quantum mechanics: Identical particles and multielectron atoms: …of Ψ remains unchanged, the wave function is said to be symmetric with respect to interchange; if the sign changes, the function is antisymmetric.

probability theory: The symmetric random walk: A Markov process that behaves in quite different and surprising ways is the symmetric random walk. A particle occupies a point with integer coordinates in d-dimensional Euclidean space. At each time t = 1, 2,… it moves from its present location to…

quantum mechanics: Identical particles and multielectron atoms: …of Ψ remains unchanged, the wave function is said to be symmetric with respect to interchange; if the sign changes, the function is antisymmetric.

fold: A symmetrical fold is one in which the axial plane is vertical. An asymmetrical fold is one in which the axial plane is inclined. An overturned fold, or overfold, has the axial plane inclined to such an extent that the strata on one limb are overturned.…

rug and carpet: Materials and technique: The Turkish, or symmetrical, knot is used mainly in Asia Minor, the Caucasus, Iran (formerly Persia), and Europe. This knot was also formerly known as the Ghiordes knot. The Persian, or asymmetrical, knot is used principally in Iran, India, China, and Egypt. This knot was formerly known as the…

formal logic: Classification of dyadic relations: …is true is called a symmetrical relation (example: “is parallel to”). If the relation ϕ is such that, whenever it holds between one object and a second, it fails to hold between the second and the first—i.e., if ϕ is such that (∀x)(∀y)(ϕxy ⊃ ∼ϕyx) —then ϕ is said to…

Spalacotherium: The genus Spalacotherium has a symmetrodont dentition, characterized by molar teeth with three cusps arranged in a triangle. The symmetrodonts are among the oldest known mammals and also among the most common European faunas of the time.

Spalacotherium: The genus Spalacotherium has a symmetrodont dentition, characterized by molar teeth with three cusps arranged in a triangle. The symmetrodonts are among the oldest known mammals and also among the most common European faunas of the time.

protist: Reproduction and life cycles: …mirror-image, type of fission (symmetrogenic fission). The ciliates, on the other hand, basically divide in a point-by-point correspondence of parts (homothetogenic fission), often seen as essentially transverse or perkinetal (across the kineties, or ciliary rows). Many amoebas exhibit, in effect, no clear-cut body symmetry or polarity, and thus their…

Hermann Weyl: …came to the fore in Symmetry (1952), a profusely illustrated work that examines symmetry in art and nature. He once said, “My work has always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.”

symmetry, in biology, the repetition of the parts in an animal or plant in an orderly fashion. Specifically, symmetry refers to a correspondence of body parts, in size, shape, and relative position, on opposite sides of a dividing line or distributed around a central point or axis. With the

symmetry, In geometry, the property by which the sides of a figure or object reflect each other across a line (axis of symmetry) or surface; in biology, the orderly repetition of parts of an animal or plant; in chemistry, a fundamental property of orderly arrangements of atoms in molecules or

symmetry, in crystallography, fundamental property of the orderly arrangements of atoms found in crystalline solids. Each arrangement of atoms has a certain number of elements of symmetry; i.e., changes in the orientation of the arrangement of atoms seem to leave the atoms unmoved. One such element

formal logic: Classification of dyadic relations: …is true is called a symmetrical relation (example: “is parallel to”). If the relation ϕ is such that, whenever it holds between one object and a second, it fails to hold between the second and the first—i.e., if ϕ is such that (∀x)(∀y)(ϕxy ⊃ ∼ϕyx) —then ϕ is said to…

symmetry, in physics, the concept that the properties of particles such as atoms and molecules remain unchanged after being subjected to a variety of symmetry transformations or “operations.” Since the earliest days of natural philosophy (Pythagoras in the 6th century bce), symmetry has furnished

subatomic particle: Hidden symmetry: Throughout the 1950s, theorists tried to construct field theories for the nuclear forces that would exhibit the same kind of gauge symmetry inherent in James Clerk Maxwell’s theory of electrodynamics and in QED. There were two major problems, which were in fact related.…

