Rabbits use both spectral and temporal cues to discriminate the fundamental frequency of harmonic complexes with missing fundamentals

Abstract

The pitch of harmonic complex tones (HCTs) common in speech, music, and animal vocalizations plays a key role in the perceptual organization of sound. Unraveling the neural mechanisms of pitch perception requires animal models, but little is known about complex pitch perception by animals, and some species appear to use different pitch mechanisms than humans. Here, we tested rabbits’ ability to discriminate the fundamental frequency (F0) of HCTs with missing fundamentals, using a behavioral paradigm inspired by foraging behavior in which rabbits learned to harness a spatial gradient in F0 to find the location of a virtual target within a room for a food reward. Rabbits were initially trained to discriminate HCTs with F0s in the range 400–800 Hz and with harmonics covering a wide frequency range (800–16,000 Hz) and then tested with stimuli differing in spectral composition to test the role of harmonic resolvability (experiment 1) or in F0 range (experiment 2) or in both F0 and spectral content (experiment 3). Together, these experiments show that rabbits can discriminate HCTs over a wide F0 range (200–1,600 Hz) encompassing the range of conspecific vocalizations and can use either the spectral pattern of harmonics resolved by the cochlea for higher F0s or temporal envelope cues resulting from interaction between unresolved harmonics for lower F0s. The qualitative similarity of these results to human performance supports the use of rabbits as an animal model for studies of pitch mechanisms, providing species differences in cochlear frequency selectivity and F0 range of vocalizations are taken into account.

NEW & NOTEWORTHY Understanding the neural mechanisms of pitch perception requires experiments in animal models, but little is known about pitch perception by animals. Here we show that rabbits, a popular animal in auditory neuroscience, can discriminate complex sounds differing in pitch using either spectral cues or temporal cues. The results suggest that the role of spectral cues in pitch perception by animals may have been underestimated by predominantly testing low frequencies in the range of human voice.

INTRODUCTION

Many natural sounds such as speech, animal vocalizations, and the sounds of musical instruments contain harmonic complex tones (HCTs) in which all the frequency components are integer multiples of a common fundamental. HCTs with fundamental frequencies (F0s) between ∼30 and 4,000 Hz typically evoke a pitch percept that is matched to a pure tone at F0, even if the complex contains no energy at F0 (“missing fundamental” phenomenon) (1–3). The pitch of HCTs plays important roles in speech and music perception and in the perceptual organization of sound. In particular, harmonicity is a powerful grouping cue in forming perceptual objects, whereas differences in F0 facilitate the perceptual segregation of sound sources (4, 5).

The missing fundamental phenomenon is not unique to humans but is also observed in experimental animals. Several vertebrate species including cats (6–8), macaques (9, 10), marmosets (11, 12), chinchillas (13, 14), ferrets (15), mice (16), bats (17), songbirds (18), and goldfish (19) can discriminate the F0 of missing-fundamental stimuli. Animals can also detect deviations from harmonicity in a tone complex [gerbil (20, 21), ferret (22), birds (23), bullfrog (24)], and some birds excel at this task, with performance exceeding that of humans. However, there is evidence for differences in pitch perception of HCTs between humans and experimental animals that go beyond simple differences in overall level of performance. Pitch percepts can be produced either by HCTs containing low-order harmonics that are individually resolved by the mechanical frequency analysis in the cochlea or by HCTs consisting entirely of high-order, unresolved harmonics whose interactions give rise to a periodicity at F0 in the temporal envelope (1, 5). In human listeners, the pitch produced by resolved harmonics is generally stronger and less dependent on phase relationships among the harmonics than the pitch produced by unresolved harmonics (25–28). In contrast, experimental animals including chinchillas (29, 30), ferrets (15), and marmosets (11) appear to rely more on the periodicity cues produced by unresolved harmonics for F0 discrimination. These differences in pitch perception mechanisms have been linked to differences in cochlear frequency selectivity between humans and experimental animals (31–34), but see Ref. 35 for a contrary opinion.

Rabbits (Oryctolagus cuniculus) are a relatively popular model in auditory neuroscience because of their good low-frequency hearing (36, 37) and because their temperament makes them ideal for neurophysiological recordings in unanesthetized preparations (38). The rabbit has also proven to be an excellent model for studies of electric hearing and neural plasticity with cochlear implants because they tolerate the implants well and can be studied for long periods of time (39–41). However, nothing is known about the perception of HCTs with missing fundamentals by rabbits. Carney et al. (42) measured behavioral thresholds for detection of amplitude modulation (AM) by rabbits. Although both AM tones (43) and AM noise (44) can produce a pitch percept at the modulation frequency in humans, Carney et al. (42) focused on AM detection and did not test for discrimination of AM stimuli differing in pitch. A main goal of the present study was to test whether rabbits can discriminate the F0 of HCTs with missing fundamentals in the same way as other vertebrate species.

Recent single-unit studies in the auditory midbrain of unanesthetized rabbits (45, 46) identified three potential neural codes for the F0 of HCTs: 1) a rate-place code for resolved harmonics dependent on cochlear frequency selectivity and tonotopic mapping; 2) tuning of firing rates to a particular range of envelope repetition rates; and 3) a temporal code in the form of phase locking to the envelope repetition rate. The last two codes are likely derived from peripheral envelope periodicity cues created via the interaction of unresolved harmonics. The availability of the three codes depends on F0: the rate-place code for resolved harmonics is most prevalent at higher F0s (>600 Hz), the temporal code for envelope repetition rate at lower F0s (<500 Hz), and rate tuning to envelope repetition rate at intermediate F0s (50–1,500 Hz). These neurophysiological results suggest 1) that rabbits should be able to use both resolved and unresolved harmonics for discriminating F0s and 2) that the relative effectiveness of the two pitch cues will depend on the F0 range. A second purpose of the present study was to test these hypotheses.

We tested behavioral discrimination of the F0 of HCTs with missing fundamentals by rabbits with operant conditioning. The tested stimuli spanned a wide range of F0s (200–1,600 Hz) and included both conditions containing resolved harmonics and conditions in which all the harmonics were likely unresolved. We used a novel behavioral task in which rabbits had to track spatial gradients in F0 dependent on their location within the testing booth to obtain a food reward, much as rabbits and other animals track odor gradients when foraging for food in natural environments (47, 48) and bats and other echolocating animals track changes in the properties of the reflected sounds for foraging (49–51). Results suggest that rabbits can discriminate F0 using either resolved or unresolved harmonics and that the relative effectiveness of the two cues depends on F0. Preliminary reports have been presented (52).

METHODS

Animal Subjects

Six adult Dutch Belted rabbits (5 female) were used in this study. Age at the beginning of behavioral training ranged from 6 to 16 mo, except for one rabbit aged 2 yr, 9 mo (Table 1). To ensure the rabbits’ motivation to obtain food rewards during behavioral sessions, food restriction was gradually implemented over several weeks until each animal approached 80% of their ad libitum weight. Rabbit weights were measured two to five times per week, and the daily ration of food pellets was regularly adjusted to maintain their weight within 5% of the target. Once trained, the rabbits received a portion of their daily pellet rations (5TVM, TestDiet) as food rewards during the behavioral sessions and were provided the remainder of their food ration (Hi-Fiber Rabbit, Scott’s Distributing, Inc.), if any, after the session, at the end of the day. To complement the food pellets, rabbits were also given unlimited water and 30 g of hay (Timothy) every day.

Table 1.

Rabbit training and testing history

Rabbit ID	Sex	Age at Training Onset, mo	No. of Initial Training Sessions	Experiment 1		Experiment 2		Experiment 3		Age at End of Testing, mo
				No. of train. sessions	No. of test sessions	No. of train. sessions	No. of test sessions	No. of train. sessions	No. of test sessions
A	F	16.5	213	30	15	55	22	0	30	60.9
B	F	10.3	108	5*	16	7*	16	2*	23	46.2
C	M	5.9	43	0*	16	5*	18	1	20	21.3
C27	F	10.2	25	N/A	N/A	N/A	N/A	N/A	N/A	12.5
N3	F	5.9	91	N/A	N/A	N/A	N/A	N/A	N/A	14.2
C55	F	33.0	12	N/A	N/A	N/A	N/A	N/A	N/A	33.6

^*In addition to the training sessions listed in the table, rabbit B performed 101, 61, and 63 sessions using the stimuli of experiments 1, 2, and 3, respectively, but with a fundamental frequency (F0) step when entering the target zone. Rabbit C performed 79 and 32 additional sessions with an F0 step using the stimuli of experiments 1 and 2, respectively. Since the data from these sessions are not included in this report, they could be considered as additional “training sessions.” All the sessions for rabbit A were performed with an F0 step. N/A, not applicable, denotes rabbits that did not progress past initial training.

Throughout the duration of testing, auditory brain stem responses (ABRs) were measured biannually under anesthesia (35 mg/kg ketamine im + 6 mg/kg xylazine sc +1.5% isoflurane in 0.8 L/min O₂) to verify the stability of the thresholds for 5-ms tone pips with frequencies ranging from 0.5 to 16 kHz in octave steps. The rabbits that were successfully trained participated in 235–438 sessions, and their age at the last testing session was 1.8–5.1 yr (Table 1). All procedures were approved by the Animal Care Committee of Massachusetts Eye and Ear.

Experimental Setup

During a behavioral session, the rabbit moved freely within a 1.65 × 1.05 × 2.05-m sound-treated chamber (SE 2000 Series, WhisperRoom Inc.). The chamber’s walls and ceiling were lined with acoustic foam (SONEX) to reduce acoustic reflections. Sound stimuli were presented via an overhead loudspeaker (Yamaha MSP5 Studio Monitor) attached to the ceiling. During experimental sessions, the rabbit was continuously monitored remotely via a camera (Creative Live! Webcam, VF0790) affixed to the chamber ceiling. The rabbit’s highly contrasting white fur was tracked digitally throughout each behavioral trial, and every 100 ms the rabbit’s current location was estimated as the center of the fur. A food dispenser mounted on one corner of the chamber released two 0.11-g food pellets into a bowl whenever the rabbit successfully completed a trial.

Stimuli

The primary stimuli used during this study were HCTs with equal-amplitude harmonics presented in cosine phase with the fundamental frequency (F0) omitted. All HCT stimuli were presented with threshold-equalizing noise (50–16,000 Hz) to mask cochlear distortion products at F0. The noise masker had a nominally flat spectrum for frequencies below 1 kHz and then rolled off at −3 dB/octave so the noise energy in a constant-Q filter would be the same across center frequencies. This masking noise would be adequate to mask cochlear distortion products in humans (see discussion).

