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. 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. In casual discourse, as German composer and music theorist Paul Hindemith stressed,
The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.

Definitions

The opposition between consonance and dissonance can be made in different contexts:
  • In acoustics or psychophysiology, the distinction may be objective. In modern times, it usually is based on the perception of harmonic partials of the sounds considered, to such an extent that the distinction really holds only in the case of harmonic sounds.
  • In music, even if the opposition often is founded on the preceding, objective distinction, it more often is subjective, conventional, cultural, and style – or period – dependent. Dissonance can then be defined as a combination of sounds that does not belong to the style under consideration; in recent music, what is considered stylistically dissonant may even correspond to what is said to be consonant in the context of acoustics. A major second would be considered dissonant if it occurred in a J.S. Bach prelude from the 1700s; however, the same interval may sound consonant in the context of a Claude Debussy piece from the early 1900s or an atonal contemporary piece.
In both cases, the distinction mainly concerns simultaneous sounds; if successive sounds are considered, their consonance or dissonance depends on the memorial retention of the first sound while the second sound is heard. For this reason, consonance and dissonance have been considered particularly in the case of Western polyphonic music, and the present article is concerned mainly with this case. Most historical definitions of consonance and dissonance since about the 16th century have stressed their pleasant / unpleasant, or agreeable / disagreeable character. This may be justifiable in a psychophysiological context, but much less in a musical context properly speaking: Dissonances often play a decisive role in making music pleasant, even in a generally consonant context – which is one of the reasons why the musical definition of consonance/dissonance cannot match the psychophysiologic definition. In addition, the oppositions pleasant/unpleasant or agreeable/disagreeable evidence a confusion between the concepts of "dissonance" and of "noise".
While consonance and dissonance exist only between sounds and therefore necessarily describe intervals, such as the perfect intervals, which are often viewed as consonant. Occidental music theory often considers that, in a dissonant chord, one of the tones alone is in itself deemed to be the dissonance: It is this tone in particular that needs "resolution" through a specific voice leading procedure. For example, in the key of C Major, if F is produced as part of the dominant seventh chord, it is deemed to be "dissonant" and it normally resolves to E during a cadence, with the G7 chord changing to a C Major chord.

Acoustics and psychoacoustics

Scientific definitions have been variously based on experience, frequency, and both physical and psychological considerations. These include:
; Numerical ratios: In classical antiquity, these mainly concerned string-length ratios. From the early 17th century onwards, the ratios were more often expressed as the equivalent ratios of frequencies. Consonance often is associated with the simplicity of the ratio, i.e. with ratios of lower simple numbers. Many of these definitions do not require exact integer tunings, only approximation.
; Fusion: Perception of unity or tonal fusion between different tones and / or their partials.
; Coincidence of partials: With consonance being a greater coincidence of partials. By this definition, consonance is dependent not only on the width of the interval between two notes, but also on the combined spectral distribution and thus sound quality of the notes. Thus, a note and the note one octave higher are highly consonant because the partials of the higher note are also partials of the lower note.

Music theory

Consonances may include:
  • Perfect consonances:
  • * unisons and octaves
  • * perfect fourths and perfect fifths
  • Imperfect consonances:
  • * major thirds and minor sixths
  • * minor thirds and major sixths
Dissonances may include:
  • Dissonance
  • * major seconds and minor seventh
  • * tritones
  • * minor seconds and major sevenths
File:Krenek's chord classification from Studies in Counterpoint.png|thumb|upright=1.4|Ernst Krenek's classification, from Studies in Counterpoint, of a triad's overall consonance or dissonance through the consonance or dissonance of the three intervals contained within. For example, C–E–G consists of three consonances and is ranked 1 while C–D–B consists of one mild dissonance and two sharp dissonances and is ranked 6.

