#### 3.1. Olfactory Profiles from Fragrantica and the H&R Guide

The frequency of terms used by Fragrantica for the main accords of perfumes studied here is shown in

Table 2, as well as the occurrence of attributes for the description of all 453 feminine fragrances contained in the H&R guide. Interestingly, the set of recurrent descriptors was basically the same, as well as those applied with a lower frequency. As an exception, the occurrence of “fruity” was much higher in the H&R guide (33.1%) than in Fragrantica (7.1%), while the opposite applied to “citrus”, which might be explained by the semantic and sensory similarity of both descriptors. Actually, as citrus is a type of fruit, they were presumably used interchangeably to a certain extent.

It turns out that

X_{balsamic} and

X_{amber} are correlated (

r_{137} = 0.22,

p = 0.009; the subscript of Pearson’s correlation coefficient indicates the number of observations). Curiously, “balsamic” was applied more often by Fragrantica (36.4%) than by the H&R guide (13.9%), while the opposite applied to “amber” (

Table 2). The reason seems to be that both descriptors refer to oriental scents and, hence, they were applied indifferently to some extent, like in the case of “fruity” and “citrus”. Consistent with this interpretation, an online fragrance guide [

27] contains a major class called “ambery–oriental”. Moreover,

Ed_{oriental} yielded the highest correlation with

I_{sweet} (

r_{140} = 0.53),

O_{vanilla} (

r_{140} = 0.53), and

X_{balsamic} (

r_{137} = 0.44,

p < 0.0001). Oriental perfumes often contain heavy blends of balsamic resins, opulent flowers, sweet vanilla, and musks [

12].

The use of Pearson’s correlation coefficient here is arguable because it measures the strength of linear relationship between two variables with a normal distribution. When using dichotomous variables, it seems more convenient a priori to apply similarity coefficients [

28]. Different coefficients of this type have been proposed in the literature, and several statistical tests like ANOSIM are available. A detailed discussion about which method best applies here is out of the scope of the present work. Furthermore, the issue becomes more complex here because some variables are continuous and others are dichotomous. Thus, in order to find those descriptors that yield the strongest similarity with a given variable, it was decided to compute Pearson’s correlation coefficient for simplicity, assuming the limitations of this method.

The relative frequency of “floral” in the H&R guide was 98.9%, which agrees with the marked feminine character of floral scents. However, “woody” was labeled more often (83.6%) than flowery descriptors (80.7%) in Fragrantica (

Table 2), which was unexpected because woody notes are more typically found in men’s fragrances. Nevertheless, woody ratings computed from this website seem to be reliable because

X_{woody} yields the highest correlation with

Z_{chypre} (

r_{137} = 0.42) and

X_{earthy} (

r_{137} = 0.38,

p < 0.0001), which is consistent with the correlation of “woody” versus “earthy” (

r_{309} = 0.39,

p < 0.0001) in the olfactory profiles compiled by Boelens and Haring [

29]. A multivariate analysis of this directory, which will be referred to hereafter as the BH database, allowed the classification of 309 compounds into 27 groups [

30], and a further study attempted to establish structure–activity relationships [

31].

#### 3.2. Olfactory Profiles from Osmoz and the H&R Guide

The H&R catalog indicates which attributes best apply to describe the odor character of a fragrance (

Table 2). Moreover, it also provides the main ingredients that are supposed to be responsible for the scent. The list of such ingredients (

Table 3) is basically coincident with the 96 terms encountered in Osmoz descriptions. Frequencies are highly skewed to particular materials labeled very frequently. It is noteworthy that “amber” and “aldehyde” were more recurrent in the H&R guide (

Table 3), which is consistent with

Table 2.

A few unexpected similarities were identified, which are not consistent with the experience of perfumers (n is the number of occurrences of the descriptor):

O_{amber} (n = 40) was neither significantly correlated with X_{balsamic} (p = 0.9) nor Ed_{oriental} (p = 0.6), which is nonsense because amber and balsamic scents are related and characteristic of oriental perfumes.

