the relation between the human frequency-following response and the low pitch of complex tones

The relation between the human frequency-following response and the low pitch of complex tones

Ron D. Chambers

Department of Speech and Hearing Science, University of Illinois, 901 South Sixth Street, Champaign, Illinois 61820

Lawrence k. Feth

Department of Speech, Language, Hearing: Sciences and Disorders, University of Kansas, Lawrence, Kansas 66045

Edward M. Burns

Department of Speech and Hearing Sciences (JG15), University of Washington, Eagleson Hall, Seattle, Washington 98195

(Received 26 July 1985; accepted for publication 30 June 1986)

The relation between the auditory brain stem potential called the frequency-following response (FFR) and the low pitch of complex tones was investigated. Eleven complex stimuli were synthesized such that frequency content varied but waveform envelope periodicity was constant. This was accomplished by repeatedly shifting the components of a harmonic complex tone upward in frequency by Afof 20 Hz, producing a series of six-component inharmonic complex tones with constant intercomponent spacing of 200 Hz. Pitch-shift functions were derived from pitch matches for these stimuli to a comparison pure tone for each of four normal hearing adults with extensive musical training. The FFRs were recorded for the complex stimuli that were judged most divergent in pitch by each subject and for pure-tone signals that were judged equal in pitch to these complex stimuli. Spectral analyses suggested that the spectral content of the FFRs elicited by the complex stimuli did not vary consistently with component frequency or the first effect of pitch shift. Furthermore, complex and pure-tone signals judged equal in pitch did not elicit FFRs of similar spectral content.

PACS numbers: 43.66.Hg

INTRODUCTION

The ear can hear a complex tone as a single percept with low pitch approximately equal to that of the fundamental for the complex, even in the absence of spectral energy at the fundamental. This phenomenon has been called "the missing fundamental" (Fletcher, 1924). Various investigators have referred to the unitary pitch of complex tones by other terms which are consistent with their experimental orienta- tions, such as residue pitch (Schouten, 1938, 1940a,b), periodicity pitch, low pitch (Thurlow, 1958, 1963; Bilsen, 1977), or musical pitch (Houtsma and Goldstein, 1972).

Experimental evidence indicates that neither orthodox place nor temporal theory is tenable when considered the sole mechanism underlying the low pitch of complex tones. Although strict advocates of place theory suggest that the missing fundamental is reconstituted in the ear by nonlinear distortion in the form of difference tones (Helmholtz, 1863; Fletcher, 1924; Bekesy, 1960), considerable evidence demonstrates that the power spectrum in the inner ear need not contain the fundamental component for low pitch to be heard (Schouten, 1938; Licklider, 1954; Thurlow and Small, 1955; Small and Campbell, 1961; Patterson, 1969). Classic temporal or periodicity explanations suggest that low pitch is derived from the unresolved higher components which interact to produce the periodicity of the stimulus waveform at the cochlear output (Schouten, 1938, 1940a,b; de Boer, 1956a, 1976; Schouten et al., 1962). However, psychophys-

ical research has not confirmed that the period of the fundamental in the cochlear output is necessary for low pitch perception.

A line of evidence which demonstrates the unaccepta- bility of classic place and temporal theory comes from experiments in which a harmonic complex tone with the fundamental absent is shifted repeatedly over a small frequency distance A f (de Boer, 1956a,b, 1976; Schouten et al., 1962; Smoorenburg, 1970; Patterson, 1973). This transforms the harmonic signal into a series ofinharmonic signals with constant interpartial spacing and constant waveform envelope periodicity. Subjects report that the low pitch for these signals changes slightly with each increase in A f. The perceived pitch follows a sawtooth function varying about the pitch corresponding to the fundamental of the harmonic complex. The variation in pitch, known as "the first result of pitch shift," excludes the possibility that low pitch is derived from a difference tone or from waveform envelope periodicity.