During a behavioral trial, an HCT was played continuously and its F0 was updated every 100 ms depending on the rabbit’s location within the chamber in relation to a virtual target location (see details below). To implement an F0 update, the frequency of each harmonic was gradually swept from its preupdate value to its postupdate value over 100 ms to avoid any waveform discontinuity and maintain harmonicity at all times. Because the frequency range of harmonics was strictly limited for each stimulus, it was possible for a new harmonic to appear or an existing harmonic to disappear after an F0 update. For example, after an increase in F0, a low harmonic could enter the specified frequency range from below or a high harmonic could exit at the upper end of the specified range. When this happened, the amplitude of each entering or exiting harmonic was ramped linearly over 100 ms in synchrony with the frequency sweep. Thus, the dynamic HCT stimuli contained no audible clicks or discontinuities as the F0 changed with rabbit position.

Behavioral Task

Our choice of a behavioral task was inspired by observations that animals can use spatial gradients in properties of sensory stimuli to acquire food. For example, bats use spatial gradients in the acoustic properties of the reflections from their echolocating calls to forage for food (51, 53) and mice can learn to utilize spatial gradients in the properties of a sound stimulus to find a hidden sound target and obtain a food reward (54). Similarly, the rabbit’s task in our experiment was to reach a virtual target by utilizing a spatial gradient in the F0 of an HCT stimulus, much as in the children’s game of “hot and cold.” At the beginning of each trial, a 35-cm-diameter virtual target was randomly placed by the computer within the testing chamber. The rabbit was continuously presented with an HCT throughout the duration of the trial. The frequency of the missing F0 varied inversely to the rabbit’s distance to the target over a range of 1 octave (Fig. 1C) and was updated every 100 ms based on the measured position of the rabbit. A successful trial (Fig. 1A) required the rabbit to reach the target within 45 s and stay in the target area for at least 2 s. We only tested ascending F0 gradients, i.e., the target was always the stimulus with the highest F0. The trial ended and the stimulation ceased either when the rabbit successfully reached the target or after a maximum duration of 45 s, whichever came first. Successful trials were rewarded with two 0.11-g food pellets delivered by an automatic dispenser located near a corner of the room. The rabbit was given 6 s after each successful trial to eat the pellets before the next trial began. If the rabbit was unable to reach the target within 45 s (failed trial; Fig. 1B), an 8-kHz pure tone was presented for 2 s, followed by an 8-s timeout before the next trial began.

Figure 1.

A and B: example paths of a rabbit inside the testing booth during a successful trial (A) and a failed trial (B). The fundamental frequency (F0) of the sound stimulus increased or decreased as the rabbit approached or moved away, respectively, from the randomly placed virtual target. To receive a food reward, the rabbit had to enter and remain within the target zone for 2 s before the 45-s time limit of the trial. C: contour line illustration of the F0 gradient for a virtual target near a corner of the testing booth. For this target location, F0 increased from ∼450 Hz at the lower left side of the room to 800 Hz within the target zone (yellow). HCT, harmonic complex tone.

Behavioral sessions were conducted three to five times per week and typically consisted of 150–250 trials, ending either after 3 h had passed or when the rabbit reached its daily food limit, whichever occurred first.

Behavioral Training

Each rabbit was first habituated to the testing chamber with the food bowl filled with reward pellets for 1 h at a time. Once the rabbit was comfortable moving around the chamber and eating pellets from the bowl, which could take up to 15 sessions, it was introduced to a much easier version of the behavioral task using an HCT stimulus with harmonics in the range 800–16,000 Hz. These training trials utilized an enlarged target, an F0 range wider than 1 octave, and a longer time limit, which served to habituate the rabbits to the stimuli and encourage them to move around the chamber. Most rabbits quickly learned to approach the food reward bowl when the sound stopped at the end of a successful trial. The task parameters were then gradually tightened to make the task more difficult whenever performance exceeded a 65% success rate, until the rabbit was able to succeed in at least 65% of trials using the standard parameters. Control trials in which an HCT with a randomly chosen constant F0 was presented throughout the trial were introduced with low probability (∼5%). Successful control trials were rewarded in the same way as trials with an F0 gradient. Performance on trials with an F0 gradient was compared with performance on control trials (constant F0) to verify that performance was based on the F0 gradient rather than random searching. The rabbits required up to 100 training sessions to attain a 65% success rate with the standard stimulus. After this initial training, additional stimuli differing in either F0 range or harmonic composition were introduced over ∼25 sessions, with the new stimuli having a gradually increasing probability of occurrence until all the stimuli (except control) were equiprobable. The probability of control trials never exceeded 10% in order to preserve motivation.

The rabbits were initially trained to do the task with an additional cue: the missing F0 would step up by 1/3 octave when the rabbit entered the target zone. The step was applied both on control trials and on trials with an F0 gradient. When we realized that some rabbits relied on this step cue more than on the F0 gradient to find the target, the step cue was eliminated, and the rabbits were retrained until they reached 65% correct without a step. Only results obtained without a step are reported in this article, with the exception of results from rabbit A, which had already completed all the experiments and was no longer available when the step was eliminated. However, it was clear from the results that rabbit A relied strongly on the F0 gradient to find the target.

Acoustic Stimuli Calibrations

To calibrate the stimulus delivery system including room acoustics, a 1/4-in. microphone (model 2520, Larson-Davis) was placed at five locations within the testing chamber to record the acoustic waveform resulting from HCTs presented through the ceiling loudspeaker. The microphone was positioned at the centers of each quadrant of the testing chamber as well as the overall center and placed at a height of 15 cm to approximate the rabbits’ ear level during the experiments. Static HCT stimuli with F0s of 200, 400, 800, and 1,600 Hz were presented both with and without the noise masker. For each HCT, the average power level of each harmonic was measured by averaging 100 power spectra collected from 100-ms segments of the stimuli. Figure 2 shows the average power spectra measured from one room location for HCTs with F0s of 200, 400, 800, and 1,600 Hz, including the added masking noise. The red trace in Fig. 2 shows the spectrum of the ambient noise, which contained significant low-frequency energy due to the presence of air conditioning and fans of electrical equipment in the room surrounding the testing booth. For each F0, the harmonics differ substantially in amplitude because of the frequency response of the speaker and sound transmission characteristics of the booth. For the 400-Hz F0, the average amplitude of each harmonic across all frequencies (range: 800–16,000 Hz) and all five room locations was 54.5 dB SPL with a standard deviation of 2.7 dB (Table 2). Similar values were obtained for the other F0s. To quantify the noise level around the missing F0, the power spectra of the masked stimuli were averaged over the average equivalent rectangular bandwidth (ERB) of rabbit auditory nerve fibers (55) at the frequency of the missing F0. Across F0s, the noise levels ranged from 39.8 to 49.4 dB SPL, which corresponds to −5.6 to −11.9 dB relative to the level of the harmonics.

Figure 2.

Acoustic measurements on the harmonic complex tone (HCT) stimuli used in the behavioral experiments. A: power spectra of the HCT stimuli with added masking noise measured with 10-Hz resolution from 1 location within the sound chamber for 4 different fundamental frequencies (F0s) labeled on left. The HCT included harmonics in the range 800–16,000 Hz. The red curve shows the power spectrum of the ambient noise in the absence of stimuli. B: envelope modulation depth at F0 as a function of F0 measured both at the input to the loudspeaker (red) and at 5 locations within the sound booth (blue). Symbols show the average modulation depth across the 5 locations; error bars represent ±1 SD. Left: a series of “Broadband” stimuli comprising all harmonics between the 2nd and 16 kHz. Right: a series of “High Harmonics” stimuli consisting entirely of harmonics above the 8th. See Fig. 3A for examples of Broadband and High Harmonics spectra when F0 = 600 Hz.

Table 2.

Average sound pressure levels of harmonics and noise in ERB centered at F0

F0, Hz	Mean Harmonic Level, dB SPL	ERB, Hz	Noise Level near F0, dB SPL	SNR, dB
200	54.5 ± 2.9	56.5	49.4	5.6
400	54.5 ± 2.7	112.9	49.6	11.9
800	54.7 ± 2.3	223.7	39.8	15.0
1,600	54.5 ± 2.2	402.7	48.2	6.3

Harmonic level values are means ± SD. ERB, equivalent rectangular bandwidth; F0, fundamental frequency; SNR, signal-to-noise ratio.

These acoustic measurements were also used to characterize the modulation depths of the stimulus envelope at the five chamber locations and compare them with the modulation depth at the input to the loudspeaker. Periodic envelope modulation at F0 is an important pitch cue for HCTs consisting entirely of unresolved harmonics. The envelope modulation depth was defined as twice the ratio of the F0 component of the full-wave rectified acoustic signal to its DC component. When the envelope modulation is sinusoidal, this method is consistent with the standard definition of modulation depth for amplitude-modulated tones (e.g., Ref. 56). Envelope modulation depth was computed as a function of F0 over the range 200–1,600 Hz and then averaged across the five room locations for each F0. This was done for both a set of “Broadband” HCTs comprising equal-amplitude harmonics from the second to 16 kHz, and “High Harmonics” HCTs comprising harmonics from the eighth to 16 kHz.

Figure 2B shows the average envelope modulation depth expressed in decibels [20 × log₁₀(m)] as a function of F0 for the Broadband and High Harmonics stimuli. Modulation depths were similar for Broadband and High Harmonics stimuli having the same F0, with <2-dB difference in favor of the Broadband stimuli. The modulation depth at the input to the loudspeaker was > 0 dB for all F0s, as expected for HCTs with harmonics in cosine phase. In contrast, the modulation depths measured inside the sound booth were substantially lower and decreased with increasing F0. The attenuation in modulation depth due to room acoustics ranged from 6–8 dB for F0 = 200 Hz to ∼20 dB at 1,600 Hz. This increased attenuation in modulation depth at higher F0s is consistent with the well-known low-pass filtering effect of room reverberation on the envelope of acoustic signals (57, 58). Similar trends were observed for alternative measures of modulation depth, including the peak factor [ratio of peak amplitude to root mean square (RMS) amplitude] and a measure derived from the RMS amplitude envelope computed over a sliding temporal window with a width equal to one-quarter of the F0 period (not shown). The modulation depth values obtained by these alternative methods were somewhat higher than with the F0 method because these metrics take into account the contributions of harmonics of F0 in the envelope waveform, whereas the F0-based method only includes the fundamental component of the envelope. Thus, if rabbits rely on envelope modulation to discriminate F0, performance should be better for low F0s than for high F0s.

Data Analysis

Success rate was used as the main measure of performance. Success rate was averaged over all trials and all testing sessions for each animal and stimulus type. We then used a mixed-effect generalized linear model (GLM) to separate the variance caused by interanimal differences from the effect of stimulus type. The model contained the stimulus type as a fixed factor and animal as a nested random factor. The model treated success rate as a random variable with a binomial distribution and used a logit link function. MATLAB’s fitglme function was used to fit the model to the data [MATLAB version 9.4.0.813654 (R2018a), Toolbox version 11.3]. Likelihood ratio tests were used to compare the goodness of fit of the full model with those of reduced models including only one of the two terms (animal or stimulus) to verify that adding a second term significantly improved goodness of fit. After the full GLM was fitted, the MATLAB function coefTest was used to perform post hoc F tests (with Bonferroni corrections for multiple comparisons) to compare the GLM coefficients for pairs of stimuli or other contrasts.

