Music has been called both the most mathematical and the most abstract of the arts. Unlike words, pictorial images, and bodily movements, however, musical tones in themselves have no concrete associations, and only gain meaning when they are combined into musical patterns. Philosophers have always been intrigued by the problems inherent in attempts to define music. Three centuries before the birth of Christ the Greek philosopher Aristoxenes distinguished between speculations on the nature of music and attempts to explain actual musical practice. Like most medieval theorists and their Greek predecessors, Boethius (c. 480-c. 524) held a very broad view, dividing music into the harmony of the universe, the harmony of soul and body, and the harmony of sounding tones. Through the centuries various philosophers have attempted to integrate theories on the essence of music within their particular world views. Many non-Western cultures and some Western writers as well--believing the power of music to be less tied to the material world than the other arts and sciences--have perceived it as an inherently mystical or occult force, able to unlock elemental truths or principles that cannot be otherwise translated into written or graphic form. "Music is born of emotion," Confucius observed. Whether vocal or instrumental, music has also been viewed both literally and figuratively as a form of language or speech, with less specificity than the spoken word but possessing subtler shades of meaning and more emotive force. It is not a "universal language," however, but rather, like speech, an acquired one for which humans have innate capacity. Down to the present day, debate continues as to whether music is fundamentally a means for the expression of ideas, experiences, and feelings, or, rather, a distinct system or way of thinking in its own right, through which such elements as ideas and feelings can pass. Some recent definitions of music include "organized sound," "sounding form in motion," and "time given shape by the energy of sound." Of course, no single definition can encompass all the diverse practices of music, or be free of some aesthetic bias. Music often includes noise (for example, the sound of a cymbal) as well as pitched tones, structured silence as well as sound, even purposeful chaos as well as form. Music is variously a form of personal expression, of communication, of common understanding or ritual, and of mode of thought. Robert Schumann noted that "perhaps it is precisely the mystery of her origins which accounts for the charm of her beauty." Archaeologists have discovered musical instruments dating back almost 30,000 years. Ceremonial music--incorporated within religious rites, public gatherings and amusements, dance and story telling--predates recorded history and, according to certain theories, may predate human speech. Folk music is also common to all societies. While folk songs, too, can be associated with certain functions (work songs, spiritual music, and so on), they are often performed solely for the pleasure they bring. More structured musical traditions evolve from ceremonial, folk, and related types of practice to become, over time, classical (or "art music") traditions. The music is now increasingly performed for its own sake, in its own time and place, and it has its own meaning. To comprehend and enjoy a musical performance, one must have some familiarity with its choice of sounds, its nuances and organizing principles, and a grasp of its function--of how the music is intended to be heard. Categories such as those mentioned above can be initially useful, but they should not be applied too rigidly or too casually, for there are many individual works and types of music that cut across such simplified distinctions. To cite but one example, jazz is at once a popular, folk, and art music tradition. Questions of how music is composed, heard, and understood involve several areas of study. When considering the quality of a sound or of a musical passage, it is often necessary to distinguish among the acoustical properties of the source, the subjective mental perception of what is heard, and the ways in which musical training and experience color a listener's response. These considerations involve such disciplines as acoustics (the science of physical properties of sound) and psychoacoustics (the study of how sounds are interpreted). Music theories are attempts to codify the elements, techniques and forms of music. Musicology traces the historical development of styles and forms. Aesthetics examines artistic values and judgments. Branches of psychology and sociology consider broader issues in the relation of music to mental processes and social changes. The remainder of this article surveys important facets of music making and listening: the sound and elements of music; the translation of these elements into written symbols; the historical development of organizing principles and performance medium in Western music; differences between Western musical practices and attitudes and those of other cultures; and the results of interactions between distinct traditions. More detailed information on major historical periods, (for example, \Tbaroque music\t), composers, musical forms, and national musics (\TRussian music\t, \TChinese music\t, and so forth) can be found in separate articles. THE ELEMENTS OF MUSIC Sound results from the vibration of elastic bodies such as violin string or human vocal chords. The vibrating pattern is transmitted through wavelike variations in air pressure to the inner ear, where it is converted to electrical impulses fired to the brain. The physical qualities of sound include duration; amplitude (a measure of force or strength) and its temporal envelope, or evolution (attack, sustaining, and decay characteristics); frequency (the fundamental rate of vibration, measured in cycles per second, also called hertz); and the frequency