ACUSTICA· acta acustica Vul. ~(\ (2000) 515 - 525 © S. Hirzel Verlag· EAA 515 Psychophysical Validation of a Proprioceptive Device by Cross-Modal Matching of Loudness Patrick Susini IRCAM-CNRS, I place Igor Stravin;;ky, F-75004 Paris, France Stephen McAdams Laboratoire de Psychologie Experiffi<~ntale(CNRS), Universite Rene Descartes, EPHE, 28 ruc Scrpente, F-75006 Paris, France and IRCAM- CNRS, I place Igor Stravinsky, F-75'J04 Paris, France Summary A large number of studies performed by S. S. Stevens, 1. C. Stevens and their collaborators have estimated the intensity of one sensory modality by way of another one related to the proprioceptive sensation of muscular force and limb position. As such, using a cross-modal matching procedure, it should be possible to associate a proprioceptive sensation with an auditory sensation (e.g. loudness, brightness, roughness) having an equivalent strcngth. A new proprioceptive cstimation devicc for the continuous unidimensional judgment of non stationary sounds has been developed, and in this paper we establish an individual calibration method and the loudness scale of stationary, I-kHz pure tones by a cross- modal matching paradigm using the new device. The loudness scale and the proprioceptive scale related to muscular force applied to a unidimcnsional joystick with forcc feedback were cvaluated independently by direct estimation techniques: ratio and magnitude production, absolute magnitude estimation. The proprioceptive function obtained is characterized by a power function with an exponent of 1.77. The results obtained with ratio scaling and cross-modal techniques are similar. Hc,wever, the set of results obtained with the cross-modal technique appear more stable and less dependent on experimental conditions. Finally, these results allow us to envisage the use of this device for different auditory assessment applications. PACS no. 43.66.Cb, 43.66.Ym 1. Introduction power law seems to be applicable without exception to any physical continuum involving a variation in sensory intensity, For sounds lasting a few seconds or considered stationary, tra- at least for values not too close to threshold where certain ditional procedures of subjective evaluation [1,21 and mea- adjustments are often necessary (ef. [Ill for loudness). The surement [31 have been used. They yield reliable and robust construction of direct scales can thus be reduced to determin- results. For example, several experiments [4,5, 6, 7, 8, 9] ing the exponent of the power function. However, the problem have been performed to evaluate the loudness of I-kHz pure with direct scaling resides in the ability of the subject to de- tones based on techniques intwduced by S. S. Stevens in tect and transmit the right ratios corresponding to his or her the I950s. The most well-known are the magnitude estima- sensations. A review of the psychophysical literature con- tion and production techniques. With these, S. S. Stevens cerning ratio-scaling techniques [11,12,13,14,15] reveals a produced the sone scale corre:;ponding to a measure of variability of the results in the subjects' judgments according perceived acoustic intensity. Several experiments performed to the type of technique, the level or the value of the reference with these direct evaluation techniques have given the power sound, the presence or absence of a reference sound, and the law relating physical to perceptual magnitudes proposed by range of stimuli presented, among other factors. S. S. Stevens S. S. Stevens [10]: [16] proposed a cross-modal matching (CMM) method for confirming the power law relation which docs not require \Ii = k<.l>", (1) the subject to make numerical judgments. The task consists in matching two sensations coming from different sensory where \)i corresponds to subjective intensity, <.I>corresponds modalities, one of which has been calibrated beforehand by to physical intensity, k is an arbitrary constant to adjust the a direct estimation method [16, 17, 18]. scale, and a is the exponent tt.at depends on the sensory The use of this CMM method with an adequate force- modality and conditions of stimulation. For example, the feedback proprioceptivel device has three main advantages. psychophysical function obtained that expresses the sensa- Firstly, as S. S. Stevens emphasized, on the basis of knowl- tion of acoustic intensity as a function of physical intensity edge concerning the function for a sensory modality, it is of a 3-kHz pure tone, corresponds to a power function with an exponent of 0.67. Experiments performed by S. S. Stevens in different sensory domains have given exponents varying 1 "Proprioception" literally means "perception of one's self" and from 0.33 (visual brightness) to 3.5 (electric shock). The is used in expcrimental psychology and sensory neuroscience to refer to the perception by an organism of stimuli relating to its own position, posture, equilibrium, or internal condition. We usc it here Reccived 6 April 1998, to refer to a combination of