Учебники / Auditory Perception - An Analysis and Synthesis Warren 2008

Periodicity theory of pitch 75

harmonic components stimulating regions associated with other pitches. Also, the fundamental frequency still characterizes the pitch of a complex tone even when it is not present as a component of the stimulus. Helmholtz (1954/1877) described the generation of difference tones (that is, creation of frequencies corresponding to the difference between sinusoidal components) which could account for perception of the absent fundamental (although Helmholtz does not seem to have used difference tones explicitly as an explanation of this problem). However, Fletcher (1924) did claim that the distortion within the ear could produce a frequency corresponding to a missing fundamental – which thus would not be missing at the level of the receptor cells.

Experiments conducted after Fletcher made this claim have shown that a pitch corresponding to the missing fundamental is heard under conditions making it highly unlikely that the fundamental is generated within the ear. These experiments have led to the development of temporal or periodicity theories of pitch perception, which consider that iterated patterns of neural response can produce a sensation of pitch corresponding to the repetition frequency.

Periodicity theory of pitch

Schouten (1938) demonstrated in an elegant fashion that a pitch corresponding to the fundamental of a complex tone was heard even when this frequency was absent at the level of the receptor cells. He prepared a complex tone with a fundamental of 200 Hz, and first removed the fundamental by the addition of the appropriate intensity of a second 200 Hz sinusoidal tone that was 180 out of phase with the fundamental. Following this acoustic cancellation, a 206 Hz sinusoidal tone was added as a probe to determine whether the 200 Hz fundamental was present at the level of the receptor cells – if a 200 Hz tone were generated within the ear, it would interact with the probe to produce periodic fluctuations in amplitude (or beats) at the rate of 6 Hz. The probe verified the absence of the fundamental. Yet a pitch corresponding to the missing fundamental could be heard clearly, although the quality associated with this pitch was quite different from that of a sinusoidal tone corresponding to the fundamental. These observations led Schouten to his concept of ‘‘residue pitch’’ which will be discussed shortly.

Schouten’s experiments, showing that the pitch of the missing fundamental is carried by higher harmonics, requires subjects skilled in matching the pitch of tones having different qualities. Licklider (1954) demonstrated the same basic phenomenon in a manner which did not require such skills. At a meeting of the Acoustical Society of America, he first let the audience hear a

76Perception of acoustic repetition: pitch and infrapitch

recognizable melody consisting of a sequence of complex tones lacking lower harmonics. In order to show that the melody was carried by the upper harmonics, he then added a band of low frequency noise of sufficient intensity to mask any distortion products corresponding to the fundamental and lower harmonics: the melody could still be heard quite clearly. Subsequent quantitative studies also have used low frequency masking noise to ensure that the spectral fundamental did not contribute to the pitch produced by higher harmonics of complex tones (Small and Campbell, 1961; Patterson, 1969).

Schouten’s residue pitch

In a number of experiments, Schouten (1938, 1939, 1940a) verified and extended Seebeck’s suggestion that higher harmonics of pulse trains could combine to produce the pitch of an absent fundamental.

Schouten first tried using an acoustic siren to generate pulses (as did Seebeck), and found that, while he could hear the auditory phenomena described by Seebeck, there was much variability in the stimulus and some undesired noise was produced. Schouten designed an ‘‘optical siren,’’ in which rotating masks of different shapes determined the pattern of light reaching a photosensitive cell, which then controlled the waveform of a signal driving a loudspeaker. The optical siren could produce intact pulse trains, and the construction of appropriate masks permitted deletion of desired lower harmonics. (Fine adjustments in the masks were made with the help of a wave analyzer that measured the strength of individual spectral components.) As the result of his experiments, Schouten (1970) came to the following conclusions.

(1)The ear follows Ohm’s law (i.e., can hear out individual harmonics) for frequencies wider apart than, say, a full tone (12 percent). In a harmonic series, from 8 to 10 lower harmonics can be perceived by the unaided ear.

(2)Higher harmonics are heard collectively as one subjective component (one percept) called the residue.

(3)The residue has a sharp timbre.

(4)The residue has a pitch equal to that of the fundamental tone. If both are present in one sound they can be distinguished by their timbre.

