page_title: Consonance and dissonance
section_title: Physiological basis
hierarchical_section_title: Consonance and dissonance / Physiological basis
caption_attribution_description: English: ii-V-I turnaround in C. Français&#160;: ii-V-I turnaround en C.
context_page_description: In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, consonance is typically associated with sweetness, pleasantness, and acceptability; dissonance is associated with harshness, unpleasantness, or unacceptability although this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. As Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.
context_section_description: Two notes played simultaneously but with slightly different frequencies produce a beating "wah-wah-wah" sound. This phenomenon is used to create the Voix céleste stop in organs. Other musical styles such as Bosnian ganga singing, pieces exploring the buzzing sound of the Indian tambura drone, stylized improvisations on the Middle Eastern mijwiz, or Indonesian gamelan consider this sound an attractive part of the musical timbre and go to great lengths to create instruments that produce this slight "roughness" (Vassilakis 2005, p. 123).
  Sensory dissonance and its two perceptual manifestations (beating and roughness) are both closely related to a sound signal's amplitude fluctuations. 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 amplitude fluctuations (Vassilakis 2005, p. 121).
  "Amplitude fluctuations can be placed in three overlapping perceptual categories related to the rate of fluctuation. Slow amplitude fluctuations (≈≤20 per second) are perceived as loudness fluctuations referred to as beating. As the rate of fluctuation is increased, the loudness appears constant, and the fluctuations are perceived as "fluttering" or roughness. As the amplitude fluctuation rate is increased further, the roughness reaches a maximum strength and then gradually diminishes until it disappears (≈≥75–150 fluctuations per second, depending on the frequency of the interfering tones).
  Assuming the ear performs a frequency analysis on incoming signals, as indicated by Ohm's acoustic law (see Helmholtz 1954b; Levelt and Plomp 1964,), the above perceptual categories can be related directly to the bandwidth of the hypothetical analysis filters (Zwicker, Flottorp, and Stevens 1957,; Zwicker 1961,). 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:
  If the fluctuation rate is smaller than the filter bandwidth, then a single tone is perceived either with fluctuating loudness (beating) or with roughness.
  If the fluctuation rate is larger than the filter bandwidth, then a complex tone is perceived, to which one or more pitches can be assigned but which, in general, exhibits no beating or roughness.
  Along with amplitude fluctuation rate, the second most important signal parameter related to the perceptions of beating and roughness is the degree of a signal's amplitude fluctuation, that is, the level difference between peaks and valleys in a signal (Terhardt 1974,; Vassilakis 2001,). The degree of amplitude fluctuation depends on the relative amplitudes of the components in the signal's spectrum, with interfering tones of equal amplitudes resulting in the highest fluctuation degree and therefore in the highest beating or roughness degree.
  For fluctuation rates comparable to the auditory filter bandwidth, the degree, rate, and shape of a complex signal's amplitude fluctuations are variables that are manipulated by musicians of various cultures to exploit the beating and roughness sensations, making amplitude fluctuation a significant expressive tool in the production of musical sound. Otherwise, when there is no pronounced beating or roughness, the degree, rate, and shape of a complex signal's amplitude fluctuations remain important, through their interaction with the signal's spectral components. This 
caption: Perfect authentic cadence (V-I with roots in the bass and tonic in the highest voice of the final chord): ii-V-I progression in C About this soundPlay (help·info).
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