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 (i.e. sounds with harmonic partials).

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 do 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 (e.g. a major triad in 20th century atonal music). A major second (e.g. the notes C and D played simultaneously) 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 (or pitch) 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". (See also Noise in music and Noise music.)

While consonance and dissonance exist only between sounds and therefore necessarily describe intervals (or chords), such as the perfect intervals, which are often viewed as consonant (e.g., the unison and octave). 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 (G7, which consists of the pitches G, B, D and F), 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. Tonal fusion occurs when a listener perceives two or more tones as one tone.

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 (i.e., the musical tuning), but also on the combined spectral distribution and thus sound quality (i.e., the timbre) of the notes (see Critical band). 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

A stable tone combination is a consonance; consonances are points of arrival, rest, and resolution.

An unstable tone combination is a dissonance; its tension demands an onward motion to a stable chord. Thus dissonant chords are "active"; traditionally they have been considered harsh and have expressed pain, grief, and conflict.

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 sevenths

tritones

minor seconds and major sevenths

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 (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.

"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 (fluctuations between about 20 per second and 75–150 per second).

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, 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 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:

Instruments producing non-harmonic overtone series

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.

According to John Gouwens, the carillon's harmony profile is summarized:

Consonant: minor third, tritone, minor sixth, perfect fourth, perfect fifth, and possibly minor seventh or even major second

Dissonant: major third, major sixth

Variable upon individual instrument: major seventh

Interval inversion does not apply.

In history of Western music

Dissonance has been understood and heard differently in different musical traditions, cultures, styles, and time periods. Relaxation and tension have been used as analogy since the time of Aristotle till the present.

The terms dissonance and consonance are often considered equivalent to tension and relaxation. A cadence is (among other things) a place where tension is resolved; hence the long tradition of thinking of a musical phrase as consisting of a cadence and a passage of gradually accumulating tension leading up to it.

Various psychological principles constructed through the audience's general conception of tonal fluidity determine how a listener will distinguish an instance of dissonance within a musical composition. Based on one's developed conception of the general tonal fusion within the piece, an unexpected tone played slightly variant to the overall schema will generate a psychological need for resolve. When the consonant is followed thereafter, the listener will encounter a sense of resolution. Within Western music, these particular instances and psychological effects within a composition have come to possess an ornate connotation.

The application of consonance and dissonance "is sometimes regarded as a property of isolated sonorities that is independent of what precedes or follows them. In most Western music, however, dissonances are held to resolve onto following consonances, and the principle of resolution is tacitly considered integral to consonance and dissonance".

Antiquity and the middle ages

In Ancient Greece, armonia denoted the production of a unified complex, particularly one expressible in numerical ratios. Applied to music, the concept concerned how sounds in a scale or a melody fit together (in this sense, it could also concern the tuning of a scale). The term symphonos was used by Aristoxenus and others to describe the intervals of the fourth, the fifth, the octave and their doublings; other intervals were said diaphonos. This terminology probably referred to the Pythagorean tuning, where fourths, fifths and octaves (ratios 4:3, 3:2 and 2:1) were directly tunable, while the other scale degrees (other 3 prime ratios) could only be tuned by combinations of the preceding. Until the advent of polyphony and even later, this remained the basis of the concept of consonance versus dissonance (symphonia versus diaphonia) in Western music theory.

In the early Middle Ages, the Latin term consonantia translated either armonia or symphonia. Boethius (6th century) characterizes consonance by its sweetness, dissonance by its harshness: "Consonance (consonantia) is the blending (mixtura) of a high sound with a low one, sweetly and uniformly (suauiter uniformiterque) arriving to the ears. Dissonance is the harsh and unhappy percussion (aspera atque iniocunda percussio) of two sounds mixed together (sibimet permixtorum)". It remains unclear, however, whether this could refer to simultaneous sounds. The case becomes clear, however, with Hucbald of Saint Amand (c. 900 ce), who writes:

"Consonance (consonantia) is the measured and concordant blending (rata et concordabilis permixtio) of two sounds, which will come about only when two simultaneous sounds from different sources combine into a single musical whole (in unam simul modulationem conveniant) ... There are six of these consonances, three simple and three composite, ... octave, fifth, fourth, and octave-plus-fifth, octave-plus-fourth and double octave".

According to Johannes de Garlandia:

Perfect consonance: unisons and octaves.

(Perfecta dicitur, quando due voces junguntur in eodem tempore, ita quod una, secundum auditum, non percipitur ab alia propter concordantiam, et dicitur equisonantiam, ut in unisono et diapason.

