d Statistical analyses

At first glance, the distribution of ratings for both the GEMMES and GEMS scales did not follow a normal distribution. Both were zero-inflated distributions due to the tendency of our participants to associate each excerpt with only a part of the items proposed, leaving the rest at the minimum value. This had two consequences: first, statistical comparison of the raw ratings required non-parametric testing (permuta-tion testing and Spearmann correla(permuta-tion). Second, we artificially created a binomial

distribution by characterizing each scale of each trial as "1" or "0". A scale was set to "1" if the corresponding raw rating was superior or equal to the middle of the rating scale (4, noted for the participants as "neither relevant nor irrelevant"), and set to "0" otherwise. Afterwards, we also determined for each excerpt the best emo-tional scale from the GEMS and metaphorical category from the GEMMES based on the frequency of positive binary ratings.

We computed a set of acoustical and musical features on all musical excerpts using the MIR toolbox (Lartillot & Toiviainen, 2007). This set of 36 features had been used in previous studies and is adapted for studying musical acoustic features (Eliard, 2017). Additionally, we also received a set of perceptual features for each excerpt as part of another distinct experiment (Aljanaki & Soleymani, 2018). The set contained 7 features: articulation, atonality, dissonance, melody, mode, rhythm complexity, and rhythm stability (cf (Aljanaki & Soleymani, 2018); for methodol-ogy). We performed three principal component analyses (PCA) in order to reduce the dimensionality of our models. The first PCA extracted two components for the acoustic and musical features (Supplementary Material E.5.b, E.5.c). The second PCA extracted two components for the perceptual features (Supplementary Material E.5.b, E.5.c). Finally, the last PCA extracted one component for the entrainment questionnaire (Supplementary Material E.5.b, E.5.c).

We computed generalized linear mixed models (GLMM) to estimate the propor-tion of positive binary ratings of each scale based on a variety of different fixed-effects. GLMMs take advantage of the modelling of random effects to improve precision of the model and allow for the computation of models with non-normal distribution. We computed our models using a binomial distribution. It is impor-tant to note that, for such models, an estimated value of 0.5 correspond to the chance level. Therefore, significant effects deviated from this value either positively or negatively. The random intercept effects in our models encapsulated the vari-ability related to each participant and each musical excerpt. We used a step-up strategy while building the model to compare the different combinations of fixed effects. This comparison was computed using chi-square difference tests between different models with increasing complexity to investigate the contribution of ex-plained variance for each variable and their interactions. We report the effect sizes in accordance with the approach of Nakagawa and Schielzeth (2013), implemented in the "MuMIn" R package (Nakagawa & Schielzeth, 2013). They developed an approach based on two indicators, a marginal and a conditional R² (R²_m and R²_c, respectively), allowing comparability with standard methods, while considering the

E.3. RESULTS 145 variance explained by the random effects. R²_m is the variance explained by the fixed factors, whereas R²_c is the variance explained by the entire model (both fixed and random effects). We calculated them for each effect in our statistical models. Each excerpt was characterized by different labels that were later used as fixed effects.

The excerpts represented each, by design, a single emotion from the GEMS. Ad-ditionally, they could be labelled as high or low based on their computed value in each of the following conditions: the acoustic features components, the perceptual features components, the entrainment component, as well as the perceived emo-tions. This distinction was based on the max-min normalized value and "high"

excerpts corresponded to a value of 0.5 and above. For example, "The Imperial March" by Williams was by design labelled as Power, and characterized by high Power, high Tension, low Tenderness, high entrainment, and high component 1 for perceptual features. Finally, we computed correlations between the different scales and components. Since different participants rated the scales on the two different questionnaires (metaphors versus emotions), straightforward correlations could not be computed. Therefore, we randomly rearranged a thousand times the order of par-ticipants’ ratings for each scale and computed Spearmann correlations between each item (emotions, metaphors, entrainment, acoustic, and perceptual components).

Then, we extracted the mean correlation for each pair from the normal distribution created by the random permutation. We used these correlation values as inputs in a multi-dimensional scaling method (MDS). The results of the MDS were sub-sequently clustered using a k-mean clustering with city block method in order to group emotions, metaphors, and features by meaningful associations.