O_{musk} (

n = 45) was not correlated with

X_{animalic} (

p = 0.8) but it yielded certain association with

P_{summer} (

r_{137} = 0.19,

p = 0.02), which was unexpected because “musk” and “animalic” refer to similar scents that are preferred for wintertime, as discussed in

Section 3.3.

I_{sensual} (n = 19) was supposed to be correlated with X_{musky} or X_{animalic} given the sensual character of such scents, but this was not the case (p > 0.4).

O_{coriander} (n = 27) was neither correlated with X_{fresh-spicy} (p = 0.3), S_{cool} (p = 0.09), nor X_{citrus} (p = 0.9), being associated with X_{musky} (r_{137} = 0.32, p = 0.0002). These relationships are not consistent with the fresh–spicy smell of coriander essential oil, resembling lavender and linalool (citrus).

O_{sandalwood} (n = 81) yielded a slight correlation with X_{floral-total} (r_{137} = 0.22, p = 0.01) but not with X_{woody} (p = 0.6), which is not consistent with the woody smell of sandalwood oil.

O_{cedar} (n = 52), likewise, was associated with S_{floral} (r_{118} = 0.37, p < 0.0001) but not with X_{woody} (p = 0.5), which does not agree with the smell of cedarwood oil.

I_{warm} (n = 32) was correlated with O_{patchouli} (r_{140} = 0.54) and Z_{chypre} (r_{140} = 0.47, p < 0.0001) but, unexpectedly, neither with X_{warm-spicy} (p = 0.2) nor with P_{night} (p = 0.1).

These seven dichotomous variables mentioned (

O_{amber},

O_{musk},

I_{sensual},

O_{coriander},

O_{sandalwood},

O_{cedar}, and

I_{warm}) were removed due to the unclear interpretation of their similarities. A much higher sample size should be necessary for an accurate study of these relationships, but it is out of the scope of the present work. We should keep in mind that dichotomous variables are less suitable for characterizing the similarities between variables, compared with descriptors rated on a continuous scale [

15].

#### 3.3. Preference for Nighttime versus Wintertime Wear

A positive correlation was found between

P_{night} and

P_{winter} (

r_{137} = 0.83,

p < 0.0001) (

Figure 1a), which is intuitively appealing because oriental perfumes smell warm and are ideal for cool weather and formal nighttime wear [

14,

26,

32]. Accordingly,

P_{night} yielded an inverse correlation with

P_{summer} (

r_{137} = –0.63,

p < 0.0001). These relationships were affected by the presence of outliers; many of them correspond to perfumes rated by a number of votes (

N_{votes}) too low (

Figure 1a) because they were not available commercially in 2007 when Fragrantica’s website was created. As discussed in a previous study [

24], it seems that at least 70 votes are required to assume that consumer preference from Fragrantica is reliable enough. By discarding 20 outlying fragrances rated by < 70 people, the correlation coefficient in

Figure 1a became

r_{117} = 0.92 (

R^{2} = 0.86).

Aimed at further understanding the correlation between

P_{night} and

P_{winter}, stepwise regression was applied for fitting

P_{night} as a function of

P_{winter} and further variables. The resulting model (Equation (1),

R^{2} = 0.88) revealed that musky scents increase the preference for nighttime wear, while the opposite applies to perfumes rated as

X_{green} > 1, which were coded by means of the indicator variable

I_{green>1}. In this model, the

p-value of regression coefficients (

p_{rc}) was very low (

p_{rc} < 0.006).

Equation (2) was fitted to estimate

P_{winter} (

R^{2} = 0.59,

p_{rc} < 0.002), not considering the effect of

P_{night}. Nine outlying fragrances were removed, eight of them rated by <59 consumers. Variables summed together corresponded to related odors with similar regression coefficients.

Similarly, Equation (3) predicted

P_{night} (

R^{2} = 0.53,

p_{rc} < 0.0009), not including

P_{winter}. Eight outliers were removed, seven of them assessed by <49 people. Descriptors in Equations (2) and (3) are basically equivalent given the tight association shown in

Figure 1a, which supports the notion that warm balsamic and animalic scents increase the preference for wintertime, while “green” and “citrus” odors are ideal for daytime wear. These effects are well known by perfumers, but few studies have quantified such relationships statistically [

24].

