1 Kejind

Consonant 4th Music Definition Essay

Harmony, in music, the sound of two or more notes heard simultaneously. In practice, this broad definition can also include some instances of notes sounded one after the other. If the consecutively sounded notes call to mind the notes of a familiar chord (a group of notes sounded together), the ear creates its own simultaneity in the same way that the eye perceives movement in a motion picture. In such cases the ear perceives the harmony that would result if the notes had sounded together. In a narrower sense, harmony refers to the extensively developed system of chords and the rules that allow or forbid relations between chords that characterizes Western music.

Musical sound may be regarded as having both horizontal and vertical components. The horizontal aspects are those that proceed during time such as melody, counterpoint (or the interweaving of simultaneous melodies), and rhythm. The vertical aspect comprises the sum total of what is happening at any given moment: the result either of notes that sound against each other in counterpoint, or, as in the case of a melody and accompaniment, of the underpinning of chords that the composer gives the principal notes of the melody. In this analogy, harmony is primarily a vertical phenomenon. It also has a horizontal aspect, however, since the composer not only creates a harmonic sound at any given moment but also joins these sounds in a succession of harmonies that gives the music its distinctive personality.

Melody and rhythm can exist without harmony. By far the greatest part of the world’s music is nonharmonic. Many highly sophisticated musical styles, such as those of India and China, consist basically of unharmonized melodic lines and their rhythmic organization. In only a few instances of folk and primitive music are simple chords specifically cultivated. Harmony in the Western sense is a comparatively recent invention having a rather limited geographic spread. It arose less than a millennium ago in the music of western Europe and is embraced today only in those musical cultures that trace their origins to that area.

The concept of harmony and harmonic relationships is not an arbitrary creation. It is based on certain relationships among musical tones that the human ear accepts almost reflexively and that are also expressible through elementary scientific investigation. These relationships were first demonstrated by the Greek philosopher Pythagoras in the 6th century bce. In one of his most famous experiments, a stretched string was divided by simple arithmetical ratios (1:2, 2:3, 3:4,…) and plucked. By this means he demonstrated that the intervals, or distances between tones, that the string sounded before and after it was divided are the most fundamental intervals the ear perceives. These intervals, which occur in the music of nearly all cultures, either in melody or in harmony, are the octave, the fifth, and the fourth. (An octave, as from C to the C above it, encompasses eight white notes on a piano keyboard, or a comparable mixture of white and black notes. A fifth, as from C to G, encompasses five white notes; a fourth, as from C to F, four white notes.) In Pythagoras’s experiment, for example, a string sounding C when cut in half sounds C, or the note an octave above it. In other words, a string divided in the ratio 1:2 yields the octave (c) of its fundamental note (C). Likewise, the ratio 2:3 (or two-thirds of its length) yields the fifth, and the ratio 3:4, the fourth.

These notes—the fundamental and the notes a fourth, a fifth, and an octave above it—form the primary musical intervals, the cornerstones on which Western harmony is built.

The roots of harmony

The organized system of Western harmony as practiced from c. 1650 to c. 1900 evolved from earlier musical practices: from the polyphony—music in several voices, or parts—of the late Middle Ages and the Renaissance and, ultimately, from the strictly melodic music of the Middle Ages that gave rise to polyphony. The organization of medieval music, in turn, derives from the medieval theorists’ fragmented knowledge of ancient Greek music.

Although the music of ancient Greece consisted entirely of melodies sung in unison or, in the case of voices of unequal range, at the octave, the term harmony occurs frequently in the writings on music at the time. Leading theorists such as Aristoxenus (flourished 4th century bce) provide a clear picture of a musical style consisting of a wide choice of “harmonies,” and Plato and Aristotle discuss the ethical and moral value of one “harmony” over another.

In Greek music a “harmony” was the succession of tones within an octave—in modern usage, a scale. The Greek system embraced seven “harmonies,” or scale types, distinguished from one another by their particular order of succession of tones and semitones (i.e., whole steps and half steps). These “harmonies” were later erroneously called modes, a broader term involving the characteristic contours of a melody, as well as the scale it used.

Harmony before the common practice period

By the 9th century the practice had arisen in many churches of performing portions of plainchant melodies with an added, harmonizing voice—possibly as a means of greater emphasis, or of reinforcing the sound to carry through the larger churches that were being built at the time. This harmonizing technique, called organum, is the first true example of harmony. The first instances were extremely simple, consisting of adding a voice that exactly paralleled the original melody at the interval of a fourth or fifth (parallel organum).

Within a short time the new technique was explored in far greater diversity. Added harmonic lines took on melodic independence, often moving in opposite, or contrary, motion to the given melody. This style was called free organum. In such cases it was impossible to maintain at all times the accepted harmonies of fourth, fifth, and octave. These intervals were considered consonances—i.e., intervals that, because of their clear sonority, implied repose, or resolution of tension. In free organum they were used at the principal points of articulation: the beginnings and ends of phrases and at key words in the text. In between occurred other intervals that were relatively dissonant; i.e., they implied less repose and more tension.