E.3 Results

The goal of this study was to describe the relationships between the musical metaphors reported in the GEMMES, the musical emotions assessed with the GEMS, and a multitude of musical descriptors including acoustic parameters, per-ceptual features, and subjective entrainment. First, we verified that our participants correctly labelled the excerpts chosen for their emotional qualities. We also high-lighted the metaphors associated with those emotional qualities. Furthermore, we reported metaphors associated with high and low values of the aforementioned mu-sical descriptors. Second, we assessed for each metaphor the best subset of descrip-tors using multi-regressions. Finally, we computed correlation between the different scales to assess multi-collinearities. Based on this information, we also performed a

multidimensional scaling to investigate the global structure of the different measures.

All participants, regardless of the type of questionnaire, were categorized as ei-ther musicians or non-musicians based on their answers to a series of questions:

"Do you consider yourself a music lover?," "Are you a musician?," "How long have you been playing?," and "How often do you play?," Musicians answered "yes" to the first two questions, played their instrument for more than 5 years, and prac-ticed for at least one hour per week. The difference in ratings for both musi-cians and non-musimusi-cians were neither significant using permutation testing for each GEMS subscales (Z_range = [−1.00,1.52],p_range = [0.13,0.79]), nor for the GEMMES (Z_range = [−1.19,0.59], p_range = [0.23,0.75]), nor for the VA (Z_range = [0.49,1.14], prange = [0.25,0.62]) (Supplementary Material E.5.d). Half of all participants (N = 81) received the GEMMES questionnaire. They first needed to answer the VVIQ to evaluate their ability to imagine mentally vivid images (Marks, 1973).

There were divided into two groups, participants with high vivid imagination and participants with low vivid imagination, based on the mean value obtained for the questionnaire, since the scores followed a normal distribution. A participant with low vivid imagination scored lower than the average value for our participants. Most metaphors ratings were not affected by how vivid the imagination of our partici-pants was (Zrange = [−2.46,0.23],prange = [0.013,0.82]). Only the metaphor family Wandering was rated significantly higher for high imagination than low imagination participant. Related to the zero-inflated distribution and before binomial segrega-tion of the raw ratings, we observed that zeros counted for around 32% of responses on the GEMS, 16% on the GEMMES, and 6% for Valence and Arousal. Finally, over the 18 musical excerpts, the reliability of ratings on each item ranged from standardized α_cronbach = 0.70 to0.90(Supplementary Material E.5.e).

To evaluate if the participants accurately labelled the emotionally connoted ex-cerpts we presented, we performed a GLMM using the binary values. A model encompassing the interaction between the labels participants gave and the labels pre-selected by the music expert, and the main effects associated, statistically out-performed the model with only the main effect (χ²(83, N = 81) = 3069.5,p <0.001, R_m² = 0.31, R²_c = 0.44, AIC_{GEM S∗}ExcerptGEM S = 13019, AICGEM S+ExcerptGEM S = 15960; BIC_{GEM S∗}ExcerptGEM S = 13640, BICGEM S+ExcerptGEM S = 16102). Partici-pants gave significantly higher ratings for the specific emotion associated with the excerpt presented (Supplementary Material E.5.f, E.5.g, E.5.h). Similarly, we re-ported that a model encompassing the interaction between the metaphors chosen and the emotion labels, and the main effects associated, outperformed a model

E.3. RESULTS 147 with only the main effects (χ²(47, N = 81) = 1710.3, p < 0.001, R²_m = 0.27, R_c² = 0.45, AIC_{GEM M ES∗}ExcerptGEM S = 7559, AICGEM M ES+ExcerptGEM S = 9205;

BIC_{GEM M ES∗}ExcerptGEM S = 7882, BICGEM M ES+ExcerptGEM S = 9308). Participants evaluating excerpt labelled as Joyful activation reported significantly more Move-ment and less Interior (FigureE.1, Supplementary Material E.5.i). Nostalgia was associated with less Force, Movement, and Wandering. Participants labelled peace-ful excerpts with more Flow and less Force and Movement. Power was associated with more Force and less Flow. Sadness excerpts were labelled with more Interior and less Force, Movement, and Wandering. Participants labelled Tenderness ex-cerpts with more Flow and less Force. Tension was associated with more Force and Movement, and less Flow and Interior. "Transcendence was only associated with more Flow. Finally, Wonder was associated with more Force and Movement, and less Interior.

