THE STABILITY OF LOUDNESS

The third aspect in which tones can differ is in their loudness. Moreover, loud-ness is a quality in which, according to common usage, the same sound can vary.

Timbre and pitch can be considered as inherent characteristics of a tone, whereas loudness is much less specific, strongly dependent on environmental conditions (such as distance and reflections). Loudness generally refers to audi-tory intensity. It seems to be the least “intelligent” attribute of sounds, and therefore our discussion of it here is short.

The loudness of a tone is primarily determined by its sound-pressure level.

However, this is only a rough, first-order approximation. Two tones of the same physical intensity can still differ considerably in their perceived loudness, de-pending on their spectral structure. The more the intensity is spread over a wider frequency range, the louder the tone seems to be. The most extreme dif-ference in perceived loudness is between a sinusoidal tone without harmonics and a tone consisting of a large range of strong harmonics—the sound level of the sinusoidal tone may need to be as much as 12 dB higher in order to be heard as equally loud as the complex tone.

A characteristic property of loudness is its rapid increase beyond the hearing threshold. This has been investigated by asking listeners to express the loudness of tones in numbers. Starting at a level of 10 to 20 dB above hearing threshold, an increase in level of about 9 dB is usually accepted as representing a factor two in loudness.

The most remarkable aspect of loudness manifests itself when two or more sound streams, such as two voices, are present simultaneously. We may expect that the varying extent to which they mask each other will be reflected in continuous loudness variations of the individual sounds. However, as our daily experience shows, this is not the case. We have the impression that there is no interaction be-tween simultaneous sounds with respect to their individual loudness.

This stability can be explained partly by the fact that, as a result of the ear’s frequency-resolving power, tones interact only when they are near in frequency.

Figure 2.9, based on data published by Scharf (1964), illustrates how the loud-ness of a sinusoidal tone of variable frequency is influenced by an equally in-tense 160-Hz band of noise centered at 1,000 Hz. We see that this influence is

limited to frequencies within a quite narrow frequency range. Nevertheless, as the loudness of a tone is determined by all its harmonics together, we would ex-pect that it is strongly affected by, for example, noise bursts masking a substan-tial part of its spectrum. However, that is not the case. Apparently, the hearing process, in its attempt to reconstruct the original sounds, ignores these differ-ences in loudness. More is said about this in the next chapter.

DISCUSSION

This chapter was devoted to the three basic perceptual qualities of tones: timbre, pitch, and loudness. We found that timbre is the perceptual correlate of the wave-form (representing the spectrum), pitch the correlate (but not a derivative) of the period, and loudness the correlate of the amplitude of the sound. These corre-spondences illustrate how closely our perception is tuned to the outer world. To a large extent the three physical parameters are independent of each other. Move-ments of the vocal folds determine the frequency of voiced speech sounds, whereas vocal-tract shapes create spectral distinctions between speech sounds.

The same is true for musical instruments—each instrument can be used to create differences in pitch, whereas the shapes and materials used in different types of in-struments give them their characteristic timbres. In all cases, the level of a sound can be varied without affecting its spectrum or periodicity.

FIG. 2.9. Sound-pressure level of a sinusoidal tone without noise, plotted as a function of fre-quency, sounding equally loud as tone of the same frequency presented together with a narrow band of noise centered at 1000 Hz. The loudness matching was carried out at four (equal) lev-els of the latter tone and the noise band (based on data from Scharf, 1964).

It should be mentioned that this is a somewhat simplified picture of the psychoacoustical reality. Particularly for sinusoidal sounds, it is known that there is some pitch dependence on sound level. Also, because hearing threshold is not the same over the entire frequency range, there is a minor interdepen-dence of timbre and loudness. However, these are second-order effects practi-cally imperceptible in everyday situations.

Our discussion of timbre has especially been oversimplified. It cannot be as-sumed that the neat steady-state tone pulses of the laboratory are representa-tive of the sounds we hear every day. Musical tones and spoken vowels are dynamic sounds that can vary substantially in time. This means that differences in timbre are not fully accounted for by spectral differences. The significance of additional parameters has been demonstrated convincingly for musical tones.

For example, Iverson and Krumhansl (1993) compared the timbre contribution of the onsets of orchestral instrument tones with the contribution of the re-mainder of the tones. Their finding that both contributions are roughly compa-rable demonstrates the substantial role of dynamic factors, most manifest in onset differences between the string and wind instruments. Sustained notes from a violin and a trumpet are spectrally quite similar, but we hear them as very different sounds due primarily to the dynamic properties of their onsets.