“Green” is applied to describe the smell of recently cut leaves or grass. Such scents are usually regarded as fresh, invigorating, nature inspired, and reminiscent of the outdoors [

11], which is consistent with Equations (3) and (4). Curiously, different studies have reported that fresh scents are associated with the leafy green color [

33,

34]. Another piece of research carried out with 21 fragrances found that extroverted subjects preferred fresh perfumes that evoked green and yellow colors [

35].

“Warm” and “fresh” refer to dissimilar odor categories [

19], with the former being associated with balsamic/oriental fragrances. This polarity is consistent with the negative regression coefficients of

X_{green} and

X_{citrus} (fresh scents) in Equations (2) and (3), while positive coefficients refer to warm odors. The Fragrance Wheel is based on 14 categories structured in four main groups; two of them, “fresh” and “oriental”, appear as opposite classes of the same underlying polarity. Furthermore, the categories “green”, “citrus”, “fruity”, and “watery” are grouped within the “fresh” group [

12], which is a common criterion in perfumery. Equation (3) suggests that

P_{night} could be considered as an indirect assessment of the warm character of a given fragrance. Conversely, since

P_{day} = 100 −

P_{night}, it could be inferred that preference for daytime wear is associated with the “fresh” odor character, which is well established in perfumery [

14], though this term is somewhat subjective for naive subjects.

Regarding

Ed_{fresh}, it yielded the strongest correlation with

P_{day} (

r_{125} = 0.24,

p = 0.007), which agrees with the resulting model (Equation (4),

R^{2} = 0.45,

p_{rc} < 0.004).

Ed_{fresh} ranges from 0 to 3, and the constant 0.6 is nearly coincident with the midpoint of this interval. This equation confirms the fresh character of “green” and “fruity” scents [

15]. The presence of

O_{galbanum} in Equation (4) is intuitively appealing because this material smells leafy green.

#### 3.4. Preference for Daytime versus Summertime Wear

The relationship shown in

Figure 1a is purely linear but, curiously, it becomes quadratic by comparing

P_{day} versus

P_{summer} (

Figure 1b). After discarding eight outlying perfumes (

N_{votes} < 59),

X_{green} was the only additional variable entering in Equation (5) (

R^{2} = 0.75,

p_{rc} < 0.0003).

The predictive model for

P_{summer} (Equation (6),

R^{2} = 0.48,

p_{rc} < 0.003) is quite similar to Equation (2) and it was obtained after discarding basically the same nine outliers.

X_{animalic} and

X_{leather} were summed given their similar regression coefficient and because the latter presents certain animalic notes. Likewise,

X_{woody} was merged with

X_{warm-spicy} because both refer to odors sharing a warm character; actually, “woody” is correlated with “balsamic” (

r_{309} = 0.37) and with “spicy” (

r_{309} = 0.32,

p < 0.0001) in the BH database. Results evidence that warm balsamic and animalic scents decrease

P_{summer} and, hence, increase the preference for wintertime.

The variable X_{green} was included in Equations (2)–(5), but its effect was not statistically significant in Equation (6), nor in the case of I_{green} (p > 0.2). This result suggests that green notes are more powerful to evoke daytime conditions than citrus notes, according to Equation (5). Actually, by excluding perfumes rated by less than 70 people, it turns out that P_{day} was more strongly correlated with X_{green} (r_{110} = 0.48, p < 0.0001) than X_{citrus} (r_{110} = 0.16, p = 0.09). Conversely, citrus scents present a higher refreshing character (i.e., more suitable for summertime) according to Equation (6).

#### 3.5. Multivariate Analysis of the Olfactory Matrix

The final matrix of olfactory descriptors was heterogeneous regarding the statistical distribution of variables, because some were continuous and others were categorical. Hence, it is uncertain if multivariate tools adapted to nonlinear data (e.g., multiple correspondence analysis or nonlinear PCA) might be more appropriate rather than standard PCA. It was decided to use the latter because PCA is one of the most common multivariate approaches for the analysis of olfactory profiles [

2], and it does not require a particular model of distribution for the variables.

