Rhona P. Hellman
Northeastern University and Veterans Administration,
INTRODUCTION
Zwislocki’s interest and contribution to our understanding of the loudness-intensity relation were sparked by his early studies with Lüscher (Lüscher & Zwislocki, 1948a, 1948b, 1951) and the development of his comprehensive theory of temporal auditory summation which assumes that loudness is directly proportional to neural activity within the auditory system (Zwislocki, 1960, 1969). These pioneering endeavors led him to determine the role of the slope of the loudness function in temporal summation and its extension to central masking, to assess the relation between the acoustic-reflex growth function and loudness, and more generally, to search for the key to an understanding of the form of the sensation-magnitude functions in all sensory systems (Zwislocki, 1965, 1972, 1973, 1974). Underlying much of Zwislocki’s loudness work is the assumption that Stevens’ power law (1953, 1975), based primarily on direct magnitude-scaling procedures, is determined by the stimulus transformation to a neural loudness code.
One way to ascertain if the outcome of direct magnitude scaling is related to the output of the auditory system is to measure the growth of loudness in cochlear pathology. Cochlear pathology not only produces an elevated threshold, but in the region of impaired hearing it markedly alters the overall shape of the loudness function. This well-documented phenomenon known as loudness recruitment is usually measured by loudness matching (e.g., Fowler, 1928, 1936; Hallpike, 1967; Miskolczy-Fodor, 1960; Reger, 1936).
Although an overall description of the loudness-intensity relation can be derived from measured loudness levels, these indirect loudness determinations cannot disclose the actual rate of growth or shape of the loudness functions (Hellman, 1976; Hellman & Zwislocki, 1968), nor can they provide information about the growth of loudness in bilaterally symmetrical impaired hearing (e.g., Marshall, 1981). Thus, despite their significant theoretical and practical ramifications, loudness-growth data spanning the dynamic range of hearing are seldom obtained for the vast majority of the hearing-impaired population. To help solve this thorny but important problem, several recent studies have demonstrated that direct magnitude scaling advocated by Stevens (1959a, 1975) for the measurement of loudness in auditory pathology can be applied to individuals and groups with cochlear-impaired hearing (Hellman, 1988; Hellman & Meiselman, 1990, 1992, 1993). This chapter presents additional evidence confirming the validity of magnitude scaling for measuring loudness in cochlear impairment. In the first section, equal-sensation functions derived from magnitude scaling are shown to be consistent with the results of intramodality matching. The second section shows that the rate of loudness growth is dependent on threshold sensitivity in the region of impaired hearing but not in the region of normal hearing. Finally, the third section shows that Zwislocki’s (1965) generalized loudness equation gives a good account of the growth of loudness in cochlear impairment. The results are compared to those predicted by the modified power law in the form L = K (P2 − P02)θ (Ekman, 1956; Luce, 1959; Stevens, 1959b) and to predictions by the alternative form L = K (P2θ − P02θ) subsequently introduced to describe the sensation-magnitude functions in quiet (Zwislocki & Hellman, 1960) and in noise (Lochner & Burger, 1961).
EQUAL-SENSATION FUNCTIONS IN COCHLEAR-IMPAIRED HEARING
Under conditions of minimal experimental constraints and biases Hellman and Zwislocki (1961, 1963, 1964, 1968) showed, in agreement with Stevens (1959a, 1966), that a similar underlying behavior was involved in loudness balances and magnitude scaling, namely matching. The coincidence of equal-sensation matches derived from magnitude scaling with those obtained from direct loudness matching was accomplished by eliminating the confounding effects imposed by either explicit or implicit reference standards and by averaging the individual raw data without any normalization. On the basis of their initial studies, Hellman and Zwislocki postulated that people have the capacity to pair the perceived magnitudes of numbers to sensation magnitudes on an absolute scale. Hence, they reasoned that the outcome of magnitude-scaling experiments can determine both the slope and absolute position of loudness curves on log-log coordinates. Later experiments corroborated the earlier findings and provided a further demonstration that equal-sensation functions consistent with the results of direct matching procedures can be derived from absolute magnitude scaling (Bolanowski, Zwislocki, & Gescheider, 1991; Collins & Gescheider, 1989; Hellman, 1976; Verrillo, Fraioli, & Smith, 1969; Zwislocki, 1983; Zwislocki & Goodman, 1980). The latter studies were all performed with people who had normal sensory functioning. The present experiments show that the mechanics of absolute scaling also hold for individuals with impaired auditory systems.