Free organum is an early example of harmonic motion from repose to tension to repose, basic to Western harmony. The emphasis on consonances at the end of compositions set the final points of arrival in strong relief and reinforced the idea of the cadence, or the finality of the keynote of a mode (on which pieces normally ended).

Rise of the intervals of the third and the sixth

Until the late 14th century the attitude toward consonance, especially among continental composers, adhered largely to the Pythagorean ideal, which accepted as consonances only intervals expressible in the simplest numerical ratios—fourths, fifths, and octaves. But in England the interval of the third (as from C to E) had been in common use for some time, although it is not expressible as such a simple ratio. A kind of English organum known as gymel, in which the voices move parallel to each other at the interval of a third, existed in the late 12th century; and in the famous Sumer is icumen in canon of the 13th century, a remarkably elaborate piece for the time, the harmonic style is almost entirely centred on thirds. The sixth (as from E to C), an interval closely related to the third, was also common in English music. These two intervals sounded much sweeter than did the hollow-sounding fourths, fifths, and octaves.

By the early 15th century, in part because of the visits of the illustrious English composer John Dunstable to the courts of northern France, the third and sixth had become accepted in European music as consonant intervals (prior to this time they were considered mildly dissonant). The result was an enrichment of the harmony in musical compositions.

This was a time, too, of a developing awareness of tonality, the concept of developing a composition with a definite keynote used as a point of departure at the beginning and as a point of arrival at the final cadence.

At this time there also began the tendency by composers to think of harmony as a “vertical” phenomenon, to regard the sound of notes heard simultaneously as a definite entity. Although the basic style of composition was primarily linear—i.e., concerned with counterpoint—the chords that emerged from the coincidences of notes in contrapuntal lines took on a personality of their own. One phenomenon that bears out this development is fauxbourdon (French: “false bass”), or, in England, faburden. This was a musical style in which three voices move parallel to one another. The middle voice consisted of a succession of notes in parallel organum a fourth below the top voice, and the lowest voice paralleled the sequence a third below the middle voice, producing a chord such as G–B–E, known as a 6/3, or first inversion, chord. This was originally an English development adopted in the 15th century by continental composers seeking to enrich their harmonies. It combined the continental fondness for “pure” intervals such as the fourth (here, B–E) with the English taste for parallel thirds (here, G–B) and sixths (here, G–E).

The weakening of the modes

A final phenomenon in early 15th-century harmonic practice clearly foreshadowed the end of the ancient modal system in favour of the major and minor modes of the later common practice period. The old modes were used by composers of the time, and they persisted to some extent until the end of the 16th century. But their purity became undermined by a growing tendency to introduce additional notes outside the mode. This was achieved by writing either a flat or sharp sign into the manuscript, or by leaving the performer to understand that he was expected to improvise accordingly. The effect of this musica ficta (Latin: “invented music”), as the technique of introducing nonmodal notes was called, was to break down the distinction between modes. A mode owes its distinctive character to its specific pattern of whole and half steps. Introducing sharps and flats upsets the mode’s normal pattern by placing half steps at unusual points. In many cases the resulting change made one mode resemble another. For example, adding an F♯ to the medieval Mixolydian mode (from G to G on the white keys of the piano) made that mode’s intervals identical with those of the Ionian mode (from C to C on the white keys), which in turn is identical with the modern major scale.

Likewise, adding a B♭ to the Dorian mode (from D to D) made its intervals equivalent to those of the Aeolian (A to A) mode, which is identical with one form of the modern minor scale. As this practice became increasingly prevalent, the major and minor modes gradually became predominant over the medieval church modes. The process is especially observable in the music of the late Renaissance.

New uses of dissonance

At the same time there emerged a more sophisticated attitude toward dissonance, favouring its use for expressive purposes. By the time of the Flemish Josquin des Prez, the leading composer of the Renaissance, contrapuntal music had assumed a more resonant texture through the use of four-, five-, and six-part writing instead of the older three-part scoring. The increased number of voices led to further enrichment of the harmony. A typical Josquin device using harmony for expressive purposes was the suspension, a type of dissonant harmony that resolved to a consonance. Suspensions arose from the chords occurring in contrapuntal music. In a suspension one note of a chord is sustained while the other voices change to a new chord. In the new chord the sustained, or “suspended,” note is dissonant. One or two beats later the suspended voice changes pitch so that it resolves into, or becomes consonant with, the chord of the remaining voices. The following illustration from Jean d’Okeghem’sMissa prolationum shows a suspension at the cadence.