The final dataset was comprised by 80 descriptors, seven of which were removed as explained in

Section 3.2. It was found that

Ed_{oriental} and

P_{winter} exerted an excessive influence in PC1, and the same occurred with

Ed_{floral} and

Z_{chypre} in the case of PC2. They appeared in the loading plot as extreme points, which might be confusing and is not convenient for the purpose of obtaining a meaningful sensory map. Thus, a coefficient of 0.9 was applied in order to reduce the variance of these descriptors so that they appear closer to the rest of variables. Next, a new PCA was fitted. PC1, PC2, PC3, and PC4 explained 11.3%, 9.5%, 5.4%, and 4.4%, respectively, of the overall data variability. Higher values were obtained in the analysis of the BH database (PC1: 17.5%; PC2: 14.2%; PC3: 8.4%; PC4: 6.6%) because odor descriptors were measured on a continuous 0–9 scale [

15], which allowed a better characterization of the relationships between variables.

The PC1/PC2 loading plot (

Figure 2) reflects the similarities and dissimilarities between variables. Descriptors appearing close to each other are expected to be positively correlated, which implies that they are often applied together in the description of scents. It is intuitively appealing that those variables from different sources referring to the same smell (e.g.,

X_{aldehydic},

I_{aldehydic},

O_{aldehydic}, and

Z_{aldehyde}) are located near to each other in

Figure 2. Thus, such descriptors were joined together by means of a polygon, and the legend “aldehydic” was indicated only once inside the plot.

PC1 basically describes the preference for daytime versus nighttime wear, while PC2 discriminates floral versus chypre perfumes. The latter are characterized by the presence of oakmoss, which smells mossy–woody and explains the correlation between

Z_{chypre} and

O_{oakmoss} (

r_{140} = 0.55,

p < 0.0001). The woody–earthy odor of vetiver [

26] agrees with the position of

O_{vetiver} close to chypre descriptors (

Figure 2). The location of

O_{patchouli}, intermediate of chypre and sweet descriptors, is intuitively appealing because the scent of patchouli oil is woody–earthy and sweet–balsamic [

26]. Galbanum oil smells leafy green, which justifies the similarity of

O_{galbanum} versus

X_{green} (

r_{137} = 0.38,

p < 0.0001) and its position in the plot close to the “green” cluster; but it presents spicy–woody and balsamic undertones [

26], which might explain the lower correlation with

P_{day} (

r_{137} = 0.24,

p = 0.005). The position of

O_{tonka} agrees with the warm, sweet caramelic odor of tonka beans. It appears next to

O_{benzoin} in

Figure 2, which is consistent with the balsamic, sweet chocolate odor of benzoin resinoid [

26]. Although perfumers usually choose sweet-smelling materials as a standard for “balsamic” [

36], some other references for this descriptor, like olibanum, do not smell sweet, which would explain why

I_{balsamic} was not correlated with

X_{sweet} (

p = 0.6) and, hence, it is located far away from

Ed_{oriental}.

Next,

t(1) and

t(2) scores were obtained with the software for all 140 perfumes. It turned out that

t(1) was correlated with

X_{hexag} (

r_{89} = 0.62,

p < 0.0001) but not with

Y_{hexag} (

p = 0.3). Conversely,

t(2) had a reasonable correspondence with

Y_{hexag} (

r_{89} = 0.54,

p < 0.0001). Thus, the projection of perfumes onto PC1 and PC2 had a rather good agreement with their position in Dragoco’s Hexagon. Nevertheless, the correlation was not very strong, which implies that the Hexagon could be improved. The location of “chypre” next to “oriental” in the original Hexagon (

Figure 3a) is not consistent with

Figure 2, and a better match would result by swapping “chypre” and “floral–spicy”. A new class called “light floral” was incorporated in the modified version proposed of the Hexagon (

Figure 3a), becoming a sensory wheel with seven families. As the floral–green category accounts for the most “refreshing” (daytime) fragrances, a different position, slightly rotated, was proposed in the modified Hexagon to make it coincident with the horizontal axis. Hence, this axis can be interpreted as a factor discriminating fragrances preferred for daytime versus nighttime wear. The “floral– fruity” category was renamed as “white-floral–fruity”, which refers to sweet–floral odors as discussed below.