spectrum (a measurement of all of the frequency components--the overtones, or partials, and their relative strengths--that are present in a sound). Audible vibrations occur within a range of roughly 20 to 20,000 hertz (Hz), although few people can hear pure frequencies at either extreme. Sounds with a well-defined pitch vibrate periodically (regularly) at a particular frequency; the lowest and highest tones of the piano vibrate, respectively, at frequencies of 27.5 and 4,186 Hz. As most light rays consist of several wavelengths, however, so the complex vibrating patterns of natural sounds actually contain many frequencies, called partials, of varying strength. In sung tones, and in most tones produced by stringed and wind instruments, most or all of these particles are harmonically related by simple integer ratios (double the fundamental frequency, three times the fundamental, four times, and so on). Most percussive, spoken, and noiselike sounds, by contrast, result from more complicated, less-regular vibrating patterns. Their partial frequencies are not harmonically related, and so one does not hear a well-defined fundamental pitch. A straightforward relationship exists between frequency and \Tpitch\t: the higher the fundamental frequency, the higher the perceived pitch. Other musical qualities, however, cannot be related so directly to a single physical source. Loudness depends both upon amplitude and upon the frequency spectrum, since sounds with more high frequency energy are perceived as more intense. Timbre is the characteristic tonal quality of a sound, which enables one to distinguish the voices of two people, or a clarinet from a flute, regardless of pitch or performance inflections. Several physical factors influence the perception of timbre. These include the envelope (particularly the attack, which often includes noiselike elements not related to the fundamental vibration); the frequency spectrum; and the formants, one or more regions in an instrument that resonate and amplify any frequencies that pass through them. Formants are determined by the physical shape of an instrument. They are also critical in the production of spoken and sung vowels. The melodies and harmonies of a culture's music consists of a limited number of pitched tones that reflect a tuning system. This collection of available tones can be arranged in ascending or descending order to form a scale. The scales of ancient Greece and the Middle Ages comprised seven tones, Such scales, corresponding to the white keys of the piano, are termed diatonic, and remain the basis for most Western music. Since the 16th century, however, Western music has made increasing use of five additional chromatic tones (the black keys), which lie between the original seven. Non-Western cultures employ different tuning systems, which may consist of as few as two or three tones (in some African tribal music) or of more than twelve (in some Asian music). Scales of five, six, or seven tones are most common. The characteristic sound of a scale is determined by the intervals (distances) between adjacent tones. The most basic musical interval is the octave, which occurs when the frequency of any tone is doubled or halved. Two tones an octave apart create a feeling of identity, or the duplication of a single pitch in a higher or lower register. The Greek mathematician Pythagoras discovered similar simple ratios for other important intervals (for example, a 2/3 ratio for the perfect fifth). These acoustically "pure" intervals, however, lead to mistunings and other problems in chromatic music. Various temperaments--tuning systems in which minor adjustments are made in the size of Pythagorean intervals--have been devised to deal with this problem. The system of equal temperament, first proposed in the 1500s, became standardized during the 18th and early 19th centuries. This system divides the octave into twelve equally spaced intervals. The interval between any two adjacent tones (a frequency ratio of 1.05946) is called a half-step. An interval equal to two half-steps (such as between two white keys separated by a black key) is termed a whole-step. Diatonic scales consist of patterns of five whole steps and two half steps. Several such scales, called modes, were used in medieval and Renaissance music (for example, the Ionian \Tmode\t, an octave of white notes beginning at C, which is today the C major scale; and the Aeolian mode, an octave of white notes beginning at A, which is today the A minor scale). The distinctive intervallic pattern of each mode resulted in characteristic melodic patterns. Medieval theorists, like their Greek predecessors, attributed particular expressive qualities and suitabilities to each mode. Any number of scales are possible. The chromatic scale, for example, consists of the twelve semitones of the octave--all the white and black keys--played in succession; the pentatonic is made up of five notes within the octave; whole tone scales are made up of six tones within the octave, each a whole tone apart; microtonic scales divide the octave into intervals smaller than a semitone; and there are many others (see \Tscale\t). Scales are usually rooted on a central tone, to which melodies frequently return and on which they end. \Ttonality\t--the relationship of all scale tones to a home tone--is among the few principles common to all musical cultures. The term is also used is a more restricted sense, however, to refer to the particular harmonic system of major-minor tonality. This system governed virtually all Western art music between the mid-17th and the early 20th centuries, and remains the basis for most popular and much concert music. Tonal music employs only two diatonic modes, (where the step arrangement on the piano is 1-1- 1/2-1-1-1-1/2) and minor 1-1/2-1-1-1-1-1/2). Melodies and chord progressions are always heard in relation to the tonal center, which is called the tonic, or