Running head: ENSEMBLE CODING IN AUDITION 1
 Ensemble Coding in Audition

In vision, humans use summary statistics (e.g., average facial expression) to efficiently perceive the “gist” of groups of features. Here, we present direct evidence that ensemble coding is important for auditory processing. We found that listeners could accurately estimate the mean frequency of a set of logarithmically spaced pure tones presented in a temporal sequence (Experiment 1) but that their performance was severely reduced when only a subset of tones from a given sequence was presented, demonstrating that ensemble coding is based on a substantial number of the tones in a sequence (Experiment 2). This precise ensemble coding occurred despite very limited representation of individual tones from the sequence: listeners were poor at identifying specific individual member tones (Experiment 3) and at determining their positions in the sequence (Experiment 4). Together, these results indicate that summary statistical coding is not limited to visual processing and is an important auditory mechanism for extracting ensemble frequency information from sequences of sounds. 
 Keywords: ensemble coding; auditory perception; statistical summary; frequency Running head: ENSEMBLE CODING IN AUDITION 3
 Ensemble Coding in Audition Humans frequently encounter ensembles or groups of objects (e.g., crowds of people, peaches at a fruit stall, cars in traffic) and are able to quickly process them with ease. However, the task of rapidly combining numerous features into a coherent percept is an incredible computational challenge. Because many natural scenes are composed of multiple objects that are similar and therefore highly redundant, it is efficient for the visual system to compress these scenes by encoding information about summary statistics instead of features of individual objects (for a review, see Alvarez, 2011). This ensemble coding has been shown to be important for perceiving the “gist” of visual scenes, and it occurs across an impressive variety of visual features. For example, humans can quickly extract the average size (Ariely, 2001; Chong & Treisman, 2003), brightness (Bauer, 2009), orientation (Parkes, Lund, Angelucci, Solomon, & Morgan, 2001), location (Alvarez & Oliva, 2008), color (de Gardelle & Summerfield, 2011), speed (Watamaniuk & Duchon, 1992), and motion direction (Williams & Sekuler, 1984) of a set of objects. Humans can even extract the mean emotion, gender (Haberman & Whitney, 2007), identity (de Fockert & Wolfenstein, 2009), and biological motion (Sweeny, Haroz, & Whitney, in press) of a crowd of people. Summary statistics in vision are computed across both space and time (Albrecht & Scholl, 2010; Haberman, Harp, & Whitney, 2009), and certain temporal properties of a visual sequence (such as its overall duration) can impact its summary representation (Haberman et al., 2009). Although ensemble coding is an important and widely studied phenomenon in vision, little is known regarding ensemble representations in other sensory domains. Auditory scene analysis is an extremely difficult task because the brain must segregate multiple streams of information and assign them to distinct objects, even though they often overlap in pitch, time, Running head: ENSEMBLE CODING IN AUDITION 4
 and space (Bregman & Campbell, 1971; Bregman, 1990; Micheyl & Oxenham, 2010). There is some evidence for statistical processing of auditory ensembles: statistical information in tone sequences influences the phonetic categorization of subsequent speech sounds (Holt, 2006), and McDermott and Simoncelli (2011) have reported time-averaged statistical processing of sound textures in the auditory periphery (although at a very fine, sub-second timescale, involving statistics of activation of individual cochlear channels). In addition, humans can estimate the mean frequency from a series of tones (Albrecht, Scholl, & Chun, 2012), but it is not known how many of the tones subjects use to make their estimate and to what extent this ability is based on encoding of individual tones as opposed to a summary statistic. In particular, no previous studies have measured the efficiency of listeners’ estimates of the mean frequency of auditory sequences and compared them to their memory of individual tones in the sequence. Given the importance of ensemble coding for vision, we hypothesized that it would also be present in auditory processing. Research on auditory statistical learning has shown that listeners can acquire statistical information from tone sequences that are repeated multiple times (Saffran et al., 1999; Loui, Wessel, & Hudson-Kam, 2010). In addition, many years of exposure to the statistics inherent in speech in a particular linguistic community can subsequently influence one’s perceptual interpretation of ambiguous sounds, such as the tritone paradox (Deutsch, 1991; Dolson, 1994). However, this type of statistical learning is fundamentally distinct from statistical “gist” perception. The former involves the acquisition of statistical information from an assortment of sounds heard previously over a prolonged training period, whereas the latter refers to listeners’ nearly instantaneous, moment-to-moment extraction of summary statistics from a given sensory environment. In an experimental setting, statistical summary perception of an auditory stimulus would occur within a single experimental trial. Running head: ENSEMBLE CODING IN AUDITION 5
