is a good correlation between C80 and perceived clarity. When one increases, so does the other. This behaviour can also be seen, although to a lesser extent, for MM2 and MM5, whose slope is not as steep. The most remarkable result is that of MM3, where the slope is practically zero. This is due to the fact that the mode of the participants’ responses is the same for four out of six C80 levels rated. Finally, in Room B, it can be noted that the linear regressions have the lowest values for all musical motifs, except for MM5.

3.2. Cochran-Mantel-Haenszel test

Two complementary CMH analyses were carried out to study the relationship between the three listening test variables (i.e., the musical motif, the C80 level and the perceived clarity) and how one of them may affect the relation between the other two. In the first analysis, we studied whether for the same C80 level, participants gave the same response ratio for all the motifs. This assessment allows us to understand whether participants perceived different levels of clarity depending on the musical motif used in the evaluation. The second CMH analysis evaluates whether for the same musical motif, participants gave different ratios for different C80 levels. It gives us information on whether participants can perceive changes in clarity with a particular motif. This analysis can be considered to evaluate a similar aspect to that studied in the regression.

Table 5 presents the results obtained for the first CMH analysis carried out. The analysis returns six v2 and p-values, one for each C80 level used in the evaluation of a room. If the p-value is low enough for the results to be considered statistically significant, it means that participants gave for a C80 level different ratios of perceived clarity when evaluated with different musical motifs.

The p-values obtained for the three rooms show that in the case of Rooms A and B there are two significant C80 levels, while in Room C there are four. It is also worth noticing that there are two p-values very close to significance for Rooms A and B. The individual assessment of each sub-table indicates that participants gave different responses of perceived clarity for one C80 level in

multiple evaluations. The only parameter that changed between evaluations was the musical motif used. In addition, the global p- value estimated for the three rooms is significant. This means that the response ratios given for each musical motif were different.

The second CMH analysis returns five v2 and p-values, one for each musical motif. The results are presented in Table 6. If the p- value is significant it means that participants gave, for a single musical motif, different ratios of perceived clarity for different C80 levels. This evaluation tells us whether participants were able to perceive changes in clarity when the C80 level was changed.

The global p-value estimates are very low, indicating that in all rooms participants were able to distinguish changes in clarity. Nevertheless, when referring to the individual values of each sub-table, it can be observed that for all three rooms there are two musical motifs where the p-value is not significant: MM3 and MM5.

4. Discussion

Research results have shown that the musical motif used to evaluate the C80 level of a room has a significant effect on the clarity perceived by the participants. These results are consistent with the findings in [8,11].

The second CMH and the regression analyses give complementary information on the participants’ ability to differentiate between changes in clarity. In the case of the p-values calculated for each sub-table of the CMH analysis, it can be seen that there are two motifs for which these values are not significant: MM3 and MM5. This is consistent with the regression analysis, where both motifs have extremely low R2 values for all rooms. This means that participants are not able to differentiate between changes in C80 level. Despite this, it should be noted that the p-values for the regression analysis for both motifs are almost all nonsignificant, which means that changes in the clarity of the venue may not be the cause of the changes in perceived clarity reported by participants. MM3 and MM5 correspond to the two orchestral passages. In the case of MM3, the difficulties encountered in the evaluation of C80 might be due to the musical simplicity of the

M. Larrosa-Navarro, D. de la Prida and A. Pedrero

piece. It presents very clear melodic lines, with long notes and a very marked accompaniment by the winds. The simple melody and the constant tempo could soften the effect that a not very large increase or decrease in clarity could have in comparison with other motifs. On the contrary, MM5 is a fragment played by a full orchestra with very short time value notes and a fast tempo. The difficulty in assessing the changes in clarity in this motif may be due to the musical complexity of the piece. Another possible reason for the difficulty in perceiving changes in clarity is the large number of melodic lines played by different instruments. The different timbres of the instruments, as well as the melodies and accompaniments played by them, can increase the complexity of the piece, making it more difficult to understand the clarity of the room in which it is played. The only difference between the two analyses is that, in the case of the linear regression, the R2 value obtained for MM3 in Room C is considerably high, while the p-value for the CMH analysis in this case is not significant. Among the results obtained for the two analyses, we consider the CMH to be more reliable. This is based on the fact that it does not require a statistical reduction of the data, as the regression does, but rather the analysis is carried out with the individual responses of all participants.

