Sixty-eight individuals (23 males and 45 females with a mean age of 26.75 (standard deviation: 12.75)) took part in the experiments. No participants reported any impairment that could affect their sense of smell (i.e., cold or flu). Participants were briefed about potential allergens and breaks (a minimum of a 10-minute break halfway through, or if the participant felt like they have a reduced sense of smell). They were instructed not to wear any scented deodorant/perfume on the day of the experiment. The experiment lasted about one hour. It was approved by the University of Liverpool and conducted under the declaration of Helsinki’s standards for medical research involving human subjects. Participants gave written informed consent before taking part in the experiment. Participants were recruited via mass e-mail and the University of Liverpool’s experiment participation requirement (EPR). Participants recruited through the EPR system did so in exchange for class credit.

All results were obtained through a graphical user interface programmed in MATLAB R2018b. Participants were placed in a lightproof anechoic chamber equipped with an overhead luminaire (GLE-M5/32; GTI Graphic Technology Inc., Newburgh, NY) during the experiment. The lighting in the room was kept consistent by using the daylight simulator of the overhead luminaire. The speakers were JBL Desktop speakers; the color stimuli were shown on a calibrated EIZO ColorEdge CG243W monitor. The results were analyzed using MATLAB R2018b.

Participants were instructed to associate a given odor with a value along each of the following dimensions: visual shapes (angularity), textures, pleasantness (using a Likert scale), pitch, musical genres, and emotions. For the musical genres and emotions, participants were asked to select the most dominant choice. The aromas were presented in a random order (determined by a random number generator in MATLAB), and all associations were assessed in the same order for a given aroma. Participants were presented with the stimuli as long as was necessary for them to make their decision. At the end of the experiment, participants were asked to identify the odor from a precompiled list (classification task). A neutral option was available for four experimental tests—visual shapes, texture, pleasantness, and the emotion task. However, participants were strongly discouraged from using this option.

We first standardized the ratings into z-scores so all the scales were in the same units; ratings were centered on each individual scale’s respective grand mean. Figure 1. shows the mean ratings (transformed to z-scores) for angularity, smoothness, pleasantness, and pitch for each of the ten odors. Separate one-way repeated measures ANOVAs (Greenhouse–Geisser corrected, α = 0.05) were conducted on the z-scores of the angularity, smoothness, pleasantness, and pitch ratings to test if the odors influenced the ratings. This revealed that the odors significantly affected all ratings—angularity (F (7.09, 475.52) = 16.59, p < 0.001, η² = 0.19), smoothness (F (7.98, 534.87) = 5.53, p < 0.001, η² = 0.07), pleasantness (F (6.97, 467.23) = 10.48, p < 0.001, η² = 0.13), and pitch (F(8.58, 406.788) = 10.23, p < 0.001, η² = 0.148). Post hoc, one-sample t-tests (Bonferroni corrected, α = 0.005 (0.05/10)) were conducted to determine which of the odors were significantly different from 0 (the original scale’s grand mean); each tested modality (i.e., the angularity of shapes) was tested independently from one another. The significantly “rounded” odors are caramel (t(67) = −9.88, p < 0.005) and coffee (t(67) = −3.87, p < 0.005). The significantly “angular” odors are peppermint (t(67) = 8.62, p < 0.005) and lemon (t(67) = 3.43, p < 0.005) (Fig. 1(A)). The significantly “rough” odor is black pepper (t(67) = −3.22, p < 0.005) whereas caramel (t(67) = 4.64, p < 0.005) is associated with “smooth,” as shown in Fig. 1(B). The significantly pleasant odors were lemon (t(67) = 4.27, p < 0.005) and orange (t(67) = 6.87, p < 0.005) whereas black pepper (t(67) = −5.84, p < 0.005) is “unpleasant,” as shown in Fig. 1(C). In the unstandardized data, there is a bias toward pleasant odors, with nine out of ten of the odors being considered pleasant. The significantly “higher pitch” odor is peppermint (t(59) = 3.47, p < 0.005), while “lower pitch” is linked with coffee (t(59) = −5.64, p < 0.005) and caramel (t(59) = −4.60, p < 0.005), as shown in Fig. 1(D). Our hypothesis of consistent crossmodal associations between odors and the angularity of shapes, smoothness of texture, perceived pleasantness, and pitch is therefore supported. All tests not reported in this manuscript are included in the supplementary materials.