Schouten (1940a) realized that one possible objection to his explanation for residue pitch in terms of periodicity of the entire waveform could be that the difference between successive harmonics of a complex tone with a fundamental frequency of 200 Hz is also 200 Hz, and that this difference might be responsible for the pitch of the residue. He then produced a train of pulses of alternating polarity having a fundamental frequency of 200 Hz (see Figure 3.6).

78 Perception of acoustic repetition: pitch and infrapitch

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Figure 3.7 Behavior of a hypothetical pitch extractor that measures intervals between main peaks in a waveform. The waveform shown is that of a complex tone corresponding to the sinusoidal modulation of a carrier tone having a frequency ten times that of the modulation frequency. Some of the possible pitches are considered to be based on the intervals sl, s2, and s3. (Adapted from Schouten, Ritsma, and Cardozo, 1962.)

expected. When he increased each component by 50 Hz to produce the complex of 850, 1,050, 1,250, 1,450, 1,650 Hz, the pitch heard was increased to about 210 Hz. De Boer offered an explanation for the pitch shift in terms of a central pitch extractor which constructed a harmonic series most closely approximating the inharmonic complex. In the example given above, this would correspond to 833.3, 1,041.7, 1,250, 1,458.3, 1,666.7 Hz, with a missing fundamental of approximately 208.3 Hz (close to the experimentally found value). De Boer suggested that the pitch extractor employed place information for spectral components having low harmonic numbers that stimulated discrete loci, and temporal information for those components with high harmonic numbers that cannot be resolved by place of stimulation.

Schouten, Ritsma, and Cardozo (1962) proposed a somewhat different model. They took amplitude-modulated signals consisting of three harmonically related components, such as 1,800, 2,000, 2,200 Hz, and then shifted the frequency of each component by the same amount to produce an inharmonic sequence. Pitch shifts similar to those reported by de Boer for his fivecomponent signals were observed. They also reported that while a harmonic three-component complex such as that described above (1,800, 2,000, 2,200 Hz) had a dominant pitch corresponding to the amplitude-modulation envelope (200 Hz), several fainter pitches could be heard as well (see Figure 3.7). Schouten and his associates suggested a model in which the ambiguity was attributed to a pitch processor that measured time intervals between peaks as shown in the figure. They noted that increasing component frequencies by a fixed amount did not change the envelope repetition frequency of 200 Hz but did change the fine structure within the envelope. Since the pitch does change, they reasoned that fine structure must enter into pitch judgments.

Complex tones on the basilar membrane 79

Spectral dominance

Since harmonic components of complex tones can generate a pitch matching that of the spectral fundamental, there have been attempts to determine which harmonics play the leading role in generating the pitch. Experiments by Ritsma (1962, 1963) suggested that components with low harmonic numbers play a dominant role. Subsequent experiments by Ritsma and by other investigators indicated that harmonic numbers from about three to five usually were the most important in establishing pitch (for reviews, see Ritsma, 1970; Plomp, 1976). However, the dominant harmonics change to some extent with fundamental frequency (Plomp, 1967a; Patterson and Wightman, 1976). In general, the dominant harmonics are resolvable along the basilar membrane and also overlap in critical bands, so that two types of temporal information as well as spatial information might be generated by these components, as will be discussed next.

Complex tones and local temporal patterns on the basilar membrane

In dealing with the possible bases for the residue pitch heard when all components were delivered to the same ear or ears, Schouten (1940c) considered the basilar membrane as a tuned resonator in which lower harmonics stimulated isolated regions without interaction with neighboring harmonics, while several of the higher harmonics stimulated the same region. Figure 3.8 shows the local pattern of excitation produced by a pulse train according to this model.

Plomp (1966) employed a more refined model of the basilar membrane response to a 200 Hz pulse train, using a set of 1/3-octave filters to approximate the width of critical bands. Figure 3.9 shows tracings obtained in our laboratory using Plomp’s method with pulses of 100 ls duration and 1/3-octave filters having attenuations of 30 dB one octave from the center frequencies of the filters. The tracings resemble closely those obtained by Plomp for the same stimulus. The responses of the filters, of course, still are not intended to represent the actual patterns along the basilar membrane in a quantitative fashion. However, the tracings do illustrate clearly some effects of the bandpass filtering occurring within the cochlea.