quasicrystal: Translational periodicity and symmetry: Fivefold symmetry axes are forbidden in ordinary crystals, while other axes, such as sixfold axes, are allowed. The reason is that translational periodicity, which is characteristic of crystal lattices, cannot be present in structures with fivefold symmetry. Figures 1 and 2 can be used to illustrate…

capacitor dielectric and piezoelectric ceramics: Piezoelectric ceramics: …as an inversion centre, or centre of symmetry—that is, a centre point from which the structure is virtually identical in any two opposite directions. In the case of BaTiO3, the centre of symmetry is lost owing to the transition from a cubic to a tetragonal structure, which shifts the Ti4+…

symmetry: Symmetry in animals: …the five-armed sea stars), any plane passing through this axis will divide the animal into symmetrical halves. Animals having three, five, seven, etc., parts in a circle have symmetry that may be referred to, respectively, as three-rayed, five-rayed, seven-rayed, etc.; only certain planes through the axis will divide such animals…

Lambert Simnel was an impostor and claimant to the English crown, the son of an Oxford joiner, who was a pawn in the conspiracies to restore the Yorkist line after the victory of Henry VII (1485). A young Oxford priest, Richard Symonds, seeing in the handsome boy some alleged resemblance to Edward

Symonds Yat, low-lying neck of land, 12 miles (19 km) south of Ross-on-Wye, Herefordshire unitary authority, Eng., in a great meander loop of the River Wye. Yat Rock (500 feet [150 metres]) to the south has a famous scenic

John Addington Symonds was an English essayist, poet, and biographer best known for his cultural history of the Italian Renaissance. After developing symptoms of tuberculosis while a fellow of Magdalen College, Oxford, Symonds traveled extensively for his health, settling in Davos, Switz., in 1880.

Lambert Simnel: A young Oxford priest, Richard Symonds, seeing in the handsome boy some alleged resemblance to Edward IV, determined to exploit him. In 1486, the rumour that the “princes in the Tower,” Edward’s children, were still alive, suggested that Simnel might be passed off as one of them. A year…

The Cosby Show: …and the irresistible Olivia (Raven-Symoné, who later starred in the Disney Channel’s That’s So Raven, 2003–07) was eventually introduced as Cliff and Clair’s five-year-old step-grandchild.

Ukraine: Kuchma’s presidency: …Kuchma defeated Communist Party leader Petro Symonenko by a resounding margin. Politically, Kuchma had benefited from the splintering of the left among several candidates. He also had campaigned vigorously, using all the means available to him, particularly the media. Indeed, a strong bias in favour of Kuchma became evident in…

Sir Roland Theodore Symonette was a Bahamian politician who served as the first premier of The Bahamas (1964–67). Symonette was educated at a day school on Eleuthera and became a shipyard owner and a contractor for the construction of roads, wharves, and harbours in The Bahamas. He was elected in

A.J.A. Symons was a British author and biographer best known for his brilliant and unconventional biography The Quest for Corvo (1934). Family economic difficulties obliged Symons to leave home and learn a trade at an early age. For three years he lived a life of drudgery, working as an apprentice

A.J.A. Symons was a British author and biographer best known for his brilliant and unconventional biography The Quest for Corvo (1934). Family economic difficulties obliged Symons to leave home and learn a trade at an early age. For three years he lived a life of drudgery, working as an apprentice

Arthur Symons was a poet and critic, the first English champion of the French Symbolist poets. Symons’s schooling was irregular, but, determined to be a writer, he soon found a place in the London literary journalism of the 1890s. He joined the Rhymers’ Club (a group of poets including William

Arthur Symons was a poet and critic, the first English champion of the French Symbolist poets. Symons’s schooling was irregular, but, determined to be a writer, he soon found a place in the London literary journalism of the 1890s. He joined the Rhymers’ Club (a group of poets including William