 We hypothesized that summary statistical representation of frequency information in auditory scenes may be an important property of auditory perception, and we designed several experiments to assess whether there is ensemble coding in audition. Specifically, we assessed whether listeners could extract the mean frequency (on a logarithmic scale) of a tone sequence despite limited access to information about the individual tones that comprise the sequence. Experiment 1: Listeners Extract the Mean Frequency of Auditory Sequences Method Listeners. 23 listeners (four male, ages 18-34) participated in the experiment, all of whom were affiliates of the University of California, Berkeley. Listeners gave informed consent to participate in the experiment and were compensated for their time. All experimental procedures were approved by the Committee for the Protection of Human Subjects at the University of California, Berkeley. All listeners had normal hearing, and none had absolute pitch (self-report). On average, listeners had 7.8 years of musical training (SD = 5.8) and initiated training at age 7.7 (SD = 2.8). All but two listeners were naïve as to the purpose of the experiments. In our study, “naïve” means that the listeners were given no information about the hypotheses, methods, or any other aspects of the study before beginning the experiment. For participants who completed more than one experiment, they were unaware of the methods of each individual experiment until the beginning of the experimental procedures and were not given information about the overall purpose or hypotheses of the study until data collection was complete. To eliminate effects of experiment order on performance, we counterbalanced the order in which participants completed the different experiments throughout the study (for those Running head: ENSEMBLE CODING IN AUDITION 6
 subjects who participated in multiple experiments), except for eleven of the participants in Experiment 1, who were added after the original round of counterbalanced data collection and had already participated in Experiment 2. Stimuli and procedure. We assessed listeners’ abilities to estimate the mean (log) frequency of a temporal sequence of six pure tones. All stimuli were sine wave tones (Figure 1) generated in MATLAB and presented at a comfortable listening level via closed headphones. In each trial, the mean frequency of the sequence was randomly chosen from the range 110 to 1174.7 Hz (A2 to D6 on a piano keyboard; darkest shaded area in Figure 1). The individual tones in each sequence were chosen from a wider range of fifty-two possible tones (82.4 Hz to 1568 Hz; E2 to G6) and were always -5, -3, -1, +1, +3, or +5 semitone units from the mean. Thus, all tones in the sequence were separated by at least two semitones, an interval that greatly exceeds normal two-tone discrimination thresholds for successive pure tones (Moore, 2004), which we confirmed in a preliminary experiment. In addition, no two members of a sequence were ever more than one octave apart, thereby eliminating possible octave confusions. We chose a logarithmic (i.e., semitone, or musical) spacing between tones because auditory frequency discrimination of pure tones follows an approximately logarithmic scale (Moore, 2004), and results from a preliminary experiment indicated that listeners tend to report that the logarithmic mean sounds more like the true “mean” of a sequence of pure tones than the linear mean. From here onward, the term “mean frequency” will be used to refer to mean frequency on a logarithmic (semitone) scale. Each trial consisted of two intervals—“sequence” and “test”—which were always separated by a 500 ms silent interval. During the “sequence” interval, the six tones in the sequence were played in random order, each for 300 ms with a 100 ms pause between successive Running head: ENSEMBLE CODING IN AUDITION 7
 tones. In the subsequent “test” interval, a single comparison tone was played for 300 ms, and listeners reported whether this tone was higher or lower than the mean frequency of the sequence (two alternative forced choice; 2AFC). Test tones differed from the true sequence mean by +/-5, +/-3, +/-2, +/-1, or +/0.5 semitones. Measuring discrimination between the mean frequency of the sequence and the test tone across this range of differences allowed us to determine how precisely listeners could estimate the mean frequency. The frequency difference between the test tone and the mean of the sequence was counterbalanced across trials. Listeners completed either 300 or 240 trials over two runs. No feedback was provided in any of the experiments. Results We fit a psychometric function to each listener’s data (Figure 2A) using a logistic equation. For each psychometric function, we generated a bootstrapped distribution of model fit parameter values by resampling the data with replacement 1,000 times and fitting a new curve for each iteration (as in Fischer and Whitney, 2011) to obtain a bootstrapped slope for each listener, corresponding to the listener’s sensitivity for estimating the mean frequency of the sequence. Higher slopes indicate better discrimination of mean frequency. If listeners were completely unable to discriminate the mean frequency of the sequence from the test tone, the slope of the psychometric function would be zero. Every individual listener performed significantly above chance (least significant was slope = 0.21, with more than 99% of the bootstrapped estimates > 0). As a group, listeners performed above chance in reporting whether a test tone was higher or lower than the mean frequency of the preceding sequence (Figure 2B; One-Sample Wilcoxon Signed Ranks Test, p < .001, Cohen’s d = 1.60). These data indicate that listeners could estimate the mean frequency of the sequence, consistent with the findings of Albrecht, Scholl, & Chun Running head: ENSEMBLE CODING IN AUDITION 8