The pitch shift does approximate the "pseudoperiod" of the cochlear waveform, which is based on the stimulus temporal fine structure. Fine structure may also relate to pitch ambiguity for inharmonic complex tones, i.e., the observa- tion of multimodal pitch selections for one tone (de Boer, 1956a,b; Schouten et al., 1962). However, evidence of a spectral "existence region" and "dominance region" for low pitch (Ritsma, 1962, 1967; Plomp, 1964, 1967, 1976; Bilsen, 1970, 1973; Smoorenburg, 1970; Houtsma and Goldstein,

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1971 ) and the role of combination tones in low pitch genera- tion ($moorenburg, 1970) point to the importance of spectral information from lower frequency components which are resolved in the cochlea. Furthermore, the sensation of low pitch may occur under conditions which prohibit peri- pheral interaction of adjacent components. Dichotic presentation of white noise with an interaural delay (Cramer and Huggins, 1958) or dichotic presentation of only two harmonics (Houtsma and Goldstein, 1972) can produce low pitch. A single pure-tone signal can produce low pitch under specific conditions of low signal-to-noise ratio (Houtgast, 1976). The nonsimultaneous presentation of successive harmonics of a fundamental may also elicit low pitch (Hall and Peters, 1981 ).

Current models of pitch perception describe a central mechanism which operates on patterns derived from the spectrum of the stimulus rather than its waveform (Gold- stein, 1973; Wightman, 1973; Terhardt, 1974). The hypoth- esized central mechanism operates on neural activity based on stimulus components resolved by the cochlea. Whether this neural activity is encoded by place (s) of activity, periodicity of neural discharge, or both is unsettled. It is known that information about the frequency of the resolved components is encoded at the VIII nerve level in both forms (Rose et al., 1967; Hind et al., 1967).

Several investigators have searched for electrophysiological correlates of pitch perception by evaluating the rela- tionship between the frequency-following response (FFR) recorded from humans and the low pitch of complex tones (Smith et al., 1978; Hall, 1979; Greenberg and Marsh, 1979, 1980). The FFR is a stimulus-related auditory brain stem potential which reproduces the waveform of low-frequency sound stimuli. The human scalp-recorded FFR is observed over a range of frequencies extending from about 70 Hz to not greater than 1500 Hz (Starr and Hellerstein, 1971; Glaser et al., 1976). The amplitude is largest for vertex placement and for frequencies of 500 Hz and below (Mou- shegian et al., 1973; Marsh et al., 1975; Smith et al., 1975; Huis in't Veld et al., 1977). The threshold for the scalp- recorded response is high, between 30-60 dB SL, relative to the behavioral threshold for the stimuli. The onset latency for stimuli of moderate intensity is about 6 ms (Moushegian et al., 1973; Marsh et al., 1975; Smith et al., 1975; Gerken et al., 1975; Glaser etal., 1976; Daly etal., 1976). Although the neural events which generate the FFR are not unequivocally established, evidence suggests it to be an aggregate of the individual activity of a group of phase-locking neurons within major brain stem auditory nuclei (Smith et al., 1975; Glaser et al., 1976; Huis in't Veld et al., 1977; Sohmer et al., 1977; Stillman et al., 1978; Gardi et al., 1979). The FFR has been utilized in the study of auditory perception as an indi- cant of brain stem neural events which phase lock to sound with low rates of waveform periodicity.

Smith et al. (1978) recorded the FFR for a complex wave with the fundamental absent. Spectral analysis of the FFR records revealed that the majority of the spectral energy was at the frequency of the fundamental, while the frequencies of the partials were not significantly represented. Spectra for FFRs elicited by a pure tone corresponding to

the frequency of the absent fundamental were characterized by similar spectral content. The investigators inferred that the waveform envelope periodicity of the missing fundamental is available at the brain stem and is related to pitch perception.

Hall (1979) pointed out that the two stimuli utilized by Smith et al. (1978) had the same waveform envelope periodicity, so the FFR and its spectra corresponded to both the pitch and the waveform envelope. Hall (1979) found that the FFR for three complex stimuli with different waveform periodicities but constant perceived pitch correlated well with the periodicity of the waveform envelope, but not the perceived pitch. He concluded that the FFR represents the encoding of waveform envelope periodicity but not the perception of the missing fundamental.