key note. The other diatonic and chromatic tones, and chords built on them, serve as points of departure, intermediate goals, and means of return for the tonic note. The most important elements of music are rhythm, melody, counterpart, harmony, form, and tone color. Other elements, such as dynamics (variations in loudness), texture, and density can also be identified, but these are usually employed to underscore formal or expressive patterns. Rhythm A rhythmic pulse marks off divisions of time. Pulses may be stressed or unstressed. Many early medieval and some Renaissance works are unstressed, with subtly shifting accents determined by the sung text. Most familiar musical styles, however, feature regularly patterned groupings of accented and unstressed pulses, which result in a number of common meters. Duple meters, with alternating stressed and unstressed beats, are characteristic of marches, triple meters (in which every third beat is stressed) of waltzes. Before the early 20th century almost all Western music employed relatively simple metrical patterns of two, three, four, or six beats. However, great variety in durational patterns and in the use of secondary types of accents is possible with such simple frameworks. Asymmetric meters, typically of five or seven beats, are widespread in Asian music and in eastern European folk traditions. Rhythmic complexity, including polyrhythms in which the accents, meters, or sometimes even beats between different parts do not coincide, is characteristic of \TAfrican\t drumming music. These and other alternatives to simple metrical frameworks have been widely exploited in 20th century concert music. (See also \Trhythm\t.) Melody A MELODY is a succession of tones in rhythm. Common to all societies and the most memorable aspect of most music, melody often proves curiously resistant to detailed analysis. Melodies are structured into phrases, each of which ends with a cadence, a relaxation or breathing point. In vocal music, cadences usually coincide with the end of a line of text. Melodic continuity can be achieved in many ways, but most often results from an interplay between repetition and contrast. Sometimes a fragmentary but incisive pitch or rhythmic figure of a few notes, called a motive, is repeated several times. Motives, phrases, or entire melodies can also be varied (repeated with alterations) or developed (broken into smaller units that are combined in new ways or transposed to a new pitch level). Melodic contour, the overall shape of upward and downward pitch motion, generally creates a clear profile, so that melodies are frequently referred to as "lines." In large-scale works the principal melodies are called themes. "Originality" in melodic construction is highly prized in the West, but is some traditions melodic invention takes the form of variations on well-known melodic formulas, motivic figures, or scale like models. The ragas of Indian music, for example, consist of particular, often inconsecutive arrangements of scale tones (some of which may be repeated) in ascending and descending forms. Midway between a fragmentary melody and a scale, the rage provides a structural and expressive framework for continuous improvisational variations. The development of rhythmic and melodic resources in many Asian and African cultures has led to many intricate tuning systems and rhythmic structures. The development of Western music, by contrast, has been characterized by fascination with combining tones and melodies in ever new ways. The techniques of combining simultaneous melodies are termed \Tpolyphony\t ("many sounds") and \Tcounterpoint\t ("point against point"). The separate melodies, usually called "voices" even in instrumental works, maintain independent contours and may end at different places, but they are also interrelated to produce a composite formal design. The voices in some contrapuntal works are developed from separate figures and may contrast sharply. More often, however, melodic ideas pass from one voice to another, a technique called imitation that leads to patterns of statement-and-reply. Imitative techniques are not always obvious to the ear. Common imitative procedures include transposition to different pitch level, rhythmic differentiation (such as a reply that moves at double or half the original speed), inversion (an "upside-down" repetition in which ascending intervals become descending intervals), and other types of transformation. Harmony Groups of tones sounded together create \Tharmony\t. Harmonic practice, which evolved out of melodic and polyphonic procedures, is among the most unique features of Western music, and is found only occasionally in other cultures. The basic unit of harmony is the chord, two or more tones that fuse into a single musical sound,. The harmonic quality of a chord is determined by the intervals between its tones, and by its relation to other chords in a passage. Consonant intervals which generally result from simpler frequency ratios, produce a sense of stability or relaxation, whereas dissonant intervals create a feeling of tension and a need for resolution. Despite their acoustical basis, consonance and dissonance are relative concepts. Intervals and chords that are perceived as dissonant in one era or culture are often treated as consonances in other times and places. Furthermore, an acoustically consonant chord can function as a dissonant harmony in certain contexts, especially if it is unexpected. Since the early 18th century, when chords were first recognized as musical building blocks in their own right, harmonic practice has been closely tied to the principles of tonality. The basic chord of tonal music is the triad, consisting of three tones each two diatonic scale steps apart (fore example, tones 1,3, and 5 of a major or minor scale). Triads, and more complex chords with additional tones, can be built on any scale or chromatic tone. Every chord