 (2012). However, it is unclear how many of the tones in the sequence contributed to this estimate and whether this estimate relied on explicit memory of each of the tones. In Experiment 2, we determined the number of tones that contributed to listeners’ mean estimates by varying the proportion of tones that were presented from each sequence. In Experiments 3 and 4, we measured listeners’ memory capacity for the frequency and position of individual tones in the sequence. Experiment 2: Listeners’ Estimates of the Mean Incorporate a Substantial Number of the Tones in a Sequence In Experiment 2, we tested the hypothesis that listeners use multiple tones to estimate the mean frequency of a sequence of tones — ensemble coding. This experiment is necessary to rule out the possibility that in Experiment 1, listeners used only a single tone (and simply ignored or disregarded the other five tones) to estimate the average, which could have resulted in some ability to estimate mean frequency but would not constitute summary statistical perception. This concern has been important in the study of visual summary statistics (e.g., Myczek & Simons, 2008), and it is equally important in this investigation. To directly test whether estimates were based on multiple tones, we restricted the number of tones that listeners could use to estimate the mean frequency of the full 6-tone sequence. Specifically, we generated 6-tone sequences as in Experiment 1, and on a given trial, either a subset of tones from the full sequence (1, 2, or 4) or all 6 tones were presented. We asked whether a listener’s percept of the average frequency improves when more information about that average is available. If a listener’s estimate of the mean frequency improves with increasing number of presented tones, this would indicate that they use those additional tones in their Running head: ENSEMBLE CODING IN AUDITION 9
 ensemble judgment. Because a single randomly selected tone from the sequence is a poor representative of the full 6-tone sequence, we expected estimates of the mean to be poor when only one tone was presented. If listeners integrate multiple tones into an ensemble code, then estimates of mean frequency should improve when more tones are presented from the full sequence (e.g., 2, 4, or all 6), as these tones provide more information about the ensemble average. Alternatively, if listeners rely on only a single tone to estimate the mean even when more than one tone from the full sequence are presented, then behavioral performance should not vary as a function of the proportion of presented tones in each sequence. Method Listeners. 11 listeners (two male, ages 24-34) from the University of California, Berkeley gave informed consent to participate in the experiment and were compensated for their time. All had normal hearing, and none had absolute pitch (self-report). On average, listeners had 10.1 years of musical training (SD = 4.9) and initiated training at age 7.0 (SD = 1.8). All listeners also participated in Experiment 1, and all but two listeners were naïve regarding the purpose of the experiment. Stimuli and procedure. All sequences were generated as in Experiment 1 (with 6 tones), but we varied how many of those 6 tones were presented from each sequence—1, 2, 4, or all 6 of the tones. As in Experiment 1, each sequence was followed by a single test tone, differing from the true mean of the full sequence of 6 tones by +/-5, +/-3, +/-2, +/-1, or +/0.5 semitones. The number of presented tones and the frequency difference between the test tone and the mean of the full sequence were counterbalanced across trials. Listeners were told to use any strategy to determine whether the test tone was higher or lower than the average frequency of the sequence. The correct mean was always defined as the mean of the full sequence (including those tones that Running head: ENSEMBLE CODING IN AUDITION 10
 were not presented, for trials with only 1, 2, or 4 tones). On trials in which only 1 tone was presented, the correct mean was never equal to the single tone. All listeners completed 880 trials over 4 runs. Results Listeners performed the same task as in Experiment 1, but only a subset of the full tone sequence was presented on each trial (1, 2, 4, or all 6 tones). We fit psychometric functions to the data for each of the four conditions (1, 2, 4, or 6 tones) using the same method as in Experiment 1 and compared slopes across the four conditions (Figure 3). The average slope for the 6-tone condition was significantly greater than the slope for the 1-tone (Wilcoxon Signed Ranks Test, p < .01, Cohen’s d = .71) and the 2-tone condition (p < .05, Cohen’s d = .57), but it was not significantly greater than the slope for the 4-tone condition (p = .50). This indicates that listeners integrated over a substantial number (at least 3) of the tones, and it shows that encoding only 1 or 2 tones was insufficient to achieve optimal estimation of the mean frequency of the full 6-tone sequence. In other words, listeners used an ensemble code to estimate the mean frequency of the sequence. For those listeners who participated in both Experiment 1 and Experiment 2, we found very high test-retest reliability of slopes for the identical 6-tone conditions in the two experiments (Cronbach’s alpha = .94; maximum alpha value is 1; Cronbach, 1951). Experiment 3: Listeners Do Not Reliably Encode Individual Frequencies in a Sequence Experiment 2 demonstrated that listeners used at least three tones to make estimates of mean frequency. It is possible that rather than encoding a summary statistic, listeners estimated the mean frequency by employing an auditory working memory strategy that involved encoding the individual tones. Auditory working memory capacity has been widely studied (Miller, 1956; Running head: ENSEMBLE CODING IN AUDITION 11