In addition to success rate, we analyzed the time to success, i.e., the trial duration for successful trials. (By definition, the duration of a failed trial is always 45 s.) Time to success might be interpreted as a measure of the ease of the task and could potentially differentiate performance in stimulus conditions when the success rate is near ceiling. As for success rate, we analyzed the data for time to success using mixed-effect GLMs with stimulus type as a fixed factor and animal as a random factor. Because the time to success data were well fit by a gamma distribution, we used a “complementary log-log” link function, which was found empirically to make the data distribution nearly Gaussian after mapping by the link function.

To test whether rabbits were attending to the sound stimulus even on trials in which they failed to reach the target, we compared the average distance to the target in the first and second half of each failed trial. If rabbits are tracking the F0 gradient, the mean distance to the target should, on average, be shorter in the second half than in the first half. On the other hand, for control trials in which there is no F0 gradient, the mean distance to target should be the same in both halves of the trial. To test this prediction, we computed the difference in mean distance to target in the two halves of each failed trial and fit a mixed linear model to this difference with F0 gradient (with or without) as fixed factor and animal as random factor. We used a linear model because the distribution of distance differences was nearly Gaussian but used the MATLAB GLM tool (with a linear link function) to fit the model for consistency with other analyses reported in this article. For display purposes (but not for quantitative analysis), we also averaged the mean distance to target over each half-trial across all trials and all sessions for each stimulus condition (see Fig. 10).

Figure 10.

A–C: scatterplots of the mean distance from rabbit to target during the first half of failed trials in experiment 1 against the mean distance during the second half for rabbits A, B, and C, respectively. The distance was first averaged over each half-trial duration for each trial and then averaged across all failed trials in which a given stimulus was presented.

RESULTS

Each of the six rabbits (Table 1) was first trained to perform the behavioral task using broadband HCTs with F0s ranging between 400 and 800 Hz and containing harmonics covering a wide frequency range (800–16,000 Hz). Three rabbits (A, B, and C; 2 females) were trained successfully, consistently achieving success rates ≥65% with the training stimulus. These three rabbits provide the data reported in this article. Training was terminated in the other three rabbits (all female) after they failed to consistently perform the task over several sessions. One rabbit failed to habituate to the testing chamber and was even reluctant to eat from the food reward bowls; training was ended after 12 sessions. A second rabbit was able to perform an easy version of the task for short periods of time but would spend most of the session sitting still in the chamber; training ended after 25 sessions. The third rabbit seemed to understand the task but would frequently stop moving around the chamber during a training session. Attempts to retrain this rabbit by making the task easier were unsuccessful. Training was discontinued after 91 sessions.

Each of the three rabbits that were successfully trained completed three separate experiments in which the training stimulus was supplemented with two to five additional stimuli differing in harmonic composition (experiment 1), F0 range (experiment 2), or both F0 range and harmonic composition (experiment 3). For each trial, the stimulus was selected at random from the experiment’s stimuli set with specified probabilities. When transitioning into a new experiment, several training sessions were conducted using the new experiment’s stimuli set until performance (success rate) reached an asymptote (Table 3).

Table 3.

Stimulus characteristics for experiment 1

Stimulus Type	F0 Range, Hz	Harmonics Range, Hz	Percentage of Trials
			Rabbit A		Rabbit B	Rabbit C
			Main	Suppl.
Broadband	400–800	800–16,000	24.0	28.7	27.8	28.2
Low Harm	400–800	800–5,000	23.6	5.7	27.8	28.4
High Harm	400–800	6,400–16,000	23.4	30.1	28.1	27.1
Pure tone	400–800	Fundamental only	24.7	30.4	8.4	8.1
Control	400–800 (constant)	800–16,000	4.2	5.0	7.8	8.1
		Total trials	2,592	3,948	2,722	3,560

F0, fundamental frequency; Harm, harmonics; Suppl., supplementary experiment.

The order in which the experiments were performed differed in the three rabbits. Rabbit A performed experiments 1, 2, and 3 in that order with an F0 step cue when entering the target area (see methods). Rabbit B first performed the experiments in the order 1, 2, 3 with the F0 step cue and then repeated the three experiments in the same order without the step cue. Rabbit C performed experiments 1 and 2 with the step cue and then experiments 2, 3, and 1 without the step cue. In rabbits B and C, only results obtained without the F0 step cue are presented since they yielded much larger differences in performance between stimuli. The different orders in which the experiments were performed and the fact that two rabbits repeated some of the experiments are expected to attenuate any learning effect resulting from a fixed order.

Experiment 1: Effect of Harmonic Resolvability

Rationale.

In human listeners, pitch percepts can be produced by either HCTs containing low-order, resolved harmonics or HCTs consisting entirely of high-order, unresolved harmonics, with the former generally giving rise to a stronger pitch (26–28). However, some experimental animals appear to rely more on the temporal envelope cues resulting from the interaction between unresolved harmonics when discriminating HCTs differing in F0 (11, 15, 29, 59). The purpose of experiment 1 was to test the degree to which rabbits can use resolved versus unresolved harmonics when discriminating the F0 of HCTs with missing fundamentals by manipulating the harmonic composition of the stimuli. The F0 range (400–800 Hz) of the stimuli was chosen because it is contained within the reported range of rabbit vocalizations (60–62).

Stimuli and procedures.

Three types of HCTs differing in harmonic content were used in experiment 1 (Table 3). Figure 3A shows schematized power spectra of the three HCT stimuli for an F0 of 600 Hz (the center of the range). Figure 3B shows the corresponding model excitation patterns computed with a bank of linear gammatone filters with equivalent rectangular bandwidths (ERBs) matching the average ERBs of rabbit auditory nerve fiber tuning curves (55). The Broadband stimulus (the same as used for training in the behavioral task) contained all harmonics between 800 and 16,000 Hz (excluding these limits). The excitation pattern shows that this stimulus contained both resolved (red circles in Fig. 3B) and unresolved harmonics. The Low Harmonics stimulus contained harmonics between 800 and 5,000 Hz. For F0 = 600 Hz, this band contained harmonics 2–8, which were all resolved in the model excitation pattern. In contrast, the High Harmonics stimulus contained harmonics between 6,400 and 16,000 Hz, which were all unresolved according to the excitation pattern model. A harmonic was considered to be resolved when the valleys in the excitation pattern on both sides of the harmonic peak were at least 2 dB deep (63).

Figure 3.

A: schematized magnitude spectra of the harmonic complex tone (HCT) stimuli from experiment 1 with equal-amplitude harmonics and varying harmonic composition for fundamental frequency (F0) = 600 Hz. The gray area represents the spectrum of the noise used to mask cochlear distortion products at F0. B: model rabbit excitation patterns for the stimuli in A. The excitation patterns were generated with gammatone filters with equivalent rectangular bandwidths (ERBs) matching the average ERBs of rabbit auditory nerve fibers (11). Red circles represent resolved harmonics, assuming that a harmonic is resolved if its amplitude exceeds the flanking valleys by at least 2 dB. The dashed gray line, left, shows the excitation pattern for a pure tone at the 600-Hz missing F0.

In addition to these three HCT stimuli, we also presented a pure tone at the missing fundamental of the HCT stimuli, i.e., in the range 400–800 Hz. The pure tone was introduced to test whether rabbits would generalize the F0 discrimination learned with HCT stimuli to a stimulus with a very different timbre. It also served to assess the possibility that the rabbits could perform the F0 discrimination task by tracking the frequency of an individual harmonic.

To verify that rabbits utilize the F0 gradient to perform the task, we introduced control trials in which a Broadband stimulus was presented with a fixed F0 selected at random on each trial over the range 400–800 Hz. By comparing chance performance on control trials to performance on trials with an F0 gradient, we can assess whether the rabbits made use of the gradient to perform the task.

Each animal performed a total of 2,600–3,600 trials over 15 or 16 sessions (Table 3). For rabbit A, all four stimuli, excluding control trials, had the same probability of ∼24%. The probability of control trials was set low at 4.2% to maintain motivation by keeping the overall success rate high. Since performance with pure tones was found to be poor in rabbit A, their probability was reduced to ∼8% for the other two rabbits, again with the goal of maintaining motivation. As a result, the probability of each HCT was raised to 28%, and the probability of control trials was also increased to 8%. The effect of altering stimulus probabilities was addressed in a supplementary experiment performed in rabbit A only. Results of this supplementary experiment are presented after those of the main experiment.

Results.

Figure 4, A–C, show the percentage of trials in which rabbits A, B, and C, respectively, successfully reached the target for each stimulus condition. (The light blue bars in Fig. 4A show performance for the supplementary experiment and are discussed below.) Performance ranged between 40% success for control trials in rabbits B and C to ∼80% success for the Broadband stimulus in all three rabbits. Although the chance performance on control trials may seem high, it results from our choice of keeping overall performance high so as to preserve the rabbits’ motivation to move within the testing booth. Performance tended to be higher in rabbit A than in the other two rabbits, especially on control trials. Rabbit A had an additional cue for performing the task in the form of a 1/3-octave F0 step when entering the target zone, and this cue was available on control trials as well as on gradient trials. This step cue was not available to the other two rabbits. Except for this difference, the pattern of performance across stimuli was similar in all three rabbits. Importantly, performance was better for all three HCT stimuli than for control trials, indicating that the rabbits were able to utilize information in the F0 gradient for finding the target. In this sense, the rabbits were able to discriminate the F0 of missing-fundamental stimuli. Among the HCT stimuli, performance was better for the Broadband and Low Harmonics stimuli, which likely contained resolved harmonics, compared with the High Harmonics stimulus, which consisted entirely of unresolved harmonics. Performance for pure tones was generally poorer than for HCTs and did not exceed chance performance (control trials) in rabbits A and B.

Figure 4.

A–C: % of successful trials for each stimulus type in experiment 1 for rabbits A, B, and C, respectively. Error bars represent 95% confidence intervals for binomial variables. A also shows success rates for supplementary experiment 1, which was performed in rabbit A only. Asterisks in A show the levels of significance for comparisons of main vs. supplementary experiment success rates using chi-squared tests. D: combined success rates across the 3 rabbits in experiment 1. Bars show the generalized linear model (GLM) coefficients (stimulus effects) converted into success rates by inverting the link function. Error bars represent 95% confidence intervals. Asterisks show the GLM-determined level of significance of comparisons of success rates between select pairs of stimuli: *P < 0.05, **P < 0.01, ***P < 0.001.

A GLM on the binomial variable success rate with stimulus type as a fixed factor and animal as a random factor was used to quantitatively analyze the results. We first compared the goodness of fit for the full model including both stimulus and animal factors to that for a reduced model with only animal as a factor. A likelihood ratio test showed a highly significant improvement in goodness of fit (P < 0.0001; see Table 4) for the full model, justifying the inclusion of stimulus as a factor in the model. A second likelihood ratio test showed that the full model fit the data significantly better than a reduced model containing only stimulus as a factor (P = 0.0006; Table 4), justifying the inclusion of animal as a factor in the model.