The suspension, which became a standard musical device, creates tension because the expected harmony is delayed until the suspended voice resolves. Its use as the next to last chord of a cadence, or stopping point, was favoured by composers as a way to enhance, through dissonance resolving to consonance, the sense of completeness of the final chord. The use of suspensions indicates a growing awareness of chords as entities, rather than coincidences, that have expressive potential and of the concept that harmony moves through individual chords toward a goal. This concept was developed in the harmony of the common practice period.

At the end of the 16th century there was an upheaval in musical style. Contrapuntal writing was frequently abandoned, and composers sought out a style that placed greater emphasis on an expressive melodic line accompanied, or supported, by harmonies. This style, called monody, brought about no marked changes in the harmonic language (the particular chords used), although such composers as the Italian Claudio Monteverdi did experiment with a heightened use of dissonance toward expressive ends. The major change at this time was in the conception of harmony. The bass line became the generating force upon which harmonies were built. It was often written out with figures below it to represent the harmonies to be built upon it. From this single line—plus figures, known variously as figured bass, basso continuo, or thorough bass—the accompanying instrumentalists were expected to improvise, or “realize,” a full harmonic underpinning for the melody of the topmost voice or voices. There was, thus, a polarization between the melodic and bass lines, with everything in the middle regarded as harmonic filling-in. This contrasts markedly with the older concept, in which all voices were regarded as of equal importance, with the harmony resulting from the interweaving of all parts.

Classical Western harmony

The approach to harmony according to which chords are purposely built up from their bass note marked the beginning of the common practice period of Western harmony. The transition began around 1600 and was nearly complete by 1650. Certain new concepts became important. These had their roots in the harmonic practices of the late Middle Ages and Renaissance and in the medieval modal system. They include the concepts of key, of functional harmony, and of modulation.

A key is a group of related notes belonging to either a major or minor scale, plus the chords that are formed from those notes, and the hierarchy of relationships among those chords. In a key the tonic, or keynote, such as C in the key of C—and thus the chord built on the keynote—is a focal point toward which all chords and notes in the key gravitate. This is a further development of the idea of a harmonic goal that appeared in the music of the late Renaissance and that ultimately developed from the medieval idea that modes have characteristic final notes.

In the new system keys further assumed relationships to one another. The larger organizational system embracing keys, key relationships, chord relationships, and harmonic goals was called tonality, or the major-minor system of tonality, because the keys were built on major and minor scales. In the tonal system, given chords assumed specific functions in moving toward or away from harmonic goals, and the system assigning goals to all chords was called functional harmony. The main goal was the keynote, or tonic, of the principal, or tonic, key. Modulation, or change of key, became an important factor in composition because it allowed the composer to exploit the listener’s ability to sense the relations between keys.

Rameau’s theories of chords

The approach to harmony that emerged about 1650 (the bass-note approach) was soon formalized in one of the most important musical treatises of the common practice period, Traité de l’harmonie (1722), by the French composer Jean-Philippe Rameau. The crux of Rameau’s theory is the argument that all harmony is based on the “root” or fundamental note of a chord; for example, D. Other notes are placed a third (as D–F or D–F♯) and a fifth (as D–A) above the root. A chord formed in this way is a triad (as D–F–A or D–F♯–A), the basic chord type of the common practice period. The third and fifth above the triad can be placed within the same octave as the root (close position) or can be spread out over several octaves (open position) in compound intervals such as an octave plus a third or two octaves plus a fifth. A triad can exist in its basic, or root position, with the root as the lowest, or bass, note (as D–F♯–A). It can also exist in inversions or rearrangements of its notes placing the third or fifth in the bass, as F♯–A–D (first inversion) and A–D–F♯′ (second inversion).

Theorists after Rameau observed that inverted chords are less stable than chords in root position; at the end of a composition, for example, they do not have sufficient finality. Although Rameau’s monumental work contains certain elements that later practices tended to disprove, his writing remains the basis for the study of common-practice harmony.

By Rameau’s time no vestige remained of the ancient modal system, which was replaced by 12 major and 12 minor keys beginning on each of the 12 notes of the piano keyboard (C, C♯, D,…A♯, B). The invention in the late 17th century of equal temperament (seetuning and temperament) made it possible to play keyboard and other instrumental music in all 24 keys of the chromatic system, the system embracing all possible notes of the 24 scales. Such a work as J.S. Bach’sWell-Tempered Clavier was, among many things, a set of exercises to acquaint keyboard players with this newfound freedom. Equal temperament also made it possible for a composer to modulate freely from one key to another to obtain contrast in works of an extended nature. Modulation was no new invention, but it now became of prime importance.