functions with respect to the home key, serving either to create tonal motion to secondary harmonic goals or to prepare the return of the tonic triad. Extended tonal motion may result in modulation, a temporary shift into some other key. In later 19th century music increasing use of chromatic inflections, strings of dissonant or coloristic harmonies, and prolonged passages of restless tonal movement gradually weakened the underlying principles of tonality. Several alternative methods of harmonic organization--some linked to tonal practice, others based on new procedures--have been employed in 20th-century music. Form Form is the architectural structure of music--the process through which principal ideas are developed and expanded into a convincing, complete musical statement. Formal processes generally incorporate both unifying and contrasting elements, and operate at many levels: the distinctive construction of initial ideas; the establishment of structural goals and pacing to points of climax and resolution; the interrelation of phrases, sections, and individual movements into ever larger patterns; and, finally, the overall design of a work. The form of a particular work is a unique process of growth and synthesis. Formal principles can be grouped into two broad categories, outlines and procedures. An outline, or scheme, consists of a general sequence of events. The most important arrival points are full cadences--the points of closure that mark off sectional divisions. Two-part forms present a statement and response. The second section may begin with contrasting ideas, or with a restatement of the initial material. In either case, it will lead to a strong final closure and the resolution of all the material that has been introduced. Most three-part forms are derived from the related principle of statement, contrast, and return (A-B-A). Individual sections may themselves contain exact or varied repetitions, groups of themes, transitions and developmental passages, and internal two-or-three-part patterns. In tonal music, unity, contrast, and overall structure result primarily from harmonic motion between secondary tonal goals and the tonic chord. Many common forms, however, are based on particular procedures rather than on a given sequence of events. Imitations, for example, is the primary organizing principle in many polyphonic and contrapuntal works, and is the basis for such forms as the \Tfugue\t and \Tcanon\t. Individual fugues vary widely in the number and placement of thematic statements, modulations, and cadences, but they share a common method of development. Sometimes confused with forms, musical genres are particular performance mediums, such as the string quartet or accompanied song. Genre categories include vocal and instrumental music; solo, chamber (small ensemble), and large ensemble works; and large-scale (lengthy, often multimovement) compositions, as well as shorter, more intimate types of performances. Different idiomatic resources are suggested by different performing mediums. Vocal melodies, for example, are generally characterized by a smaller pitch range than instrumental melodies. During certain periods, some genres are associated with particular forms. Most 18th- and 19th-century string quartets, for example, follow a roughly similar formal outline. The musical language, conventions, and working procedures of a culture, historical period, or individual composer or performer constitute a musical style. Styles reflect the responses of musicians to the values and aspirations of their society. A musician's use of common forms, methods of tonal organization, and musical formulas are the general characteristics against which one can measure his or her unique achievements. DEVELOPMENT OF WESTERN MUSICAL FORMS Throughout the long period of \Tmedieval music\t, encompassing roughly a thousand years from the early Christian era to the mid-15th century, the Roman church was the dominant and unifying force in Western music. The most important musical developments were the establishment and codification of the repertory of \Tplainsong\t chants of the Mass and Offices, which would serve as the structural basis for countless secular as well as sacred compositions in ensuring centuries; the rise of polyphonic techniques and forms; and the development of metrical rhythms and principles of rhythmic organization. \Torganum\t, the earliest form of polyphony, featured the addition of one, two, or three melodic lines to a plainsong melody in the tenor voice (the lowest voice in two and three part polyphony, the second lowest in four-voice works). Originally (c. 900-1050) consisting of simple doublings of the chant melody at fixed intervals of the fourth or fifth, the newly composed voices gained increasing contour and rhythmic independence during the 12th and 13th centuries, particularly with the introduction of modal rhythms (a way of notating that clearly set forth short, repeated rhythmic patterns) by the composers Leonin and Perotin. This technique was extended to the principle of isorhythm (longer reiterated rhythmic patterns) in the major genre of medieval polyphony, the \Tmotet\t. \Tcantus firmus\t techniques, in which the "fixed melody" (usually borrowed, most often from plainsong) is sung or played in the tenor voice against more rapid, freely-composed upper voices, remained a common basis for most polyphonic forms until the late 16th century. During the 12th and 13th centuries an independent tradition of secular songs developed among \Tminstrels\t at feudal courts. The musical structures of the Ballade, Rondeau, Virelai, and other types of songs were derived from the French poetic forms of the same names. During the ars nova period (French music of the first half of the 14th century), expressive two-, three-, and four-part settings of ballades and rondeaux, often incorporating two instrumental parts, were composed by Guillaume de Machaut and