In 1979, Greenberg and Marsh recorded the FFR from the human scalp during presentation of a series of two-component tones. They reported that FFR amplitude varied in a manner consistent with Bilsen's perceptual model of pitch strength and harmonic number, i.e., response amplitude was largest for the tone composed of the third and fourth harmonics and progressively declined for tones of increasing harmonic rank. As in the investigators' 1978 study, the periodicity of the FFR records corresponded to both stimulus waveform envelope and the perceived pitch. In addition, psychophysical measurement of pitch and pitch strength for the test signals was not carried out. In a separate study, Greenberg and Marsh (1980) reported that the degree to which the FFR is sensitive to stimulus amplitude modula- tion for three-component complex tones may vary as inter- harmonic spacing and stimulus level vary. All subjects, however, did not show the same pattern.

In the current study, we attempted to extend these find- ings by evaluating if variation in the spectral content of the FFRs evoked by a group of complex stimuli is associated with a similar variation in low pitch. For this purpose, we used inharmonic stimuli like those used in investigations of the so-called first effect of pitch shift, as described earlier. These stimuli have a common waveform envelope, but differ in frequency content, temporal fine structure, and subjective pitch. We used these signals to investigate whether the neural periodicity reflected in the FFR covaries with pitch. Our experimental design specified the psychophysical measurement of pitch as well as the electrophysiological recording of the FFR for the same signals for each subject.

I. METHODS

A. General design

The experiment proceeded in four stages. Stage one involved the synthesis and calibration of complex and sinusoidal stimuli. Pitch-shift functions for the complex tones were determined during stage two. During stage three, frequency- following responses (FFRs) were recorded for both complex and pure tones. The complex stimuli used to elicit the FFR were those whose pitch marked the most divergent points on each subject's pitch-shift function. The pure-tone stimuli were those with pitch judged equal to those of the two complex tones which were judged as having the most diver-

1674 J. Acoust. Soc. Am., Vol. 80, No. 6, December 1986 Chambers eta/.: FFR and complex pitch 1674


gent pitches. The FFR records were analyzed for frequency composition during stage four.

B. Subjects

Four adults (three females and one male, between 19 and 22 years of age) with extensive musical training served as subjects. Each subject had hearing thresholds no poorer than 15 dB HL (ANSI, 1969) for the octave frequencies from 0.25-8 kHz. The subjects were paid for their participa- tion.

C. Stimuli

The complex and pure-tone stimuli were generated on a Cromemco Z-2D microcomputer using a 12-bit D to A converter. Eleven complex six-component tones of the form

5

s(t) = •/1 sin 2•r[ (4 4- m)200 4- 20i]t m=O

were generated for values of i between 0 and 10. Component amplitudes were synthesized to be equal and all components started at sine phase. Following acquisition of psychophysical data, pure-tone stimuli at frequencies which had been judged equal in pitch to the extreme points of the pitch function determined for each subject were also synthesized. Digi- tal sampling frequency for all tones was 20 kHz. All stimuli were of 50-ms duration, with 5-ms rise and decay times.

D. Transducer system

To eliminate electrical pickup from the earphone during measurement of the FFR, a special earphone-tubing system was constructed. With an otoscope speculum firmly at- tached by a Plexiglas holder to the grid of a TDH-49 earphone, the earphone was enclosed in a can constructed of multiple layers of ferromagnetic shielding. The otoscope speculum was connected to a section of Tygon tubing. The other end of the tube was connected to a second otoscope speculum, which was mounted in the center of a Plexiglas holder formed to fit snugly into an MX41/AR cushion. The shielding and separation (67 cm) between the electrical signal and the electrodes effectively eliminated the contribution of stimulus artifact to the response. The response characteristics of the transduction system were examined within a sound-treated room by placing the earphone cushion on an NBS 9A coupler sound level meter (Bruel and Kjaer, model 1613) and directing the output to a wave analyzer (Hewlett- •ackard, model 35SIA). A •hi•d-u•ave-band graphic equalizer (MXR) was used to compensate for the high-frequency roll-off of the earphone-tubing system. The response of the system with the equalizer is shown in Fig. 1. A periodicity with a fundamental of about 250 Hz is evident, prob- ably related to the resonance characteristics of the tubing- speculum section. The amplitude of these peaks in the frequency region of the stimulus components (0.8-2 kHz ) is never more than about 3 dB.

