Schroeder's algorithm can produce harmonic tone complexes (HTCs) with a flat temporal envelope and either upward- or downward-sloping instantaneous frequency sweeps within periods of the fundamental frequency (F0), depending on the polarity of the phase-scaling parameter C (Schroeder, 1970) (Fig. 1). Early on, it was discovered that HTCs generated with positive (downward-sweeping frequency) and negative (upward-sweeping frequency) C values differ in the extent to which they mask behavioral thresholds for pure-tone detection in humans, with lower thresholds by up to 20 dB for the positive C value compared to negative (Kohlrausch and Sander, 1995; Smith et al., 1986). Less masking by Schroeder HTCs with positive C values is not explainable by traditional power-spectrum models of masking (Fletcher, 1940) because Schroeder HTCs generated with opposite C values have identical magnitude spectra; these signals share the same waveform when one signal is time reversed.

The underlying reason for masking differences between Schroeder C polarities remains uncertain. One hypothesis is that the difference originates from asymmetry of mechanical filtering by the mammalian cochlea (Smith et al., 1986). Specifically, recordings of basilar membrane motion in response to clicks show that the impulse response of the cochlea can exhibit an upward-sweeping instantaneous frequency glide – a property associated with asymmetry in the shape of pure-tone frequency tuning curves (Recio et al., 1998; Strube, 1985). Filters with an upward-gliding impulse response are expected to produce more prominent response envelope fluctuations (i.e., “peakier” temporal-response profiles) for Schroeder HTCs with positive C values compared to negative. The deeper and longer low-amplitude periods in the cochlear response to maskers with positive C values could potentially provide opportunities for detection of an added low-level tone, thereby leading to the observed lower masked threshold for the positive-C condition.

Animal models have been used to test the hypothesized contribution of cochlear filtering asymmetries to Schroeder-masking differences between opposite C polarities, but so far have yielded an incomplete understanding of underlying mechanisms. Studies in chinchilla and guinea pig recorded basilar membrane motion in response to Schroeder HTCs to test for the predicted difference in response envelope fluctuations between opposite C polarities (Recio and Rhode, 2000; Summers et al., 2003). Results were partly consistent with an explanation based on cochlear impulse responses, showing the expected larger fluctuations for responses to Schroeder HTCs with positive C values compared to negative. However, measurements were restricted to basal cochlear regions with characteristic frequencies (CFs) above the frequency range of target signals typical of human behavioral studies. Note that for CFs below 1 kHz in cat and chinchilla (this “transition” frequency may vary between species), the cochlea appears to transition to downward-sweeping frequency glides of the impulse response based on auditory-nerve-fiber recordings (Carney et al., 1999; Recio-Spinoso et al., 2005). Filters with downward-gliding impulse responses should theoretically produce a peakier response to Schroeder HTCs with negative C values rather than positive, and consequently less masking for the negative-C condition. However, it remains unknown whether these species show behavioral differences in Schroeder masking across test frequencies because animal behavioral studies have not been conducted. Furthermore, all of these physiological studies focused largely on supra-threshold Schroeder responses rather than thresholds for Schroeder-masked detection, complicating direct comparison to behavioral results. In summary, the lack of (1) complementary behavioral and physiological data in the same species and (2) physiological thresholds for Schroeder-masked detection are major impediments to our understanding of masking by Schroeder HTCs. Consequently, it remains unclear whether asymmetry of cochlear filtering can explain observed behavioral masking differences between Schroeder C polarities.

Birds provide an interesting animal model for studies of Schroeder masking because many species use vocalizations containing rapid frequency changes as part of their social communication system and can perform complex auditory detection and discrimination tasks (Dooling et al., 2000). In contrast with human results, the few behavioral studies of Schroeder masking in birds have found minimal threshold differences for tones masked by Schroeder HTCs with opposite C values. In budgerigars, thresholds were determined for detection of 1, 2.8, and 4-kHz tones masked by Schroeder HTCs with positive or negative C values, for comparison with human thresholds determined using the same stimuli (Leek et al., 2000). Whereas human subjects showed the expected lower threshold of up to 15-20 dB for positive-C Schroeder maskers compared to negative C values, budgerigar thresholds were either similar between opposite C values or slightly lower for maskers with negative C values. In two follow-up studies, budgerigars, zebra finches, and canaries were tested across a wider range of stimulus conditions including higher F0s up to 400 Hz (Dooling et al., 2001), and multiple, intermediate C values between -1 and +1 (Lauer et al., 2006). Note that lower absolute C values produce stimuli with reduced duty cycles and, consequently, faster instantaneous frequency sweeps within F0 periods, with C of zero producing an impulse train associated with all components in cosine phase (Fig. 1). Even over this wider range of conditions, which included faster rates of instantaneous frequency change that were potentially better suited to the mechanics of the avian inner ear, birds showed little appreciable difference in masking between Schroeder HTCs generated with opposite C values (Dooling et al., 2001; Lauer et al., 2006).