other leading figures. In Italy, the primary 14th-century forms were the Ballata with a refrain structure; the Caccia, which involved continuous imitation between the upper two voices against a slower-moving tenor; and the \Tmadrigal\t (not to be confused with the 16th-century form of the same name). In contrast to such rigid late Gothic techniques as isorhythm, \TRenaissance music\t (c. 1450-1600) is characterized by imitative polyphonic styles of seamless textures, rhythmically flowing lines, equality among voice parts, and a growing emphasis on sonorous harmonies. The two major genres of sacred polyphony, the motet and settings of the Ordinary of the \TMass\t, were brought to their highest levels of mastery by \TJosquin des Prez\t and \TPalestrina\t. The principal formal procedures of Mass settings were cantus firmus and parody techniques, the latter incorporating melodies or complete polyphonic sections of motets or secular works. Following the Reformation, Martin Luther and his followers assembled collections of \Lchorale\ls (Protestant hymns), derived mostly from secular songs and Catholic hymns and designed for congregational singing. The humanistic spirit of the Renaissance is reflected in the rise of distinct secular styles and forms. Polyphonic secular songs, including the French chanson, the Italian frottola, the German polyphonic lied, the Spanish villancico, and the Italian and English madrigal, were lighter in texture (with a solo singer on each part) as well as spirit. Instruments were no longer used only to accompany or replace singers. Repertoires of keyboard music (often played on \Lorgan\ls, \Lharpsichord\ls, or \Lclavichord\ls) and \Tlute\t music developed in such forms as the fantasia, ricercar, canzona, and sets of \Tvariations\t on secular tunes. A similar repertoire was composed for \Lconsort\ls of instruments, both among instruments of a single family (usually viols or recorders) and among mixed ensembles of winds and strings. Major developments at the beginning of the period of baroque music (c. 1600-1750) were concentrated in vocal music. The simplified vocal style of monody, with a solo vocal line in speechlike rhythms over a sparse harmonic accompaniment, provided the basis for the first \Lopera\ls, notably those of Claudio \TMonteverdi\t. Distinct national and regional serious and comic operatic forms arose, comprising \TArias\t, \Lrecitative\ls, and choruses, as well as less elaborate types of music such as the English \Tmasque\t. The \Toratorio\t, originally similar in outline to opera (but without stage action), and the \Tcantata\t, a narrative work in several movements for soloists, chorus, and orchestral accompaniment, incorporated operatic forms and conventions but gradually evolved during the 17th century into distinct genres on either religious or dramatic subjects. The stylistic characteristics of later baroque opera and oratorio traditions are best known today through the works of George Frideric \THandel\t. Chorale melodies were incorporated within the church cantata, passion, and other genres of Lutheran music chorale melodies (see \Tchoral music\t), and functioned in the manner of cantus firmus in many organ works. Vivid emotional portrayals characterized many vocal works. The fundamental formal principle in most instrumental works, however, was the contrast in patterns between opposing groups, sections, dynamic levels, soprano and bass voices, or other elements of structure. The sonata ("sound piece"), a term originally used to designate various types of music for instruments, evolved into the most important genre of \Tchamber music\t and music for harpsichord, notably in the work of Domenico \TScarlatti\t. Sonatas for violin and continuo, and trio sonatas, typically for two violins and continuo, included three or four contrasting slow and fast movements. (The continuo was the instrument or instruments providing the bass line. It was usually an organ of harpsichord, sometimes reinforced by a cello or bassoon. See \Tfigured bass\t.) The \Tconcerto\t ("contrasting instrumental bodies"), a term originally applied to vocal works with instrumental or organ accompaniment, evolved in the works of Antonio \TVivaldi\t and his contemporaries into an orchestral form similar in outline to the sonata. The distinguishing feature of the baroque concerto, however, was the continuous alternation between a small group of instruments and the larger string ensemble (the concerto grosso), or between the soloist (usually a violinist) and an orchestra. The keyboard forms of the late 16th century remained popular, but new forms also developed, notably the \Ttoccata\t, a "touch piece" for organ or harpsichord featuring rapid scale-like runs and similar idiomatic figures. The long history of Renaissance and baroque imitative polyphony culminated in the development of the fugue, a formal procedure employed in organ, chamber, orchestral, and choral works by J. S. \TBach\t. Sonata procedures that were first developed in the \Tclassical period in music\t (C. 1750-1825) dominated major instrumental genres through the early 20th century, and remain vital components of many recent works. The sonatas for piano or for solo instrument with piano accompaniment of Franz Joseph \THaydn\t, Wolfgang Amadeus \TMozart\t, and Ludwig van \TBeethoven\t are expansive three- or (in many of Beethoven's works) four-movement cycles featuring clearly articulated tonal schemes and extensive thematic development. These features are most prominent within the first movement of the cycle, where they constitute a structural procedure known as the sonata form. (The principles of sonata form, through which a single movement is developed, should not be confused with the overall multimovement scheme, or "form," of the sonata as a whole. This distinction is clarified further in the article \Tsonata\t.) The formal outline of the sonata, and the procedures of sonata form, were