 Crowder, 1993), and recency effects on tone memory are well-known and robust (Crowder, 1993). In Experiments 3 and 4, we measured how many tones listeners could remember from the same stimuli that were used in Experiments 1 and 2. Specifically, we tested whether listeners could accurately identify the frequency or position of individual tones within the sequence. Poor performance on these tasks would suggest that the ensemble code is formed implicitly, without access to individual tones. Method Listeners. Ten listeners (five listeners from Experiment 1, two listeners from both Experiments 1 and 2, and three additional listeners) participated in Experiment 3. All listeners (six male, ages 18-33) gave informed consent to participate in the experiment and were compensated for their time. All listeners had normal hearing, and none had absolute pitch (selfreport). On average, listeners had 5.2 years of musical training (SD = 5.3) and initiated training at age 7.4 (SD = 3.6). All but one listener were naïve as to the purpose of the experiment. Stimuli and procedure. The sequences were generated and presented in exactly the same way as in Experiment 1, except that each “test” interval contained two comparison tones (each with a 300-ms duration and separated by 100 ms): a member of the sequence and a new lure tone that differed by at least 1 semitone (well above the just-noticeable difference for frequency) from any member of the sequence. The temporal order of the lure and the target was counterbalanced across trials. Listeners reported which of the two tones was a member of the sequence (2AFC). All listeners completed 192 trials over two runs. Results When asked to identify which of two test tones was present in the preceding sequence, listeners performed significantly, but only slightly, above chance levels (Figure 4A; One-Sample Running head: ENSEMBLE CODING IN AUDITION 12
 Wilcoxon Signed Ranks Test, p < .05, Cohen’s d = 1.12), indicating limited access to frequency information about individual tones in the sequence. We estimated the mean number of tones that were effectively accessible to the listener at the time of report, assuming a linear relationship between number of remembered tones and percentage correct. Specifically, we divided the difference between perfect and chance performance (100% 50% = 50%) by the number of tones in the sequence (6), resulting in 8.3%. A performance level of 58.3%, or 8.3% above chance (8.3% + 50% = 58.3%), is consistent with representation of a single tone, performance of 66.6% (8.3% + 8.3% + 50% = 66.6%) corresponds to representation of two tones, etc. Our listeners’ average accuracy rate was 57.7%, or 7.7% above chance. By dividing 7.7% by 8.3% (which corresponds to representation of one tone), we determined that on average, listeners had access to approximately one of the individual tones in the sequence (0.93 tones, SEM = 0.26) at the time of report, a number that is insufficient to explain the mean discrimination accuracy in Experiments 1 and 2 (see Discussion). Experiment 4: Listeners Cannot Reliably Identify a Single Tone’s Position Within a Sequence Method Listeners. Ten individuals from Experiment 1 (including four from Experiment 3 and none from Experiment 2) participated in Experiment 4. All listeners (two male, ages 18-24) gave informed consent to participate in the experiment and were compensated for their time. All listeners had normal hearing, and none had absolute pitch (self-report). On average, listeners had 4.3 years of musical training (SD = 5.6) and initiated training at age 9.1 (SD = 3.7). All listeners were naïve as to the purpose of the experiment. Running head: ENSEMBLE CODING IN AUDITION 13
 Stimuli and procedure. The method of generating and presenting the sequences was the same as in Experiment 1, except the “test” stimulus was always one of the tones from the sequence. Listeners were asked to identify the position (1-6) of the test tone in the preceding 6tone sequence (6AFC). Listeners completed 180 trials over two runs. Results Overall, listeners correctly identified the position of the test tone in the sequence 33.1% of the time, slightly but significantly above chance (Figure 4B; One-Sample Wilcoxon Signed Ranks Test, p < .01, Cohen’s d = 1.14). As in Experiment 3, we estimated the mean number of tones that were accessible to the listener at the time of report. To do this, we again divided the difference between perfect and chance performance (100% 16.6% = 83.4%) by the number of tones (6), resulting in 13.9%. A performance level of 30.5%, or 13.9% above chance (13.9% + 16.6% = 30.5%), is consistent with representation of a single tone, performance of 44.4% (13.9% + 13.9% + 16.6% = 44.4%) corresponds to representation of two tones, etc. The fact that actual