The chart called Analogies of Feminine Fragrances was developed by the Swiss company Givaudan around 1985 [

11] (p. 276). It displays 113 perfumes, 65 of which are included in the sample set studied here. Their coordinate position was obtained on a continuous arbitrary scale. If this odor map is rotated –45 degrees approximately (

Figure 3b), it turns out that the projection of perfumes over the

x axis yields the maximum correlation (

r_{65} = 0.6,

p < 0.0001) with

t(1) scores. Strikingly, the position of five major classes in Givaudan’s map (

Figure 3b) is coincident with equivalent descriptors in

Figure 2 and with the modified Hexagon (

Figure 3a).

#### 3.6. Study of Further Components

By visually inspecting the PC3/PC4 loading plot (

Figure 4), it was found that PC3 basically reflects the contrast between “aldehydic” and “fruity” descriptors. According to Müller [

26], aldehydes are used especially in perfumes that feature elegant feminine notes. This feminine character is reflected by the fact that “aldehydic” is encountered more often in women’s perfumes (in the H&R guide: 52.8% of women’s versus 25.3% of men’s). Given the preference of ladies for aldehydic and floral scents, these descriptors are usually located close to each other in perfumery odor maps [

16,

37], but both appear as distinctive (far apart) polygons in

Figure 2. The reason seems to be the marked nonsweet (dry) odor character of aldehydes [

11] (p. 278), which explains the negative correlation between

Z_{aldehyde} and

X_{sweet} (

r_{137} = –0.26,

p = 0.003). Such dissimilarity of “aldehyde” versus “sweet” is also apparent in the BH database (

r_{312} = –0.36,

p < 0.0001) and in

Figure 4.

Conversely, X_{sweet} yielded the highest similarity with X_{fruity} (r_{137} = 0.44, p < 0.0001), which explains the opposite character between fruity and aldehydic descriptors revealed by PC3. Fruity, sweet, and spicy descriptors appear with low p(3) loadings, and they are typically encountered in foodstuffs. On the opposite side, aldehydes and animalic notes are characterized by a certain unpleasant character. Hence, PC3 might be interpreted in some way as an underlying dimension related with “edible” scents.

PC4 basically reflects a dissimilar character between citrusy descriptors (i.e.,

X_{citrus},

O_{lemon}, and

O_{bergamot}) with respect to “green” variables (

I_{green},

O_{green}, and

X_{green}). Both categories are usually regarded as fresh and enhance the preference for daytime wear (Equation (3)). In the BH database, “fresh” is similar to “green” (

r_{312} = 0.43) and “citrusy” (

r_{312} = 0.43,

p < 0.0001), but the correlation between both variables is very weak (

r_{312} = 0.12,

p = 0.03), which reveals a distinct odor character. Accordingly,

X_{citrus} and

X_{green} are slightly dissimilar (

r_{137} = –0.18,

p = 0.04) in Fragrantica’s profiles, which justifies their divergent position in

Figure 2;

Figure 4. “Citrus” is located close to the center of

Figure 2 because it is not correlated with

P_{day} (

p = 0.3). It is appealing that

O_{mandarin} appears in

Figure 4 closer to

X_{sweet} because mandarins smell much sweeter than lemons.

PC5 did not provide additional relevant information because it basically discriminated floral versus balsamic descriptors, which are distinct odors as already reflected by

Figure 2 and

Figure 4. Further components are not of interest.

#### 3.7. Study of Floral Descriptors

“Rose” was the most frequent floral term encountered in Osmoz descriptions (

Table 3). Actually, rose oil is commonly considered as the preferred reference material for “floral” by perfumers [

36], which implies that certain correlation should be expected between

O_{rose} and

X_{floral-total}. However, this was not the case (

p = 0.2,

n = 93), which is consistent with the position of

O_{rose} very close to the origin of coordinates in

Figure 2. Thus, it seems that the information of

O_{rose} is not relevant here, probably because it was labeled too often.

