The early Greeks considered music to be of mathematical and cosmic significance as well. Pythagoras of Samos (circa 500 B.C.) discovered the frequency proportions that define the intervals we hear today. For example, two notes whose frequencies are in a ratio of 2 to 1, sound one octave apart. A ratio of 3 to 2 produces a fifth, a ratio of 4 to 3 produces a fourth, and a ratio of 9 to 8 produces a major second. Greek musicians and philosophers used a single-string instrument, known as the monochord, to produce the various intervals. Pythagorean philosophers believed that these ratios also governed the movement of celestial bodies and other cosmic matters. Thus, music came to be revered as the highest of intellectual and artistic pursuits. Music theorists of the second century A.D. such as Nicomachus of Gerasa and Claudius Ptolemy wrote extensively about the mathematical, moral, and cosmic significance of music. Ptolemy's treatise, Harmonics, is the most useful extant reference on ancient Greek music theory. Interpretations of ancient treatises have yielded common ground on the matter of rhythmic notation but much disagreement and speculation on the interpretation of pitch. The Greeks used a system of modes known as tonoi which may or may not be similar in concept to the scales we use today.

Music of the Early Roman Church

There is little evidence that Ancient Romans contributed much to music history other than the development of brass instruments used in the military. The Romans conquered Greece in 146 B.C. and assimilated and adapted Greek music and religion. Writings of Cicero, Quintilian, and others document the use of music for purely entertainment purposes at large festivals with choruses and instrumental ensembles. The gradual decline of Rome after 200 A.D. took place as the popularity of Christianity was increasing. The emperor Constantine I, who ruled from 306 to 337 A.D., adopted Christianity and legalized it for the first time in the Roman empire. Rome had for centuries exerted a peaceful and unifying influence on Europe but that was gradually disintegrating as barbarians increasingly threatened the security of the empire. When the Roman empire was permanently divided in 395 A.D., Christianity became the only major cultural force unifying the still vital eastern empire in Byzantium with the rapidly dissolving western empire in Europe. By the time the last Roman emperor, the young Romulus Augustulus, was finally deposed in 476, the papacy had established itself in Rome and was asserting jurisdiction over the Christian church. The music of the Christian church was for centuries the only cultivated art music in existence in Europe. Early Christian music, largely monophonic chant influenced by the Jewish cantorial tradition, was entirely vocal as the church attempted to purge the masses of the instrumental music associated with competing religions. Latin translations by Boethius (circa 480-524) and Cassiodorus (circa 490-585) of Greek literature on music theory also contributed to the theoretical foundations of early Christian chant. It is from these origins that the history of western art music properly begins.

Western Music

Music in the Western Culture is the result of various influences, including the formalization of improvised traditions; the growth of notation; the development of tuning systems; the treatment of text; innovative approaches to form; the role of patronage; the absorption of various cultures into the style; the growth of technology; investigations of performance practice; and various other factors.

Western music also benefits from various dualities: sacred and secular traditions; monophonic and polyphonic textures; conservative and progressive tendencies; popularism and elitism; canon and non-canonic works; and other polarities. The western tradition is complicated by these various influences and perspectives, and formal musicological study often becomes a point of departure for other, more individualized investigations of music.

The western tradition of music has its origins in the chant tradition of the early Christian era. The monophonic music of chant dominated the middle ages, and included the composition of sequences and tropes. In the high middle ages, organum emerged, thus introducing polyphonic textures into liturgical music. By the thirteenth century, the motet became a seminal polyphonic composition and included liturgical and secular texts as well as a chant cantus firmus. In the Ars Nova of the thirteenth and fourteenth centuries, secular music was composed polyphonically, and resulted in elaborate contrapuntal devices and notational practices.

In the fifteenth century the early Renaissance polyphony showed evidence of a new style influenced on fauxbourdon and based on previously improvised traditions. At this time textures grew from a reliance on lower voices to treble-dominated textures. Renaissance motets and madrigals have their origins in the music of the Netherlands composers (Obrecht, Ockeghem, Busnois, Binchois) and the idiom culminates in the work of Josquin Desprez. With the late Renaissance, more national and secular music emerged, as found with the English madrigal and the French chanson.

The late sixteenth-century music included attempts to return to Greek drama. The latter resulted in the formulation of monody for declaiming music which was at the core of early opera (Caccini, Peri) and became a vehicle for composers like Monteverdi to take forward the nascent genre of opera. Italian opera (opera seria, opera buffa) soon dominated the early baroque style of the seventeenth century, which extended to the composition of oratorios on sacred subjects. In France opera soon took root, and a national style evolved starting with Lully.