In normal, or functional, harmony, the succession of chords is analyzed by the distance, or interval, between their roots. The most common movement from chord to chord is through “strong” intervals: fourths (as C to F), fifths (as C to G), and seconds (as C to D). A movement from one chord to another having this root relation is strong because the two chords have the fewest notes in common and therefore contrast more with each other. Movement by “weak” intervals—thirds (as C to E) and sixths (as C to the A above it)—is weaker, or less pronounced, because the two chords in this case usually share two out of their three notes; for example, C–E–G and E–G–B, or C–E–G and A–C–E. Similarly, modulation from one key to another in the course of a piece was most characteristically from one key to another whose keynote is a strong interval apart from that of the first key, as from C to G. Usually the modulation was to the key built on the fifth note, or dominant, of the original scale. A work in C major, for example, tended to move toward the area of G. In works in a minor key, the modulation might be to the dominant minor key (A minor to E minor, for example); or it might be to the relative major key (the key that shares the same scale notes as the minor scale but arranging them in major scale order rather than minor scale order [A minor and C major, for example]). In the second case the contrast of major and minor mode appeared to compensate for the weak modulation (A and C are a third apart).

Harmony and modulation in the 18th century

By the early 18th century these modulatory principles were well established and were made use of in musical form. In the keyboard sonatas of Domenico Scarlatti, for example, or the instrumental dance movements in Bach’s partitas, the opening key is well established at the beginning of the piece. There then begins a movement to a new key, normally the dominant key. This is characteristically achieved by an emphasis on chords common to both keys (known as “pivots”), plus a strong musical statement in the new key leading to a cadence in that key. After the modulation there is a process of return to the initial key. During this process the harmonic motion tends to be more rapid, passing quickly through many chords and often including momentary diversions into many new keys, thus lending greater impact to the eventual return to the original key. Such a composition is said to be in “binary form.” In binary form compositions in a minor key, there occasionally occurred an exception to the rule of return to the home key. The composer could at his option return to the tonic major, the major key built on the same keynote, or tonic, as the original minor key—A major from A minor, for example. But even in this case the harmonic goal toward the tonic note (A in this case) remained the same.

This basic modulatory scheme from tonic key to dominant key back to tonic key formed the basis of the large-scale musical forms that developed during the 18th century and persisted well into the 19th. The sonata forms of Mozart and Haydn, with their exposition, development, and recapitulation, adhere closely to this plan, often greatly expanded. Here the movement from the tonic to the dominant key or to the relative major key made up the exposition; the rapid harmonic movement en route back to the tonic made up the development; and the return to the tonic key—usually reinforced by a return of the initial thematic (melodic) material—signalled the start of the recapitulation. An optional final coda, or concluding section, further strengthened the sense of the tonal journey’s having come to an end. In the large, multi-movement works from this period, there was usually a further contrast achieved by having one of the inner movements in another key, but the final movement almost invariably was once again in the same key as the first movement.

Romantic changes in classical harmony

This clear and logical system of organization seemed highly consistent with an age that took its cues from the clarity and balance of ancient classical architecture. It was not so consistent, however, with the ideals of the ensuing era of Romanticism. Already in the mature works of Beethoven, there is the beginnings of a breaking-down of the classic modulatory scheme; the opening movement of the Waldstein Sonata, Opus 53 (completed, 1804), for example, is built on a modulation from the tonic, C major, to the sharply contrasting key of E major, instead of the expected key of G. Much of the individual harmonic language of Franz Schubert is based on his purposeful disavowal of modulation via the smooth succession of pivot chords and his fondness, instead, for dropping suddenly into unrelated, and therefore unexpected, keys, as C major to E flat major in the opening movement of the String Quintet in C Major, Opus 163 (1828); C major to E minor in the opening movement of the Symphony No. 9 in C Major (1828), known as the Great Symphony.

Throughout the 19th century there was also a great increase in the use of chromatic tones—tones not belonging to the scale of a given key and that formed “foreign,” sometimes dissonant, harmonies with the notes of that key. In addition to the triad, the typical chord of functional harmony, other more complex chords were used, the harmonic functions of which were extremely ambiguous to the listener. As a result the sense of clearly established tonality created by traditional harmonies began to vanish from the musical language—doubtless in line with composers’ greater obsession with music and all arts as something mysterious and personalized.

By the time of the German composer Richard Wagner, the sense of tonality as the unifying musical force showed definite signs of disintegration. For one thing, Wagner’s idea of the “endless melody” led him in his late works to abjure almost completely, except at the end of acts, the full cadence that establishes tonality. A seeming approach to a cadence in Tristan und Isolde or the Ring des Nibelungen tetralogy is more often than not thwarted by a quick and unprepared switch to a sharply contrasting key and a continuation of the music in that new area. For another, Wagner’s passion for complex chords subject to more than one functional interpretation made the tonality of even short passages difficult to assess.

