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Page 46 ï~~Loudness of musical sounds in a reverberant environment Jan Chomyszyn CCRMA, Stanford University firstname.lastname@example.org Abstract. Widespread use of reverberant devices in computer music awoke awarness of possible influence of distance of sound on loudness perception, and arose interest in the cognition of this phenomenon. The results of research pursuing this issue are reported in this paper. Creation of convincing auditory perspective is an important element of computer music; it can make the sound lively and expressive. Many factors contribute to the impression of space and the location of sound sources, including appropriate reverberation, and balance of loudness and timbres of the sounds used in the composition. Some of the parameters that provide cues to distance of the sound sources are correlated in a natural reverberant environment. A typical example is intensity and direct-to-reverberant sound energy ratio, which change reciprocally along the physical distance between the sound source and the listener. However, the percepts arising from the physical cues do not always follow the same relationship. Since the beginning of this century researchers have been aware that changes in loudness and changes in distance may sometimes form equivalent concepts for the listeners [Gamble, 1909]. As a part of his "physical correlate theory" Warren  noticed that loudness judgements of his stimuli (speech) depended on the degree of reverberation. Recently Chowning  observed that loudness constancy might take place in room environment in an analogous way to the size constancy in vision. In visual perspective, to preserve the impression of size constancy of an object, the physical size of the object has in fact to be diminished in proportion to the provided perspective. Is this also the case in auditory perspective? Imagine sounds in a room varying as to the playing effort induced by the player and, the amount of reverberation, proportional to the distance from the listener.From the work of Mershon and King  we know that the reverberation invokes the sensation of distance and auditory perspective. In such conditions, if "size constancy" appears in the auditory world, the loudness of the sound source will be perceived rather than the loudness of the sound wave at the listeners' ears in a loudness judgement of such sounds. For the two sounds of equal intensity (and the same, or similar timbre), the sound played with a greater effort and carrying a higher amount of reverberation would be perceived as louder. According to the hypothesis, for the listeners these cues should suggest that the sound was played from a greater distance, hence it must have been louder at the source. Four short percussive-like sounds were generated for the test by using the physical model of the wave digital hammer striking a membrane with different forces [Van Duyne et al., 1994]. Varied force produced increase in power by 3 dB, spectral changes (increase of spectral bandwidth), and sharpening of the attack, among other things. By varying the force the playing effort was simulated. In this way the sounds corresponded to the four different playing efforts. Reverb was then added to the sounds by using the Yamaha SPX1000 digital reverberation room model. Four sounds were created from each of the four dry prototypes in such a way that, for a constant effort, the powers decreased by approximately 6 dB. The most powerful of the reverberated sounds were also the closest ones, and their powers were equal to the powers of the least Psychoacoustics, Perception 46 ICMC Proceedings 1994
Page 47 ï~~effort dry sound. The direct-to-reverberant sound energy ratios were calculated accordingly by using an inverse square law formula [Beranek, 1954], assuming the power of the sound sources changing with the effort by 3dB, so that all the 16 sounds could be thought of as being played and heard at different distances in the room. Distance ratios between the sound source and the listener's position for all the sounds depend on both effort, and power level (see Tab. 1). The distance ratios between the power levels differ by a factor of two (except for the two most distant sounds). relative power level in dB 0 -6 -11R -17.4 1 -174 effort 1.0 2.0 1.3 2.6 2.0 4.0 2.7 5.7 4.0 5.7 8.3 12.0 8.3 12.0 184.108.40.206 8.3 9.2 9.4 12.5 Table 1. Distance ratios relative to the closest sound (effortl/power level 0). The last column contains the ratios between the farthest and the closest sounds. The sounds were next presented in a formal listening test through loudspeakers. During the test, the sounds were reproduced in pairs; in each pair the sounds were played in alternation in a loop. Subjects attempted to match the loudness of the second sound to the loudness of the first sound in the pair by using a slider on a computer screen, which allowed them real-time gain control. Once the match was achieved, the decision had to be confirmed by pressing a button, and the next pair was presented. The gain factor, by which the second sound was rescaled during the procedure, was stored in a disk file along with the information about the sound effort and power level. The test consisted of four parts. During the first part only the four dry prototypes were presented. The subjects were supposed to match the loudness of each of the three dry prototypes, which were +3dB,+6dB, and +9dB above the smallest effort sound (0dB) to the loudness of this sound. The sequence was repeated 16 times (differently randomized). During this part each subject created four dry, equally loud reference sounds, and the (mean) gain factors were further used to re-create the reference sounds in the successive parts of the test. During the second part, the subjects were exposed to the reverberated sounds. In each pair the dry reference sound to be matched was made of the same dry prototype as the reverberated sound.Therefore, we can think about the sounds in each pair as being played with the same effort, but at varying distances. In this way spectral differences other than those introduced by reverberation were eliminated in the loudness match. The subjects were given each of the different effort sounds at four different power levels, reflecting four different distance positions in the room. The subjects were instructed to imagine a room and two players in this room, a distant and a close one. They were supposed to match the loudness of the close player (the loudness of the sound's source) to the loudness of the distant one. To help them with this task, a sequence of four reverberated sounds (same effort) receding in distance, was played before each loudness match. During the third part, the reverberated sounds were presented in a similar fashion, but no leading sequence was included before each presentation. The subjects were also instructed not to think about any room, or players, but to match the loudness of the sounds as they appeared at their ears. Half of the subjects took the second part first, and the other half took the third part first. In the fourth part, only dry sounds were presented. They were made from the dry prototypes in such a way, that for each effort the powers of the dry sounds were equal to the powers of the reverberated sounds (ie., 0, -6, - 11.8, - 17.4 dB - see Tab.l1). As before, the subjects were ICMC Proceedings 1994 47 Psychoacoustics, Perception
