In music Music is an art form whose medium is sound. Common elements of music are pitch , rhythm (and its associated concepts tempo, meter, and articulation), dynamics, and the sonic qualities of timbre and texture. The word derives from Greek μουσική (mousike), "(art) of the Muses.", harmony is the use of simultaneous pitches Pitch represents the perceived fundamental frequency of a sound. It is one of the four major auditory attributes of sounds along with loudness, timbre and sound source location. When the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because of overtones, also known as (tones A major second ( Play ), also called a whole step or a whole tone, is a musical interval that occurs between the first and second degrees of a major scale, the tonic and the supertonic. The major second is abbreviated as M2; its inversion is the minor seventh. On a musical keyboard, a major second is the interval between two keys separated by one, notes Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis), or chords In music, a chord is any set of harmonically-related notes that is heard as if sounding simultaneously (a "harmonic simultaneity", see Simultaneity ). The most frequently encountered chords in theory and music are triads: major and minor and then the augmented and diminished triads. The descriptions "major", "minor", &.^[1] The study of harmony involves chords and their construction and chord progressions A chord progression is a series of musical chords, or chord changes that "aims for a definite goal" of establishing (or contradicting) a tonality founded on a key, root or tonic chord. Chords and chord theory are generally known as harmony and the principles of connection that govern them.^[2] Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic line A melody , also tune, voice, or line, is a linear succession of musical tones which is perceived as a single entity. In its most literal sense, a melody is a sequence of pitches and durations, while, more figuratively, the term has occasionally been extended to include successions of other musical elements such as tone color, or the "horizontal" aspect.^[3] Counterpoint In music, counterpoint is the relationship between two or more voices that are independent in contour and rhythm and are harmonically interdependent. It has been most commonly identified in classical music, developing strongly during the Renaissance and in much of the common practice period, especially in Baroque music. The term originates from, which refers to the interweaving of melodic lines, and polyphony In music, polyphony is a texture consisting of two or more independent melodic voices, as opposed to music with just one voice or music with one dominant melodic voice accompanied by chords (homophony), which refers to the relationship of separate independent voices, are thus sometimes distinguished from harmony.

Definitions, origin of term, and history of use

The term harmony derives from the Greek Greek , an independent branch of the Indo-European family of languages, is the language of the Greeks. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. In its ancient form, it is the language of classical ancient Greek literature and the New Testament of ἁρμονία (harmonía In Greek mythology, Harmonia is the immortal goddess of harmony and concord. Her Roman counterpart is Concordia, and her Greek opposite is Eris, whose Roman counterpart is Discordia), meaning "joint, agreement, concord",^[4] from the verb ἁρμόζω (harmozo), "to fit together, to join".^[5] The term was often used for the whole field of music, while "music" referred to the arts in general.

In Ancient Greece, the term defined the combination of contrasted elements: a higher and lower note.^[6] Nevertheless, it is unclear whether the simultaneous sounding of notes was part of ancient Greek musical practice; "harmonía" may have merely provided a system of classification of the relationships between different pitches. In the Middle Ages the term was used to describe two pitches sounding in combination, and in the Renaissance the concept was expanded to denote three pitches sounding together.^[6]

It was not until the publication of Rameau's Jean-Philippe Rameau was one of the most important French composers and music theorists of the Baroque era. He replaced Jean-Baptiste Lully as the dominant composer of French opera and is also considered the leading French composer for the harpsichord of his time, alongside François Couperin 'Traité de l'harmonie' (Treatise on Harmony) in 1722 that any text discussing musical practice made use of the term in the title, though that work is not the earliest record of theoretical discussion of the topic. The underlying principle behind these texts is that harmony sanctions harmoniousness (sounds that 'please') by conforming to certain pre-established compositional principles.^[7]

Current dictionary definitions, while attempting to give concise descriptions, often highlight the ambiguity of the term in modern use. Ambiguities tend to arise from either aesthetic considerations (for example the view that only "pleasing" concords may be harmonious) or from the point of view of musical texture (distinguishing between "harmonic" (simultaneously sounding pitches) and "contrapuntal" (successively sounding tones).^[7] In the words of Arnold Whittall:

While the entire history of music theory appears to depend on just such a distinction between harmony and counterpoint, it is no less evident that developments in the nature of musical composition down the centuries have presumed the interdependence—at times amounting to integration, at other times a source of sustained tension—between the vertical and horizontal dimensions of musical space. —^[7]