Table 4.

Statistical tests for success rate

Test	Statistic	Experiment 1	Experiment 2	Experiment 3
Likelihood ratio, full model vs. animal only	χ2	614	384	526
	df	4	3	6
	P value	<0.0001	<0.0001	<0.0001
Likelihood ratio, full model vs. stimulus only	χ2	11.7	303	71.3
	df	1	1	1
	P value	0.0006	<0.0001	<0.0001
GLM, % variance accounted	R 2	97.6	92.1	89.1
GLM ANOVA, stimulus effect	F	143.1	125	85.0
	df1, df2	4, 10	3, 8	6, 14
	P value	<0.0001	<0.0001	<0.0001

GLM, generalized linear model.

Figure 4D shows the average performance across the three rabbits (as determined from the best-fitting GLM coefficients) for each stimulus condition. An analysis of variance (ANOVA) was used to test the null hypothesis that all model coefficients representing the fixed effect (stimulus type) are equal. The ANOVA revealed a highly significant effect of stimulus type (P < 0.0001; Table 4), and the GLM accounted for 97.6% of the variance in the data. Post hoc paired comparisons with Bonferroni corrections showed that performance for each of the three HCT stimuli was significantly better than performance on control trials (all P < 0.0001), confirming that rabbits utilize information in the F0 gradient to perform the task. All paired comparisons between HCTs also yielded significant differences (P < 0.0001 for High Harmonics vs. Broadband or Low Harmonics, P = 0.029 for Broadband vs, Low Harmonics). Importantly, performance was significantly better for Low Harmonics than for High Harmonics stimuli. These results suggest that rabbits can discriminate F0 using either resolved or unresolved harmonics but perform better when the stimulus contains resolved harmonics, at least for F0s in the 400–800 Hz range. This pattern of performance is similar to the human pattern but contrasts with reports from studies in other experimental animals.

Performance for pure tones was significantly poorer than performance for any HCT stimulus (P < 0.0001 compared with Broadband or Low Harmonics, P = 0.038 compared with High Harmonics) but still significantly better than chance (P = 0.0057, as determined from control trials). One possible explanation for this result is that the pure tone differed so much in timbre from the HCT stimuli that rabbits had trouble extending to pure tones the frequency discrimination task learned with HCTs. This explanation may also apply to the High Harmonics stimuli, which differed sharply in timbre from the Broadband HCT used for training because of the absence of low harmonics. To address this possibility, we modified the stimulus probabilities in a supplementary experiment to give rabbit A additional experience with the stimuli giving the poorest performance in the main experiment 1.

Supplementary experiment.

A supplementary experiment was performed with rabbit A to address the possibility that the poor performance with pure tones and High Harmonics stimuli in the main experiment was due to the strong differences in timbre relative to the Broadband stimulus along with the more limited experience of the rabbit with these stimuli. The stimulus set was the same as in the main experiment 1, but the stimulus probabilities were altered. Specifically, probabilities of the pure tone and High Harmonics stimuli were increased to 28%, whereas the probability of the Low Harmonics stimulus (which gave good performance in the main experiment) was decreased to 5% (Table 2). Rabbit A completed 24 sessions in this supplementary experiment. Only data from the last 16 sessions (comprising 2,611 trials) are reported, to ensure that the data represent performance after the rabbit had time to adapt to the change in stimulus probabilities.

Figure 4A compares rabbit A’s success rates for each stimulus in the main and supplementary experiments. There was an improvement in performance for the pure-tone and High Harmonics stimuli in the supplementary experiment, consistent with the additional experience with these stimuli resulting from increased probabilities. However, there was also a small increase in performance for the Low Harmonics stimulus despite a major drop in probability, suggesting that there may have been an overall learning effect as well. Performance was unchanged for the Broadband stimulus and control trials.

A GLM with fixed factors stimulus type and experiment (main vs. supplementary) was fit to rabbit A’s success rate data. This analysis identified significant main effects of both experiment [F(1,4) = 28.7, P = 0.0058] and stimulus type [F(4,4) = 51.0, p = 0.0011]. Post hoc paired comparisons with Bonferroni corrections showed that, across both experiments, performance for pure tones was significantly lower than performance for Broadband and Low Harmonics stimuli (P = 0.021 or lower) but not statistically distinguishable from performance for High Harmonics stimuli (P > 0.05). The latter was significantly lower than performance for Broadband and Low Harmonics stimuli (P = 0.029 or lower). Performances for Broadband and Low Harmonics stimuli did not statistically differ (P = 0.54).

Because the structure of the data did not allow testing for interactions between experiment and stimulus, we used two-sample binomial tests with Bonferroni corrections to compare performance for each stimulus in the two parts of the experiment. Success rates for the pure tone [χ²(1) = 24.2, P < 0.0001] and the High Harmonics stimulus [χ²(1) = 9.89, P = 0.008] were significantly increased in the supplementary experiment compared with the main experiment, but there was no significant change in the other stimulus conditions (P > 0.05). As a result, performance for the pure tone in the supplementary experiment no longer differed statistically from performance for the Low Harmonics stimulus [Tukey honestly significant difference (HSD) test for multiple proportions: q = 3.75, P > 0.05], although it was still lower than performance for the Broadband stimuli (Tukey HSD test, q = 9.50, P < 0.01). Importantly, performance for the High Harmonics stimulus in the supplementary experiment remained significantly lower than performance for Low Harmonics (Tukey HSD test, q = 4.00, P < 0.05).

In summary, although providing additional experience with the pure-tone and High Harmonics stimuli by increasing their probabilities in the supplementary experiment improved performance for these two stimuli, the overall pattern of results in rabbit A was not greatly altered between the two parts of the experiment and was also consistent with the pattern in the main experiment across the three animals tested: Success rates were higher for HCTs containing low-frequency, presumably resolved harmonics and lower for HCTs consisting entirely of high-frequency, unresolved harmonics. Because altering stimulus probabilities had only modest effects in rabbit A, the supplementary experiment was not repeated in the other two rabbits.

Experiment 2: Effect of F0 Range

Rationale.

Experiment 1 showed that rabbits can discriminate the F0 of missing-fundamental stimuli in the F0 range 400–800 Hz. Although data on rabbit vocalizations are scant, F0 values in the range 400–1,200 Hz have been reported in the literature (60–62). If the ability to discriminate missing-fundamental stimuli is linked to the perception of conspecific vocalizations, this ability should be reduced for F0s outside of the range of vocalizations. Another reason why F0 discrimination may depend on F0 is that relative cochlear frequency selectivity [as measured by the Q factor = characteristic frequency (CF)/bandwidth] is not constant across the tonotopic axis but rather tends to increase with characteristic frequency (55, 64–66). As a result, the number of resolved harmonics increases with F0. If good performance in F0 discrimination is dependent on the presence of resolved harmonics, performance should also improve with increasing F0. On the other hand, if rabbits rely primarily on temporal envelope cues to discriminate F0, performance is expected to be poorer at higher F0s because the envelope modulation depth is reduced at higher F0s because of room acoustics. Experiment 2 tested these hypotheses by comparing F0 discrimination for three octave ranges extending both below and above the 400–800 Hz range used in experiment 1.

Stimuli and procedures.

The stimulus set in experiment 2 included three HCTs differing in F0 range but in which the equal-amplitude harmonics occupied the same wide frequency band, 800–16,000 Hz (Table 5). Figure 5A shows schematic power spectra for the stimuli at the center of each F0 range, and Fig. 5B shows the corresponding model excitation patterns computed from filters with rabbit auditory nerve fiber ERBs. Stimuli in the mid-F0 range (400–800 Hz) were identical to the Broadband stimuli in experiment 1. The lower F0 range extended from 200 to 400 Hz and the higher range from 800 to 1,600 Hz. Both included F0s outside the reported range of rabbit vocalizations. Figure 5B shows that the number of resolved harmonics increases from 2 for the stimulus at the center of the lower F0 range (300 Hz) to 6 for a 600-Hz F0 and 7 for a 1,200-Hz F0 at the center of the higher F0 range. Thus, if F0 discrimination is dependent on resolved harmonics, performance should be better for the mid-F0 and higher F0 ranges than for the lower F0 range. On the other hand, because only the mid-F0 range is wholly contained within the reported range of rabbit vocalization, performance should be better for the mid-F0 range than for the lower and higher F0 ranges if F0 discrimination is linked to perception of conspecific vocalizations.

Table 5.

Stimulus characteristics for experiment 2

Stimulus Type	F0 Range, Hz	Harmonics Range, Hz	Percentage of Trials
			Rabbit A	Rabbit B	Rabbit C
200–400 Hz	200–400	800–16,000	30.6	30.2	29.8
400–800 Hz	400–800	800–16,000	31.4	30.4	30.1
800–1,600 Hz	800–1,600	800–16,000	30.4	29.7	30.7
Control	400–800 (constant)	800–16,000	7.7	9.7	9.5
		Total trials	3,808	3,329	4,173

F0, fundamental frequency.

Figure 5.

A: idealized power spectra of harmonic complex tone (HCT) stimuli from experiment 2 for the 3 fundamental frequencies (F0s) at the centers of each F0 range. B: model rabbit excitation patterns for the stimuli in A. The number of resolved harmonics (red circles) increases with F0.

Each rabbit performed 3,330–4,170 trials over 16–22 sessions in experiment 2 (Table 5). All three HCT stimuli had a probability of ∼30%. On control trials, which occurred with ∼10% probability, an HCT with a fixed F0 was selected at random from the 400–800 Hz range.

Results.

Figure 6, A–C, show the success rates for each stimulus in experiment 2 for rabbits A, B, and C, respectively. Figure 6D shows the average success rates across the three rabbits as determined by the best-fitting GLM. In all three rabbits, success rate for each F0 range was higher than the chance performance on control trials. In rabbits B and C, performance was best for the mid-F0 range, followed by the higher F0 range and then the lower F0 range. In rabbit A, which had the additional step cue when entering the target area, performance was higher overall and the differences between stimulus conditions were less pronounced than in the other two rabbits.

Figure 6.

A–C: success rates for each stimulus in experiment 2 for rabbits A, B, and C, respectively. D: combined experiment 2 success rates across the 3 rabbits. Same format as in Fig. 4. Asterisks show the GLM-determined level of significance of comparisons of success rates between select pairs of stimuli: ***P < 0.001.

A mixed-effect GLM for the binomial variable success rate was used for quantitative analysis. As in experiment 1, likelihood ratio tests comparing goodness of fit for the full, two-factor model with those for reduced models omitting one of the two factors justified inclusion of both stimulus and animal terms into the model (Table 4). An ANOVA on the full model coefficients showed a highly significant effect of stimulus condition (P < 0.0001; Table 4), with the model accounting for 92.1% of the variance in the data. Post hoc paired comparisons with Bonferroni corrections confirmed that the performance for each F0 range was higher than the performance on control trials (all P < 0.0001). Performance in the mid-F0 range was higher than performance in both the lower F0 (P = 0.0001) and higher F0 (P = 0.0007) ranges. However, performance did not statistically differ between the lower F0 and higher F0 ranges (P = 0.569).