performance was only 33.1% indicates that, on average, listeners had access to the position of approximately one of the individual tones in the sequence (1.18 tones, SEM = 0.33) at the time of report. This is remarkably consistent with Experiment 3 (in particular, a bootstrapped permutation test indicated no significant difference between the mean number of accessible tones in the two experiments, p > .20). In conclusion, both Experiments 3 and 4 indicate that listeners have access to approximately one tone. This very limited auditory working memory capacity for the tone sequences we have employed cannot account for the discrimination performance in Experiments 1 and 2 (see Discussion). We also found a significant recency effect: listeners were significantly more likely to successfully report the position of the test tone when it was the final tone in the sequence Running head: ENSEMBLE CODING IN AUDITION 14
 compared to when the test tone position was any of the first five tones (Related-Samples Wilcoxon Signed Ranks Test; after Bonferroni correction, p < .05 for all five comparisons). Together, the results of Experiments 3 and 4 indicate that listeners’ ability to report information about the frequencies of individual tones in the sequence was severely limited. Discussion Our results provide the first direct evidence of ensemble coding in the auditory domain. Listeners reliably estimated the mean frequency of a sequence of six sinewave tones. This ability was severely reduced when we restricted the proportion of these six tones that were presented to listeners, indicating that ensemble coding occurred over a substantial number (at least three) of the tones in the sequence. This finding rules out cognitive strategies for estimating the mean frequency such as basing judgments on a single tone in the sequence. Listeners performed poorly when asked to identify either the frequency or the position of individual tones in a sequence, indicating that the ensemble code was not based on explicit memory of the individual tones that comprised the sequence. Instead, listeners’ representations of those tones were transformed into a concise summary representation of the mean frequency. Previous work on visual statistical summary demonstrates that the number of items in a set that subjects can integrate is equal to approximately the square root of the total set size (Dakin, 2001). Experiment 2 showed that listeners used at least 3 out of the 6 tones in a sequence to estimate the mean, a value that is generally consistent with √N (i.e., √6 is ~2.5). Future work using sequences with a greater number of tones will help elucidate whether, as in vision, this square-root relationship holds for various lengths of auditory sequences. Running head: ENSEMBLE CODING IN AUDITION 15
 Auditory frequencies convey crucial information in various social contexts, and ensemble coding of frequency may provide a computationally efficient means of obtaining perceptual information that is essential for communication. Pitch is an important social cue in speech processing: it can indicate emotional tone (Curtis & Bharucha, 2010; Fairbanks & Provonost, 1939), level of interest (Wennerstrom, 2001), gender (Abitbol, Abitbol, & Abitbol, 1999), and even sexual infidelity (O’Connor, Re, & Feinberg, 2011). For instance, the frequency of a single pure tone can influence the perceived gender of a visually androgynous face (Smith, Grabowecky, & Suzuki, 2007). In the natural world, auditory information is broadband, containing multiple frequencies. Here, we show that humans can accurately perceive ensemble frequency even when information about individual frequencies is not explicitly encoded. Given that natural environments and stimuli, including speech, contain complex sequences of pitches comprised of multiple frequencies, our ability to encode ensemble frequency may have evolved to facilitate perception of social stimuli. Ensemble frequency encoding may also be a fundamental mechanism underlying music processing, even in individuals without music training. When we hear a tonal sequence (i.e., a melody in a particular key, like E Major), statistical likelihood and hierarchical pitch schemas constrain our understanding of which pitches belong in the sequence, and which do not (Krumhansl & Kessler, 1982; Krumhansl, 1990; Krumhansl & Cuddy, 2010; Temperley, 2007). Even listeners without musical training can reliably judge how well a given pitch fits into a particular key context (Krumhansl & Kessler, 1982). Our results extend these findings by showing that statistical mechanisms are also involved in the perception of sequences that are not traditionally tonal (i.e., not belonging to a single major or minor key). This gist encoding was independent of musical training (we found no significant correlation between musical training Running head: ENSEMBLE CODING IN AUDITION 16
 and performance in any of our experiments), suggesting the operation of a basic mechanism for rapidly perceiving an ensemble of tones. We have shown that ensemble coding is a powerful mechanism for perceiving the auditory environment, and we propose that perceiving auditory “gist” may be critical for social interactions and music perception. Our findings demonstrate that ensemble coding is a useful strategy beyond the visual domain and may represent a general mechanism for efficient representation of the environment. Running head: ENSEMBLE CODING IN AUDITION17
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