E. Procedures

1. Preliminary

Behavioral thresholds for the complex tones were obtained during a preliminary session for each subject. Thresh-

10 dB m

10 1 O0 1000 10000

Frequency (Hz)

FIG. 1. Frequency response of the earphone (TDH-49) and tubing system with frequency roll off compensated by the equalizer.

olds for the pure-tone signals used to elicit the FFR were measured following determination of pitch-shift functions. Using a method of limits with a 2-dB step size, thresholds were estimated as the lowest level at which the subject re- sponded to three stimulus presentations on ascending trials. Complex stimuli were presented at 60 dB relative to behavioral threshold for both pitch shift and FFR measures. The FFR recordings for pure tones were obtained at 55 dB SL due to output limitations. Peak-to-peak voltage for the experimental signals was monitored prior to each session.

2. Psychophysical procedures: Pitch-shift functions

The digitized complex tones were low-pass filtered (8 kHz) and then bandpass filtered (0.5-3 kHz) for monaural presentation. A sinusoidal comparison tone produced by a voltage-controlled generator (Wavetek, model 164) alter- nated with a complex tone after a 200-ms interstimulus interval. An electronic switch (Coulbourn, model S84-04) kept the duration and envelope of the pure tone equal to that of the six-tone complex. The microcomputer controlled signal timing and presentation. Subjects used a ten-turn potentiometer to control the frequency of the matching sinusoid. For each match, the starting position of the potentiometer was selected randomly by the experimenter. The complex and pure-tone stimuli were attenuated separately. The matching tone was presented at a level that was judged by the subject to be approximately equal in loudness to the complex tone with the lowest component at 800 Hz.

The pitch-matching portion of the study was carried out over several sessions. Each subject was instructed to listen to the alternating signals and adjust the dial of the potentiometer until the pure tone was subjectively equal in pitch to that of the complex tone. After a match was completed, the frequency of the matching tone was read from a frequency counter. Each of the six-component complex tones, presented in random order, was matched for pitch at least two times in each session. Subjects were instructed to use a bracketing approach and were permitted to take as much time as needed to reach a match. If the subject heard more than one pitch in the complex tone, s/he was instructed to match to the dominant pitch (Patterson, 1973).

Each session lasted 45 min, and approximately 25 matches were performed each session. There was one 5-min rest period after the first 20 min. Pitch matching for each subject required initial training sessions which continued



until intermatch differences for each complex tone were 5 Hz or less. Following the training sessions, each subject completed at least eight additional matches per complex which were averaged to obtain the low pitch for each complex.

3. Electrophysiologic procedures: Frequency-following responses

The complex and pure-tone signals used to elicit the FFR were produced and filtered for monaural presentation through the same experimental setup used in pitch matching. For each subject, the FFR was obtained for the two complex signals which showed the most divergent mean pitch values on the pitch-shift function, i.e., the two com- plexes between which the dominant pitch matches dropped from above to below fo. These were chosen to improve the probability of resolving differences in the spectral content of the respective FFRs. For comparison purposes, the FFRs to pure-tone frequencies with pitch judged equal to each of these complex tones were also recorded. In addition, FFRs to the harmonic complex with the lowest harmonic at 800 Hz were recorded for each subject, and FFRs to the pure tone judged equal in pitch to the harmonic complex were obtained for subjects 2, 3, and 4. The FFR to the latter stimulus was not recorded for subject 1 due to time limitations. The FFR for each complex tone was recorded at least twice for each subject.

The neuroelectric responses were recorded as the potential difference between a scalp vertex disk electrode and a reference electrode placed on the ipsilateral neck, 10 cm cau- dal to the mastoid. A ground electrode was affixed to the contralateral neck. The potentials were amplified and filtered (0.1-3 kHz) by an amplifier (Grass P511J) with' a gain of 200 000. The output was bandpass filtered (Krohn- Hite, model 3350) between 0.1 and 2.5 kHz. The amplified signal was fed to the microcomputer for signal averaging, using a 12-bit A to D converter. The averaging window was 70 ms, and each average consisted of 5000 responses. The averager was triggered externally on a trapezoidal waveform produced by the Wavetek generator for a stimulus repetition rate of five per second. During the sessions, a control run for the stimulus artifact was completed by averaging as usual with the tubing of the earphone transduction system clamped.