George James Symons was a British meteorologist who strove to provide reliable observational data by imposing standards of accuracy and uniformity on meteorological measurements and by substantially increasing the number of reporting stations. Symons was elected a member of the British

sympathetic nervous system, division of the nervous system that functions to produce localized adjustments (such as sweating as a response to an increase in temperature) and reflex adjustments of the cardiovascular system. Under conditions of stress, the entire sympathetic nervous system is

human nervous system: Enteric nervous system: …two types of sensory neurons: sympathetic neurons, which originate from dorsal-root ganglia found at the thoracic and lumbar levels; and parasympathetic neurons, which originate in the nodose ganglion of the vagus nerve or in dorsal-root ganglia at sacral levels S2–S4. The former innervate the gastrointestinal tract from the pharynx to…

eye disease: Ocular injuries: …of inflammation following injury, called sympathetic ophthalmia, is of particular importance. In this condition an injured eye causes the other, previously normal eye to take part in the inflammation, with resulting impairment of vision. Sympathetic ophthalmia can occur weeks, months, or years after the initial injury. The cause of sympathetic…

eye disease: Ocular injuries: …of inflammation following injury, called sympathetic ophthalmia, is of particular importance. In this condition an injured eye causes the other, previously normal eye to take part in the inflammation, with resulting impairment of vision. Sympathetic ophthalmia can occur weeks, months, or years after the initial injury. The cause of sympathetic…

human nervous system: Sympathetic nervous system: …sometimes referred to as the thoracolumbar outflow.) The axons of these neurons exit the spinal cord in the ventral roots and then synapse on either sympathetic ganglion cells or specialized cells in the adrenal gland called chromaffin cells.

stringed instrument: The production of sound: and the sitar, possess numerous sympathetic strings tuned according to the notes of the mode being played. The South Asian fiddle, sarangi, has some two to three dozen sympathetic strings; the Norwegian Hardanger fiddle (Hardingfele) has four or five sympathetic strings; and the viola d’amore typically has seven. Sympathetic strings…

human nervous system: The peripheral nervous system: …ganglia are located in the sympathetic trunks, two long chains of ganglia stretching along each side of the vertebral column from the base of the skull to the coccyx; these are referred to as paravertebral ganglia. Prevertebral motor ganglia are located near internal organs innervated by their projecting fibers, while…

adrenergic drug, any of various drugs that mimic or interfere with the functioning of the sympathetic nervous system by affecting the release or action of norepinephrine and epinephrine. These hormones, which are also known as noradrenaline and adrenaline, are secreted by the adrenal gland, hence

Mark Ruffalo: …Festival for his directorial debut, Sympathy for Delicious, about a paraplegic DJ who discovers that he has a talent for faith healing. In addition, his performance as the laid-back sperm donor who fathered the teenage children of a lesbian couple in The Kids Are All Right (2010) brought him an…

speciation: Sympatric speciation: …alternative to allopatric speciation is sympatric speciation, in which reproductive isolation occurs within a single population without geographic isolation. In general, when populations are physically separated, some reproductive isolation arises. How genetic divergence can happen within a population of individuals that are continually interacting with one another is usually difficult…

gibbon: >Symphalangus. Molecular data indicate that the four groups are as different from one another as chimpanzees are from humans.

siamang, (Symphalangus syndactylus), arboreal ape of the gibbon family (Hylobatidae), found in the forests of Sumatra and Malaya. The siamang resembles other gibbons but is more robust. The siamang is also distinguished by the webbing between its second and third toes and by a dilatable hairless

hurdy-gurdy: Secular, one-man forms, called symphonia, appeared in the 13th century. It was fashionable during the reign of Louis XIV as the vielle à roue (“wheel fiddle”) and was played into the 20th century by folk and street musicians, notably in France and eastern Europe. The Swedish nyckelharpa is a…