In summary, all three rabbits were able to achieve good performance for all three F0 ranges, showing that they can discriminate the F0 of HCTs over a range of at least 3 octaves. That the performance was significantly better for the mid-F0 range than for the lower and higher F0 ranges is consistent with the idea that F0 discrimination is related to the perception of conspecific vocalizations, since only the mid-F0 range was wholly included within the reported range of rabbit vocalizations. However, despite the large numbers of trials performed in experiment 2, the rabbits (especially rabbit A) had more experience with stimuli in the mid-F0 range than those in the outer ranges because the mid-F0 range stimulus was the same as the Broadband stimuli of experiment 1 as well as that used for initial training, so the differences in performance may just reflect the amount of experience with each F0 range. Moreover, an effect of resolvability cannot be ruled out, since in rabbits B and C performance was better for the higher-F0 stimuli (which contained more resolved harmonics) than for the lower-F0 stimuli, although the difference did not reach significance. Experiment 3 tested the interaction between F0 range and resolvability directly by independently varying both F0 range and the frequency range of harmonics.

Experiment 3: Interaction between F0 Range and Harmonic Resolvability

Rationale.

Because relative cochlear frequency resolution (Q factor) increases from apex to base, the number of resolved harmonics in a broadband HCT is expected to increase with F0, especially for lower F0s (Fig. 5B). This observation leads to the prediction that F0 discrimination performance for HCTs containing low-order harmonics should improve with increasing F0 if harmonic resolvability contributes to F0 discrimination. On the other hand, F0 discrimination performance for HCTs consisting of high-order, unresolved harmonics should degrade for higher F0s because, as shown in Fig. 2B, envelope modulation depth decreases with increasing F0 because of the low-pass filtering effect of room acoustics. Experiment 3 tested these predictions by measuring F0 discrimination for HCTs in which both the F0 range and the frequency range of harmonics were varied independently. Only two F0 ranges (200–400 Hz and 400–800 Hz) were tested, both to keep the number of stimulus conditions manageable and because the effect of F0 on resolvability was expected to be stronger for lower F0s (Fig. 5B).

Stimuli and procedures.

The stimulus set for experiment 3 consisted of six HCTs representing every combination of two F0 ranges (200–400 Hz and 400–800 Hz) and three ranges of harmonics: Broadband, Low Harmonics, and High Harmonics (Table 6). For the 400–800 Hz F0 range, the stimuli were the same as in experiment 1. For the 200–400 Hz F0 range, the lower frequency cutoffs for all three stimuli and the upper cutoff for Low Harmonics stimuli were all lowered by 1 octave relative to the cutoffs for the 400–800 Hz F0 so that the cutoff harmonic ranks would match for both F0 ranges. However, the upper cutoff of the Broadband and High Harmonics stimuli was kept at 16,000 Hz for both F0 ranges.

Table 6.

Stimulus characteristics for experiment 3

Stimulus Type	F0 Range, Hz	Harmonics Range, Hz	Percentage of Trials
			Rabbit A	Rabbit B	Rabbit C
Broadband 200–400 Hz	200–400	400–16,000	14.3	14.8	14.9
Broadband 400–800 Hz	400–800	800–16,000	16.8	17.3	17.8
Low Harm 200–400 Hz	200–400	400–2,500	15.4	14.5	14.8
Low Harm 400–800 Hz	400–800	800–5,000	15.2	15.4	14.8
High Harm 200–400 Hz	200–400	3,200–16,000	15.2	15.5	14.8
High Harm 400–800 Hz	400–800	6,400–16,000	15.3	14.6	14.7
Control	200–800 (constant)	800–16,000	7.9	7.9	8.3
		Total trials	4,833	5,114	4,671

F0, fundamental frequency; Harm, harmonics.

Each rabbit performed 4,670–5,110 trials over 20–30 sessions with these stimuli. Each of the six stimuli was presented with ∼15% probability (Table 6). On control trials, which had 8% probability, a broadband HCT with a fixed F0 was selected at random over the range 200–800 Hz. Because the rabbits had already been presented with similar stimuli in experiments 1 and 2, experiment 3 started immediately after experiment 2 with no intervening training sessions.

Results.

Figure 7 shows the success rates for each animal and each stimulus condition. Performance for both Broadband stimuli was the highest and was similar in both F0 ranges. For Low Harmonics and High Harmonics stimuli, there was an interaction between F0 and frequency content. Specifically, for Low Harmonics stimuli, performance was better for 400–800 Hz F0 than for 200–400 Hz F0 in all three rabbits, consistent with the notion that the 400–800 Hz F0 stimuli contain more resolved harmonics. In contrast, for the High Harmonics stimuli performance was better for 200–400 Hz F0 than for 400–800 Hz F0, consistent with the idea that the decrease in envelope modulation depth with increasing F0 impairs the rabbits’ ability to use temporal envelope cues at higher F0s.

Figure 7.

Average success rate for each rabbit and each stimulus type in experiment 3. Colored lines indicate individual animals, and black lines show the generalized linear model (GLM)-determined combined performance across the 3 rabbits. Solid lines show performance for the 400–800 Hz fundamental frequency (F0) range and dashed lines for the 200–400 Hz range. Error bars represent 95% confidence intervals for binomial variables.

As in experiments 1 and 2, the success rates from experiment 3 were analyzed with a mixed-effect GLM with factors stimulus and animal. Likelihood ratio tests comparing goodness of fit for the full model versus reduced models including only one term justified the inclusion of both terms into the model (Table 4). An ANOVA on the full model coefficients showed a highly significant effect of stimulus type (P < 0.0001; Table 4), with the model accounting for 89.1% of the variance in the data. Performance for each of the six stimuli was significantly better than performance on control trials (post hoc comparisons with Bonferroni corrections: P = 0.0128 for High Harmonics with 400–800 Hz F0, P < 0.0001 for all other stimuli).

In rabbits A and C, performance for the Broadband 200–400 Hz stimulus was higher than performance for the High Harmonics stimulus in the same F0 range. This result seems inconsistent with the idea that performance in the 200–400 Hz F0 range is driven primarily by unresolved harmonics. There may be a synergistic interaction between the weak low-frequency cues to resolved harmonics and the envelope periodicity cues available at high frequencies so that performance is higher when both cues are available in the Broadband stimulus. Alternatively, the good performance with the Broadband 200–400 Hz F0 stimulus may be due to its similarity of timbre with the Broadband 400–800 Hz stimulus used for initial training.

Results were further analyzed using three orthogonal contrasts: an F0 contrast, a harmonics range contrast, and a contrast testing for interactions between F0 and harmonics range. The F0 contrast compared performance between the three stimuli with 400–800 Hz F0 and the three stimuli with 200–400 Hz F0. The harmonics range contrast compared performance for the two Low Harmonics stimuli with performance for the two High Harmonics stimuli. The interaction contrast compared performance for the Low Harmonics 400–800 Hz F0 and High Harmonics 200–400 Hz F0 stimuli against performance for the Low Harmonics 200–400 Hz F0 and High Harmonics 400–800 Hz F0 stimuli. All three contrasts were highly significant [F0 contrast: F(1,14) =29.1, P = 0.0009; Harmonics Range contrast: F(1,14) = 91.0, P < 0.0001; interaction contrast: F(1,14) =94.6, P < 0.0001; all P values Bonferroni corrected].

The most important result is the presence of a significant interaction between F0 range and harmonics range, which is consistent with the hypothesis that resolved harmonics strongly contribute to F0 discrimination in rabbits and that the smaller number of resolved harmonics in the 200–400 Hz F0 range compared with the 400–800 Hz range (because of the frequency dependence of cochlear Q factors) results in poorer discrimination performance for Low Harmonics stimuli in the 200–400 Hz F0 range. The better performance for High Harmonics stimuli in the 200–400 Hz F0 range compared with the 400–800 Hz range likely results from the lower envelope modulation depth of the stimuli in the 400–800 Hz range (Fig. 2B). The overall effect of F0 identified by the contrast test occurred because the performance advantage of the 400–800 Hz F0 over the 200–400 Hz F0 with Low Harmonics is larger than the performance decrement from the 200–400 Hz F0 to the 400–800 Hz F0 with High Harmonics.

Stability of Success Rate across Experiments

Because similar HCT stimuli were used across experiments, it is of interest to test whether the success rates were stable over the long duration of the series of experiments (Table 1). Our analysis focused on the Broadband 400–800 Hz F0 stimulus, which was used for initial training and was tested in all three experiments. Figure 8 compares the success rates for this stimulus across experiments for each rabbit. Performance was high (>80%) and highly consistent across experiments for rabbits A and C. Performance for rabbit B was lower overall and more variable across experiments.

Figure 8.

Success rate in each of the 3 experiments for the Broadband stimulus with 400–800 Hz fundamental frequency (F0). Error bars show 95% confidence intervals for binomial variables.

These data were analyzed by a separate chi-square test for differences in proportions in each rabbit. There was no significant effect of experiment on success rate for rabbits A and C (A: χ² = 0.870, df = 2, P = 0.647; C: χ² = 0.327, P = 0.849), but the differences in success rates across experiments were significant in rabbit B (χ² = 25.37, P < 0.0001). A post hoc Marascuilo test for pairwise comparisons of multiple proportions in rabbit B showed that success rate was much higher in experiment 1 than in experiment 2 (P < 0.0001) whereas the success rate differences between experiments 1 and 3 and between experiments 2 and 3 barely reached statistical significance (P = 0.038 for both).

We have no explanation for the difference in performance across experiments in rabbit B. Learning effects are unlikely since the experiments were performed in the order 1, 2, 3, while performance was worst in experiment 2. An effect of task difficulty is also unlikely since experiment 2 had the smallest number of stimuli and therefore should have been the easiest. The lower performance in experiment 2 for rabbit B was not limited to one stimulus but was also observed for the Broadband 200–400 Hz F0 stimulus used in both experiments 2 and 3 (not shown). We speculate that rabbit B experienced long-term fluctuations in its level of motivation that were reflected in performance.

Overall, performance was highly stable over the course of the experiments in two rabbits. Although the third rabbit showed fluctuations in performance across experiments, these effects were modest relative to the range of performance across stimuli in each experiment.

Additional Measure of Performance: Time to Success

Although we have focused so far on success rate as a measure of F0 discrimination performance, our behavioral paradigm also records the rabbit’s trajectory within the testing chamber over the course of each trial, from which additional measures of performance were derived. Such measures may provide information about a rabbit’s ability to discriminate F0 when success rate is uninformative, e.g., because it is near chance or near ceiling. Here, we report results for the time to success on successful trials, which was the most informative of several metrics analyzed. Average time to success may be interpreted as being inversely related to task difficulty.

