Auditory Roughness  (adapted from Vassilakis, 2005)

DEFINITION

The term auditory roughness was introduced in the acoustics and psychoacoustics literature by Helmholtz (1885) to describe the buzzing, harsh, raspy sound quality of narrow harmonic intervals. Within the Western musical tradition, auditory roughness constitutes one of the perceptual correlates of the multidimensional concept of dissonance, concept that has cognitive, historical, and cultural bases, along with physical and physiological ones (Vassilakis, 2001, 2005). The dimension of dissonance correlating best with auditory roughness has been termed sensory dissonance (Plomp & Levelt, 1969) or auditory dissonance (Hutchinson & Knopoff, 1978), to mark its dependence more on physical and physiological, rather than cognitive, historical, or cultural considerations.

A familiar example of a signal corresponding to a rough sound would be the signal of a harmonic minor second performed, for instance, on two flutes. Although a harmonic minor second will sound rough regardless of the sound sources involved, steady state sources such as singing voices, bowed strings, or winds (as opposed to impulse sources such as percussion, plucked strings, etc.) result in more salient roughness sensations (von Béckésy 1960; Terhardt 1974). At relatively low registers, wider intervals such as major seconds and minor thirds can also sound rough and, within the Western musical tradition, are usually avoided as dissonant. For example, the general practice in Western art music orchestration of spacing out harmonic intervals more at low registers than at high registers has its basis on roughness considerations.

More broadly, the term roughness can be used to describe the buzzing sound quality of a variety of signals, beyond those of narrow harmonic intervals (e.g. signals corresponding to fast trills, fast vibrato, percussive rolls, rattles, etc.). Roughness is one of the perceptual manifestations of interference and, in the physical frame of reference it is usually described as a function of a signal's amplitude envelope (i.e. amplitude fluctuation rate and depth) and corresponding spectral distribution. As such, auditory roughness can also be considered a dimension of timbre.

The reason all complex signals, including the signals of chords, harmonic intervals, etc., exhibit amplitude fluctuations is physical and is related to the phenomenon of interference. The reason why some of these signals correspond to rough sounds is physiological and has to do mainly with the properties of the inner ear (review in Vassilakis, 2001).

INTERFERENCE - AMPLITUDE FLUCTUATION - ROUGHNESS

Amplitude fluctuations describe variations in the maximum value (amplitude) of sound signals relative to a reference point and are the result of wave interference. The interference principle states that the combined amplitude of two or more vibrations (waves) at any given time may be larger (constructive interference) or smaller (destructive interference) than the amplitude of the individual vibrations (waves), depending on their phase relationship.
In the case of two or more waves with different frequencies, their periodically changing phase relationship results in periodic alterations between constructive and destructive interference, giving rise to the phenomenon of periodic amplitude fluctuations. Figure 1a shows an example of a signal with steady amplitude over time, while Figure 1b shows a signal whose amplitude fluctuates over time.

Figure 1: Illustration of a sound signal with (a) steady amplitude and (b) amplitude that fluctuates over time.

ROUGHNESS, AMPLITUDE FLUCTUATION RATE, & CRITICAL BANDS

Amplitude fluctuations can be placed in three overlapping perceptual categories related to the rate of fluctuation. Slow amplitude fluctuations (≈≤15 per second) are perceived as loudness fluctuations referred to as beating. As the rate of fluctuation is increased, the loudness appears to gradually become constant and the fluctuations are perceived as "fluttering," "buzzing," or roughness. As the amplitude fluctuation rate is increased further, the roughness reaches a maximum strength and then gradually diminishes until it almost disappears (≈≥75-150 fluctuations per second, depending on the frequency of the interfering waves) (von Béckésy 1960; Zwicker, 1961; Plomp, 1964; Vassilakis, 2001).