Physiological basis

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".
Sensory dissonance and its two perceptual manifestations are both closely related to a sound signal's amplitude fluctuations. Amplitude fluctuations describe variations in the maximum value 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 at any given time may be larger or smaller than the amplitude of the individual vibrations, 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.
"Amplitude fluctuations can be placed in three overlapping perceptual categories related to the rate of fluctuation:
  1. Slow amplitude fluctuations are perceived as loudness fluctuations referred to as beating.
  2. As the rate of fluctuation is increased, the loudness appears constant, and the fluctuations are perceived as "fluttering" or roughness.
Assuming the ear performs a frequency analysis on incoming signals, as indicated by Ohm's acoustic law, the above perceptual categories can be related directly to the bandwidth of the hypothetical analysis filters, For example, in the simplest case of amplitude fluctuations resulting from the addition of two sine signals with frequencies and, the fluctuation rate is equal to the frequency difference between the two sines and the following statements represent the general consensus:
  1. If the fluctuation rate is smaller than the filter bandwidth, then a single tone is perceived either with fluctuating loudness or with roughness.
  2. 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. 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.
"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."
  • Frequency ratios: When harmonic timbres are played in one of the just intonations, ratios of higher simple numbers are more dissonant than lower ones. However, the farther the timbre departs from the harmonic series, and/or the farther than the tuning departs from a Just Intonation, the less the "frequency ratio" rule applies.
In human hearing, the varying effect of simple ratios may be perceived by one of these mechanisms:
  • Fusion or pattern matching: fundamentals may be perceived through pattern matching of the separately analyzed partials to a best-fit exact-harmonic template, or the best-fit subharmonic, or harmonics may be perceptually fused into one entity, with dissonances being those intervals less likely mistaken for unisons, the imperfect intervals, because of the multiple estimates, at perfect intervals, of fundamentals, for one harmonic tone. By these definitions, inharmonic partials of otherwise harmonic spectra are usually processed separately, unless frequency or amplitude modulated coherently with the harmonic partials. For some of these definitions, neural firing supplies the data for pattern matching; see directly below.
  • Period length or neural-firing coincidence: with the length of periodic neural firing created by two or more waveforms, higher simple numbers creating longer periods or lesser coincidence of neural firing and thus dissonance. Purely harmonic tones cause neural firing exactly with the period or some multiple of the pure tone.
  • Dissonance is more generally defined by the amount of beating between partials. Terhardt calls this "sensory dissonance". By this definition, dissonance is dependent not only on the width of the interval between two notes' fundamental frequencies, but also on the widths of the intervals between the two notes' non-fundamental partials. Sensory dissonance is associated with the inner ear's inability to fully resolve spectral components with excitation patterns whose critical bands overlap. If two pure sine waves, without harmonics, are played together, people tend to perceive maximum dissonance when the frequencies are within the critical band for those frequencies, which is as wide as a minor third for low frequencies and as narrow as a minor second for high frequencies. If harmonic tones with larger intervals are played, the perceived dissonance is due, at least in part, to the presence of intervals between the harmonics of the two notes that fall within the critical band. The sensory consonance or dissonance of any given interval, in any given tuning, can be adjusted by adjusting the partials in the timbre to be maximally aligned or mis-aligned, respectively, with the notes of the related tuning.
  • Dissonance sensation is a result of brain's response to unusual or rare sound perceptions. The brain is remembering and ranking the sound patterns that usually enters the ears, and if an unusual sound is listened to, a well known EEG pattern emerges indicating an oddball event. This causes slight stress in the listener, which is causing the sensation of dissonance. In the same paper, Pankovski and Pankovska show by a software simulated neural network that the brain is capable of such remembering and ranking of the sound patterns, thus perfectly reproducing the well known Helmholtz's list of two-tone intervals ordered by consonance/dissonance, for the first time in the history of studying these phenomena. As a consequence, Pankovski and Pankovska suggest that the consonance and dissonance are biologically dependent for the more consonant sounds, and culturally dependent for the more dissonant sounds.
Generally, the sonance 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. The sonance of the interval between two notes can be maximized by maximizing the alignment of the two notes' partials, whereas it can be minimized 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. cadence, the authentic cadence, dominant to tonic, is in part created by the dissonant tritone created by the seventh, also dissonant, in the dominant seventh chord, which precedes the tonic.
File:Dominant seventh tritone resolution.png|thumb|Tritone resolution inwards and outwards
File:Ii-V-I turnaround in C.png|thumb|center|Perfect authentic cadence : ii–V–I progression in C