians most likely shared the same metaphors. Similar to musical expertise, having a vivid imagination did not seem to affect the evaluation of metaphors, except in the case of Wandering. It is likely that in a judgment study like the one we performed, musician and non-musician used very similar everyday metaphorical representations. Since human conceptual system is in essence thought to be metaphorical (Lakoff & Johnson, 1980), with figurative language and metaphors occurring during spoken discourse about once every 25-30 words (Graesser, Mio, & Millis, 1989), everyone should be capable of evaluating the metaphorical content of a musical piece. However, it might not be the case in the context of musical performances or musical training, in which musician use more complex metaphorical representations. The example of Wandering, as a more complex metaphor in a sense that its reliability is lower than the other four, shows that not all metaphors are understood in a similar way. This is the main drawback of using metaphors, in the context of music teaching, for example, where students could struggle to understand a teacher’s metaphorical language (Persson, 1996). Furthermore, such mechanisms of metaphor or affective evaluations would be strongly impacted by cultural differences. It would be interesting to address these questions in future studies.

Taking together the results from the generalized linear mixed models, the mul-tiple regression, and the multidimensional scaling, we can confidently link musical metaphors to emotions, acoustic, and perceptual features. We believe that both musical metaphors and emotions, as parts of musical meaning, are grounded in em-bodied cognition and experiences (Aksnes, 2002; Borgo, 2004b; Chuck, 2004; A. Cox, 2001; M. L. Johnson, 1997; Walker, 2000). In this work, the metaphors of Force (de-scribed by "impressive," "empowerment," "amplify," "immense," "grandeur," and

"intense") and Movement (described by "to move," ‘rhythm", "body movement,"

and "jump") were associated with emotions of Power, Tension, Joyful activation, a feeling of Arousal, and in the case of the Movement metaphors to Valence and Wonder. Both metaphors and affects seems to be engrained within the physicality of human experiences, which consolidate both concepts. For example, Tension requires

E.4. DISCUSSION 157