“Floral” and “white floral” are different descriptors in Fragrantica. It turns out that

X_{floral} is dissimilar to

X_{sweet} (

r_{137} = –0.20,

p = 0.02) and it is associated with:

X_{green} (

r_{137} = 0.33, p = 0.0001),

P_{day} (

r_{137} = 0.27,

p = 0.001),

O_{violet} (

r_{137} = 0.26,

p = 0.002), and

O_{hyacinth} (

r_{137} = 0.26). Considering that “green”, “fresh”, and “light” are related concepts in perfumery, applied to odors evoking daytime conditions, “floral” was renamed as “light floral” for clarity purposes, as explained in

Section 2.2. The observed correlations indicate that violet and hyacinth are the lightest floral scents in the database. Both materials smell leafy green [

26], which justifies the similarity between

O_{hyacinth} and

I_{green} (

r_{140} = 0.48,

p < 0.0001). The correlation of O

_{lily-valley} versus

P_{day} (

r_{137} = 0.25,

p = 0.003) is explained by the light floral, fresh green scent of lily-of-the-valley [

11] and is consistent with the proximity of

Ed_{fresh} in

Figure 4.

According to Fragrantica, “white flower” refers to the heady, sweet–floral scent common in jasmine and orange blossom. Jasmine absolute was the reference for “floral” in the BH database, which yielded the highest correlation with “sweet” (

r_{312} = 0.28,

p < 0.0001). The variable

X_{white-floral} correlated with

O_{tuberose} (

r_{96} = 0.54,

p < 0.0001),

O_{orange-blossom} (

r_{137} = 0.42,

p < 0.0001), and

X_{sweet} (

r_{137} = 0.34,

p < 0.0001), but not with

O_{jasmine} (

p = 0.2), perhaps because “jasmine” was encountered too often (59.1%) in Osmoz descriptions. Jasmine, tuberose, and orange blossom are flowers of white color that display a floral–sweet, honey-like scent [

26].

The flowery descriptors mentioned next (i.e.,

O_{iris},

O_{carnation},

O_{ylang}, and

O_{heliotrope}) are neither correlated with

S_{floral} nor

X_{floral-total} (

p > 0.1), which indicates a lower floral character and is consistent with their position in

Figure 2 and

Figure 4:

O_{iris} correlated with

X_{powdery} (

r_{137} = 0.31,

p = 0.0003) and

O_{violet} (

r_{140} = 0.15,

p = 0.08). These similarities are intuitively appealing because the powdery facet of orris is well known [

12,

38]. Moreover, orris (iris) oil displays a woody, violet-like odor [

26].

O_{carnation} yielded the highest similarity with

I_{spicy} (

r_{140} = 0.18,

p = 0.03), which agrees with the spicy, clove-like character of carnation flowers [

38].

O_{ylang} correlated with O_{vanilla} (r_{93} = 0.21, p = 0.04), consistent with the floral–narcotic and sweet–spicy smell of ylang-ylang flowers.

O_{heliotrope} yields the strongest correlation with X_{sweet} (r_{137} = 0.26, p = 0.002), which can be explained by the sweet scent of heliotrope flowers, being reminiscent of marzipan, vanilla, and cherry pie.

The continuous variable

S_{floral} obtained from sensory experiments [

14,

25] yielded the strongest correlation with

X_{floral-total} (

r_{116} = 0.62) and

X_{light-floral} (

r_{116} = 0.52,

p < 0.0001), which evidences that Fragrantica’s profiles are consistent with experimental ratings. Equation (7) was obtained by applying stepwise regression (

R^{2} = 0.82,

p_{rc} < 0.006) after removing five moderate outliers. The correlation between

S_{floral} and

P_{day} (

r_{116} = 0.44,

p < 0.0001) agrees with the position of “floral” in a reported fragrance map [

11] (p. 280). By contrast, oriental and sweet scents are preferred for nighttime wear, which justifies their negative coefficients in Equation (7).