applied in orchestral and chamber form as well. Thus the \Tsymphony\t may be considered a sonata for orchestra; the classical concerto a sonata for soloist and orchestra; and the \Tstring quartet\t (and such related genres as the piano trio and string quarter) a sonata for small ensemble. The overall design of each of these genres consists of a fast movement in sonata form; a slow movement; a third movement (not included in concerti or early sonatas) in \Tminuet\t-and-trio or \Tscherzo\t-and-trio form; and a finale, most often in \Trondo\t, sonata-rondo, or theme-and-variation form. Sonata-form procedures were also widely employed in simplified form within single-movement \Loverture\ls. Opera remained the primary genre of vocal music, given new life through the reforms first implemented by Christolph Willibald \TGluck\t. The comic opera and singspiel attained greatest expressive power in the works of Mozart. Oratorios, masses (intended for concert rather than liturgical use), and various song and chorale genres were widely performed. Classical forms underwent considerable expansion during the period of \Tromanticism\t (c. 1830-1910). Such composers as Felix \TMendelssohn\t and Johannes \TBrahms\t, seeking to extend classical practice, maintained the broad outlines, procedures, and balance of these forms while incorporating a more expansive harmonic palette. Other romantics--including Hector \TBerlioz\t, Frederic \TChopin\t, Franz \TLiszt\t, and Richard \TWagner\t--believed that the enriched, often highly chromatic tonal language of the age and the romantic imperative for intense personal expression required free adaptation or the development of new forms, sometimes based on literary or pictorial themes. Programmatic symphonies led to the development of single-movement \Lsymphonic poem\ls, loosely structured around poetic or dramatic subjects. Conceiving of opera as a "total art work" (Gesamtkunstwerk) for the portrayal of mystical truths, Wagner replaced conventional, set numbers with vocal lines midway between aria and recitative, accompanied by continuous, constantly evolving orchestral colors and textures. Giuseppi \TVerdi\t, by contrast, accepted the conventions of Italian serious opera, composing "singers' operas" with rapid stage action and melodramatic plots. The tendencies toward increased brilliance and breadth, also reflected in the virtuosic piano works of Liszt, were counterbalanced by an opposing desire for intimate expression in simple forms, most notably in the flowering of the romantic lied (German art song). The lieder of Franz \TSchubert\t, Robert \TSchumann\t, and later composers served as models for lyrical instrumental themes, and in the development of many types of character pieces, brief piano works that depict particular moods or qualities. Popular genres of this type included "songs without words," impromptus, \Lnocturne\ls, \Lintermezzo\ls, rhapsodies, and \Lprelude\ls. The years immediately before and after World War I marked a watershed in the development of Western musical forms. The principles of tonality, stretched to the breaking point in many later 19th-century works, and the romantic aesthetic that had spurred musical imaginations for nearly a century were challenged by an array of aesthetic, stylistic, and structural alternatives. The resulting musical pluralism, in which style becomes a matter of choice rather than of accepted conventions, has been the most prominent characteristic of a fertile but unsettled artistic age that continues through the present day. Some composers have embraced this freedom, forging highly individual styles based on intuitive procedures. Declaring that "music is not something that can be cast into a traditional or fixed form. Music consists of colors and rhythms..." Claude \TDebussy\t sought to create musical forms that evolve organically and continuously out of opening figures or a "precise sound" (ton juste). The early ballets of Igor \TStravinsky\t (especially Le Sacre du Printemps, 1913) unleashed a torrent of asymmetric rhythmic energy, bristling dissonances, and orchestral color within highly sectional structures. While the music of Debussy and (early) Stravinsky often maintained tonal references, Arnold \TSchoenberg\t carried the dense chromaticism of late German romanticism to its final stage, employing all twelve tones equally and consciously avoiding tonal implications. Schonberg's atonal ("without tonal center") works often featured transformations of three- or four-note melodic cells (see \Tatonality\t). Seeking a more systematic method of atonal composition, Schoenberg formulated the principles of serial composition, in which a particular ordering of the twelve tones, repeated in various transformations and combinations throughout a work, results in recurrent intervallic relationships. Adopted in both rigorous and freer forms by Schoenberg's pupils Anton von \TWebern\t, Alban \TBerg\t, and Stravinsky--as well as many later composers--serial principles were later applied to rhythmic procedures and other structural elements (see \Tserial music\t). Composers seeking clarity of design and well-defined frameworks have frequently discovered new vitality in tonal forms and materials, selecting particular historical models and reworking and updating them. Between 1920 and 1950 this movement was termed "neoclassicism," although baroque procedures such as the fugue were employed nearly as often as classical forms and genres. Within the past decade, several leading composers previously associated with more complex styles have also adopted tonal syntaxes, and have sometimes quoted directly from well-known masterworks, most often choosing 19th-century models. Tone color has become an increasingly significant element of structure, and an ever broader range of noise-like sounds have been employed to create particular musical gestures. Seeking "to focus interest on the harmonies of sound