Abstract
An important phenomenon for models of pitch perception is that adult listeners can extract pitch from complexes containing only unresolved harmonics (UH). Although 3-month-olds discriminate resolved harmonics on the basis of missing fundamental (MF) pitch, their ability to discriminate UH is unknown. This study investigated the ability of adults, 7- and 3-month-olds to perceive the pitch of UH using an observer-based method. Stimuli were MF complexes that were bandpass filtered with a −12 dB/octave slope, combined in random phase, and presented at 70 dB SPL for 650 ms with a 50 ms rise/fall and a pink noise to mask distortion products. The experiment had two conditions: 1) “low” UH between 2500–4500 Hz based on MFs of 160 Hz (H17-H26) and 200 Hz (H13-H22) and 2) “high” UH between 4000–6000 Hz based on MFs of 190 Hz (H22-H31) and 200 Hz (H20-H29). To demonstrate MF pitch discrimination, participants were required to ignore spectral changes in complexes with the same fundamental and respond only when the fundamental changed. Interestingly, variable performance in the “high” condition was observed with adults. However, nearly all infants tested categorized complexes by MF pitch in both conditions, suggesting discrimination of unresolved harmonics at 3 months.
INTRODUCTION
Harmonic complex sounds such as a musical note or a vowel in speech produce a unitary pitch percept that corresponds to its fundamental frequency (F0). Whether the auditory system uses a spectral representation of the F0 or a temporal representation of the waveform to produce this pitch percept has been much debated. The pitch of unresolved harmonics is restricted to a temporal representation and has therefore been of theoretical importance to models of pitch perception.
Since the bandwidth of auditory filters increase with center frequency (e.g. Glasberg and Moore, 1990), low number harmonics in a complex sound fall within different auditory filters and are resolved by the cochlea while high number harmonics fall within the same filter and are unresolved. The auditory system can provide a code for the pitch of resolved harmonics based on temporal information (e.g. Licklider, 1951; Meddis and Hewitt, 1991), spectral information (e.g. Goldstein, 1973; Terhardt, 1979), or both (e.g. Shamma and Klein, 2000). However, the pitch of unresolved harmonics is likely derived from a temporal representation of the envelope of the waveform resulting from harmonic interaction on the basilar membrane (Plack and Oxenham, 2005).
While we know that adult listeners can extract pitch from complexes containing only unresolved harmonics (e.g. Carlyon and Shackleton, 1994; Ritsma, 1962), less is known about infants’ ability. Clarkson and Rogers (1995) presented 7- and 8-month-old infants with either low-frequency resolved harmonics or high-frequency unresolved harmonics in a missing fundamental (MF) pitch categorization task. They found that more infants were able to discriminate the MF of low-frequency resolvable complexes (67%) than high frequency resolvable complexes (17%). Recently, Lau and Werner (2012) demonstrated that infants as young as 3 months of age were able to discriminate resolved harmonics on the basis of the MF but their ability to discriminate unresolved harmonics is unknown.
The purpose of this study is to investigate the ability of 3-month-olds, 7-month-olds, and adults to perceive the pitch of unresolved harmonics using an observer-based method. A missing fundamental pitch categorization task was presented to infants in one of two conditions: 1) low unresolved harmonics between 2500 and 4500 Hz and 2) high unresolved harmonics between 4000 and 6000 Hz.
METHOD
Subjects
The participants in the low unresolved harmonics condition were 12 3-month-old infants and 10 7-month-old infants. The participants in the high unresolved harmonics condition were 8 3-month-old infants, 13 7-month-old infants, and 6 adults. All infants passed their newborn hearing screening and had no history of health or developmental concerns. Adult participants were between 18 and 30 years of age, reported normal hearing bilaterally, had less than 2 years of musical training and no prior experience as participants in psychoacoustic experiments. All participants were required to pass a tympanometric screen at each test session.
Stimuli
Stimuli were harmonic complexes that were bandpass filtered with a −12 dB/octave slope, combined in random phase, and presented for 650 ms with a 50 ms rise/fall and with a continuous pink noise to mask distortion products. Table 1 shows the harmonic structure of the stimuli used across test phases in each condition. For the low condition, harmonics between 2500 and 4500 Hz based on MFs of 160 Hz and 200 Hz were used. For the high condition, harmonics between 4000 and 6000 Hz based on MFs of 190 Hz and 200 Hz were used. All complexes were presented monaurally at a flat-weighted level of 70 dB SPL through an Etymotic ER-2 insert earphone in the right ear. Testing was conducted in a double-walled, sound attenuating booth.
TABLE 1.
Harmonic structures of stimuli in the two conditions: low unresolved and high unresolved.
| Phase | Low Unresolved Harmonics | High Unresolved Harmonics | ||
|---|---|---|---|---|
| MF 160 Hz | MF 200 Hz | MF 190 Hz | MF 200 Hz | |
|
| ||||
| 1 | F0+H2-H9 | F0+H2-H9 | F0+H2-H9 | F0+H2-H9 |
| 2 | F0+H2-H9 | F0+H2-H9 | F0+H2-H9 | F0+H2-H9 |
| 3 | H17-H22 | H13-H18 | H22-H27 | H20-H25 |
| H18-H23 | H14-H19 | H23-H28 | H21-H26 | |
| H19-H24 | H15-H20 | H24-H29 | H22-H27 | |
| H20-H25 | H16-H21 | H25-H30 | H23-H28 | |
| H20-H26 | H17-H22 | H26-H31 | H24-H29 | |
F0 is the fundamental frequency; Hn refers to the other component frequencies by harmonic number.