Although Wagner’s specific harmonic concepts were not universally accepted, during his time or afterward, the blurring of the tonal sense by one means or another became prevalent throughout Western music by the last decades of the 19th century. Even in the works of the Italian Giuseppe Verdi, whose music was regarded as the opposite pole from Wagnerian techniques, this abandonment of clear tonal outlines may be noted: the sudden changes to unrelated keys, the piling up of dissonances that leave the sense of key obscured for minutes at a time, the emergence in his late works of a continuous melodic style that avoided regular, key-defining cadences. In France the blurring of clear outlines characteristic of Impressionist painters found its musical counterpart in the music of Claude Debussy, who employed such devices as the scale consisting entirely of whole tones as a means of sidestepping the tonal feeling created by traditional scales. In the music of later French composers, especially the members of the post-World War I group known as “Les Six,” a common practice was polytonality, or the sounding of two tonalities simultaneously, each defined with relative clarity but neither dominating the other. Similar polytonal methods also occur in the works of the Hungarian-born Béla Bartók and the Russian émigré Igor Stravinsky.

Schoenberg’s 12-tone row

The Wagnerian influence continued most directly, via the music of Gustav Mahler, into the serial techniques developed in the 1920s by Arnold Schoenberg and his Viennese school. In Schoenberg’s serialism the 12 notes of the chromatic scale are arranged into an arbitrary series, or 12-tone row, that becomes the basis for the melodies, counterpoint, and harmonies of the composition. Of these 12 notes no single note is allowed to predominate. This is in complete contrast to the predominance of the tonic, or keynote, in the music of the late Renaissance and the common practice period. Serialism thus completely and systematically obliterated traditional harmonic organization. With no single note serving as a musical goal, tonality—at least as it was known from the 15th century—ceased to be a unifying musical force. Other elements, including serialization of rhythms and tone colours as well as of notes, came to prevail.

For other uses, see Literary consonance, North/South Consonance Ensemble, and Dissonance (disambiguation).

In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Consonance is associated with sweetness, pleasantness, and acceptability; dissonance is associated with harshness, unpleasantness, or unacceptability.

The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and reciprocally. 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" (Hindemith 1942, p. 85).

The opposition 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- and/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 (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, Noise music and Noise (acoustic).)

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.

Consonance[edit]

Consonances may include:

The definition of consonance has been variously based on experience, frequency, and both physical and psychological considerations (Myers 1904, p. 315). These include:

  • Frequency ratios: with ratios of lower simple numbers being more consonant than those that are higher (Pythagoras[full citation needed]). Many of these definitions do not require exact integer tunings, only approximation.[vague][citation needed]
  • Coincidence of partials: with consonance being a greater coincidence of partials (Helmholtz & 1954 [1877],[page needed]). 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 the entry under 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 (Roederer 1995, p. 165). Although Helmholtz's work focused almost exclusively on harmonic timbres and also the tunings, subsequent work has generalized his findings to embrace non-harmonic tunings and timbres (Sethares 1992; Sethares 2005[not in citation given][page needed]; Milne, Sethares, and Plamondon 2007,[page needed]; Milne, Sethares, and Plamondon 2008,[page needed]; Sethares et al. 2009,[page needed]).
  • Fusion: perception of unity or tonal fusion between two notes (Stumpf 1890, pp. 127–219; Butler and Green 2002, p. 264).

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

— Roger Kamien 2008, p. 41

Dissonance[edit]

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.

— Roger Kamien 2008, p. 41

In Western music, dissonance is the quality of sounds that seems unstable and has an aural need to resolve to a stable consonance. Both consonance and dissonance are words applied to harmony, chords, and intervals and, by extension, to melody, tonality, and even rhythm and metre. Although there are physical and neurological facts important to understanding the idea of dissonance, the precise definition of dissonance is culturally conditioned—definitions of and conventions of usage related to dissonance vary greatly among different musical styles, traditions, and cultures. Nevertheless, the basic ideas of dissonance, consonance, and resolution exist in some form in all musical traditions that have a concept of melody, harmony, or tonality.[citation needed] Dissonance being the complement of consonance it may be defined, as above, as non-coincidence of partials, lack of fusion or pattern matching, or as complexity.

Additional confusion about the idea of dissonance is created by the fact that musicians and writers sometimes use the word dissonance and related terms in a precise and carefully defined way, more often in an informal way, and very often in a metaphorical sense ("rhythmic dissonance"). For many musicians and composers, the essential ideas of dissonance and resolution are vitally important ones that deeply inform their musical thinking on a number of levels.[citation needed]

Despite the fact that words like unpleasant and grating are often used to explain the sound of dissonance, all music with a harmonic or tonal basis—even music perceived as generally harmonious—incorporates some degree of dissonance. The buildup and release of tension (dissonance and resolution), which can occur on every level from the subtle to the crass, is partially responsible for what listeners perceive as beauty, emotion, and expressiveness in music.[citation needed]

Musical style[edit]

The concept of dissonance does not belong to the domain of harmony as it is presented us by Nature [harmonic series], but is derived from voice leading [guidelines], which is an essential constituent of Art.