Like success rate, the time to success data from each experiment were analyzed by a mixed-effect GLM with stimulus as a fixed factor and animal as a random factor (see methods). ANOVAs on the full model coefficients showed highly significant effects of stimulus for all three experiments (all P < 0.0001; Table 7). However, the percentages of variance accounted for by the GLMs were much smaller for time to success (0.75–3.7%) than for success rate (89–98%), reflecting the large across-trial variability in time to success (Table 7). Time to success is measured for each trial, whereas success rate is an average across all trials for a given stimulus. Across-trial variability in time to success is unsurprising since the rabbit’s initial distance and head orientation relative to the target differ for every trial and rabbits sometimes passed near the target without reaching it, forcing them to turn back.

Table 7.

Statistical tests for time to success

Test	Statistic	Experiment 1	Experiment 2	Experiment 3
Likelihood ratio, full model vs. animal only	χ2	28.8	10.7	31.0
	df	4	3	6
	P value	<0.0001	0.0137	<0.0001
Likelihood ratio, full model vs. stimulus only	χ2	8.1	127	217
	df	1	1	1
	P value	0.0044	<0.0001	<0.0001
GLM, % variance accounted	R 2	0.75	3.7	2.0
GLM ANOVA, stimulus effect	F	6.85	33.1	<0.0001
	df1, df2	4, 5,736	3, 7,470	7, 9,513
	P value	<0.0001	<0.0001	<0.0001
Correlation with success rate	Pearson corr.	−0.91	−0.74	−0.63
	P value	0.033	0.256	0.131

GLM, generalized linear model.

Despite these limitations, there was usually a monotonic or nearly monotonic relationship across the stimulus set between the mean time to success across all trials and animals and the corresponding average success rate (Fig. 9, A–C). For the most part, the higher the success rate, the lower the mean time to success. The monotonic relation was tight in experiments 1 and 2 (Fig. 9, A and B) but more scattered (and not statistically significant; Table 7) in experiment 3 (Fig. 9C). In experiments 1 and 2, the success rate for control trials was lower than expected from the general trend, or, equivalently, rabbits found the target faster than expected from the trend line on those control trials in which they found the target by chance. In addition, in experiment 3, rabbits took the longest to find the target for the High Harmonics 200–400 Hz F0 stimulus, even though the success rate for this stimulus was higher than those for two other stimuli. We have no explanation for this deviation from a monotonic relationship.

Figure 9.

A–C: relationship between the mean success rate and the mean time to success across all trials and animals for each of the stimuli of experiments 1–3, respectively. Harm, harmonics.

In summary, time to success was clearly dependent on stimulus type, suggesting that, even when rabbits successfully reach the target, the difficulty with which they do so depends on the stimulus. Time to success tended to be negatively correlated with success rate but with much greater across-trial variability, and therefore less sensitivity to the stimulus. This metric also provided evidence of a qualitatively different behavior during control trials, unsurprisingly given the lack of an F0 gradient in this condition.

Were Rabbits Attending to the Stimulus on Failed Trials?

Sometimes, rabbits failed to reach the target on a given trial, even if the overall success rate for the presented stimulus was high. Such failures could reflect either a lack of attention to the stimulus during the trial or errors in tracking the F0 gradient, e.g., by heading in the wrong direction from the target. To distinguish between these two possibilities, we compared the mean distance from the rabbit to the target in the first half of each failed trial to the mean distance in the second half of the trial. If rabbits attend to the F0 gradient, they should be closer to the target on average in the second half of the trial than in the first half. On the other hand, if rabbits are not attending to the stimulus or if there is no F0 gradient (on control trials), the mean distance to target should be similar, on average, for both halves of each trial. This analysis was only performed for failed trials because the mean distance to target will necessarily be shorter in the second half of the trial when the rabbit successfully reaches the target. Indeed, the mean distance to target dropped by 35–40% in the second half of successful trials relative to the first half when averaged across all stimuli and all rabbits.

Figure 10 shows the average distance to target in the second half of failed trials of experiment 1 plotted against the average distance in the first half. The distances were averaged over the 22.5-s half-trial duration for each trial and then averaged over all failed trials for each animal and stimulus type. For all three rabbits, data points from stimuli with an F0 gradient (except pure tones in rabbit B) lay below the diagonal line of equality, meaning that the average distance to target was shorter in the second half of the trial, as predicted if the rabbits were tracking the F0 gradient. In contrast, for control trials, in which there was no F0 gradient, the mean distance to target was similar for both halves of the trial, suggesting that the rabbits were moving at random in the sound chamber. The mean distance to target in both halves of the trial was also larger for control trials than for trials with a gradient. The one exception to this rule is the data point for pure tones in rabbit B, which lies on the equality line, suggesting that rabbit B was either not attending to or unable to use the F0 gradient for pure tone stimuli.

To minimize the possible effects of irrelevant factors such as animal or across-session differences in level of motivation, we computed the difference in mean distance to target between the second and first half of each failed trial. These difference data were analyzed by a linear, mixed-effect model with F0 gradient (with or without) as fixed factor and animal as random factor. The “without gradient” class consisted of control trials, and the “with gradient” class included all other stimulus conditions, including pure tones. The model identified a highly significant effect of F0 gradient (P < 0.0001; see Table 8). For conditions with an F0 gradient, the mean distance to target was 5.8 cm shorter on average in the second half of failed trials than in the first half, and this difference was highly significant by a post hoc t test (P < 0.0001; Table 8). In contract, for control trials the average distance difference was only −0.71 cm, which was not significantly different from zero (P = 0.474; Table 8). Overall, these results support the hypothesis that the rabbits were attending to the F0 gradient when it was available during failed trials of experiment 1, whereas they made no progress in approaching the target over the course of a trial when there was no F0 gradient.

Table 8.

Comparison of mean distance to target in the two halves of failed trials

Test	Statistic	Experiment 1	Experiment 2	Experiment 3
ANOVA, % variance accounted	R 2	0.57	2.26	1.52
ANOVA, F0 gradient effect	F	15.85	20.91	11.45
	df1, df2	1, 2,784	1, 3,427	1, 3,427
	P value	<0.0001	<0.0001	0.0007
Mean distance difference = 0 for conditions with F0 gradient	Mean, cm	−5.83	−6.78	−6.38
	t	−13.04	−3.76	−4.05
	P value	<0.0001	0.0002	<0.0001
Mean distance difference = 0 for conditions without F0 gradient	Mean, cm	−0.84	−2.23	−2.96
	t	−0.72	−1.13	−1.64
	P value	0.474	0.261	0.100

F0, fundamental frequency.

This analysis was repeated for the data from experiments 2 and 3 and yielded similar results. For both experiments, there was a significant effect of F0 gradient on the distance difference between the two halves of failed trials (Table 8; F tests). Moreover, the mean distance difference was significantly negative for conditions with an F0 gradient, whereas it did not significantly differ from zero for control trials (Table 8; t tests). Thus there is strong evidence that, in all three experiments, the rabbits were attending to the F0 gradient when it was available even when they failed to reach the target.

DISCUSSION

We tested F0 discrimination for harmonic complex tones with missing fundamentals using a novel behavioral paradigm inspired by the observation that animals utilize information in sensory gradients when foraging for food. Three of the six rabbits tested successfully learned the task and were able to discriminate F0 in the sense that they harnessed the F0 gradient to achieve better-than-chance performance in finding a hidden target. Rabbits were able to discriminate F0s over a wide range (200–1,600 Hz) and for both stimuli presumed to contain harmonics resolved by the cochlea and stimuli consisting entirely of unresolved harmonics. There was also an interaction between F0 range and harmonic resolvability in that resolved harmonics were the stronger cue for F0 discrimination at higher F0s but not lower F0s (experiment 3), consistent with the improvement in relative cochlear frequency selectivity (Q factor) with increasing frequency.

Acoustic Cues Used for F0 Discrimination

Although rabbits were able to discriminate F0 of harmonic complexes, this does not necessarily mean that they did so by forming a percept associated with the missing F0, since several other stimulus properties covaried with F0. Here, we discuss the cues used by rabbits to perform this discrimination.

In behavioral experiments with missing-fundamental stimuli, it is important to minimize the influence of combination tones created by nonlinear mechanical interactions in the cochlea. In the present experiments, low-pass noise was added to all complex tone stimuli to mask cochlear distortion products (DPs) at F0. Depending on F0, the stimulus harmonics were 6–15 dB above the masking noise level in the ERB centered at the missing F0 (Table 2). Only a few studies in humans have directly measured the amplitudes of the perceived DPs produced by HCTs containing many harmonics (67–70). Using the beat cancellation method for complex tones with an F0 of 100 Hz and containing no harmonics below the 15th, Pressnitzer and Patterson (70) found that the DP at F0 could be as high as 15 dB below the primaries, although its amplitude was highly dependent on the number of components and the phase relationships among the harmonics. Similarly, using HCTs containing no frequency components below 1 kHz, Norman-Haignere and McDermott (67) found that DP amplitude decreased with increasing DP frequency regardless of its harmonic rank. The largest DP at F0 for F0 = 100 Hz was ∼20 dB below the primaries for HCTs with harmonics in cosine phase and ∼10 dB lower than cosine phase for harmonics in Schroeder phase. Using complex tones with an F0 of 1,000 Hz and containing no components below 6,000 Hz (similar to our “High Harmonics” stimuli of experiments 1 and 3), Oxenham et al. (69) found that the level of the largest cubic distortion product (at 5,000 Hz) was at least 30 dB below the primaries, but they did not measure the amplitude of the DP at F0. Based on these results, it is likely that our noise was effective in masking cochlear DPs if we assume that combination tones behave similarly in rabbits as in humans. Unfortunately, no data are available on perceptual DPs in rabbits. Even if the noise in our experiments was not fully effective in masking cochlear DPs in some conditions, the poor discrimination performance with pure tones in experiment 1 makes it unlikely that rabbits relied primarily on the cochlear DP at F0 to perform the discrimination.

For each stimulus condition, the stimulus components were always confined to a fixed frequency range as F0 varied, making it unlikely that rabbits used the spectral center of gravity or sharpness of timbre to discriminate F0. In principle, rabbits could track the frequency of a single harmonic covarying with F0, most likely either the lowest or the highest harmonic since they stand out perceptually. Such a strategy would not be effective in most stimulus conditions because the relationship between F0 and the frequency of the lowest or highest harmonic was nonmonotonic and therefore the harmonic frequency provided an ambiguous cue to F0. For example, as F0 varied from 400 to 800 Hz, the highest harmonic of the Broadband and High Harmonics stimuli of experiment 1 was in turn the 39th, the 38th, … down to the 19th as each of these harmonics successively reached the upper frequency limit of 16,000 Hz. Similarly, the lowest harmonic of the High Harmonics stimuli was successively the 17th, the 16th, down to the 9th as each of these harmonics in turn reached the 6,400-Hz lower frequency limit as F0 increased from 400 to 800 Hz. The only case when the lowest harmonic was monotonically related to F0 in experiment 1 was the 2nd harmonic of Broadband and Low Harmonics stimuli, which increased from 800 to 1,600 Hz as F0 varied from 400 to 800 Hz. Although we cannot rule out that rabbits tracked the lowest harmonic to perform the F0 discrimination for these two stimuli, the poor performance with pure tones at the missing F0 in experiment 1 makes this strategy unlikely. Additionally, rabbits performed better with High Harmonics stimuli than with Low Harmonics stimuli for F0 = 200–400 Hz in experiment 3, even though the strategy of tracking the lowest harmonic would be ineffective for High Harmonics stimuli because the lowest harmonic was not monotonically related to F0. Thus, the rabbits likely relied on the overall spectral pattern of harmonics (and covarying cues such as envelope periodicity) rather than tracking a single salient harmonic to perform the F0 discrimination.