Another question not addressed in this chapter is the role of nonlinear dis-tortion in hearing, the phenomenon where the output amplitude of a signal is not exactly proportional to the input amplitude. Since Helmholtz’s extensive discussion of the nonlinearity of the ear’s mechanical sound transmission (von Helmholtz, 1863/1954), the topic has received substantial attention. Such a nonlinearity manifests itself in the creation of new tones not present in the in-put signal. For example, a sinusoidal tone with frequency f produces tones with frequencies nf, and two tones with frequencies f₁and f₂(f₂> f₁) interact result-ing in new tones with frequencies mf₁– nf₂(where m, n are integers). Particularly in the 1960s these combination tones were studied intensively, with interest also stimulated by their supposed role in the audibility of beats for slightly mistuned pairs of tones.⁴It appeared that 2f₁– f₂can be rather strong for small values of f₂ – f₁. This would indicate that simultaneous tones, as in music, strongly interact. However, although our ears are very sensitive to nonlinear distortion in the form of intermodulation in sound-transmission systems, result-ing in a reduced “transparency” of the music, this has not been shown to be the case for distortions introduced by the ear itself. This remarkable discrepancy in the perception of externally versus internally originating distortion has still not been explored properly.

4The occurrence of combination tones and beats was discussed extensively in Plomp (1976).

In addition, detection thresholds, another favorite topic of a few decades ago, did not receive much attention here. Detection thresholds, whether or not expressed in the d’ of signal-detection theory, are useful for describing the limits of the auditory system’s capacity, but they do not represent the essence of the perception process. Just-noticeable differences in frequency, amplitude, and so on can inform us about whether differences between sounds are perceived, but they do not inform us about the attributes of what is perceived, without doubt the much more important question.

As we have seen, the process of analyzing sounds into their spectral compo-nents is an essential stage in auditory perception, but it is only the first stage. An artificial system could be designed to do exactly the same. But this apparatus would be unable to reconstruct the original sounds from the sinusoidal compo-nents and to characterize them according to their timbre and pitch. Both analy-sis and syntheanaly-sis are required to perform this task. Hence, we may say that the auditory system is a quite unique sound analyzer.

Of all the phenomena discussed in this and the following chapters, the ones described in the present chapter have been most studied physiologically. How-ever, even here, our knowledge is almost exclusively limited to the ear’s fre-quency-resolving power. More than a century ago, Helmholtz (von Helmholtz, 1863/1954) exerted much effort to convince his readers that the cochlea is a fre-quency analyzer. In his view, the basilar membrane within the cochlea, extend-ing over (almost) its entire length, should be seen as a series of strextend-ings tuned from low to high frequency much like the strings of a piano. Modern research, initiated by Georg von Békésy’s (1899–1972) first successful attempts to ob-serve the membrane’s movements, has abandoned the idea of vibrating strings in favor of the concept of traveling waves with a frequency-dependent peak along the basilar membrane (von Békésy, 1960). This means that Helmholtz’s view locating frequency analysis in the peripheral ear was essentially correct.

Animal studies have abundantly demonstrated that the individual nerve fibers associated with the hair cells along the basilar membrane transfer faithfully the results of the peripheral frequency analysis to higher centers in the auditory pathway.

Our physiological knowledge of how sounds are processed does not extend significantly beyond this first stage of frequency analysis. Subsequent processes are clearly required to group components originally belonging to the same sound, to characterize the sound’s timbre, to “compute” pitch, and to mark loudness. It is obvious that these all are neural processes depending on the elec-trical inputs of large numbers of neurons. Up to now, no physiologically based description of these processes has been made. Such a description would be

par-ticularly intriguing for the pitch processor, which is surely a rather sophisticated mechanism. Only speculations based on algorithms are available.

The fact that in listening to a mixture of sounds both the pitch and timbre of each individual sound are so readily perceived demonstrates that our hearing is, even in its most elementary processes, aimed at undoing the unavoidable conse-quences of the fact that all incoming sounds are superimposed in the air. We hear these individual sounds as if they had never been mixed. Hearing, even at its most elementary level, is clearly the result of highly “intelligent” processes operating so well that extensive hearing research was required to discover their existence. This is all the more true for the perceptual separation of series of suc-cessive sounds, considered in the next chapter.

CONCLUSIONS

We have seen in this chapter that the ear and auditory system represent a rather unique frequency-analyzing system. This system manages to separate sounds entering the ear canal so perfectly by source, it is as if the sounds had reached the ear through different channels rather than as a superimposed air vibration.

This means that the peripheral ear, working as a straightforward frequency ana-lyzer, is followed by a second, neural, stage in which the spectral components originally belonging to the same sound are reunited in a single percept. Specific processes must be employed resulting in the perception of timbre as the coun-terpart of the sound’s spectrum, pitch as the councoun-terpart of its periodicity, and loudness as the counterpart of its sound level.

3

The Perception of Multiple