The reason for less masking difference between Schroeder HTCs of opposite C polarity in birds compared to humans is unclear due to limited physiological investigations. One possibility is that the avian cochlea differs from that of mammals in its impulse response, perhaps lacking a prominent instantaneous frequency glide. Consistent with this notion, impulse responses of auditory-nerve fibers in the barn owl show smaller instantaneous-frequency glides than in cat and chinchilla, and little evidence of a transition CF for glide direction (Fontaine et al., 2015). On the other hand, the barn owl has specialized high-frequency hearing and might show different cochlear processing mechanisms than budgerigars and other avian behavioral models species from prior Schroeder studies. Despite broad physiological similarities between birds and mammals in auditory-nerve frequency tuning, phase-locking limits, and other basic response properties of auditory-nerve fibers (Manley et al., 1985; Sachs et al., 1974), the sensory epithelium in birds is considerably shorter and wider than in mammals, with dozens of hair cells spanning its width in apical low-CF regions (Takasaka and Smith, 1971). If these anatomical differences result in a cochlear impulse response without a prominent frequency glide, this could explain less masking difference between Schroeder HTCs of opposite polarity. While Dooling and colleagues found stronger compound auditory-nerve action potentials for negative-C Schroeder HTCs in several bird species (Dooling et al., 2002), these gross potentials are strongly influenced by cross-channel neural synchrony and are therefore not directly relatable to current hypotheses for human masking asymmetry, based on a single-channel framework.

To gain further insight into mechanisms of Schroeder masking, and into possible reasons for minimal Schroeder masking asymmetry in birds, we performed parallel behavioral and neurophysiological experiments in budgerigars using tones masked by Schroeder HTCs. The frequency range of sensitive hearing in budgerigars extends broadly, from 0.6-5 kHz (10-dB bandwidth), and is determined by the linear transfer function of the columellar middle-ear system (Peacock et al., 2020; Saunders, 1985). Whether budgerigars show cochlear frequency glides, and changes in glide direction across CFs, are unknown. In the first experiment, behavioral studies were conducted in animals trained using operant-conditioning procedures over a wide range of F0 and C values, to improve the possibility of detecting masking differences between Schroeder C polarities if they exist. To expand upon prior studies, masking conditions included previously untested C values of ±0.5 at F0s of 200 and 400 Hz. Furthermore, stimuli were presented using a roving-level paradigm for which the overall masker level was randomly selected on each trial from a 20-dB range centered on 80 dB SPL (a typical level used in prior studies), thereby diminishing the extent to which overall loudness and/or single-channel energy cues could be used to perform the task.

In the second experiment, we made neurophysiological recordings in awake passively listening animals of extracellular activity in the central nucleus of the avian inferior colliculus (IC), which is a large and nearly obligatory midbrain processing center in the ascending auditory pathway. The IC shows pronounced temporal and rate-based encoding of acoustic-envelope fluctuations at amplitude-modulation frequencies up to several hundred Hz (Henry et al., 2017a; Joris et al., 2004), encompassing the range of envelope frequencies found in Schroeder HTCs. Moreover, a recent study of gerbil IC revealed neural selectivity for C polarity of Schroeder HTCs based on average discharge rate and spike timing (Steenken et al., 2022). The present study obtained budgerigar IC neural responses to Schroeder HTCs across widely ranging F0 and C values and evaluated the changes in neural activity that occur upon addition of a tone increment to Schroeder maskers. Thus, we were able to evaluate potential neural cues used by animals to perform the behavioral masked-detection task and test whether differences in supra-threshold responses to Schroeder HTCs of opposite polarity are clearly associated with threshold differences for detection of an added tone.