muscular, articulatory, and positional acceptcd 7 June 2000. cues deriving from an action on a resistive external device. ACUSTICA· acta acustica 516 Susini, McAdams: Cross-modal loudness matching Vo!. 86 (2000) possible to determine the psychophysical functions of other 2. Technical description of the proprioceptive device sensory modalities by cross-modal matching. For example, the psychophysical functions of different auditory attributes 2.1. Weight-related resistmce: device schema (loudness, roughness, sharpness) can be obtained by way of the proprioceptive function corresponding to the assessment In order to evaluate audit')fy sensation by a sensation of device. Secondly, the data in the literature reveal variabil- muscular resistance, a proprioceptive system was developed. ity, between and within methods [11, 12, 13, 14, 15] and This system acts on the selsitivity of muscles, bones, liga- among subjects, that can be reduced by determining for each ments, and joints, and provides information concerning the subject an individual matching function. It is necessary with equilibrium and position of limbs of the body in space. The this aim in mind that the assessment device be individually transmitted information and sensitivity depend on the type of calibratable as a function of different factors such as indi- effort and the movement provoked by the system. It is thus important in the choice of the device to specify what type of vidual sensitivity that varies with the stimulus range and the individual process of associating the two sensory modalities. effort is involved in the subject's task during the experiment. Thirdly, the intuitive and implicit nature of this assessment In other words, the subject must know to which gestural cat- procedure in comparison with other methods of numerical egory corresponds the required muscular effort as a function estimation or ratio estimation suggests its possible useful- of the device. The representation of the effort to be made is ness in procedures where rapid assessment is necessary. For different according to the manipulated object, and to each example, in the case of continuous judgment of nonstation- object is associated an appropriate scale of muscular effort. ary signals, it is important to use a method that transcribes For example, the scale will be different if one squeezes on rapidly, easily, and continuously the subjects' estimates. Fur- a water balloon or if one manipulates the handle of a pick- ther, it is interesting that this method can provide subjects axe. The schematic of the device we settled on is shown in with continuous information concerning their ratings by pro- Figure 1. viding force feedback. With this system, the subject has information on the eval- The aim of the present article is to test the psychophys- uation being made by force feedback and the position of arm ical reliability of CMM with a new proprioceptive device and shoulder. The \ever exerts a resistance as a function of developed for that purpose. We limit this study to determin- the angle of displacement, the effect of which is to create ing the loudness function of I-kHz stationary pure tones, in a proprioceptive sensation. As such, the subject associates a order to compare our results with those of the literature and combination of muscular force and displacement with any in- to validate our device with the cross-modal matching tech- tensity variation perceived by moving the lever of a "joystick" nique. In a future article [19], this technique will be applied in the direction corresponding to the auditory sensation. For to time-varying sounds and compared with other techniques. example, to an auditory sensation for which the intensity is The proprioceptive evaluation device developed for this work perceived as being two times greater, the subject doubles the is presented in section 2. In the first series of experiments proprioceptive sensation. In this way, the result related to (section 3), w~ determine the loudness scale with ratio and an intensity sensation does not depend on the ability of the magnitude production, as well as with magnitude estimation. listener to estimate the numerical magnitude related to the To obtain greater precision, we have used different methods sensation, which involves a sensory-to-conceptual matching to examine the biases due to each one. Similarly, we have process, but rather to match one sensory magnitude to an- repeated these tests with different levels and values for the other. The data obtained allow us to establish a relation be- reference sound in order to observe their influence on the tween the muscular force in Newtons and the sound pressure evaluation. We then determine the psychophysical function level in dB SPL. related to proprioceptive sensation with the ratio production The displacement of the I~veris recorded with the help of a method, on the one hand, and with magnitude estimation, 10 kD potentiometer mount~d in the axis of the lever motion. on the other hand.