— Oswald Jonas (Jonas 1982, p. 19)

Understanding a particular musical style's treatment of dissonance—what is considered dissonant and what rules or procedures govern how dissonant intervals, chords, or notes are treated—is key in understanding that particular style. For instance, harmony is generally governed by chords, which are collections of notes defined as tolerably consonant by the style. (There is likely, however, to be a hierarchy of chords, with some considered more consonant and some more dissonant.) Any note that does not fall within the prevailing harmony is considered dissonant. A given style typically pays attention to how its musical structure approaches dissonance (in steps is less jarring, a leap is more jarring), and even more to how they resolve (almost always by step), to how they fit within the meter and rhythm (dissonances on strong beats are more emphatic, those on weaker beats less vital), and to how they lie within the phrase (dissonances tend to resolve at phrase's end).[citation needed]

In traditional music[edit]

Sharp dissonant intervals and chords play a prominent role in many traditional musical cultures. Vocal polyphonic traditions from Bulgaria, Serbia, Bosnia-Herzegovina, Albania, Latvia, Georgia, Nuristan, some Vietnamese and Chinese minority singing traditions, Lithuanian sutartinės, some polyphonic traditions from Flores and Melanesia are predominantly based on the use of sharp dissonant intervals and chords. The most prominent dissonance in most of these cultures is the interval of the neutral second (which is between the minor and major seconds). This interval is known to create the maximum sharpness and is known in German ethnomusicology under the term "Schwebungsdiaphonie".

Physiological basis[edit]

Musical styles are similar to languages, in that certain physical, physiological, and neurological facts create bounds that greatly affect the development of all languages. Nevertheless, different cultures and traditions have incorporated the possibilities and limitations created by these physical and neurological facts into vastly different, living systems of human language. Neither the importance of the underlying facts nor the importance of the culture in assigning a particular meaning to the underlying facts should be understated.[citation needed]

For instance, two notes played simultaneously but with slightly different frequencies produce a beating "wah-wah-wah" sound. Musical styles such as traditional European classical music consider this effect objectionable ("out of tune") and go to great lengths to eliminate it. Other musical styles such as Indonesian gamelan consider this sound an attractive part of the musical timbre and go to equally great lengths to create instruments that produce this slight "roughness" (Vassilakis 2005,[page needed]).

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.[citation needed]

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 1885; Levelt and Plomp 1964,[page needed]), the above perceptual categories can be related directly to the bandwidth of the hypothetical analysis filters (Zwicker, Flottorp, and Stevens 1957,[page needed]; Zwicker 1961,[page needed]). 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:

  1. If the fluctuation rate is smaller than the filter bandwidth, then a single tone is perceived either with fluctuating loudness (beating) 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 (Terhardt 1974,[page needed]; Vassilakis 2001,[page needed]). 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 (Vassilakis 2001; Vassilakis 2005; Vassilakis 2007).

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.

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 (Gerson and Goldstein 1978,[page needed]) or the best-fit subharmonic (Terhardt 1974,[page needed]), 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 (Terhardt 1974,[page needed]). By these definitions, inharmonic partials of otherwise harmonic spectra are usually processed separately (Hartmann et al., 1990), unless frequency or amplitude modulated coherently with the harmonic partials (McAdams 1983). For some of these definitions, neural firing supplies the data for pattern matching; see directly below (e.g., Moore 1989, pp. 183–87; Srulovicz and Goldstein 1983).
  • 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 (Patterson 1986,[page needed]; Boomsliter and Creel 1961,[page needed]; Meyer 1898,[page needed]; Roederer 1973, pp. 145–49). 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 (called harmonics or overtones when occurring in harmonic timbres) (Helmholtz & 1954 [1877],[page needed]). Terhardt 1984,[page needed] 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 (i.e., presence of beating and/or roughness in a sound) 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 (relative to the range of human hearing) (Sethares 2005, p. 43). 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 (Roederer 1995, p. 106).

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) (Sethares 2005, p. 1). 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 (Sethares 2005, p. 1; Sethares 2009,[page needed]).

Controlling the sonance of more-or-less non-harmonic timbres in real time is an aspect of dynamic tonality. For example, in Sethares' piece C To Shining C (discussed here), the sonance of intervals is affected both by tuning progressions and timbre progressions.

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(Benward & Saker 2003, p. 54) created by the seventh, also dissonant, in the dominant seventh chord, which precedes the tonic.

Instruments producing non-harmonic overtone series[edit]

Musical instruments like bells and xylophones, called Idiophones, are played such that their relatively stiff, non-trivial[clarification needed] mass is excited to vibration by means of a blow. 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 (Gouwens 2009, p. 3).