quality alone," Edgard \TVarese\t used percussion instruments extensively in the creation of sharply drawn melodic, timbral, and rhythmic textural layers. By means of tape manipulation and other sound-processing procedures, collectively called musique concrete ("concrete music"), composers of \Telectronic music\t have altered, superimposed, and reshaped recorded sounds into various types of textural and rhythmic patterns. Sound colors, and similar timbres produced by purely electronic means, have in turn influenced such orchestral composers as Krzysztof \TPenderecki\t in the creation of vivid textural colors from traditional instruments. \Tcomputer music\t procedures have recently opened up a broad new range of timbral, compositional, and performance possibilities, enabling musicians to manipulate lifelike synthetic or processed sounds with great precision. MUSICAL NOTATION Aural traditions, in which musical practices are learned by ear through years of imitation and memorization, can be found among highly trained professional musicians as well as in preliterate societies. Many classically trained musicians of India and some of the first half of the 20th century have attained consummate performing skills without learning to read music. Most Western traditions, however, rely heavily on written notational systems to aid in the learning, dissemination, and preservation of music. Various types of notation have been devised to represent different kinds of performance practices. In improvisatory traditions, shorthand sketches are sometimes sufficient. \Ttablature\t systems employ signs that show where to position the fingers on a keyboard or stringed instrument to produce the desired notes. When several performers must realize a composer's detailed intentions, however, means of precise indication of pitch and durations, supplemented by directions for tempo, loudness, character of the music, various types of accents, special effects, and ornamentation, become necessary. In ancient and non-Western music, pitch and durational symbols have been derived from alphabetical letters, from literary scripts, and from other sources. The symbols of modern Western notation were derived from grammatical and phonetic symbols, originally placed above and below the texts of plainsong chants as memory aids to rising and falling melodic inflections. These rudimentary symbols gradually evolved into a system of neumes, signs representing single tones, groups of notes, or melodic formulas. Neumes were positioned at various heights above and below a horizontal line that designated the pitch "F." Additional lines were gradually added to indicate pitch level more precisely, and by the 13th century the familiar five-line staff appeared in notations of polyphonic music. At about the same time, a proportional system of durational values was devised, employing four square-shaped note symbols: the double-long; the long; the breve; and the semibreve. Mensural notation (c. 1450-1600) enabled composers to indicate either duple or triple division of beats. The present system, dating from the early 17th century, is based on the duple division of each successive note and rest symbol (one whole note = two half notes = four quarter notes, and so on). Meters are indicated by means of time signatures and bar lines, major and minor keys by means of key signatures (sharps and flats). Additional symbols, such as those needed for microtonal tunings or special effects, have been introduced in recent years, and alternative graphical and proportional systems, which sometimes bear little resemblance to common musical notation, are frequently employed by contemporary composers. NON-WESTERN MUSICAL TRADITIONS The term non-Western is most often applied to the music of the Far and Middle East and Africa, but it is also used to denote all musical practices outside of the European traditions, including that of Indian civilizations of the Western hemisphere. Specific practices are covered in the articles \TAfrican music\t; \TArabian music\t; \TChinese music\t; \TGreek music\t; \TIndian music\t; \LIndians of North America\ln; \TJapanese music\t; \TLatin American music\t. Some of the cultures listed above have very long musical histories. Chinese writings as old as the 6th century BC refer to musical performances. Within the Far Eastern countries distinct traditions of classical practice (concentrated in the courts, temples, and major urban centers) and related but simpler fold musics, often with pronounced regional differences, have coexisted for many centuries. When considering this vast and varied repertoire, ethnomusicologists generally seek to examine individual traditions in light of the social and musical values and cultural conditions of the society, before attempting comparative analyses. In fact, certain striking parallels between civilizations that until recently had little or no contact can be observed. These include the nearly universal recognition of the intervals of the octave and perfect fifth as having a special structural importance and constant quality, and the widespread use of similarly tuned pentatonic ("black key") scales in Chinese, African, American Indian, and other cultures. Attempts to discover universal or consistent principles beyond certain acoustical fundamentals, however, have proved elusive. Investigation of the ways in which a musical language results from the functions of music in a society is generally more illuminating than attempts to discover how a particular music sounds, or why it sounds as it does. Studies of non-Western music often require different methods of investigation from those employed in conventional musicology. Some types of African drums, for example, can produce ten or more distinct tones of varying pitch and tone color, depending upon where and how the instrument is struck. Such music cannot be transcribed in common Western notation, of course. Moreover, the