This model reflects that aldehydic notes attenuate (i.e., “soften”) the floral character, which justifies the name “soft floral” given by Edwards [

12] for aldehydic fragrances. The reason could be that the natural scent of short-chain aliphatic aldehydes is not pleasant; however, in floral fragrances, such notes combine appropriately with the powdery accents of vanilla and iris to create soft floral fragrances [

12]. In perfumery, the powdery impression is associated with particular warm–sweet scents, which explains that

X_{powdery} yields the highest correlation with

O_{iris} (

r_{137} = 0.31,

p = 0.0003) and

O_{vanilla} (

r_{137} = 0.21,

p = 0.01). A mixture of musk ketone and coumarin was the reference for “powdery” in the BH database [

29].

#### 3.8. Prediction of the Cool Odor Character

“Fresh” and “warm” are usually regarded as contrasting polarities in the perception of fragrances [

15]. However, “cool” and “warm” are also opposite terms semantically [

25]. In order to clarify these relationships,

Figure 5 reveals that fragrances with higher values of

S_{cool} (i.e., the most “cool” fragrances) tend to be preferred for daytime wear (

P_{day} > 50%) while, conversely, most sweet–oriental perfumes (black points in

Figure 5) smell warm and are best suited for the night, but not always. Both variables are linearly related, but the correlation is not very strong (

r_{116} = 0.47,

p < 0.0001). Considering that “fresh” basically accounts for informal daytime fragrances, as discussed above, the lack of a tight correlation reveals that “fresh” and “cool” refer to different concepts in perfumery.

The variable

S_{cool} obtained experimentally yielded the highest correlation with

P_{day} (

r_{116} = 0.47) and

I_{mossy} (

r_{118} = 0.40,

p < 0.0001), which explains its position in

Figure 2. The negative correlation with

Ed_{oriental} (

r_{118} = –0.52) and

I_{sweet} (

r_{118} = –0.48, p < 0.0001) evidences the warm smell of oriental fragrances [

32]. These similarities are reflected by Equation (8), which was fitted after discarding six moderate outliers rated by <68 people. The positive coefficient of

P_{day} and

Z_{chypre} in Equation (8) suggests that “cool” fragrances are intermediates of fresh and chypre perfumes but dissimilar to oriental scents, given the negative coefficient of

Ed_{oriental} and

I_{ambery}. Accordingly, the aromatic/fougère category in Edwards’s wheel is located between “chypre” and fresh families but opposed to “oriental”, which agrees with the association between “cool” and “fougère” in perfumery.

The goodness-of-fit for the prediction of S_{cool} (R^{2} = 0.54, p_{rc} < 0.008) was lower than the value obtained for S_{floral} (R^{2} = 0.82), which might indicate that the cool character of a fragrance is a particular odor quality not properly captured by those descriptors considered here. The proposed hypothesis is that “cool” basically refers to the perception of camphoraceous notes, as discussed next.

“Aromatic/fougère” is the category in Edwards’s guide with highest amount of men’s fragrances in the market [

15] (p. 243). Although the term “aromatic” is rather subjective, it is applied in modern perfumery as a synonym of “fougère”, a family developed after the well-known Fougère Royale launched in 1882. The fougère accord is based upon the interplay between lavender, oakmoss, and coumarin [

4], which justifies that

X_{aromatic} yielded the strongest similarity with

O_{oakmoss} (

r_{137} = 0.36,

p < 0.0001). Lavender seems to be the key material responsible for the cool odor character of fougère accords because it presents a marked camphoraceous smell [

38]. The cooling effect of camphor and mentholic odors is apparent [

39]. Lavender and some fresh–spicy herbs (e.g., peppermint, rosemary, and sage) share camphoraceous notes that produce a trigeminal cooling effect, which explains the similarity between

X_{fresh-spicy} and

X_{aromatic} (

r_{137} = 0.23,

p = 0.007). However, lavender and herbaceous notes are typically masculine and, hence, these scents are never dominating in women’s perfumes (

Table 2;

Table 3).