To assess if the odors affected the genre and emotion selections, separate chi-squared tests of independence (α = 0.05) were conducted. This revealed that the odors impact both the choice of genre (x²(54) = 138.20, p < 0.05, Cramer’s V = 0.18) and the participant’s emotional response (x²(90) = 187.54, p < 0.05, Cramer’s V = 0.17). Chi-squared tests for goodness of fit (Bonferroni corrected, α = 0.005 (0.05/10)) were conducted to see which of the presented stimuli were significantly different from a chance selection; the emotional and genre dimensions were tested independently from one another. The odors significantly different from a chance selection in the genre association task are black pepper (x²(6) = 22.59, p < 0.005), caramel (x²(6) = 46.06, p < 0.005), freshly cut grass (x²(6) = 21.56, p < 0.005), and orange (x²(6) = 22.79, p < 0.005) (see Figure 2(A)). All odors were significantly different from chance selection in the emotion association task—black pepper (x²(10) = 43.62, p < 0.005), caramel (x²(10) = 62.71, p < 0.005), cherry (x²(10) = 56.24, p < 0.005), coffee (x²(10) = 71.76, p < 0.005), freshly cut grass (x²(10) = 57.21, p < 0.005), lavender (x²(10) = 47.82, p < 0.005), lemon (x²(10) = 94.41, p < 0.005), orange (x²(10) = 111.56, p < 0.005), peppermint (x²(10) = 50.09, p < 0.005) and pine (x²(10) = 56.88, p < 0.005) (see Fig. 2(B)). Our data therefore supports the hypothesis of consistent crossmodal associations between odors and musical genres and emotions.

For this analysis, 343 colors from the L^∗a^∗b^∗ color space were chosen, and the user’s color selection was then mapped to one of these 343 colors based on the lowest ΔE 2000 error. The sampling points are shown in Figure 3(A). These hue selections were then used to compile a histogram of common colors, as shown in Fig. 3(B). The median hue angles for the commonly selected colors are shown in Fig. 3(C). Each participant only reported one color for each odor. One-sample t-tests (Bonferroni corrected, α = 0.005 (0.05/10)) were conducted to determine if the selected lightness values were significantly different from the scale’s midpoint and default slice of 50 (the mean lightness, which was also used as the starting point in the color selection task). The odors that yielded an L^∗ value significantly different from the mean lightness were: caramel (t(67) = 3.93, L^∗ = 59.86, p < 0.005), cherry (t(67) = 3.41, L^∗ = 58.03, p < 0.005), freshly cut grass (t(67) = 3.43, L^∗ = 56.65, p < 0.005), lavender (t(67) = 4.53, L^∗ = 59.87, p < 0.005), lemon (t(67) = 14.63, L^∗ = 76.16, p < 0.005), orange (t(67) = 11.86, L^∗ = 69.99, p < 0.005), peppermint (t(67) = 6.61, L^∗ = 66.85, p < 0.005) and pine (t(67) = 3.67, L^∗ = 58.07, p < 0.005). Due to a large number of possible hue angles, a chi-square test for independence (α = 0.05) was conducted on the frequency distribution of the binned hue angles (N = 15). This revealed that the color selections significantly differ from chance selection (x²(126) = 588.95, p < 0.05, Cramer’s V = 0.31). To determine which odor’s produced consistent color profiles, Rayleigh’s z tests (Bonferroni corrected, α = 0.005 (0.05 / 10)) were conducted on the hue angles for the commonly selected colors (Fig. 3(B)). This revealed that the color profiles for caramel (z = 5.79, p < 0.005), cherry (z = 5.32, p < 0.005), coffee (z = 6.22, p < 0.005), lemon (z = 6.67, p < 0.005) and orange (z = 6.63, p < 0.005) are non-random; thereby supporting the hypothesis of consistent crossmodal odor–color correspondences.

The participants’ task was to identify the given odor by selecting one of the 23 possible selections from a list. Retrospective twofold classification was considered, exact classification and categorical classification. The exact classification was achieved 45.74% of the time by correctly identifying the current odor. The top three correctly classified odors are peppermint (82.35%), lemon (80.88%), and orange (61.76%). The top three misclassified odors are black pepper (10.29%), pine (13.24%), and caramel (20.59%), see Figure 4. Retrospective category classification was determined by the participants’ ability to pick another odor in the same category following the fragrance classes outlined in [9]. An accuracy rating of 62.94% was achieved for category classification; each potential classification belonged to only one category.

To test if crossmodal associations are mediated by knowledge of the odor, the ratings were divided into two sets—“correct” and “incorrect” (Figure 5(A–D)). Two-way repeated measures ANOVAs (Greenhouse–Geisser corrected, α = 0.05), was conducted on the z-scores for angularity, smoothness, pleasantness, and the pitch ratings using the odors and classification sets (correct versus incorrect) as within-subject factors. Each modality was tested independently from one another. This revealed that the main effect for identification was not significant for the angularity (F(1, 6) = 3.19, p = 0.124, η² = 0.347), smoothness (F(1, 6) = 0.123, p = 0.738, η² = 0.020), pleasantness (F(1, 6) = 0.142, p = 0.74, η² = 0.18), or pitch (F(1, 6) = 0.540, p = 0.50, η² = 0.119). These results indicate that the ratings for the angularity of shapes, smoothness of texture, perceived pleasantness, and pitch are not mediated by knowledge of the odors identity.