Recordings were taken only when the subjects were rest- ing quietly or were asleep. To facilitate sleep, the subjects reclined comfortably on a cot in a semidark, soundtreated room. Overall activity level was monitored by observing the ongoing electroencephalogram (EEG) displayed on an os- cilloscope, as were the stimulus waveform and ongoing average.

4. Waveform analysis

The FFR records were analyzed for spectral content using a Nova 4 computer and Interactive Laboratory Sys- tems (ILS) programs. • The amplitude spectra provided by ILS were analyzed for spectral peaks corresponding to the mean pitch matches of each subject. The fundamental frequency of each FFR was estimated by computing the center frequency of the lobe representing the fundamental.

II. RESULTS

The pitch-shift functions for the four subjects appear in Fig. 2 (see Ref. 2). The ordinate indicates the mean frequency of the pure tone matched in pitch to each complex tone. The abscissa is marked in values representing: (1) the frequency of the lowest component of the complex, and (2)f/g, where g -- the frequency spacing between components and

f--- the center frequency of the corresponding complex tone (cf. de Boer, 1956a,b, 1976; Schouten et al., 1962; Patterson, 1973). The error bars about each mean are plus and minus one standard deviation. Most standard deviations were less

than 3 Hz. The asterisks represent single, spurious, pitch- match selections. The data represented by the diamonds in Fig. 2 will be discussed later.

Figure 2 shows that the experimental complex tones elicited a linear shift in pitch similar to that observed by previous investigators (de Boer, 1956a,b, 1976; Schouten et al., 1962; Smoorenburg, 1970; Houtsma and Goldstein, 1971; Patterson, 1973). Two pitch courses are apparent as the stimulus components shift upward over the 200-Hz range. For each subject, the gradually rising pitch jumped down during the course of the interval to a lower value and began another upward trend. The lines drawn through the points in Fig. 2 were fit to the data using a least-squares criterion. The slopes for the regression lines were determined as a function of both the lowest component in each complex stimulus and f/g. In general, the slopes of the lines which define the first rising pitch course in each function (range of 0.192-0.27 across subjects, average slope of 0.228) are somewhat steeper than those corresponding to signals which produced the second pitch course (range of0.12-0.175, average of 0.149). Only the first slope was computed for subject 2 because the second pitch course involved only two points. The mean slope value 0.228 agrees favorably with that of 0.21 reported by Patterson (1973) for six-component stimuli in the same frequency region (the fourth harmonic).

kHz

.78 .•2 .86 .90 .94 .98 1.02 .78 .82 .86 .90 .94 .98 1.02 , , i ,

.22 - Subject•,•• .21

.2o • .19

i

I Subj;ct 3 ' • •

i

' •Subject2 T •e•, Subject 4 .24 • -

.21

/ i i i i i

f/g

FIG. 2. Pitch-shift functions for six-component complex tones and the fundamental frequency of FFRs elicited by associated complex tones for four subjects. Filled-in circles denote mean pitch values. Error bars mark plus and minus one standard deviation from the mean. Regression lines fit by least-squares criterion. The abscissa is marked in values representing: ( 1 ) the frequency of the lowest component of the complex and (2) f/g, where g - the frequency spacing between components and f- the center frequency of the corresponding complex tone. Fundamental frequencies on the FFRs denoted by diamonds. Asterisks represent single pitch judgments.

1676 J. Acoust. Soc. Am., Vol. 80, No. 6, December 1986 Chambers eta/.' FFR and complex pitch 1676


The distribution of pitch matches in response to each complex tone was usually unimodal for each subject. How- ever, two or more pitch percepts were reported for repeated presentations of several test stimuli by subjects 3 and 4, producing bimodal distributions of matches. Subject 3 chose pitch values clustered around means of 227 and 188 Hz for the complex with a lowest component of 920 Hz. Of the eight matches completed for this complex, five were for the lower pitch value. For the purposes of this study, the lower value was considered dominant in the percept. The stimuli chosen as most divergent in pitch had lowest components of 900 and 920 Hz and respective pitches of 221 and 188 Hz. Bimodal pitch selections for subject 4 were equally distributed between high and low values for several signals. The break in the pitch-shift function was considered to occur between the stimuli with lowest components at 940 and 960 Hz. For the complex with 940 Hz, pitch selections clustered around mean values of 237 and 190 Hz. The stimulus with a 960-Hz

component had a unimodal pitch of 193 Hz. These observa- tions of pitch ambiguity are consistent with those reported by Schouten et al. (1962) and Patterson (1973).