The view that modern tonal harmony in Western music began in about 1600 is commonplace in music theory. This is usually accounted for by the 'replacement' of horizontal (of contrapuntal In music, counterpoint is the relationship between two or more voices that are independent in contour and rhythm and are harmonically interdependent. It has been most commonly identified in classical music, developing strongly during the Renaissance and in much of the common practice period, especially in Baroque music. The term originates from) writing, common in the music of the Renaissance The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Florence in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historic era, but since the changes of the Renaissance were not uniform across Europe, this is a general use of the, with a new emphasis on the 'vertical' element of composed music. Modern theorists, however, tend to see this as an unsatisfactory generalisation. As Carl Dahlhaus Carl Dahlhaus , a musicologist from Berlin, has been one of the major contributors to the development of musicology as a scholarly discipline during the post-war era puts it:

It was not that counterpoint was supplanted by harmony (Bach’s tonal counterpoint is surely no less polyphonic than Palestrina’s modal writing) but that an older type both of counterpoint and of vertical technique was succeeded by a newer type. And harmony comprises not only the (‘vertical’) structure of chords but also their (‘horizontal’) movement. Like music as a whole, harmony is a process. —^[8][9]

Descriptions and definitions of harmony and harmonic practice may show bias towards European Europe is one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally divided from Asia to its east by the water divide of the Ural Mountains, the Ural River, the Caspian Sea, the Caucasus region (Specification of borders) and the Black Sea to the southeast. Europe is bordered by the Arctic Ocean and (or Western Western culture refers to cultures of European origin) musical traditions. For example, South Asian art music (Hindustani Hindustani classical music is the Hindustani or erstwhile North Indian style of Indian classical music. Originating in the Vedic period, it is a tradition that has been evolving from the 12th century AD, in what are now northern India, Bangladesh, and Pakistan, and also Nepal and Afghanistan, and is today one of the two parts of Indian classical and Carnatic music Carnatic music is a system of music commonly associated with the southern part of the Indian subcontinent, with its area roughly confined to four modern states of India: Andhra Pradesh, Karnataka, Kerala, and Tamil Nadu. It is one of two main sub-genres of Indian classical music that evolved from ancient Hindu traditions; the other sub-genre being) is frequently cited as placing little emphasis on what is perceived in western practice as conventional 'harmony'; the underlying 'harmonic' foundation for most South Asian music is the drone In music, a drone is a harmonic or monophonic effect or accompaniment where a note or chord is continuously sounded throughout most or all of a piece. The word drone is also used to refer to any part of a musical instrument that is just used to produce such an effect, a held open fifth (or fourth) that does not alter in pitch throughout the course of a composition.^[10] Pitch simultaneity in particular is rarely a major consideration. Nevertheless many other considerations of pitch are relevant to the music, its theory and its structure, such as the complex system of Rāgas Rāga refers to melodic modes used in Indian classical music. It is a series of five or more musical notes upon which a melody is made. In the Indian musical tradition, rāgas are associated with different times of the day, or with seasons. Indian classical music is always set in a rāga. Non-classical music such as popular Indian film songs or, which combines both melodic and modal considerations and codifications within it.^[11] So although intricate combinations of pitches sounding simultaneously in Indian classical music The origins of Indian classical music can be found from the oldest of scriptures, part of the Hindu tradition, the Vedas. It has also been significantly influenced by Indian folk music, and Hindustani music has been influenced by Persian music. The Samaveda, one of the four Vedas, describes music at length. The Samaveda was created out of Rigveda do occur they are rarely studied as teleological Teleology is the philosophical study of the idea that final causes exist, of evidence that design and purpose are inherent in nature. The word comes from the Greek τέλος - telos, root: τελε-, "end, purpose." harmonic or contrapuntal In music, counterpoint is the relationship between two or more voices that are independent in contour and rhythm and are harmonically interdependent. It has been most commonly identified in classical music, developing strongly during the Renaissance and in much of the common practice period, especially in Baroque music. The term originates from progressions, which is the case with notated Western music. This contrasting emphasis (with regard to Indian music in particular) manifests itself to some extent in the different methods of performance adopted: in Indian Music improvisation takes a major role in the structural framework of a piece,^[12] whereas in Western Music improvisation has been uncommon since the end of the 19th century,^[13]. Where it does occur in Western music (or has in the past), the improvisation will either embellish pre-notated music or, if not, draw from musical models that have previously been established in notated compositions, and therefore employ familiar harmonic schemes.^[14]