Christianity: The views of Eusebius of Caesarea: …of the Christian church as symphōnia, or “harmony.” The church recognized the powers of the emperor as protector of the church and preserver of the unity of the faith and asserted its own authority over the spiritual domain of preserving Orthodox doctrine and order in the church. The emperor, on…

concerto: The Baroque vocal-instrumental concerto (c. 1585–1650): …the three sets of Schütz’s Symphoniae sacrae, or Sacred Symphonies (1629, 1647, and 1650), works that reveal all the variety of treatment to be found in Schein’s sacred concerti, except for Schein’s interest in the chorale. The first two of Schütz’s sets consisted of few-voice settings, mostly one to three…

Symphonic Dances, Op. 45, symphony for orchestra by Russian composer Sergey Rachmaninoff that premiered in the United States in 1940 and was the last of his major compositions. Rachmaninoff had left his homeland forever soon after the Russian Revolution of 1917. Symphonic Dances was first performed

symphonic poem, musical composition for orchestra inspired by an extra-musical idea, story, or “program,” to which the title typically refers or alludes. The characteristic single-movement symphonic poem evolved from the concert-overture, an overture not attached to an opera or play yet suggestive

Robert Schumann: The early years: …and the Études symphoniques (1834–37; Symphonic Studies), another work consisting of a set of variations.

Gunther Schuller: …pieces and in 1955 composed Symphonic Tribute to Duke Ellington. He often collaborated with John Lewis, notably with the Modern Jazz Quartet and the Modern Jazz Society.

symphonie concertante, in music of the Classical period (c. 1750–c. 1820), symphony employing two or more solo instruments. Though it is akin to the concerto grosso of the preceding Baroque era in its contrasting of a group of soloists with the full orchestra, it rather resembles the Classical solo

Édouard Lalo: …composer, best known for his Symphonie espagnole and notable for the clarity of his orchestration.

Symphonie fantastique, Op. 14, orchestral work by French composer Hector Berlioz, widely recognized as an early example of program music, that attempts to portray a sequence of opium dreams inspired by a failed love affair. The composition is also notable for its expanded orchestration, grander

Symphonie fantastique, Op. 14, orchestral work by French composer Hector Berlioz, widely recognized as an early example of program music, that attempts to portray a sequence of opium dreams inspired by a failed love affair. The composition is also notable for its expanded orchestration, grander

Hector Berlioz: Mature career of Hector Berlioz: …Symphonie funèbre et triomphale (Funeral Symphony) for military band, chorus, and strings, commissioned for the 10th anniversary (1840) of the July Revolution of 1830—was intended as a partial solace for the defeat of Benvenuto Cellini. A few years before, Berlioz’s literary gifts had won him the post of music…

André Gide: Great creative period: …Strait Is the Gate), and La Symphonie pastorale (1919; “The Pastoral Symphony”) reflect Gide’s attempts to achieve harmony in his marriage in their treatment of the problems of human relationships. They mark an important stage in his development: adapting his works’ treatment and style to his concern with psychological problems.…

electronic music: Establishment of electronic studios: …period are Schaeffer and Henry’s Symphonie pour un homme seul (1950; Symphony for One Man Only) and Henry’s Orphée (1953), a ballet score written for the Belgian dancer Maurice Béjart. These and similar works created a sensation when first presented to the public. Symphonie pour un homme seul, a descriptive…

Merce Cunningham: Symphonie pour un homme seul (1952; later called Collage) was performed to Pierre Schaeffer and Pierre Henry’s composition of the same name and was the first performance in the United States of musique concrète, or music constructed from tape-recorded environmental sounds.