#### 3.9. Towards a Standard Sensory Wheel of Women’s Fragrances

Taking into account the seven olfactory classes shown inside

Figure 3a, it seems more convenient to think about a heptagon of feminine perfumes. If each side of this heptagon is split in two parts, it obviously becomes an odor wheel with 14 categories. Interestingly, the Fragrance Wheel of Edwards [

12] is based on the same number of families, but such representation is intended to display the whole spectrum of commercial fragrances. Edwards’s wheel is probably the most popular one nowadays in perfumery; it is employed, among others, by two Spanish franchise bulk perfume companies [

13,

40] aimed at showing their customers the palette of items on sale. Nonetheless, if we focus on the subset of women’s perfume, it might be convenient to reorganize some categories of this Fragrance Wheel to better describe the perceptual space from a sensory standpoint. Accordingly, some alterations should be required to adapt such a wheel to the subset of men’s fragrances; this issue will be tackled in a further work.

Based on the results reported here, an effort was carried out to conveniently arrange the 14 Edwards’s families inside this novel Heptagon (

Figure 6). The order of categories appearing in the original Fragrance Wheel is indicated numerically close to the central hub. Following this sequence, it becomes apparent that the main difference with respect to Edwards’s wheel is the position of “fruity” and “soft floral”. The former was placed next to “green” by Edwards [

12], but fruity descriptors appear in

Figure 2 and

Figure 4 closer to “sweet” rather than to “green”, which evidences the sweet character of fruity scents as discussed in

Section 3.6. Based on this result, the fruity category was placed closer to the sweet polarity in

Figure 6. Regarding “soft floral” that accounts for aldehydic perfumes, it appears in Edwards’s wheel next to “floral oriental”, but

Figure 2 suggests a better position in between chypre/aromatic and citrus/green due to the nonsweet character of such perfumes, as already discussed.

Apart from this remarkable reorganization of categories with respect to the Fragrance Wheel, some contrasting polarities were also indicated in an effort to achieve a sensory wheel based on meaningful underlying dimensions. The horizontal axis explains preference for daytime versus nighttime wear, which is directly related with preference for summertime versus wintertime wear. Another polarity is “sweet” versus “nonsweet” (dry). Interestingly, this axis divides the chart in two parts; all floral categories are located on the upper right side, and they basically account for those scents most typically feminine. On the other hand, “woody” appears as opposite to “floral”, which agrees with Edwards’s wheel. Regarding the contrasting polarity of notes most typically feminine versus those less feminine, it does not seem to be exactly equivalent to the divergence of “floral” versus “woody”.

#### 3.10. Representativeness of the Sample of 140 Perfumes

The sample under study corresponds to quite old perfumes, which obviously constrains the results because the market of women’s fragrances has evolved since the 1990s. Taking into account that 125 out of the 140 fragrances are contained in Edwards’s guide,

Table 4 displays the number of items listed under each class of this guide (24th edition of 2008), as well as the classification corresponding to the set of perfumes under study. By comparing the relative frequencies

P_{ED} and

P_{125}, it turned out that the percentage of perfumes classified as “floral” in the sample was about half of the percentage in Edwards’s directory. Conversely, the ratio for “mossy woods” (chypre) was much higher in the sample. Interestingly, both categories are properly discriminated by PC2 and appear as opposed odor classes in

Figure 2 and

Figure 6. As the polygon of floral descriptors is broad enough, it is unclear if a larger proportion of floral perfumes in the sample might lead to a better characterization of such perceptual spectrum.

After discarding the categories “floral” and “mossy woods”, a chi-squared test was carried out with the values

N_{ED} and

N_{125} in

Table 4. As this test requires an occurrence >4, some classes appearing next to each other in the Fragrance Wheel (e.g., “woods” and “woody oriental”) were summed together prior to the test in order to achieve this condition. It turned out that the null hypothesis of independence could be accepted (

χ^{2}(6) = 9.6,

p = 0.14). Hence, this test suggests that except for “floral” and “chypre”, none of the remaining categories in the Fragrance Wheel were underrepresented in the sample. It can be assumed that

Figure 6 properly exemplifies the perceptual spectrum of women’s fragrances currently in the market. Nevertheless, a further study would be necessary to confirm this hypothesis, and to take into consideration some new trends like “gourmand” scents that have become popular in recent years.