Page 48 ï~~requested to match the loudness of the dry reference sounds to each of the dry sounds. Matching the loudness of different complex sounds, even similar in timbre, is a difficult task. Therefore, each of the 26 subjects (mostly musicians or former music students) participating in the experiment took the test twice, and the two results were compared to check the reliability. The Pearson's correlation coefficient of 0.7 between the results of the loudness match for the "room" situation ("imagine two players in a room") was assumed to be a reasonable cut off to exclude some inconsistent subjects and limit the error. Of the 26 subjects, 16 passed this criterion, and were selected for further study. For these sixteen subjects the correlation coefficient for repeated results of the other parts of the test was even higher. Only 10 of these 16 people took the fourth part of the test by the time of this report, however, and only their results are reported. The gain factors obtained during 2nd, 3rd, and 4th parts of the test were normalized by the gain factors of the dry references to show the differences in loudness between the sounds and the corresponding (equally loud) dry references. For every subject, the normalized gains of the dry sounds comparison were subtracted from the results of the two reverberated sounds comparisons ("imagine a room...", and "forget about any room..."). Spectral differences resulting from the presentation of the sounds at the four different power levels were eliminated at this stage. The gain differences so obtained, if significant, would show how the reverberation influenced the loudness judgement. Variance analysis of these loudness differences (instruction by effort by power level) was performed next. Clearly, the F-ratio appeared significant for both, effort and power level (p < 0.001), and we could conclude that they influenced the loudness judgement. The F-ratio for the instruction, however, did not justify its influence on the loudness judgement (p=O.498). The only significant interaction effect, although not very strong (p=0.036), appeared to be the interaction between the instruction and the power level. To show the significance of the loudness match in the reverberant environment, loudness differences between the gains set during "imagine room..."/"forget about any room...", and the gains set during the dry loudness match were depicted on the figures 1 and 2. 20 I I I 15 A H 10 51 0 _ _ _ I I 0 1 2 3 4 5 EFFORT Fig.l. Sounds in a room - "imagine a room..." comparison. Each dot corresponded to a mean difference between the extreme power levels (17.4 dB) calculated for a fixed effort. Standard deviations are also plotted. Distance ratios corresponding to these loudness differences at each of the efforts are included in the Table 1. All the means are significantly different from zero, which also reveals the influence of the reverberation on loudness perception. In the case of the "imagine a room..." situation a distinct trend is visible: the means increase along with the increasing distance ratios. The more different in distance the sounds were, the louder they were perceived. A similar, Psychoacoustics, Perception 48 ICMC Proceedings 1994
Page 49 ï~~but not so consistent relationship can also be seen for the "forget about any room..." test in Fig.2. 20 15 10 I11 z M 5 0 1 2 3 4 extent this problem can possibly be solved by comparing the results of the psychoacoustcal test to the changes of the physical data introduced by the reverberation, especially the spectral changes (currently under investigation). As seen today, the results seem not to support the hypothesis about loudness constancy. References [Beranek, 1954] Leo L. Beranek. Acoustics. McGraw-Hill Inc. pp. 314-315, 1954 [Chowning, 1990] John Chowning. Music form Machines: Perceptual Fusion & Auditory Perspective - for Ligeti. Report No. STANM-64, CCRMA Department of Music, Stanford University, pp. 7-14, 1990, [Gamble, 1909] E. Gamble. Minor studies from the psychological laboratory of Wellesley College, I. Intensity as a criterion in estimating the distance of sounds. Psychological Review, 16, pp. 416-426, 1909 [Mershon, and, King, 1975] D.H.Mershon, and L.E.King. Intensity and Reverberation as Factors in the Auditory Perception of Egocentric Distance. Perception and Psychophysics 18 409-415 [Van Duyne et al., 1994], Scott A.Van Duyne, John R.Pierce, Julius 0. Smith III. Traveling Wave Implementation of a Lossless ModeCoupling Filter and the Wave Digital Hammer, ICMC Proceedings,1994 [Warren, 1973] R...M.Warren. Anomalous loudness function of speech. Journal of the Acoustical Society of America, 54, pp. 390 -396, 1973 EFFORT Fig 2. Reverberated sounds matched at the ears - "forget about any room..." Concluding, the results show clearly that reverberation influences loudness perception. More distant sounds of the same intensity and similar timbre are perceived as louder than the close ones. However, the experiment does not entitle us to derive a conclusion about the reason of this phenomenon.The difference in 'instruction' was not significant for the loudness comparison, therefore we cannot explain the non-zero means by assuming that they are the result of the perception of the sound sources. In the "forget about any room..." test, the means are also non-zero, and they do not differ significantly from the "imagine a room... " test. One possible explanation is that the subjects could not consistently imagine the players. It was a difficult task, which can be seen in a fairly large standard deviation. On the other hand, we can argue the opposite, namely that the subjects were unable to get rid of the estimation of the sound source in the case of the "forget about any room..." test, because of the reverberation. To a certain ICMC Proceedings 1994 49 Psychoacoustics, Perception