Description of Experiments
Equal-sensation functions were generated indirectly from absolute magnitude estimation (AME), absolute magnitude production (AMP), and cross-modality matching (CMM) between loudness and apparent length; they were also generated directly from intramodality matching. Eight listeners with bilateral cochlear impairments of long duration participated. All had clinically normal hearing (≤-dB HL; ANSI, 1969) at one frequency enabling either interfrequency or intrafrequency loudness matches to be performed. Each listener was tested individually in a double-walled soundproof booth. Listening was monaural through a TDH-49 earphone mounted in an MX-41/AR cushion. Root-mean-square voltages to the earphone were measured daily with a Fluke (8050A) digital voltmeter.
The stimuli were tone bursts that varied in frequency from 500–3,500 Hz and horizontal lines of light displayed one at a time from 35-mm slides. Tone-burst duration was 1 sec, rise-fall time was 10 ms, and the interstimulus interval was 500 ms. The tones were generated by a Krohn-Hite (4141R) oscillator. After appropriate amplification (Crown D-75 amplifier), the levels of the tone were controlled with Hewlett-Packard (350D) attenuators. A Kodak (4600) projector was used to display the lines which were viewed in a dimly lit room through the glass window of the booth.
The experimental protocol for the determination of the sensation-magnitude functions was as follows. First, pure-tone thresholds were measured by the method of limits at two frequencies, one where thresholds were normal, and the second where thresholds were elevated. Next, to increase the stability of the loudness results and to illustrate the concept of an open-ended number scale (Hellman, 1982; Zwislocki, 1983), apparent length was judged by AME for eight previously tested lines with measured projected lengths of 0.52, 1.04, 2.08, 5.2, 10.4, 20.8, 41.6, and 65 cm (Hellman & Meiselman, 1988, 1990). After the judgments of apparent length were completed, loudness was judged by AME in separate sessions at each of the two chosen stimulus frequencies. Loudness judgments were obtained at 7 to 11 sensation levels (SL) spanning the dynamic range of hearing from 4-dB SL to the SL corresponding to the maximal output of the equipment at a sound-pressure level (SPL) of 110 dB. Within a session, AME was followed by AMP (for rationale, see Hellman & Zwislocki, 1963) and by cross-modality matching. A typical stimulus set for AMP consisted of 7 to 11 numbers, and for CMM it consisted of 6 to 7 lines. For AMP the selected stimuli were individually determined from the range of numbers used for AME of loudness; for CMM they were selected from the lines used for AME of apparent length. As in AME of loudness, judgments by AMP and CMM were obtained at each stimulus frequency in a separate session.
The AME procedure was essentially the same for apparent length and loudness. For both tasks, each listener was simply asked to match an appropriate positive number, including decimals and fractions, to the loudness (or length) of the tone (or line), regardless of the number assigned to the previous stimulus. No standard stimulus was prescribed, and no lengthy practice sessions were required. Moreover, all judgments were self-paced; that is, the listeners were permitted to hear a tone (or see a line) more than once before making a response. Order biases arising from the preceding trial are effectively reduced under these conditions (Hellman, 1976). The final averaging was obtained without normalization of the raw data. Geometric means of the second and third judgments provided the estimate of apparent length and of loudness at each stimulus level.
Similarly, the judgments of AMP of loudness and of CMM were obtained without a designated standard. For both AMP of loudness and CMM the levels of the tone were adjusted by the listener until the loudness appeared equal to the perceived magnitude of the assigned number or line. Three adjustments to each stimulus were obtained by a bracketing procedure. The adjustments were made by turning an unmarked black knob attached to a sone potentiometer (60-dB range) external to the booth. To ensure that the listener’s settings remained within the middle of the potentiometer’s range, the experimenter controlled the input SPL to the potentiometer with a supplementary Hewlett-Packard (350D) attenuator. Just as in AME, the final averages were obtained without normalization of the raw data. Decibel averages of the second and third adjustments provided the average level matched in loudness to each assigned stimulus number or line.
Intramodality matches were obtained in a third listening session with the same apparatus and adjustment procedure used for AMP and CMM. However, rather than match loudness to assigned numbers or lines, six listeners performed intrafrequency matches and two performed interfrequency matches at 6 to 10 levels. The intrafrequency matc...