To assess if explicit knowledge of the odor affected the musical genre and emotional dimensions, the relative percentage difference was first calculated using the assignment percentages from the “correct” and “incorrect” sets. This was performed because the underlying data was categorical and not numerical. One-sample t-tests (Bonferroni corrected, α = 0.005 (0.05/10)) were conducted on the relative percentage difference to determine if the incorrect and correct proportions for each odor are significantly different from 0 (no change). The musical and emotional dimensions were tested independently from one another. This revealed that only freshly cut grass (t(6) = 4.5139, p < 0.005) and lavender (t(6) = 4.8174, p < 0.005) are significantly different for the genre ratings. The significantly different odors for the emotional ratings are black pepper (t(10) = 7.9480, p < 0.005), caramel (t(10) = 4.3374, p < 0.005), cherry (t(10) = 4.3374, p < 0.005), freshly cut grass (t(10) = 3.8407, p < 0.005), lavender (t(10) = 4.8719, p < 0.005) and lemon (t(10) = 4.0871, p < 0.005). Hence, the knowledge of the odor identity affects the observer’s musical genre and emotional responses, see Figure 6.

Following the same procedure as the color analysis above, the common colors for the correctly classified odors are shown in Figure 7(A), and the common colors for the misclassified odors are shown in Fig. 7(B). To determine if the observed proportions (quantity of commonly selected colors) between the common colors for the correctly classified and misclassified odors were the same, chi-squared tests for goodness of fit (Bonferroni Corrected, α = 0.005(0.05∕10)) were conducted. This revealed that five odor–color associations are significantly different for the observed proportions between correctly classified and misclassified colors: the proportions for black pepper (x²(1) = 8, p < 0.005), cherry (x²(1) = 10, p < 0.005), lemon (x²(1) = 14, p < 0.005), peppermint (x²(1) = 10, p < 0.005) and pine (x²(1) = 8, p < 0.005) are significantly different. Comparing Fig. 7(A) with Fig. 7(B), we can see that with the knowledge of the odor’s identity, the generated color profiles are more consistent. Without knowing the identity of the odor, the generated color profiles are more diverse. Chi-squared tests for goodness of fit (Bonferroni corrected, α = 0.005 (0.05/10)) were conducted on the correctly and incorrectly classified odors’ median hues angles. This revealed that the median hue angles for all odors except for caramel are significantly different. This suggests that the explicit knowledge of an odor’s identity affects the colors associated with the odors.

Principal component analysis (PCA) was conducted to determine the perceptual similarity between the odors (Figure 8(A)) and to uncover the potential underlying relationships between the principal components (Fig. 8(B)). The PCA was conducted on the mean shape ratings, texture ratings, pleasantness ratings, pitch ratings, the color dimension (lightness), classification accuracy, the musical genre dimensions, and the emotional dimensions. Due to some of the ratings being on different scales, each independent rating (i.e., lightness and emotions) was rescaled between 1 and 9, then standardized. The Kaiser–Meyer–Olkin sampling adequacy [37, 38] is 0.86, Bartlett’s test of sphericity [3] is significant (p < 0.01), meaning the data was of high enough quality to progress with the factor analysis. Based on inspection of the scree plot, we extracted the first four principal components, explaining 81.55% of the total variance and have an eigenvalue of at least 1. The principal components 1 through 4 explain 33.31%, 25.44%, 13.88%, and 7.87% of the total variance. We did not perform any rotations on the factors produced by PCA as we believe that it better expresses the underlying data. The first two principal components are shown in Fig. 8(A); this shows the perceptual similarity between the olfactory stimuli, for example, (cherry, lemon, and orange), (lavender, freshly cut grass, and pine), (coffee and caramel) obtained similar results in most, but potentially not all ratings analyzed using PCA. We only explored the first two principal components for straightforward interpretation, as the inclusion of the 3rd and 4th components did not change the conclusion. The loadings matrix is shown in Fig. 8(B); this shows how strongly each component affects the principal components, shown in 8A. The 3rd and 4th components for both the score and loadings plot are shown in Fig. S2. The PCA loadings plot (Fig. 8(B)) suggests that hedonics plays an essential role in crossmodal correspondences, for example, the loadings of soul and metal on the smoothness rating. The loadings plot also suggests that knowledge of the odor’s identity plays a vital role in modulating the hedonic ratings. Based on inspection of the PCA loadings plot Fig. 8(B), we can see that the component “Classification Rate” has a strong loading on the first component (furthest from 0 on the x axis). This suggests that the semantic involvement (knowledge of the odor’s identity) plays an essential role in explaining the first component’s variation. The negative loadings of “Bored,” “Calm,” and “Country” onto the “Classification Rate” component suggests that knowledge of the odor’s identity mainly influences the hedonic dimensions (emotional and musical). The negative loadings of the hedonic dimensions (emotional and musical) on the “Angularity,” “Smoothness,” “Pleasantness,” and “Pitch” components suggest that they are affected more by the hedonic dimensions with little involvement from the semantic (correct classification).