A remaining question is whether the rabbit’s ability to discriminate F0 implies the formation of a pitch percept associated with the F0. McPherson and McDermott (71) have shown that “F0” discrimination by human listeners is just as accurate for inharmonic tone complexes in which the frequency of each harmonic is randomly jittered around its harmonic value as for harmonic complex tones. For inharmonic tones, “F0” refers to the average spacing between adjacent frequency components. Since inharmonic tones are aperiodic and do not produce a clear pitch, the results of McPherson and McDermott (71) imply that the formation of a pitch percept associated with F0 is not necessary for accurate F0 discrimination. McPherson and McDermott (71, 72) argue for the existence of at least two pitch mechanisms, one based on the spectral pattern of resolved components that is robust to inharmonicity and one involving the formation of an F0-based pitch. Which of the two mechanisms dominates depends on the nature of the pitch task (e.g., musical vs. nonmusical) and its memory demands. Since our F0 tracking task did not involve judgments of musical intervals and had low memory demands because each harmonic (except possibly at the spectrum edges) was presented continuously, the rabbits may have used the spectral pattern mechanism rather than the pitch-based mechanism to perform the F0 discrimination, at least when the stimuli contained resolved harmonics. For stimuli consisting entirely of unresolved harmonics, F0 discrimination was likely based on the envelope repetition rate (which is equal to F0) rather than on the spectral pattern. The possibility that F0 discrimination is based on a spectral pattern mechanism rather than a mechanism requiring the formation of a pitch percept at F0 is not unique to the present study and behavioral paradigm but is also relevant to other studies of F0 discrimination by animals.

Use of Resolved and Unresolved Harmonics for F0 Discrimination

A widely used objective behavioral test of whether a set of harmonics is resolved or not is the degree to which the F0 discrimination performance depends on the phase relationships among the harmonics (25, 26, 28). For tone complexes consisting of unresolved harmonics, F0 discrimination performance is better when all the harmonics are in sine or cosine phase, which yields a strong envelope modulation, compared with stimuli with harmonics in random or Schroeder phase, which have minimal envelope modulation. No such phase-dependent differences in performance are observed for resolved harmonics. This test for resolvability has been used not only with human subjects but also in behavioral studies of F0 discrimination by animals (9, 11, 13, 15, 29).

This objective criterion for resolved harmonics based on lack of phase sensitivity was not used in the present experiments because the room acoustics distorted the waveforms presented at the loudspeaker and attenuated the envelope modulations at F0, thereby blurring the distinction between HCTs with harmonics in cosine phase versus random phase (Fig. 2B). We instead used an indirect measure of harmonic resolvability based on an excitation pattern model with bandwidths matching those of auditory nerve fiber frequency tuning curves in rabbits (55). In other animal species, there is a fairly good match between auditory nerve fiber bandwidths and behavioral measures of frequency selectivity [guinea pig (73), chinchilla (74), cat (75), ferret (34)] despite complications related to whether the behavioral measures of frequency selectivity are based on forward or simultaneous masking. Using this excitation pattern model, we inferred that the number of resolved harmonics in our Broadband stimuli (not including the missing fundamental) increases from 2 for F0 = 300 Hz to 7 for F0 = 1,200 Hz (Fig. 5B). This increase in the number of resolved harmonics with F0 is due to the improvement in relative cochlear frequency selectivity (Q factor) with increasing characteristic frequency (CF) observed in many species (66). Specifically, in rabbits there is a steep increase in auditory nerve fiber Q10dB for CFs near 2–3 kHz (Fig. 4 in Ref. 55; see also Fig. 7F in Ref. 46), so that harmonic 5 becomes resolved once it exceeds 2,000 Hz, i.e., when F0 reaches 400–500 Hz. Consistent with this increase in the number of resolved harmonics with F0 in the model, F0 discrimination performance by our rabbits for the Low Harmonics stimuli of experiment 3 was better for F0s in the 400–800 Hz range than for F0s in the 200–400 Hz range (Fig. 7).

Although the number of resolved harmonics increases with F0, the temporal envelope periodicity cues tend to degrade with increasing F0 for both physical and perceptual reasons. As shown in Fig. 2B, the low-pass filtering effect of room acoustics on the envelope of sounds (57, 58) increasingly attenuates the periodic envelope modulations at F0 at higher F0s. In addition, the ability to detect envelope modulations tends to degrade for modulation frequencies above 50–100 Hz in humans and other species, including rabbits (42, 76, 77). In rabbits, modulation depths at detection threshold for sinusoidal modulations average −15 to −12 dB near 50 Hz and then increase to reach −10 to −6 dB at 256 Hz (42). Thus, the small modulation depths measured in the testing booth for F0s above 600 Hz (Fig. 2B) may not have been detectable, although the modulation depth metric shown in Fig. 2B underestimates the amount of modulation since it only takes into account the fundamental component of the envelope waveform, which is not sinusoidal. In two of the three rabbits (B and C) as well as in the combined results across animals, performance was significantly better than chance (control trials) for High Harmonics stimuli with F0s in the 400–800 Hz range, suggesting that rabbits were able to extract F0 information from the envelope despite the low modulation depths. Moreover, performance for High Harmonics stimuli was somewhat poorer in the 400–800 Hz F0 range than in the 200–400 Hz range, consistent with the degradation in envelope modulation depth.

In summary, the rabbits were able to use both the spectral pattern of resolved harmonics and periodicity cues available in the stimulus envelope to discriminate F0 of harmonic complexes. Performance with resolved harmonics was better for F0s in the 400–800 Hz range than in the 200–400 Hz range, consistent with the increase in the number of resolved harmonics with increasing F0 as inferred from the excitation pattern model based on auditory nerve fiber bandwidths. In contrast, although the rabbits still seemed to be able to use temporal envelope cues despite the low modulation depth of the acoustic stimuli with higher F0s, performance for stimuli consisting entirely of unresolved harmonics was poorer than performance with resolved harmonics for F0s in the 400–800 Hz range.

Comparison with Previous Studies of F0 Discrimination in Experimental Animals

Our finding that rabbits can use resolved harmonics for F0 discrimination and show better performance for stimuli containing resolved harmonics than for stimuli consisting entirely of unresolved harmonics at higher F0s is consistent with the pattern of performance in humans (25, 26, 28) and with results on F0 perception by marmosets (11) but contrasts with reports that chinchillas (13, 29, 30, 78) and ferrets (15) rely primarily on envelope periodicity cues to discriminate F0 of harmonic complexes. Because experiment 3 demonstrated an interaction between the F0 range of the stimuli and the relative effectiveness of resolved and unresolved harmonics for F0 discrimination, it is important to examine the F0s tested in these studies.

Our experiments used stimuli with dynamic F0s that contrast with the static F0 stimuli used in most behavioral studies of F0 discrimination. Although dynamic stimuli may be more ethologically realistic, they also raise the question of whether rabbits performed the task using a perceptual mechanism that relies on frequency modulation in the stimulus. Since F0 changes rapidly along the F0 gradient but does not change much in the orthogonal direction, rabbits could, in principle, use the rate of frequency changes to navigate toward the target without explicitly identifying the F0. Shackleton and Carlyon (28) compared the effects of harmonic resolvability and F0 range on pitch encoding accuracy measured in human subjects using three different tasks: one task required detecting a difference in mean F0 using a two-interval paradigm commonly used in psychophysical studies, another task required the detection of frequency modulation in a harmonic complex, and the third task required identifying the direction of frequency modulation. The pattern of performance was broadly similar for the three tasks, and, in particular, performance for all three tasks was better in conditions when the stimuli contained resolved harmonics than when they consisted entirely of unresolved harmonics. If these human results also apply to rabbits, we expect that the pattern of performance with dynamic F0 stimuli observed in the present study, and in particular the interaction between harmonic resolvability and F0 range, should also be observed with static F0 stimuli, justifying a comparison with behavioral studies that used static F0s.

Osmanski et al. (11) trained marmosets to detect one of two possible target HCTs within a background of repeating HCTs with harmonics in cosine phase (and with an F0 chosen in the range 150–900 Hz. One of the targets was a cosine-phase HCT with F0 an octave higher than the background (2F0). The other target was an HCT at F0 with harmonics in alternating phase (i.e., odd harmonics in sine phase and even harmonics in cosine phase). Because the alternating-phase HCT target has the same power spectrum as the background cosine-phase HCT at F0 but the same envelope repetition rate as the cosine-phase HCT target at 2F0, a “go” response to the alternating-phase HCT target suggests that the marmoset attends to the envelope repetition rate rather than the spectral pattern to perform the task, whereas failure to respond to the alternating-phase HCT suggests that the marmoset bases its decision on spectral cues. By varying both the F0 and the harmonic composition of the stimuli, Osmanski et al. (11) concluded that marmosets can use either spectral cues or envelope repetition rate to perform the task but use temporal envelope cues only when 1) the stimulus contains no harmonics below the 5th and 2) F0 is below ∼450 Hz. These results are consistent with our finding that rabbits, like marmosets, can use either spectral patterns or temporal envelope cues to discriminate F0 and perform better using temporal cues for the lower F0s. In both rabbits and marmosets, frequency resolution is not as fine as in humans. Based on behavioral measurements of auditory filter bandwidths by the notched-noise method (79, 80), Osmanski et al. (11) concluded that, for F0 = 150 Hz, only the first 4 or 5 harmonics are resolved in marmosets. Based on our excitation pattern model, the 5th harmonic becomes resolved in rabbits only for F0s above 400–500 Hz, whereas in humans at least the first 8 harmonics are resolved for F0s as low as 100 Hz (25). Thus, humans, rabbits, and marmosets are all able to use both resolved harmonics and temporal envelope cues for F0 discrimination, but the range of F0s over which they use spectral cues differs across species because of differences in peripheral frequency resolution.