There is no doubt, nevertheless, that the emphasis on the precomposed in European art music and the written theory surrounding it shows considerable cultural bias. The Grove Dictionary of Music and Musicians (Oxford University Press) identifies this quite clearly:

In Western culture the musics that are most dependent on improvisation, such as jazz, have traditionally been regarded as inferior to art music, in which pre-composition is considered paramount. The conception of musics that live in oral traditions as something composed with the use of improvisatory techniques separates them from the higher-standing works that use notation. —^[15]

Yet the evolution of harmonic practice and language itself, in Western art music, is and was facilitated by this process of prior composition (which permitted the study and analysis by theorists and composers alike of individual pre-constructed works in which pitches (and to some extent rhythms) remained unchanged regardless of the nature of the performance).^[16]

Historical rules

Some traditions Traditions serve to preserve a wide range of culturally significant ideas, specific practices and the various methods used by distinct cultures. The word tradition comes from the Latin traditionem which is the accusative case of traditio which means "handing over, passing on" of music performance A performance, in performing arts, generally comprises an event in which one group of people behave in a particular way for another group of people (the audience). Sometimes the dividing line between performer and the audience may become blurred, as in the example of "participatory theatre" where audience members might get involved in, composition A piece of music exists in the form of a written composition in musical notation or as a single acoustic event . If composed before being performed, music can be performed from memory, through written musical notation, or through a combination of both. Compositions comprise musical elements, which vary widely from person to person and between, and theory Music theory is the field of study that deals with how music works. It examines the language and notation of music. It seeks to identify patterns and structures found in composers' techniques, across or within genres, styles, or historical periods. In a grand sense, music theory distills and analyzes the fundamental parameters or elements of music have specific rules of harmony. These rules are often held to be based on natural properties such as Pythagorean tuning Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. Its name comes from medieval texts which attribute its discovery to Pythagoras, but its use has been documented as long ago as 3500 B.C. in Babylonian texts. It is the oldest way of tuning the 12-note chromatic scale's law whole number ratios ("harmoniousness" being inherent in the ratios either perceptually or in themselves) or harmonics A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic and resonances Acoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own natural frequencies of vibration than it does at other frequencies. As such, acoustic resonance is a branch of mechanical resonance that is concerned the mechanical vibrations in the frequency range ("harmoniousness" being inherent in the quality of sound), with the allowable pitches and harmonies gaining their beauty or simplicity from their closeness to those properties. While Pythagorean ratios can provide a rough approximation of perceptual harmonicity, they cannot account for cultural factors.^{[citation needed]}

Early Western religious music often features parallel perfect intervals; these intervals would preserve the clarity of the original plainsong Plainsong is a body of chants used in the liturgies of the Roman Catholic Church. Though the Eastern Orthodox Church did not split from its Western counterpart until long after the origin of plainchant, Byzantine chants are generally not classified as plainsong. Plainsong is also commonly used in the Anglican and Lutheran churches. These works were created and performed in cathedrals, and made use of the resonant modes of their respective cathedrals to create harmonies. As polyphony developed, however, the use of parallel intervals was slowly replaced by the English style of consonance that used thirds and sixths. The English style was considered to have a sweeter sound, and was better suited to polyphony in that it offered greater linear flexibility in part-writing. Early music also forbade usage of the tritone The tritone ( Play , tri- "three" and tone) is a musical interval that spans three whole tones. The tritone, sometimes known as the "Diabolus in Musica", refers to either the augmented fourth or the diminished fifth, which in 12-tone equal temperament are enharmonic equivalents. It is often used as the main interval of, as its dissonance was associated with the devil, and composers often went to considerable lengths, via musica ficta Musica ficta was a term used in European music theory from the late twelfth century to about 1600 to describe any pitches, whether notated or to be added by performers in accordance with their training, that lie outside the system of musica recta or musica vera ('correct', or 'true' music), defined by the hexachord system of the Guidonian hand. In, to avoid using it. In the newer triadic harmonic system, however, the tritone became permissible, as the standardization of functional dissonance made its use in dominant chords desirable.