Subjects also differed in the overall pitch range they selected. Whereas subjects 1, 3, and 4 selected both low and high pitches for these complex stimuli, high pitches were dominant for subject 2. These individual differences were stable over time, and are similar to those described by Patter- son (1973).

The FFR waveforms for subject 1 are shown in Fig. 3

Pure Tone Frequency (Hz)

219 •

219

184 • Lowest Component Frequency (Hz)

900

900

900

920

920

ß

920

800 '

CONTROL

.5 pV 10 ms

FIG. 3. The FFR waveforms for subject 1 for pure-tone and complex tone stimuli. From top to bottom: The first three waveforms were elicited by pure tones; the next six waveforms were elicited by inharmonic complex tones; the tenth waveform was elicited by a harmonic complex tone; the bottom waveform was recorded in a control condition during presentation of a harmonic complex tone with the tubing of the earphone setup clamped.

and are representative of those for each subject. The responses are arranged in two groups: those elicited by complex signals (labeled according to the frequency of the lowest component) and those elicited by sinusoidal signals. The complex signals include those inharmonic tones which subject 1 judged to be most divergent in pitch, i.e., the signal with the lowest component of 900 Hz and a perceived pitch of 219 Hz and the signal with the lowest component of 920 Hz and a perceived pitch of 184 Hz. Three recordings for each of these signals are displayed in Fig. 3. Also displayed are an FFR for the harmonic complex tone with the lowest component of 800 Hz and an averaged response obtained during a control run with presentation of the harmonic complex but with the tubing clamped. For comparison purposes, the FFR for the sinusoidal signals (219 and 184 Hz) judged by subject 1 to be equivalent in pitch to the two inharmonic signals are also shown in Fig. 3. The FFR records tend to be characterized by a relatively flat baseline followed by the onset of the FFR. The control run and the first 8-10 ms of

each FFR suggest no significant stimulus artifact. The spectral contents of the FFRs in Fig. 3 are displayed

in Fig. 4 in the same order. Initial spectral analyses carried out through 3000 Hz revealed no significant energy at the

80 Lowest

Component 8o (Pitch)

8O

8O

8O

219

8O

70

6O

5O

dB 40 30

20

10

0

219

184

• 92O (184)

80 920 (184)

80 Hz 92O

80 (184) 9OO

80 (219)

900 80 (219)

900 (219)

800 (200)

CONTROL

0 200 400 800 1000

Frequency (Hz)

FIG. 4. Spectra of frequency-following responses for subject 1 for pure-tone and complex tone stimuli. Broken vertical line denotes 200-Hz location across spectra. From top to bottom: The first three spectra are for FFRs elicited by pure tones; the next six spectra are for FFRs produced by inharmonic complex tones; the tenth spectrum is for FFR to a harmonic complex tone; bottom spectrum is for waveform recorded in a control condition. Al- ternate spectra are drawn with slightly different widths to aid in visual separation.

1677 J. Acoust. $oc. Am., Vol. 80, No. 6, December 1986 Chambers eta/.' FFR and complex pitch 1677


frequencies of the stimulus components (0.8-2 kHz). For purposes of display in Fig. 4, analyses were carried out through 1000 Hz. Adjacent spectra were drawn with slightly different line widths to assist in visual separation. The spectra are arranged to facilitate the comparison of the frequency content of the FFRs for complex tones and the FFRs for pure tones. The lowest and predominant peak (other than dc offset) of each FF R for the complex tone lies near 200 Hz, the fundamental frequency of the harmonic stimulus. The broken vertical line across the spectra indicates the 200-Hz location. The spectra for the FFR for complex tones and pure tones can be distinguished on the basis of the location of the fundamental frequency.-For all subjects, visual inspec- tion revealed that the fundamental frequency of the FFR for the higher frequency pure tones was obviously higher than those for the complex tones, including the complex tones of equal pitch.