Renaissance

In Renaissance music, the perfect fourth above the bass was considered a dissonance needing immediate resolution. The regola delle terze e seste ("rule of thirds and sixths") required that imperfect consonances should resolve to a perfect one by a half-step progression in one voice and a whole-step progression in another. The viewpoint concerning successions of imperfect consonances—perhaps more concerned by a desire to avoid monotony than by their dissonant or consonant character—has been variable. Anonymous XIII (13th century) allowed two or three, Johannes de Garlandia's Optima introductio (13th–14th century) three, four or more, and Anonymous XI (15th century) four or five successive imperfect consonances. Adam von Fulda wrote "Although the ancients formerly would forbid all sequences of more than three or four imperfect consonances, we more modern do not prohibit them."

Common practice period

In the common practice period, musical style required preparation for all dissonances, followed by a resolution to a consonance. There was also a distinction between melodic and harmonic dissonance. Dissonant melodic intervals included the tritone and all augmented and diminished intervals. Dissonant harmonic intervals included:

Major second and minor seventh

Minor second and major seventh

Augmented fourth and diminished fifth (enharmonically equivalent, tritone)

Early in history, only intervals low in the overtone series were considered consonant. As time progressed, intervals ever higher on the overtone series were considered as such. The final result of this was the so-called "emancipation of the dissonance" by some 20th-century composers. Early-20th-century American composer Henry Cowell viewed tone clusters as the use of higher and higher overtones.

Composers in the Baroque era were well aware of the expressive potential of dissonance:

Bach uses dissonance to communicate religious ideas in his sacred cantatas and Passion settings. At the end of the St Matthew Passion, where the agony of Christ's betrayal and crucifixion is portrayed, John Eliot Gardiner hears that "a final reminder of this comes in the unexpected and almost excruciating dissonance Bach inserts over the very last chord: the melody instruments insist on B natural—the jarring leading tone—before eventually melting in a C minor cadence."

In the opening aria of Cantata BWV 54, Widerstehe doch der Sünde ("do resist sin"), nearly every strong beat carries a dissonance:

Albert Schweitzer says that this aria "begins with an alarming chord of the seventh... It is meant to depict the horror of the curse upon sin that is threatened in the text". Gillies Whittaker points out that "The thirty-two continuo quavers of the initial four bars support four consonances only, all the rest are dissonances, twelve of them being chords containing five different notes. It is a remarkable picture of desperate and unflinching resistance to the Christian to the fell powers of evil."

Neo-classic harmonic consonance theory

George Russell, in his 1953 Lydian Chromatic Concept of Tonal Organization, presents a slightly different view from classical practice, one widely taken up in Jazz. He regards the tritone over the tonic as a rather consonant interval due to its derivation from the Lydian dominant thirteenth chord.

In effect, he returns to a Medieval consideration of "harmonic consonance": that intervals when not subject to octave equivalence (at least not by contraction) and correctly reproducing the mathematical ratios of the harmonic series are truly non-dissonant. Thus the septimal minor seventh, major ninth, neutral eleventh (semiaugmented fourth), neutral thirteenth, and diminished fifteenth must necessarily be consonant.

Most of these pitches exist only in a universe of microtones smaller than a halfstep; notice also that we already freely take the flat (minor) seventh note for the just seventh of the harmonic series in chords. Russell extends by approximation the virtual merits of harmonic consonance to the 12TET tuning system of Jazz and the 12-note octave of the piano, granting consonance to the sharp eleventh note (approximating the harmonic eleventh), that accidental being the sole pitch difference between the major scale and the Lydian mode.

(In another sense, that Lydian scale representing the provenance of the tonic chord (with major seventh and sharp fourth) replaces or supplements the Mixolydian scale of the dominant chord (with minor seventh and natural fourth) as the source from which to derive extended tertian harmony.)

Dan Haerle, in his 1980 The Jazz Language, extends the same idea of harmonic consonance and intact octave displacement to alter Paul Hindemith's Series 2 gradation table from The Craft of Musical Composition. In contradistinction to Hindemith, whose scale of consonance and dissonance is currently the de facto standard, Haerle places the minor ninth as the most dissonant interval of all, more dissonant than the minor second to which it was once considered by all as octave-equivalent. He also promotes the tritone from most-dissonant position to one just a little less consonant than the perfect fourth and perfect fifth.

For context: unstated in these theories is that musicians of the Romantic Era had effectively promoted the major ninth and minor seventh to a legitimacy of harmonic consonance as well, in their fabrics of 4-note chords.