Although most harmony comes about as a result of two or more notes being sounded simultaneously, it is possible to strongly imply harmony with only one melodic line through the use of arpeggios In music, an arpeggio is Italian for broken chord where the notes are played or sung in sequence, one after the other, rather than ringing out simultaneously. This word comes from the Italian word "arpeggiare" , which means "to play on a harp". Formed from scales, the arpeggio is based on the relative scale playing the " or hocket In music, hocket is the rhythmic linear technique using the alternation of notes, pitches, or chords. In medieval practice of hocket, a single melody is shared between two voices such that alternately one voice sounds while the other rests. Many pieces from the baroque Baroque music describes a style of European classical music approximately extending from 1600 to 1750. This era is said to begin in music after the Renaissance and was followed by the Classical era. The word "baroque" came from the Portuguese word barroco, meaning "misshapen pearl", a strikingly fitting characterization of the period for solo string instruments A string instrument is a musical instrument that produces sound by means of vibrating strings. In the Hornbostel-Sachs scheme of musical instrument classification, used in organology, they are called chordophones. The most common string instruments in the string family are guitar, violin, viola, cello, double bass, banjo, mandolin, ukulele, and, such as Bach's Sonatas and partitas for solo violin The Sonatas and Partitas for solo violin are a set of six works composed by Johann Sebastian Bach. They consist of three sonatas da chiesa, in four movements, and three partitas, in dance-form movements, convey subtle harmony through inference rather than full chordal structures; see below:

Types

Carl Dahlhaus Carl Dahlhaus , a musicologist from Berlin, has been one of the major contributors to the development of musicology as a scholarly discipline during the post-war era (1990) distinguishes between coordinate and subordinate harmony. Subordinate harmony is the hierarchical A hierarchy (Greek: hierarchia , from hierarches, "leader of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above," "below," or "at the same level as" one another and with only one "neighbor" above and below each of tonality Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840 (Reti, 1958; Simms 1975, 119; Judd, 1998; Dahlhaus 1990). Although Fétis used it as a general term for a or tonal harmony well known today, while coordinate harmony is the older Medieval The term medieval music encompasses European music written during the Middle Ages. This era begins with the fall of the Roman Empire and ends in approximately the early fifteenth century. Establishing the end of the medieval era and the beginning of the Renaissance is difficult; the usage in this article is the one usually adopted by musicologists and Renaissance Renaissance music is European music written during the Renaissance. Defining the beginning of the musical era is difficult, given the gradually adopted "Renaissance" characteristics: musicologists have placed its beginnings from as early as 1300 to as late as the 1470s tonalité ancienne, "the term is meant to signify that sonorities are linked one after the other without giving rise to the impression of a goal-directed development. A first chord forms a 'progression' with a second chord, and a second with a third. But the former chord progression is independent of the later one and vice versa." Coordinate harmony follows direct (adjacent) relationships rather than indirect as in subordinate. Interval cycles create symmetrical harmonies, which have been extensively used by the composers Alban Berg Alban Maria Johanne Berg was an Austrian composer. He was a member of the Second Viennese School with Arnold Schoenberg and Anton Webern, and produced compositions that combined Mahlerian Romanticism with a personal adaptation of Schoenberg's twelve-tone technique, George Perle George Perle was a composer and music theorist. He was born in Bayonne, New Jersey. A student of Ernst Krenek, Perle composed with a technique of his own devising called "twelve-tone tonality," which is different from, but related to, twelve-tone technique of the Second Viennese School of which he was an, "early admirer," and, Arnold Schoenberg Arnold Schoenberg (13 September 1874 – 13 July 1951) was an Austrian and later American composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School. He used the spelling Schönberg until after his move to the United States in 1934 (Steinberg 1995, 463), "in deference to American, Béla Bartók Béla Viktor János Bartók (pronounced /ˈbɑrtɒk/ , Hungarian pronunciation: [ˈbeːlɒ ˈbɒrtoːk]) (March 25, 1881 – September 26, 1945) was a Hungarian composer and pianist. He is considered to be one of the greatest composers of the 20th century and is regarded, along with Liszt, as his country's greatest composer (Gillies 2001). Through, and Edgard Varèse Edgard Victor Achille Charles Varèse, whose name was also spelled Edgar Varèse , was an innovative French-born composer who spent the greater part of his career in the United States's Density 21.5.

Other types of harmony are based upon the intervals used in constructing the chords used in that harmony. Most chords used in western music are based on "tertian" harmony, or chords built with the interval of thirds. In the chord C Major7, C-E is a major third; E-G is a minor third; and G to B is a major third. Other types of harmony consist of quartal harmony and quintal harmony.

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