No peaks are obvious in the spectra for the FFR for each complex tone at the frequencies chosen by subject 1 during pitch matching ( 184 and 219 Hz). Given the spectral resolution of the analysis algorithm, one would expect peaks at these frequencies to be resolved if such energy were a predominant feature of the FFR. This finding was evident for other subjects as well. For example, subject 2 chose a pitch of 239 Hz for the complex tone with the lowest component at 960 Hz. No significant peak was resolved in the region of 239 Hz.

The fundamental frequency values in Table I indicate little overlap between the range of the fundamental frequencies of the FFRs to complex tones and the fundamentals of the responses to pure tones judged equal in pitch. For example, the mean pitch match for subject 1, for a complex tone with the lowest component of 920 Hz, was 184 Hz. The fundamental frequency for the FFR to a 184-Hz pure tone for subject 1 was 185 Hz. This value is below the range of fundamental frequencies--197.5 to 200.0 Hz•derived from the FFR records for the complex tone of equally judged pitch. Similar results were apparent fo• each subject.

The fundamental frequencies of the FFRs for complex tones and the mean pitch matches for the 11 complex stimuli

for each subject are graphed in Fig. 2. Each diamond represents the fundamental frequency for one FFR record for the complex tone identified on the abscissa. It is apparent that the fundamental frequency of the FFR to complex stimuli did not covary with pitch for these stimuli. Whereas the pitch shifted in a monotonic fashion with increases in the frequency content of the components of the stimuli, the FFR fundamental frequency remained fairly constant near 200 Hz. Moreover, no other peaks in the spectra for FFRs elicited by complex tones varied consistently with frequency or pitch for any subject.

III. DISCUSSION

We are unable to relate the frequency-following responses (FFRs) recorded for complex stimuli in this study to the low pitch elicited by those stimuli. In particular, the spectral content of the FFR for our subjects did not covary with the pitch of the inharmonic complex tones frequently used to demonstrate the first effect of pitch shift.

The variability of pitch matches in the current study is somewhat larger than that of previous studies (de Boer, 1956a,b, 1976; Schouten et al., 1962; Patterson, 1973). The largest standard deviation for the pitch matches to any complex tone was 3.0 Hz for subject 1, 5.0 Hz for subject 2, 5.2 Hz for subject 3, and 7.0 Hz for subject 4. The greater variability of the current data may be related to the use of a sinusoid as the comparison tone and to the short duration stimuli. Patterson (1973), and others, used a pulse train of definite pitch for comparison because it has a timbre similar to that of the test stimuli. The sinusoid was chosen in the

current study because the research design required the FFR records elicited by the comparison as well as the complex stimuli. Rather than comparing the FFR evoked by two multicomponent signals of similar spectra, the sinusoid was selected. The stimuli in this study were of relatively short duration (50 ms) when compared to signals of several hundred ms used in most investigations of low pitch. Despite these considerations, pitch-matching variability was small relative to the size of the pitch shifts measured, and the re-

TABLE I. Fundamental frequencies of the frequency-following responses (FFR) elicited by the complex tones which marked the extreme points on the pitch-shift function for each subject and to pure tones of equal pitch. Values were taken from the spectra of one-, two-, and three-FFR records.

Lowest FFR--Center of Pure FFR--Center of

component lowest lobe (Hz) tone lowest lobe (Hz) (Hz) 1st 2nd 3rd (Hz) 1st 2nd

Subject 1 800 195.5 900 199.0 198.0 195.5 219 218.0

920 200.0 200.0 197.5 184 185.0

Subject 2 800 195.5 192.0 200 198.5 960 194.5 200.5 239 240.0

980 201.0 200.0 202.0 195 195.0

Subject 3, 800 194.0 196.0 201 201.5 900 202.0 203.0 221 219.0

920 195.5 196.5 189 187.5

Subject 4 800 198.5 197.0 198 198.0 940 200.5 197.5 239 240.0

960 200.0 201.0 195 195.0

215.5



suits are generally consistent with those in the literature. We evaluated several measures of the FFR that could be