Assuming the ear performs a frequency analysis on incoming signals, as indicated by Ohm's acoustical law (see Helmholtz 1885; Plomp 1964), the perceptual manifestations of amplitude fluctuation can be related directly to the bandwidth of the hypothetical analysis-filters, depending upon and defining what Zwicker (1961) termed critical bandwidth. For example, in the simplest case of amplitude fluctuations resulting from the addition of two sine signals with frequencies f₁ and f₂, the fluctuation rate is equal to the frequency difference between the two sines |f₁-f₂|, and the following statements represent the general consensus:
(a) If the fluctuation rate is smaller than the critical bandwidth, then a single tone is perceived either with fluctuating loudness (beating) or with roughness.
(b) If the fluctuation rate is larger than the critical bandwidth, then a complex tone is perceived, to which one or more pitches can be assigned but which, in general, exhibits little or no beating or roughness.

Psycho-physiologically, the roughness sensation can be linked to the inability of the auditory frequency-analysis mechanism to resolve inputs whose frequency difference is smaller than the critical bandwidth and to the resulting instability or periodic "tickling" (Campbell and Greated 1994: 61) of the mechanical system (basilar membrane) that resonates in response to such inputs.

ROUGHNESS & AMPLITUDE FLUCTUATION DEGREE

Along with amplitude fluctuation rate, the next most important signal parameter related to roughness is amplitude fluctuation degree, that is, the level difference between peaks and valleys in a signal such as the one in Figure 1b (Terhardt 1974; Vassilakis 2001). The degree of amplitude fluctuation depends on the relative amplitudes of the components in the signal's spectrum, with interfering components of equal amplitudes resulting in the highest fluctuation degree and the highest roughness degree.

AUDITORY ROUGHNESS AS MEANS OF MUSICAL EXPRESSION

The sensation of roughness has been explored more than any other perceptual manifestation of amplitude fluctuation and by numerous musical traditions, a practice that has only recently been documented and researched (Vassilakis, 2001, 2005). Manipulating the degree and rate of amplitude fluctuation helps create the buzzing sound of the Indian tambura drone and the rattling effect of Bosnian ganga singing, resulting in a sonic canvas that becomes the backdrop for further musical elaboration. It permits the creation of timbral variations (e.g. Middle Eastern mijwiz playing) and rhythmic contrasts (e.g. ganga singing) through gradual or abrupt changes among roughness degrees. Whether such variations are explicitly sought after, as in ganga singing and mijwiz playing, or are introduced more subtly and gradually, as may be the case in the typical chord progressions/modulations of Western music, they form an important part of a musical tradition’s expressive vocabulary. Other examples include the Quechua Haraui songs of Peru, with their frequent use of narrow harmonic intervals, and the performance of the taqara flutes of the Xingu river in Brazil, where sonic effects similar to those produced with the mizwij are produced by two or more simultaneous performers.

REFERENCES
(with some links to the sources)

von Békésy, G. (1960). Experiments in Hearing. New York: Acoustical Society of America Press (1989).

Campbell, M. and Greated, C. (1994). The Musician's Guide to Acoustics (2^nd edition). New York: Oxford University Press.

Helmholtz, H. L. F. (1885). On the Sensations of Tone as a Physiological Basis for the Theory of Music (2nd edition). Trans. A. J. Ellis. New York: Dover Publications, Inc. (1954).

Hutchinson, W. and Knopoff, L. (1978). "The acoustic component of Western consonance," Interface 7: 1-29.

Plomp, R. (1964). "The ear as a frequency analyzer," J. Acoust. Soc. Am. 36(9): 1628-1636.

Plomp, R. and Levelt, W. J. M. (1965). "Tonal consonance and critical bandwidth," J. Acoust. Soc. Am. 38(4): 548-560.

Terhardt, E. (1974). "On the perception of periodic sound fluctuations (roughness)," Acustica 30(4): 201-213.

Vassilakis, P. N. (2001). Perceptual and Physical Properties of Amplitude Fluctuation and their Musical Significance. Doctoral Dissertation. Los Angeles: University of California, Los Angeles; Systematic Musicology.

Vassilakis, P. N. (2005). "Auditory roughness as a means of musical expression," Selected Reports in Ethnomusicology 12 (Perspectives in Systematic Musicology): 119-144.

Zwicker, E. (1961). "Subdivision of the audible frequency into critical bands," J. Acoust. Soc. Am. 33(2): 248-249.