Procedure
Infants were tested using an observer-based psychophysical procedure (Werner, 1995) similar to the procedure used in Lau and Werner (2012). During testing, infants sat on a caregiver’s lap with an assistant in the booth manipulating toys to keep infants facing midline. The experimenter sat outside the booth and observed through a window. Harmonic complexes from one pitch category, the “background”, were played repeatedly to the participant from the start of the test session. The goal was to determine whether the participant detected a change in the complex to the other pitch category, the “target”. There were two trial types that occurred with equal probability during testing. On change trials the target complex with a pitch change was presented four times, while on no-change trials complexes from the background pitch category continued to play. On each trial, the experimenter, blind to trial type, decided within 4 seconds of trial onset whether a change or no-change trial had occurred, based only on the infant’s behavior. The behavior used by experimenters to make judgments varied from infant to infant. Eye movements, increases and decreases in body movement, and facial expressions like widening of the eyes were common behaviors observed. Computer feedback was provided to the experimenter at the end of a trial. During the test phases, participants’ responses were reinforced with the presentation of a mechanical toy or video for 4 seconds only if the experimenter correctly identified a change trial.
The study consisted of one training phase and two test phases presented in a fixed sequence. The first phase was a training phase used to demonstrate the association between the reinforcer and the target F0 change to the participant. The probability of a change trial was 0.80, and the reinforcer was activated after every change trial regardless of the experimenter’s response. The experimenter had to respond correctly on 4 of the last 5 change trials and 1 no-change trial to complete the training phase and progress to the test phases.
In the two subsequent test phases, the probability of change and no-change trials was 0.5, and the experimenter was required to respond correctly on 4 of the last 5 change and 4 of the last 5 no-change trials to move on to the next phase. This criterion corresponds to a hit rate of 80% and a false alarm rate of 20% on the last 5 consecutive change and no-change trials respectively. In the second phase, the task and stimuli were the same as in the training phase but the reinforcer was activated only when the experimenter correctly identified a change trial to teach the participant to produce an observable response when they heard a pitch change.
The third phase was a missing fundamental pitch categorization task. While in phases 1 and 2, the same set of harmonics was associated with each F0 on every presentation, in phase 3 each pitch category consisted of five different sets of harmonics with the same F0. One of these complexes was randomly chosen on each presentation. To demonstrate discrimination of the missing fundamental pitch, participants were required to ignore the spectral changes of complexes from the same pitch category and respond only when a complex from the other pitch category was played.
RESULTS
Two analyses were conducted to evaluate participants’ performance. The first analysis addressed whether the number of participants in each age group reaching criterion was greater than expected by chance. In the low condition, 11 of 12 3-month-olds and 9 of 10 7-month-olds reached criterion on the pitch categorization task. In the high condition, 7 of 8 3-month-olds, 12 of 13 7-month-olds, and 2 of 5 adults reached criterion on the pitch categorization task. To determine the proportion of subjects expected to reach criterion by chance, the response rate on all trials in all sessions meeting criterion was calculated for the infants tested. The overall response rate was 0.58. A simulation of 1000 sessions in which responses occurred randomly at a rate of 0.58 showed that criterion was met in only 3% of sessions. Exact binomial tests with an assumed probability of 0.03 were conducted based on the number of participants who reached criterion in each age group for each condition. Not surprisingly, more infants were found to meet criterion than expected by chance (p < 0.001) for both 3- and 7-month-olds in both low and high conditions. Interestingly, variable performance in the high condition was observed with adult participants. Only 2 of 5 adults reached criterion on the pitch categorization task. However, due to the limited number of adult participants, interpretation of results is difficult. Further data collection is in progress.
The second analysis addressed the relative difficulty of the task for 3-month-old and 7-month-old infants by comparing the average number of trials to meet criterion in the MF test phase across age groups. Figure 1 shows the mean number of trials to criterion in the low condition for each age group. Figure 2 shows the mean number of trials to criterion in the high condition for each age group. In the low condition, the difference in mean number of trials to criterion for 3-month-olds and 7-month-olds was not statistically significant. In the high condition, the difference in mean number of trials to criterion was not statistically significant for 3-month-olds, 7-month-olds, or adults.
FIGURE 1.
Mean (± 1 SEM) number of trials to criterion of successful participants for missing fundamental discrimination in low condition.
FIGURE 2.
Mean (± 1 SEM) number of trials to criterion of successful participants for missing fundamental discrimination in high condition.
CONCLUSION
These results suggest that infants at both 3- and 7-months are able to discriminate the missing fundamental pitch of unresolved harmonics and that the difficulty of the task was comparable for infants at both ages.
ACKNOWLEDGEMENTS
This work was supported by NIH grants R01 DC00396 and P30 DC04661.
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