related to low pitch. We examined the relation between the fundamental frequency of the FFRs for complex and pure tones and perceived pitch. The pure-tone signal was chosen as a relatively unambiguous token of pitch and waveform envelope periodicity. The FFRs obtained with pure tones were assumed to be relatively direct representations of peri- odieity-based neural activity. As expected, the fundamental frequency of the FFRs for pure tones approximated the pitch-matched pure tone in every instance. The fundamental of the FFRs elicited by the complex tones did not show this agreement with perceived pitch. The pure tone and complex stimuli elicited matching pitch but evoked FFRs of different fundamental frequency. The data did suggest a closer rela- tionship between stimulus waveform envelope periodicity and the FFR fundamental. In each instance, the fundamentals of the FFRs dosely approximated the frequency of the stimulus envelope.

The FFR spectra were evaluated for evidence of activity that would support the pitch ambiguity observed for some of the experimental complex tones. Sehouten ½t al. (1962) and Patterson (1973) demonstrated that the degree to which ambiguity is observed for inharmonie tones depends to some extent on the subjeet's set toward the pitch matching task, i.e., his/her training, experience, motivation, and ability in pitch judgments, as well as the instructions preparatory to the experimental task. Sehouten ½t al. (1962) instructed their subjects to adjust the pitch of the matching stimulus to search for as many pitches as possible. The pitch adjust- ments of their subjects clustered around as many as live different values for one complex stimulus. Patterson (1973) requested that his subjects focus on the dominant pitch. Even with this constraint, each subject consistently reported two pitches for some stimuli.

Pitch ambiguity has been related to ambiguity or quasi- periodicity in the temporal line structure of the stimulus waveform (Sehouten ½t al., 1962). If the FFR retteets low pitch perception, one might expect to find measurable peaks in the FFR spectra to support ambiguous pitch judgments and individual subject preferences in high- versus low-pitch values. We were unable to discern such components in our data.

The current data are not interpreted to suggest that periodicity mechanisms at the brain stem level do not contribute to pitch extraction. Rather, the data suggest that the dominant neural periodicity retteeted in the FFR as it appears at the human scalp does not directly eovary with pitch. •

ACKNOWLEDGMENTS

This research was supported, in part, by NINCDS Grant NS 15405. This publication is based upon research performed by Ron D. Chambers as partial fulfillment of the requirements for the doctoral degree at Purdue University under the advisorship of Lawrence L. Feth. The authors ap- preciate the contribution of Steve Kuhlman to this project.

lIn order to avoid contamination by onset responses in the FFR, only the latter 40 ms or eight cycles of each response were analyzed. This involved approximately 780 of the 1200 sampled data points in the original time series. With a sampling frequency of 20 kHz, the resolution of the analysis algorithm was determined to be approximately 12.8 Hz.

2See AIP document No. PAPS JASMA-80-1673-16 for 16 pages of figures and tables showing the following for each subject for the experiments reported in this paper: individual pitch-match selections, mean and standard deviation measures for pitch selections, slopes of pitch-shift functions, FFR waveforms, and FFR spectra. Order by PAPS number and journal reference from American Institute of Physics, Physics Auxiliary Publica- tion Service, 335 East 45th Street, New York, NY 10017. The price is $1.50 for each microfiche or $5.00 for photocopies of up to 30 pages with $0.15 for each additional page over 30 pages. The material also appears in Cur- rent Physics Microfilm, the Monthly Microfilm edition of the complete set of journals published by AIP, on the frames immediately following this article.

3Since preparation of this manuscript, an unpublished study by Greenberg (1980), which may be relevant, has been brought to our attention. Green- berg recorded the FFR from the scalp of two subjects using inharmonic complex tones. The FFRs were recorded with each stimulus in its original polarity and a second time with its polarity reversed. As in the present study, spectral analysis of the full FFR waveform indicated a substantial component at the difference frequency with no apparent pitch related activity. Greenberg also subtracted the FFRs elicited by the opposite polarity signals. Spectral analysis of the waveform resulting from this manipulation suggested a component in the FFR that corresponds to one of the pitches that may be produced by the inharmonic signals as well as smaller peaks at the stimulus frequencies. Greenberg (1980) noted that the result was not always replicable; he also did not measure pitch for these signals.

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the relation between the human frequency-following response and the low pitch of complex tones

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