The results of the regression analysis show that MM1 is the motif with the highest R2 values for all rooms, followed by MM4. The high correlation obtained between the C80 of each room and the perceived clarity is considered to be due to the musical characteristics of the piece. As previously described, MM1 is a passage played by a solo flute, in fast tempo, with strongly marked articulation and numerous ornaments. A decline in clarity could have easily been noticed by participants due to the blurring of notes and ornaments and the loss of musical precision. MM4 corresponds to a liturgical piece performed by a five-man choir. It is a piece sung in Latin, a language that none of the participants could understand. Despite not understanding the word of the chant, the fact that it is a word-based signal may have facilitated their ability to appreciate the changes in clarity. The other solo piece evaluated in the listening test is MM2. The R2 values obtained for two of the rooms, A and C, are approximately 60%, implying that participants were relatively able to appreciate the changes in clarity. The lowest value is found in Room B. The musical motif is played by a cello, with very long notes, a slow tempo and a legato character. The ability to understand musical lines and differentiate notes in slower, less articulate passages may persist despite a decrease in clarity. This phenomenon was also observed in Cox et al.’s research [8], where the slow-moving motif had a JND threshold twice as high as the fast one.

If we focus only on the global estimated values of the CMH analysis, it can be seen that they are all significant. This would mean that participants are generally able to differentiate between changes in the C80 for all rooms and with all musical motifs. Looking at the regression results for each room, it is noticeable that the slopes of the regression lines vary, even for the same musical motif, depending on the room. The variation of the C80 levels from the base case to the maximum in all rooms is the same, 4 dB, but it can be observed that the relationship between C80 and perceived clarity is not constant. It is possible to conclude that Room C is the venue where it is easiest for participants to detect changes in clarity. This may be due to the very low C80 range of the room. Clarity changes between extremely low values and those that might be found in concert halls, e.g., 1.9 dB, may be more easily recognizable in all motifs. The room where the changes in clarity are worst differentiated is Room B. This venue has very high C80 levels, starting at 3 dB, which implies a very high clarity range. An increase in these levels may not be as noticeable as changes in the other rooms. These differences in the ability to perceive clarity changes

Applied Acoustics 208 (2023) 109370

depending on the C80 level seem to suggest that the JND for high clarity levels may be higher than the one specified by the standard. This could be a possibility since research conducted by Martellota [12] already showed that for very low ranges of C80, the JND value is higher than the generally accepted one. Whether the JND for C80 is greater than 1 dB for very high clarity values is beyond the scope of this paper, but it is an interesting phenomenon and deserves further investigation.

The first CMH analysis performed indicates whether participants gave similar response ratios for all musical motifs when only one C80 level was tested. The p-values obtained for almost all C80 levels in all three rooms are significant. This indicates that the musical motif is a relevant factor when assessing the clarity of a room. The room with the highest number of significant p-values is Room C, which corresponds to the lowest C80 level range. As could be seen in the regression analysis, the participants were able to correctly identify changes in clarity. The combination of these two analyses means that participants noticed the changes in C80 levels and selected different levels of perceived clarity on the Likert scales. But the range of clarity indicated depended on the musical motif used in the stimuli. In the other two rooms, it can also be seen that the p-values are significant for two C80 levels and very close to significance for two others. The estimated global p- values are significant for all rooms, indicating once again that the musical motif has a high influence on the perception of room clarity.

5. Conclusions

The aim of this research is to assess whether the musical motif used during the evaluation of the clarity of a room has an effect on perceived clarity. A listening test was carried out in which the same levels of C80 were evaluated with five different musical motifs. The motifs consisted of two pieces performed by solo instruments, two orchestral pieces and a liturgical chant. The range of C80 levels evaluated was from 5.90 to 6.75 dB. 36 participants with different musical educational background took the test.

Participants’ ability to perceive changes in clarity for all musical motifs was examined using a regression analysis and a CMH analysis. In both cases it was possible to observe that the results were motif dependent. It could be seen in the regression analysis that the two solo pieces (MM1 and MM2) and the liturgical chant (MM4) were motifs with a high correlation between the C80 level and the clarity perceived by the participants. The two orchestral pieces, on the contrary, had very low R2 values. The results of the CMH analysis corroborated these statements. The global estimated p-value was significant for all rooms, which means that, in general, participants were able to perceive changes in the C80 level. Nevertheless, when each musical motif is studied individually, it can be observed that there are two of them, MM3 and MM5, for which the p-value is not significant. This difference in the ability to perceive changes in clarity may be due to the musical characteristics and different instrumentation of the motifs used.

Secondly, we wanted to study whether these motifs were a significant factor when assessing the C80 level of a stimulus and this is analyzed through a CMH analysis. Results showed whether participants gave different responses of perceived clarity for a particular C80 value depending on the piece. The individual results show that for a large number of C80 levels the musical motifs are a significant factor in assessing the clarity of the room. When evaluating the global results for each room, the global estimated p-value indicates that for all of them the musical motif is a significant factor.