Walker et al. (15) trained ferrets to discriminate two pairs of HCTs differing widely in F0 (150 vs. 450 Hz and 500 vs. 1,000 Hz) using a classification task requiring a forced choice between the lower F0 and the higher F0. The training stimuli contained many equal-amplitude harmonics in sine phase. Once they achieved good performance on the classification task for these standard “All Harmonics” stimuli, ferrets were presented with low probability “probe” HCTs that had the same F0s as the standards but differed either in having harmonics in random phase rather than in sine phase or in the frequency range of harmonics: “Low Harmonics” stimuli contained resolved harmonics, whereas “High Harmonics” stimuli consisted entirely of unresolved harmonics according to an excitation pattern model with filter bandwidths derived from ferret auditory nerve fiber data (34). The ferrets achieved good classification performance for stimuli that had strong envelope modulation at F0 (All Harmonics and High Harmonics stimuli in sine phase) but not for stimuli with weak envelope modulation (All Harmonics and High Harmonics stimuli in random phase and Low Harmonics stimuli in sine phase), suggesting that they were attending to the envelope repetition rate rather than the spectral pattern of harmonics to perform the classification. However, since both correct and incorrect responses to the probe stimuli were rewarded, this result does not prove that ferrets cannot use resolved harmonics to discriminate F0, as the authors recognize. Ferrets might learn to use spectral cues more efficiently if trained specifically with stimuli with strong spectral cues and weak temporal cues rather than with stimuli containing strong temporal cues.

Although Walker et al. (15) did not emphasize this point, their data (Fig. 5A in Ref. 15) indicate an interaction between F0 range and the relative weight of spectral and temporal cues, consistent with both our results in rabbits and expectations based on the increase in relative cochlear frequency selectivity (Q factor) with increasing frequency. Specifically, ferret performance was somewhat better for stimuli in the higher F0 range (500 vs. 1,000 Hz classification) when the stimuli contained resolved harmonics (All Harmonics in sine phase and Low Harmonics conditions), whereas performance was slightly better in the lower F0 range (150 vs. 450 Hz classification) for High Harmonics stimuli consisting of unresolved harmonics.

That the stimuli used for training can influence the cues animals attend to in a perceptual classification task is demonstrated by the experiments of Shofner and colleagues (29, 78) on the perception of “periodicity strength” by chinchillas. Shofner (29) initially trained seven chinchillas to discriminate a “signal” HCT stimulus with harmonics in cosine phase requiring a “go” response from a “standard” broadband noise requiring a “no go” response. Once the animals learned this discrimination task, they were presented with “test” stimuli with low probability to find out whether the learned discrimination generalizes to these new stimuli. The frequency of “go” responses to a test stimulus was interpreted as a measure of the perceptual similarity between this stimulus and the signal stimulus, as opposed to the standard. The test stimuli used by Shofner (29) included an HCT with the same F0 as the signal but with harmonics in random phase and infinitely iterated ripple noise (IIRN) with a loop delay of 1/F0 that would evoke a pitch at F0 in humans (81). Like HCTs, the power spectrum of IIRN has harmonically related peaks at integer multiples of F0, and its autocorrelation has local maxima at 1/F0 and its multiples. For all three F0s tested (125, 250, and 500 Hz), five of the seven chinchillas rarely responded to the random-phase HCT and IIRN test stimuli, suggesting that these stimuli were perceived as being more similar to the broadband noise standard than to the cosine-phase HCT signal. Because IIRN and random-phase HCT stimuli differ from cosine-phase HCT in that they show little envelope modulation at F0, this result suggests that the chinchillas were basing their decision on the amount of envelope modulation in the stimulus rather than the presence of harmonically related peaks in the power spectrum. In a follow-up study, Shofner et al. (78) retrained the same chinchillas to discriminate an IIRN signal from a broadband noise background and then tested generalization of the learned discrimination to HCT stimuli in cosine and random phase. Most chinchillas responded with high probability to both test HCT stimuli, showing 1) that they can discriminate random-phase HCT from broadband noise [which was not obvious from the Shofner study (29)] and 2) that they learned to use a new cue to perform the task after being retrained on a discrimination between two stimuli with minimum envelope modulation (IIRN and broadband noise). Shofner et al. (78) suggest that the new cue lies in the temporal fine structure (e.g., in the form of a peak at 1/F0 in the IIRN autocorrelation), but it could also be the harmonic pattern of peaks in the IIRN power spectrum since the autocorrelation and the power spectrum are Fourier transform pairs and contain the same information.

For the most part, the above behavioral studies used F0s in the range of human voice (100–500 Hz), which tends to be lower than the range of vocalizations in the species tested. Osmanski et al. (11) used F0s between 150 and 900 Hz, but a majority of marmoset vocalizations have F0s above 5 kHz, including the phee, twitter, and trill calls (82, 83). Although chinchilla distress calls tend to have F0s in the 300–800 Hz range (84), their exploratory, contact, and alarm calls can exceed 1,000 Hz (85, 86), which is well above the 125–500 Hz range of F0s tested by Shofner and colleagues (29, 78). Although we are not aware of any published study of ferret vocalizations, some calls can have F0s exceeding 2,000 Hz (Stephen David, personal communication), which is beyond the 150–1,000 Hz range tested by Walker et al. (15). Given the interaction between F0 and the ability to use spectral cues for F0 discrimination demonstrated in several species, the failure to test F0s extending over the full range of conspecific vocalizations in the above studies may have led to an underestimation of the importance of resolved harmonics as a cue for F0 discrimination. In the present study, we tested F0s encompassing the 400–1,200 Hz reported range of rabbit vocalizations (60–62), admittedly based on limited data, and clearly demonstrated that rabbits can use resolved harmonics for F0s above ∼400 Hz.

In summary, there are more similarities than differences among the five mammalian species (including humans) in which behavioral experiments have been designed to assess the relative importance of spectral cues (resolved harmonics) and temporal envelope cues for discriminating the F0 of harmonic complex tones. Humans, marmosets, chinchillas, and rabbits have been shown to be able to use both spectral cues (or, equivalently, temporal fine structure cues) and temporal envelope cues for F0 discrimination. The ferret is an exception in that it appears to rely primarily on envelope cues (15), but that experiment was not designed to facilitate utilization of resolved harmonics. Also, in four of five species including humans (87, 88), F0 influences the relative weight given to spectral and temporal cues, in that spectral cues are more likely to be used at higher F0s whereas temporal envelope cues are better processed at lower F0s. Here, the exception is the chinchilla, as the data of Shofner et al. (78) show no obvious dependence on F0 over the range 125–500 Hz. Perhaps higher F0s would need to be tested to demonstrate an effect in this species. There are, however, clear across-species differences in the F0 range over which spectral cues begin to dominate over temporal envelope cues with respect to F0 discrimination. In humans, the border appears to be near 50–100 Hz, in rabbits and marmosets it is near 400–500 Hz, and in ferrets and chinchilla temporal cues dominate over the entire F0 range tested (up to 500 Hz in chinchillas, up to 1,000 Hz in ferrets). These differences partly correlate with differences in the number of resolved harmonics, which depends on relative cochlear frequency selectivity.

Implications for Neurophysiological Studies of F0 Coding

Having established that rabbits, as other mammalian species, can use both the pattern of resolved harmonics and temporal envelope cues for F0 discrimination, we discuss how each type of cue is coded and ultimately extracted by the auditory system.

Spectral cues to F0 might be coded by peaks at the tonotopic locations of resolved harmonics in the profile of firing rate against CF. Such rate-place cues to resolved harmonics have been observed in the cat auditory nerve for HCTs with F0s above ∼400 Hz (89), but these cues were degraded at moderate stimulus levels in most fibers because of firing rate saturation (90). However, rate-place cues to resolved harmonics appear to be more robust to stimulus level in the rabbit inferior colliculus (IC) (46). Rate-place cues were observed for F0s as low as 300 Hz but were most prominent above 600 Hz, which is consistent with our behavioral result that F0 discrimination performance for stimuli containing resolved harmonics is better for higher F0s. Robust rate-place coding of resolved harmonics in the IC might arise through central amplification of weak rate-place cues already present in the auditory nerve by mechanisms such as lateral inhibition (46) or might be created via a transformation of temporal fine structure cues present in the firing patterns of neurons in the auditory nerve and ventral cochlear nucleus (91–94), although the site and mechanism for such a transformation remain unclear. IC neurons that exhibit rate-place coding of resolved harmonics may be a source of inputs to the pitch-selective neurons found in a restricted area of marmoset auditory cortex (95), as pitch selectivity appears to be derived from spectral cues for neurons tuned to F0s above 400–500 Hz (96).

Temporal envelope cues to F0 are initially coded via phase locking of auditory nerve fibers with CFs in the frequency region of unresolved harmonics to the envelope repetition rate (91, 97–99). This temporal code is maintained and even enhanced for some cell types in the cochlear nucleus (100, 101) but tends to be increasingly restricted to lower frequencies at higher stations in the auditory pathways (102). In the IC of unanesthetized rabbits, temporal coding of the envelope repetition rate of HCT in cosine phase is widely observed for F0s up to 400–500 Hz, although some neurons still phase locked at 900 Hz (45). This temporal coding range overlaps with the F0 range over which rabbits were shown to discriminate F0 of HCTs with unresolved harmonics in the present study. In the IC (103, 104) and also to a degree in octopus cells of the cochlear nucleus (105), another code emerges in the form of tuning of firing rate to the envelope repetition rate of stimuli with modulated envelopes. In the rabbit IC, band-pass rate tuning to the envelope repetition rate of cosine-phase HCTs and pulse trains has been observed for F0s from 50 to 1,500 Hz (45, 106), which encompasses almost the entire range of F0s tested in the present study. IC neurons showing rate tuning to envelope repetition rate may be a source of inputs to the many neurons in ferret auditory cortex in which firing rates are sensitive to the F0 of HCTs (107, 108). However, these IC neurons are unlikely to be a major source of inputs to pitch-selective neurons in marmoset auditory cortex since the rate tuning of IC neurons is also observed for pulse trains with irregular (temporally jittered) intervals (106), whereas the pitch selectivity of cortical neurons is dependent on periodicity (109).

Conclusions

Using a behavioral paradigm inspired by foraging behavior, we showed that rabbits can discriminate the F0 of harmonic complex tones with missing fundamentals over a wide range of F0 based on either the spectral pattern of resolved harmonics or temporal envelope cues arising from waveform interactions between unresolved harmonics. The broad similarity in this pattern of behavior between rabbits, humans, and other mammalian species supports the use of a variety of animal models, including rabbits, for studies of the neural mechanisms of complex pitch perception, providing the study design takes into account across-species differences in cochlear frequency selectivity and the F0 range of conspecific vocalizations.

GRANTS

This work was supported by NIH Grant DC 002258 to B.D.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

K.E.H., Y.C., and B.D. conceived and designed research; J.D.W., A.G., and K.E.H. performed experiments; J.D.W. and B.D. analyzed data; J.D.W. and B.D. interpreted results of experiments; J.D.W. prepared figures; B.D. drafted manuscript; J.D.W., A.G., K.E.H., Y.C., and B.D. edited and revised manuscript; J.D.W., A.G., K.E.H., Y.C., and B.D. approved final version of manuscript.