According to John Gouwens (2009, p. 3), 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[edit]

When we consider musical works we find that the triad is ever-present and that the interpolated dissonances have no other purpose than to effect the continuous variation of the triad.
— Lorenz Mizler 1739 (quoted in Forte 1979, p. 136)

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 (Kliewer 1975, p. 290).

One of the early composers known for use of dissonants was Monteverdi (Kempers and Bakker 1949, p. 14: "His use of dissonants was in contradiction to all known rules; his melodies showed unheard-of intervals; he even neglected the rules of counterpoint, secure in his conviction that the new subjective art form needed a new means of expression"). The use of dissonants was also practiced by Moscheles (Anon. 1826, p. 349: "It however appears, that Mr. Moscheles, according to the most esteemed writers and the rules of composition, is perfectly justified in writing it D flat. The D flat is here a diminished 7th, which, though a dissonant, is not necessarily resolved in all cases") and taught by Chopin (Eigeldinger, Howat, and Shohet 1988, p. 42: "Musical prosody and declamation; phrasing—Here are the chief practical directions as to expression which Chopin often repeated to his pupils: A long note is stronger, as is also a high note. A dissonant is likewise stronger, and equally so a syncopated note. The ending of a phrase, before a comma, or a stop, is always weak. If the melody ascends, one plays crescendo, if it descends, decrescendo. Moreover, notice must be taken of natural accents.)"

Antiquity and Middle-Ages[edit]

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) (Philip 1966, pp. 123–24). 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 degrees (other 3-prime ratios) could only be tuned by combinations of the preceding (Aristoxenus 1902, pp. 188–206 See Tenney 1988, pp. 11–12). Until the advent of polyphony and even later, this remained the basis of the concept of consonance/dissonance (symphonia/diaphonia) in Occidental 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)" (Boethius n.d., f. 13v.). It remains unclear, however, whether this could refer to simultaneous sounds. The case becomes clear, however, with Hucbald of Saint Amand (c900), 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" (Hucbald n.d., p. 107; translated in Babb 1978, p. 19).

According to Johannes de Garlandia & 13th century:

  • 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. — "[Consonance] is said perfect, when two voices are joined at the same time, so that the one, by audition, cannot be distinguished from the other because of the concordance, and it is called equisonance, as in unison and octave.")
  • Median consonance: fourths and fifths. (Medie autem dicuntur, quando duo voces junguntur in eodem tempore; que neque dicuntur perfecte, neque imperfecte, sed partim conveniunt cum perfectis, et partim cum imperfectis. Et sunt due species, scilicet diapente et diatessaron. — "Consonances are said median, when two voices are joined at the same time, which neither can be said perfect, nor imperfect, but which partly agree with the perfect, and partly with the imperfect. And they are of two species, namely the fifth and the fourth.")
  • Imperfect consonance: minor and major thirds. (Imperfect consonances are not formally mentioned in the treatise, but the quotation above concerning median consonances does refer to imperfect consonances, and the section on consonances concludes: Sic apparet quod sex sunt species concordantie, scilicet: unisonus, diapason, diapente, diatessaron, semiditonus, ditonus. — "So it appears that there are six species of consonances, that is: unison, octave, fifth, fourth, minor third, major third." The last two appear as imperfect consonances by elimination.)
  • Imperfect dissonance: major sixth (tone + fifth) and minor seventh (minor third + fifth). (Imperfecte dicuntur, quando due voces junguntur ita, quod secundum auditum vel possunt aliquo modo compati, tamen non concordant. Et sunt due species, scilicet tonus cum diapente et semiditonus cum diapente. — [Dissonances] are said imperfect, when two voices are joined so that by audition although they can to some extent match, nevertheless they do not concord. And there are two species, namely tone plus fifth and minor third plus fifth.")
  • Median dissonance: tone and minor sixth (semitone + fifth). (Medie dicuntur, quando due voces junguntur ita, quod partim conveniunt cum perfectis, partim cum imperfectis. Et iste sunt due species, scilicet tonus et simitonium cum diapente. — [Dissonances] are said median when two voices are joined so that they partly match the perfect, partly the imperfect. And they are of two species, namely tone and semitone plus fifth.")
  • Perfect dissonance: semitone, tritone, major seventh (major third + fifth). (Here again, the perfect dissonances can only be deduced by elimination from this phrase: Iste species dissonantie sunt septem, scilicet: semitonium, tritonus, ditonus cum diapente; tonus cum diapente, semiditonus cum diapente; tonus et semitonium cum diapente. — These species of dissonances are seven: semitone, tritone, major third plus fifth; tone plus fifth, minor third plus fifth; tone and semitone plus fifth.")