Given the results obtained for the listening test, it can be stated that the musical motif used in the assessment of the clarity of a room is a significant factor. This means that if subjective evalua-

M. Larrosa-Navarro, D. de la Prida and A. Pedrero

tions are to be compared, it is necessary to use motifs with similar musical characteristics. Further research is needed to determine which motifs give the best results in the evaluation of the acoustic characteristics of a room. If we take into account the results of our listening test, it would be advisable to use the solo or vocal pieces. The best results obtained when evaluating the C80 level of the rooms have been achieved with MM1. The use of the two orchestral pieces used in the listening test is not recommended. It would be advisable to continue studying orchestral pieces until we find ones that give good results for evaluating the acoustic characteristics of a venue. Many of the performances that take place in concert halls are by chamber groups or symphony orchestras. The use of pieces performed by these instrumental ensembles is vital to evaluate the characteristics of the rooms. It should also be noted, in view of [21], that these results could vary depending on the signal dynamics. It would be interesting to carry out an additional listening test to evaluate, with a reduced set of impulse responses and musical motifs of this study, the influence that changes in dynamics have on the perception of clarity. For this purpose, not only the variation in perceived clarity for the different C80 levels would be evaluated, but also the change in perceived clarity for the same motif and C80 level as a function of dynamics. With this evaluation, it could be verified whether the findings of [21] regarding the variation in perceived clarity with different dynamics can be confirmed with the stimuli and the methodology used in this article.

CRediT authorship contribution statement

María Larrosa-Navarro: Conceptualization, Software, Methodology, Formal analysis, Investigation, Resources, Visualization, Writing - original draft, Writing - review & editing. Daniel de la Prida: Conceptualization, Software, Methodology, Investigation, Resources, Writing – review & editing, Supervision, Project administration. Antonio Pedrero: Conceptualization, Methodology, Investigation, Resources, Writing – review & editing, Supervision, Project administration.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Description of the above-mentioned acoustic parameters

Reverberation time (T): duration requiered for the sound energy density of a room to decrease by 60 dB after the sound source has been turned off. It can be evaluated using a dynamic range smaller than 60 dB and then extrapolating to a decay time of 60 dB, assuming that the decay slope is constant. It is usually derived from a dynamic range of 20 or 30 dB. These parameters are labelled as T20 and T30, respectively [7].

Early decay time (EDT): it is evaluated, as the reverberation time, from the integrated impulse response curve. The slope of the decay curve is determined from the slope of the first 10 dB. It is considered to have a better correlation with the perceieved reverberation and it is more affected by very early reflections [7].

Clarity C50: this descriptor is used to quantify the perception of the clarity of speech. It is calculated as the musical clarity C80, but the time threshold that marks the end of the early sound energy and the beginning of the late sound energy is 50 ms [7].

Applied Acoustics 208 (2023) 109370

Center time (TS): is the time of the centre of gravity of the quadratic impulse response. It is measured in ms [7].

R 1tp2ðtÞdt

Ts ¼ R01p2ðtÞdt

0

Apparent source width (ASW): describes the perceived width of the sound field created by a performing entity. It can be determined by the sound energy that reach the listeners in the first 80 ms after the arrival of the direct sound in an enclosed space [7,37].

Listener envelopment (LEV): refers to the listener’s impression of being surrounded by the sound field. It is related to the reverberant field, which is considered to begin 80 ms after the arrival of the direct sound [7,37].

Early lateral energy fraction (ELEF): it is defined as [8]:

where pðtÞ is the pressure arriving at the listener at time t and h is the horizontal angle of incidence with reference to an axis drawn through the ears of the listener.

Inter-aural cross correlation (IACC): it is commonly used as the measure of spatial impression. It requires binaural recording and it is calculated by the equation [7]:

IACCt1 ;t2 ¼ maxjIACFt1 ;t2 j

for

1ms < s < 1ms

IACF is the inter-aural cross correlation function and is define as:

where pI ðtÞ is the impulse response at the entrance of the left ear canal and pr ðtÞ is the impulse response at the entrance of the right ear canal.

Appendix B. Description of the Cochran-Mantel-Haenszel analysis

The Cochran-Mantel-Haenszel analysis is used for the study of matched categorial or stratified data. It is a type of analysis that was design, in the first place, to know the effect that a categorical variable K has on the relationship between two dichotomous variables (X and Y). This is its most basic approach and the first step in the analysis is the creation of K contingency tables, which are used to analyze K categorical variables (e.g., the musical motifs in this article). These contingency tables represent the result of the experiment for each of the possible situation of the dichotomous variables [31,32,38].

Although the CMH analysis was originally described for the analysis of dichotomous variables, with a formulation that follows (following the nomenclature of Table B.7) [31,38]:

M. Larrosa-Navarro, D. de la Prida and A. Pedrero

Table B.7

Example of a CMH contingency table for one category of the K variable [38].

where CMH is the score statistic alternative to the likelihood-ratio or Wald test. The CMH analysis follows a v2 distribution.

This analysis can also be generalised to experiments where the variables X and Y are not dichotomous. In this case one would have K contingency tables of size I J, where I and J are different from two and can have different sizes [31,38].

Appendix C. Supplementary data

Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.apacoust.2023. 109370.

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