researcher may have difficulty in following the often rapid, subtle pitch shadings, or in grasping the resulting speechlike inflections of performed "drum tunes," which are not merely rhythmic patterns, nor melodies in the Western sense, but often more like percussive recitations. Western concepts of abstract music ("music for its own sake") are foreign to many other cultures. More often, music is perceived as a cohesive social force or gift, most valued for the group expression of shared beliefs that transcend contemporary political events. Indian tribes of North and South America have believed not only that music mirrored cosmic harmonies, but also that the very process of making music can increase the harmony between a community and the universe, a view paralleled in some Asian and African societies. In many folk traditions particular types of songs, dances, and instrumental music are performed in connection with particular ceremonies and entertainments associated with hunting, farming, birth, and rites of passage. Certain instruments may be associated with certain rituals and performed only by select members of the community. Within some classical traditions, to an even greater degree, elements of structure may be determined by the function of the music. Each of the hundred of Indian ragas, for example, prescribes not only unique melodic formulas, but also an emotional quality, such as happiness or longing, and suitability for performance at a certain time of day. The circumstances, time, and mental attitudes of the performers and audience must be in harmony for a successful performance to take place. When viewed as the aural embodiment of shared experience or metaphysical harmonies, music is often closely allied with other arts, which reflect this same source in visual form. African music is generally associated with dance, music of the Far East with drama. Given such musical values, at once mythic and very utilitarian, it is not surprising that musical practice in many parts of the world has remained virtually unchanged for long periods, in marked contrast to the continuous evolution of Western styles. Japanese gagaku (orchestral court) music exists today much as it did in the 8th century; kuen-chen, a 16th-century genre of music drama that dominated Chinese music for almost 400 years, can be heard today in its original form. Clues to the nature and instruments of distant classical practices that were superseded can often be found in contemporary folk music, where these elements sometimes survive for even longer periods. Within the past hundred years, world musics have increasingly been influenced by Western elements. The spread of technology, particularly of radio and recordings, has accelerated this trend. Some traditions now exist only in hybrid form, and others are passing from use. The styles and techniques of Western music are taught in Japanese schools, for example, and Japanese composers, performers, teachers, and instrument makers have achieved considerable success in Europe and North America. Fortunately, the same technological tools are now assisting scholars from many areas of the world in recording, studying, and preserving the musical heritage of diverse cultures. INTERACTIONS BETWEEN MUSICAL TRADITIONS Most Western music is goal oriented, or narrative in structure, consisting of a series of events that create listener expectations as to "where the music is going." Much of non-Western music, by contrast, is characterized by stasis--the prolongation of one quality or pattern--throughout a performance. Such performances may evoke a ritualistic or contemplative quality; a sense of timelessness or of "inner music"; or a tension brought to the breaking point through the process of uncompromising repetition. The availability of recordings and media communications, and of global travel, have enabled Western audiences to gain increased understanding and appreciation of such types of musical expression. Eastern and African influences within recent Western concert music have been extensive, and can be readily discerned in John \TCage\t's attempts to free music of personal elements, often through chance procedures (see ALEATOLRY \Tmusic\t). Minimalist music by such composers as Steve \TReich\t often feature a single, elemental formal process that unfolds continuously throughout a work. Some works also reflect the influence of \Trock music\t, which itself incorporates elements of rhythm and blues, gospel, country, and black folk music. Such interactions between musical cultures and traditions have always been an important means of renewal and a catalyst in the rise of new styles and forms. Medieval European music developed from Greek, Jewish, Oriental, and local folk sources. Nationalist composers of many periods have incorporated local folk tunes, rhythms, and harmonies within concert and operatic works, seeking to reflect in their music the character and aspirations of their native peoples. \Tjazz\t is the most outstanding recent example of a new musical tradition resulting from crossfertilization. The product of African rhythmic and melodic practices applied to European tuning, harmonic, and metrical frameworks, this black American art form has evolved rapidly into several distinct idioms, many of which have had a significant impact on contemporary concert music. Allan Schindler Bibliography: Abraham, Gerald, The Concise Oxford History of Music (1980); Apel, Willi, ed., Harvard Dictionary of Music, 2d ed. (1973); Arnold, Denis, ed., The New Oxford Companion to Music, 2 vols. (1983); Benade, Arthur, Fundamentals of Musical Acoustics (1976); May, Elizabeth, ed., Music of Many Cultures: An Introduction (1980); Read, Gardner, Music Notation: A Manual of Modern Practice, 3d ed. (1972); Sadie, Stanley, ed., Music Guide: An Introduction (1986) and The New Grove Dictionary of Music and Musicans, 20 vols. (1980); Schindler, Allan, Listening to Music (1980).