One example of imperfect consonances previously considered dissonances[clarification needed] in Guillaume de Machaut's "Je ne cuit pas qu'onques" (Machaut 1926, p. 13, Ballade 14, "Je ne cuit pas qu'onques a creature", mm. 27–31):

According to MargoSchulter (1997a):

Stable:

  • Purely blending: unisons and octaves
  • Optimally blending: fourths and fifths

Unstable:

  • Relatively blending: minor and major thirds
  • Relatively tense: major seconds, minor sevenths, and major sixths
  • Strongly discordant: minor seconds, tritonus, and major sevenths, and often minor sixths

It is worth noting that "perfect" and "imperfect" and the notion of being (esse) must be taken in their contemporaneous Latin meanings (perfectum, imperfectum) to understand these terms, such that imperfect is "unfinished" or "incomplete" and thus an imperfect dissonance is "not quite manifestly dissonant" and perfect consonance is "done almost to the point of excess".[citation needed] Also, inversion of intervals (major second in some sense equivalent to minor seventh) and octavereduction (minor ninth in some sense equivalent to minor second) were yet unknown during the Middle Ages.[citation needed]

Due to the different tuning systems compared to modern times, the minor seventh and major ninth were "harmonic consonances", meaning that they correctly reproduced the interval ratios of the harmonic series which softened a bad effect (Schulter 1997b).[clarification needed] They were also often filled in by pairs of perfect fourths and perfect fifths respectively, forming resonant (blending) units characteristic of the musics of the time (Schulter 1997c), where "resonance" forms a complementary trine with the categories of consonance and dissonance.[clarification needed] Conversely, the thirds and sixths were tempered severely from pure ratios[clarification needed], and in practice usually treated as dissonances in the sense that they had to resolve to form complete perfect cadences and stable sonorities (Schulter 1997d).

The salient differences from modern conception:[citation needed][clarification needed]

  • parallel fourths and fifths were acceptable and necessary, open fourths and fifths inside octaves were the characteristic stable sonority in 3 or more voices,
  • minor sevenths and major ninths were fully structural,
  • tritones—as a deponent[clarification needed] sort of fourth or fifth—were sometimes stacked with perfect fourths and fifths,
  • thirds and sixths (and tall stacks thereof) were not the sort of intervals upon which stable harmonies were based,
  • final cadential consonances of fourth, fifths, and octaves need not be the target of "resolution" on a beat-to-beat (or similar) time basis: minor sevenths and major ninths may move to octaves forthwith, or sixths to fifths (or minor sevenths), but the fourths and fifths within might become "dissonant" 5/3, 6/3, or 6/4 chordioids[clarification needed], continuing the succession of non-consonant sonorities for timespans limited only by the next cadence.

Renaissance[edit]

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 (Dahlhaus 1990, p. 179). 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 (Gerbert 1784, 3:353) 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[edit]

In the common practice period, musical style required preparation for all dissonances, followed by and then 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:

Thus, Western musical history can be seen as progressing from a limited definition of consonance to an ever-wider definition of consonance.[citation needed] 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" (Schoenberg 1975, pp. 258–64) by some 20th-century composers. Early-20th-century American composer Henry Cowell viewed tone clusters as the use of higher and higher overtones (Cowell 1969, pp. 111–39).

Despite the fact that this idea of the historical progression towards the acceptance of ever greater levels of dissonance is somewhat oversimplified and glosses over important developments in the history of Western music, the general idea was attractive to many 20th-century modernist composers and is considered a formative meta-narrative of musical modernism.[citation needed]

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 EliotGardiner (2013, 427) hears "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("upon sin oppose resistance"), nearly every strong beat carries a dissonance:

Albert Schweizer 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" (Schweizer 1905, 53). Gillies Whittaker (1959, 368) 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.”

According to H.C. Robbins Landon, the opening movement of Haydn’s Symphony No. 82, “a brilliant C major work in the best tradition” contains “dissonances of barbaric strength that are succeeded by delicate passages of Mozartean grace." [1]:

Mozart's music contains a number of quite radical experiments in dissonance. The following comes from his Adagio and Fugue in C Minor, K. 546:

Ernst Krenek's classification, from Studies in Counterpoint (1940), of a triad's overall consonance or dissonance through the consonance or dissonance of the three intervals contained within (Schuijer 2008, p. 138)  Play (help·info). For example, C-E-G consists of three consonances (C-E, E-G, C-G) and is ranked 1 while C-D♭-B consists of one mild dissonance (B-D♭) and two sharp dissonances (C-D♭, C-B) and is ranked 6.
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  Play (help·info).
Machaut "Je ne cuit pas qu'onques"
Xs mark thirds and sixths
Bach Preludio XXI from Well-tempered Clavier, Vol 1
A sharply dissonant chord in Bach's Well-Tempered Clavier, Vol. I (Preludio XXI)
Bach St Matthew Passion closing bars
Closing bars of the final chorus of Bach's St Matthew Passion.
Bach BWV 54, opening bars. Listen
Haydn Symphony 82 1st movement bars 51-63
Haydn Symphony 82 1st movement bars 51-64

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