Consonance and dissonance
In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise.[1] 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.[2] In casual discourse, as German composer and music theorist Paul Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied".[3] The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.[4]
For other uses, see Literary consonance, North/South Consonance Ensemble, and Dissonance (disambiguation).
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".[18]
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.[19]
"Amplitude fluctuations can be placed in three overlapping perceptual categories related to the rate of fluctuation:
Assuming the ear performs a frequency analysis on incoming signals, as indicated by Ohm's acoustic law,[20][21] the above perceptual categories can be related directly to the bandwidth of the hypothetical analysis filters,[22][23] 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:
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.[24][25] 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 interaction is manifested perceptually in terms of pitch or timbre variations, linked to the introduction of combination tones.[26][27][28]
"The beating and roughness sensations associated with certain complex signals are therefore usually understood in terms of sine-component interaction within the same frequency band of the hypothesized auditory filter, called critical band."[29]
In human hearing, the varying effect of simple ratios may be perceived by one of these mechanisms:
Generally, the sonance (i.e., a continuum with pure consonance at one end and pure dissonance at the other) of any given interval can be controlled by adjusting the timbre in which it is played, thereby aligning its partials with the current tuning's notes (or vice versa).[37] The sonance of the interval between two notes can be maximized (producing consonance) by maximizing the alignment of the two notes' partials, whereas it can be minimized (producing dissonance) by mis-aligning each otherwise nearly aligned pair of partials by an amount equal to the width of the critical band at the average of the two partials' frequencies.([37][15]
Controlling the sonance of pseudo-harmonic timbres played in pseudo-just tunings in real time is an aspect of dynamic tonality. For example, in William Sethares' piece C to Shining C (discussed at Dynamic tonality § Example: C2ShiningC), the sonance of intervals is affected both by tuning progressions and timbre progressions, introducing tension and release into the playing of a single chord.
The strongest homophonic (harmonic) cadence, the authentic cadence, dominant to tonic (D-T, V-I or V7-I), is in part created by the dissonant tritone[38] created by the seventh, also dissonant, in the dominant seventh chord, which precedes the tonic.
Musical instruments like bells and xylophones, called Idiophones, are played such that their relatively stiff mass is excited to vibration by means of a striking the instrument. This contrasts with violins, flutes, or drums, where the vibrating medium is a light, supple string, column of air, or membrane. The overtones of the inharmonic series produced by such instruments may differ greatly from that of the rest of the orchestra, and the consonance or dissonance of the harmonic intervals as well.[39]
According to John Gouwens,[39] the carillon's harmony profile is summarized: