The auditory sensation of roughness can be described as an auditory attribute that represents a rapid sequence of brief auditory events. With respect to their subjective characteristics, these events as such are poorly defined; what matters is just that they occur in rapid succession. Rapid means that, to be perceived as roughness, the time interval between successive events must be less than about 30 ms. When the time interval is greater than about 30 ms, the events are perceived as individual events, e.g., as peaks of an oscillating loudness-time pattern.
When the auditory events are physically evoked by a periodic train of sound impulses, the magnitude of roughness (briefly just termed roughness) essentially depends on (1) the shape of the individual impulses; and (2) on the pulse frequency. For a fixed pulse frequency, roughness increases when the impulses are made shorter in duration. For a given impulse duration, roughness decreases when pulse frequency is increased (e.g., Miller & Taylor 1948a, Fastl 1976d, 1977f).
So, roughness indeed is an auditory percept that represents a sound's time structure, though in a "time-integrated" manner. Time structure is aurally represented without concsious apprehension of the individual events.
For any type of sound, e.g., speech and music, it is apparent that roughness is most pronounced when the sound includes spectrally coherent fluctuations. When a sound includes spectrally coherent fluctuations, its auditory roughness can be considerably reduced by somewhat randomizing the amplitudes and phases of its Fourier components (cf., e.g. Fleischer 1976a). This is what "automatically" happens when sound is (re)produced, and listened to, in a reverberating environment. One of the benefits of adding reverberation to a sound probably emerges from this roughness-reduction effect.
As any audible sound by its very nature is an oscillating signal, any sound can be regarded as a sequence of (physical) events. Therefore the question is neither trivial nor inadequate, why some types of sound elicit roughness while others do not. For instance, it is not easy to understand why a sine tone with a frequency as low as, say, 70 Hz, does not elicit any roughness, while a harmonic complex tone such as of a musical instrument or the human voice indeed elicits roughness if the oscillation frequency is below about 300 Hz. A possible explanation may be based on the notion that it is coherence of fluctuations of the ultimate auditory stimulus along the cochlear partition which is required for roughness to occur. For an (unmodulated) steady sine tone, there indeed is little coherence, because the phase of the wave in the inner ear varies drastically as a function of location. By contrast, for a multi-component complex signal, though its auditory excitation covers a wider area of the cochlear partition, it is the fluctuation of temporal envelope that must be regarded as responsible for roughness. The fluctuations of envelopes, however, are practically coherent in a wide area of the cochlear partition.
Whatever, it is inadequate to think that roughness is an auditory sensation that is exclusively associated with modulated sounds and even is a kind of auditory representation of a sound's modulation (i.e., either AM or FM). As was mentioned just above, several types of sound occurring in real life can elicit roughness without being modulated.
The first who has seriously considered roughness as an attribute of auditory sensation, was Helmholtz (1863a). He had recognized, and outlined in his book that, and how, roughness affects musical consonance. Almost 8 decades later, Bekesy (1935a) described a number of basic observations on roughness, e.g., its "bandpass" characteristic as a function of beat frequency. Thereafter, roughness again got little or no attention in "modern" psychoacoustics, i.e., for another thirty years, until in 1965 I became concerned with the topic and was able to show that roughness, besides other parameters, is governed by auditory critical bandwidth [4], [5], [6], [10] [12] (see also Plomp & Steeneken 1968a). This way, roughness became acknowledged as one of the fundamental auditory attributes, i.e., along with pitch, loudness, and timbre.
Roughness is involved in several aspects of sound evaluation. Besides musical consonance (Helmholtz 1863a, [30], [34], [35], [63]), the "consonance" of non-musical sounds, i.e. (absence of) annoyance, was shown to be dependent on roughness [37], [52], [60], Cardozo & van Lieshout (1981a), Aures (1985a, 1985b), Vos & Smoorenburg (1985a), Betke et al. (1988a), Kohler & Kotterba (1992a), Hashimoto & Hatano (1994a), Berglund et al. (1994a), Daniel & Weber (1994a), Daniel (1995a), Springer & Weber (1995a). Moreover, applications in sound evaluation of technical systems and in medicine were described (e.g., Isshiki et al. 1969a, Zeh et al. 1987a). With respect to the importance of roughness for the evaluation of sound, several calculation procedures have been developed, e.g. by Aures (1985c), and Daniel & Weber (1997a).
Although, as mentioned above, roughness should not be conceptualized as being typical of modulated sounds, in laboratory experiments it is very useful to study the roughness elicited by modulated narrow-band sounds, in particular, AM of sine tones. A kind of "natural" AM is provided by beats, i.e., pairs of sine tones. This is why roughness was also characterized as being the auditory sensation evoked by rapid beats.
Both with beating simultaneous tone pairs and with sinusoidally amplitude modulated sine tones one finds a number of typical features of roughness, such as the following.
From these notions it becomes apparent that roughness of fluctuating narrow-band signals can be well understood, as it is governed by a few simple principles. By contrast, roughness of wide-band signals is a complicated matter as it depends both on the magnitude of local fluctuations of auditory excitation as a function of frequency, and on the relative phase of those local fluctuations. This implies that the mechanism which creates auditory excitation is strongly involved. Modeling auditory roughness primarily requires adequate modeling of auditory excitation.