Figure E.1 – Estimated binary ratings for GEMS and GEMMES based on the attributed affective content of the musical excerpts. The dotted horizontal line at 0.5 symbolized the chance level of drawing from a binary set. Values are tested to be significantly different from this value. a. GEMS ratings. b. GEMMES ratings. All contrasts are FDR-corrected [*: p <0.05, **: p <0.01, ***: p <0.001]

We complemented these results by computing models for each musical descriptor.

We labelled each excerpt as high or low in one of the different musical descriptors based on either participants’ responses or on the computed acoustical features. Mod-els encompassing an interaction between the metaphors and the descriptor, as well

at their main effect, always outperformed models with only the main effect (Supple-mentary Material E.5.j). We reported the results in polar graph to be able to char-acterize each metaphor in one glance (FigureE.2, for description of the metaphors in terms of emotional content, andFigureE.3, for a description of the metaphors in terms of acoustic and perceptual features). Participants reported significantly more Flow when excerpts were associated with more Peacefulness, Nostalgia, and Tender-ness, and less Power, Tension, Transcendence, and Arousal (Supplementary Material E.5.k). Participants reported more Force for excerpts associated with more Joyful activation Power, Tension Transcendence, and Arousal, and less Peacefulness, Nos-talgia, Sadness, and Tenderness. Participants reported more Interior for excerpts associated with more Peacefulness, Nostalgia, Sadness, and Tenderness, and less Joyful activation, Power, Tension, Transcendence, Wonder, Valence, and Arousal.

Similar to Force, participants reported more Force when excerpts were associated with more Joyful activation, Power, Tension, Transcendence, Wonder, Valence, and Arousal, and less Peacefulness, Nostalgia, Sadness, and Tenderness. Finally, partici-pants reported more Wandering for excerpts associated with more Joyful activation, Power, Tension, Wonder, Valence, and Arousal, and less Peacefulness, Nostalgia, and Sadness.

The descriptors linked to acoustical and perceptual features were principal com-ponents (PC) from three PCA computed on the acoustic features, the perceptual features, and the entrainment questionnaire, respectively. The first PCA resulted in two components for the acoustical features that explained cumulatively 48.3%

of the variance. The first PC was positively associated with the spectral centroid and brightness. The second PC was negatively associated with the intensity of the signal (RMS) and the roughness. The second PCA, based on the perceptual fea-tures, resulted also in two components that encapsulated 65.3% of the variance.

The first PC was positively associated with dissonance and negatively with melody.

The second PC was positively associated with rhythm and articulation. Finally, the last PCA integrated the entrainment questionnaire into one single component that explained 85.5% of the variance and was associated positively to feeling an-imated, wanting to move, and feeling the beat. Participants reported more Flow when excerpts were more melodious, and associated with less entrainment, articu-lation, and rhythm (Figure E.3). Participants reported more Force for excerpts that were more dissonant, entraining, articulate, and intense. They reported more Interior for excerpts that were less entraining and articulate. Participants associ-ated excerpts that were more melodious, entraining, articulate, and intense with

E.3. RESULTS 149

Figure E.2 – Polar graph of the estimated binary value of each metaphor based on the emotional content of the musical excerpts. The red shape represents the excerpts that were rated high for such emotional content. The blue shape represents the excerpts that were rated low for such emotional content. The contrasts compare the estimated value of a specific metaphor between the high value and low value excerpts for each affective term. For example, a single contrast compares the Flow values obtained for excerpts characterized as high for Nostalgia and low for Nostalgia. All contrasts are FDR-corrected [*: p <0.05, **: p <0.01, ***: p <0.001]

Figure E.3 – Polar graph of the estimated binary value of each metaphor based on the principal components of the acoustic and perceptual features associated with the musical excerpts. The red shape represents the excerpts that were rated high for such descriptors. The blue shape represents the excerpts that were rated low for such descriptors. The contrasts compare the estimated value of a specific metaphor between the high value and low value excerpts for each component. All contrasts are FDR-corrected [*:

p <0.05, **: p <0.01, ***: p <0.001]. The table summarizes the principal components resulting from the PCA on the acoustic feature, the perceptual feature, and the entrainment questionnaire. Only the features with a weight superior to 0.5 are displayed. Features with a weight superior to 0.7 a displayed not faded. Positive weights are represented in read and negative in blue.

E.3. RESULTS 151