In the seventeenth century instrumental music developed on its own, treble dominated texture of vocal music was supported by the basso continuo tradition of accompaniment. Works for instruments included keyboard suites (Froberger, Kerll) and sonatas, organ music (Frescobaldi), including various partitas and fugues, and trio sonatas (Corelli, et al.) for various combinations of instruments. Music for orchestra included sinfonias and concertos, including the concerto grosso.

The high baroque music of the eighteenth century was dominated by the genius of Bach and Handel. Bach composed music for almost every genre except opera; he left a corpus of liturgical music, including cantatas, that show the influence of the Reformation on musical style. Handel, as a German - born composer who studied in Italy and worked many years in England, shows the international aspects of the baroque style. Like Bach, he wrote in almost every genre, including opera seria and oratorio.

While Bach and Handel yet composed, a style change was taking place in the early eighteenth century. Rococo preferences moved toward simpler harmonies and more transparent textures, as well as a tendency toward instrumental music (C.P.E. Bach, J.C. Bach, Joseph Haydn). Later in the century, the Classic style of Haydn and Mozart dominated the music of Western Europe, with the symphony, sonata, and string quartet predominating, and the sonata principle at the core of musical structure. The opera seria of Handel and his generation gave way to opera buffa, as found with Mozart and others. The bel canto tradition in opera seria metamorphosed with Mozart and emerged later in the operas of Rossini, Donizetti and Bellini.

The classical style may be seen to culminate in the music of Beethoven, who is perceived as the link between the classic and romantic style. This distinction is important for the so-called common practice era from ca. 1725 to 1900, that is the period of the defining tradition of western music. Beethoven contributed to almost every genre of music at the time, including piano sonata, string quartet, and symphony. He expanded the symphony with regard to form, orchestration, texture, and aesthetics, contributing programmatic elements to an otherwise self-contained style.

As the link to the romantic era that dominated the nineteenth century, Beethoven is a point of departure for many of the trends that existed in the era. The so-called Romantic style includes the growth of a number of varied and often antithetical influences. These include the development of the symphony as a genre; program music and the ideal of absolute music; grand opera; lieder; character pieces for piano; the piano sonata; national musical style; and the expansion of tonality and harmonic practice. The early Romantic composers include Schubert, Weber, Berlioz, Mendelssohn, Schumann, and Chopin; among the later ones are Liszt, Wagner, Brahms, and Verdi.

With Wagner romantic opera expanded in terms of the orchestra, the scope of subject matter, the demands on voices, and the overall length. As a controversial figure, Wagner influenced the musical establishment, such that affinities were aligned with him and the music of the future, or with more conservative trends that reached back to Beethoven. Wagner's harmonic and timbral idiom was critical for the late romantic efflorescence at the end of the century that led to the so called end of tonality as it was generally understood in the nineteenth century.

With Wagner, the dominance of the Austro-German tradition in nineteenth-century music became apparent. The extended harmonic and formal practices of Mahler, Richard Strauss, Schonberg, and others preceded the freer treatment of dissonance in the twelve-tone music of the New Viennese School of Schonberg, Berg, and Webern. At the same time, the Impressionism of the French composers Debussy and Ravel were based on non-functional harmonic principles. Composers like Bartok introduced folk elements into music.

Twentieth-century music includes many different styles and tendencies, including neoclassicism (Stravinsky) - an important type of 20th century music is neoclassical. «Neo» means new, so neoclassical music is new music that is similar to music of the Classical period. While neoclassical music sounds modern in many ways, it is written following the basic forms and ideals of the Classical period.

A famous neoclassical composer is Igor Stravinsky. His music uses many different key signatures and time signatures, and sometimes more than one at a time. One example is the Rite of Spring;

expressionism (Berg, Webern);

serialism (Boulez);

electronic music (Stockhausen);

aleatoric music and indeterminacy (Cage) - the composer leaves a lot up to the performer. For example a composer might give each player in the band four different sheets of music. On the director's signal each player in the band could play any one of the four sheets of music, starting and stopping whenever he or she wished. Chance music is interesting because each performance is different. One important composer of chance music was John Cage. His Imaginary Landscape No. 4, consists of 12 radios all playing at the same time, but all tuned to different stations; minimalism (Reich, Glass).

At the same time, the rediscovery of the past has resulted in an explosion of interest in the authentic music of past cultures. Similarly, the eclecticism of twentieth-century culture touches upon the growth of ethnomusicology and the perspectives it offers to studies of more traditional western music.

Literature

1. Griffiths, Paul. Encyclopedia of 20th-Century Music. N.p.: Thames and Hudson, 1986.

2. Grout, Donald Jay. A History of Western Music. New York: W.W. Norton, 1960-80. 3rd ed.

3. http://music.dartmouth.edu

4. http://www.hypermusic.ca

5. http://www.stevenestrella.com