Both Figures 3.8 and 3.9 provide an impressive indication that bursts of activity having a periodicity corresponding to the pulse rate occur at cochlear loci which respond to frequencies several times higher than the spectral fundamental. Even though it is tempting to consider that the periodic bursts of activity are responsible for the detection of a pulse-train periodicity,

Complex tones on the basilar membrane 81

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Figure 3.9 Demonstration of the nature of the basilar membrane’s response to pulse trains based upon Plomp’s procedure (see text). The pulse-train waveform is shown diagramatically in broadband form as BB at the bottom of the figure. Tracings are shown of the actual waveforms obtained as output from a set

of 1/3-octave filters (center frequencies of 160, 200, 250, . . . , 6,300 Hz) stimulated simultaneously by a 200 Hz pulse train. Spectral resolution of individual harmonics can be seen for the filters with lower center frequencies, as well as the emergence of pulsate patterns with repetition frequencies of 200 Hz for filters with the highest center frequencies. The same equipment and procedures were used in preparing the tracings for nonpulsate stimuli shown in Figures 3.1, 3.3, and 3.8.

82Perception of acoustic repetition: pitch and infrapitch

nonpulsate complex tones (which also exhibit residue pitch) do not produce such bursts of activity, either broadband or when filtered. Indeed, the amplitude contours of individual critical bands of a complex tone need not be correlated in any way for them to be integrated into a unified percept of residue pitch.

Before attributing perceptual characteristics of specific sounds to their special acoustic properties, it is desirable to determine whether these characteristics are also exhibited by representative or generic stimuli lacking the special waveforms and spectral characteristics of specific types of sounds.

Let us turn for a moment to consideration of how the use of representative stimuli can help us understand the general principles governing the perception of periodic sounds.

Use of special versus model periodic stimuli

Periodic stimuli of a particular frequency can have an almost limitless number of waveforms and spectra. One of the most important special stimuli is the simple or pure tone, since it consists only of a single spectral component. These sinusoidal waveforms have proved invaluable in studying cochlear mechanics, neural physiology, and pitch perception. However, pure tones are encountered infrequently outside the laboratory, and all other periodic sounds have more than one spectral component. Also, the thresholds for pure tones become so high for frequencies less than 20 Hz that they are effectively inaudible; however, periodic waveforms having fundamental frequencies below 20 Hz can be heard if they have harmonics in the audible range.

In the nineteenth century, complex tones were generated by a siren or by a rotating Savart wheel (see Boring, 1942, p. 335), both of which could produce periodic pulses or clicks of any desired frequency. In the twentieth century, electronic pulse generators with adjustable frequency and pulse width or computer generated pulses were used frequently when complex tones with broad spectra were desired. If the width of the periodic pulse is narrow, the amplitude of higher harmonics decreases only slowly with harmonic number, as shown in Figure 3.10. However, the spectral alignment of the phases of spectral components of pulse trains produces unique patterns of auditory stimulation, as indicated in Figures 3.8 and 3.9. Also, at low tonal and infratonal frequencies, pulse trains are unique stimuli, sounding like a sequence of clicks separated by silence.

If we turn from pulses to familiar complex tones, such as the sounds employed in speech and music, we find that they each have special qualities and a limited range of repetition frequencies. Is there, then, any sound which can be considered as a model periodic stimulus?

84 Perception of acoustic repetition: pitch and infrapitch

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Figure 3.11 Simulation of the nature of the basilar membrane response to a model periodic sound. Two statements of a repeating white noise segment (period 5 ms, repetition frequency 200 Hz) are shown in unfiltered or broadband form in the bottom tracing labeled BB, with the tracings shown above obtained from the same

set of 1/3-octave filters used with the pulse train in Figure 3.9. The center frequencies of the filters are shown to the left of each response curve. Spectral resolution of the sinusoidal waveforms of the individual lower harmonics can be

seen, as well as a series of iterated complex patterns (each with a period of 5 ms) produced by individual filters with center frequencies above 800 Hz. For additional details, see the text.