Vincent d’Indy: Among his symphonic works, Symphonie sur un chant montagnard français (1886; “Symphony on a French Mountaineer’s Chant”), with solo piano, based entirely on one of the folk songs d’Indy had collected in the Ardeche district, and Istar (variations; 1896) represent his highest achievements. His 105 scores also include keyboard…

Bavarian Radio Symphony Orchestra, German symphony orchestra based in Munich and supported by the state of Bavaria. Under the aegis of the Bavarian state radio station, conductor Eugen Jochum organized the performing group in 1949, trained it to become a major orchestra, and took it to perform at

Michel-Richard Delalande: Of his instrumental music the Symphonies pour les soupers du roi was so appreciated by Louis XIV that he ordered André Philidor to copy the complete set in 1703. Delalande also wrote secular cantatas and pastorals and music for dramatic presentations of the sacred tragedies produced by the Jesuit College…

symphony, a lengthy form of musical composition for orchestra, normally consisting of several large sections, or movements, at least one of which usually employs sonata form (also called first-movement form). Symphonies in this sense began to be composed during the so-called Classical period in

Wolfgang Fortner: The Symphony (1947), an aggressive, poignant work, exemplifies the composer’s maturity. Its four movements abound in contrapuntal complexities, the resulting musical texture being harmonically and rhythmically very intense. The Phantasie über B-A-C-H for two pianos, nine solo instruments, and orchestra (1950) displays Fortner’s skill with 12-tone…

Chicago: Cultural institutions: …few more blocks north is Symphony Center (formerly Orchestra Hall), home of the Chicago Symphony Orchestra and its training ensemble, the Civic Orchestra of Chicago, as well as a venue for other musical events. Across the street sits the Art Institute of Chicago, a world-class art museum and school dating…

symphonie concertante, in music of the Classical period (c. 1750–c. 1820), symphony employing two or more solo instruments. Though it is akin to the concerto grosso of the preceding Baroque era in its contrasting of a group of soloists with the full orchestra, it rather resembles the Classical solo

Franz Schubert: Maturity of Franz Schubert: …time, destined to obscurity: the Symphony in B Minor (Unfinished), which speaks from Schubert’s heart. Two movements and a half-finished scherzo were completed in October and November 1822. In November of the same year Schubert composed a piano fantasia in which the variations are on a theme from his song…

Duke Ellington: Classical forms: …basis for the film short Symphony in Black (1935), which also features the voice of Billie Holiday (uncredited). Ellington wrote motion-picture scores for The Asphalt Jungle (1950) and Anatomy of a Murder (1959) and composed for the ballet and theatre—including, at the height of the American civil rights

symphony: The 20th century: But the Symphony in C (1940) and Symphony in Three Movements (1942–45) are unique. The former, a Neoclassical work, reinterprets in Stravinsky’s language the thematic construction and sonata form of the Classical era. The result, far from a simple parody of Classical style (such as in Sergey…

Georges Bizet: His Symphony in C Major, however, written in 1855 but subsequently lost and not discovered and performed until 1935, will bear easy comparison with any of the works written at the same age of 17 by either Mozart or Felix Mendelssohn. Flowing and resourceful counterpoint, orchestral…

Gaelic Symphony, symphony by American composer Amy Beach, premiered October 30, 1896, in Boston. It was the first symphony by an American woman composer to gain public attention, written at a time when American composers of either gender were a relative rarity on the international scene. The Gaelic

symphony: The 20th century: The Symphony in Three Movements, inspired by wartime impressions, is independent of models, yet in outward form the movements appear traditional. Two other of Stravinsky’s works deserve mention here: the Symphonies of Wind Instruments (1920, rev. 1947) and the Symphony of Psalms (1930), which includes chorus.…

James McNeill Whistler: The move to London: …considerable success in Paris when Symphony in White, No. 1: The White Girl (1862) was shown at the Salon des Refusés in 1863. This famous painting shows that if he was an exponent of realism, he was also attracted by the Pre-Raphaelite movement, which had begun in England in 1848.

Dmitri Shostakovich: Early life and works: …as a composer with the Symphony No. 1 (1924–25), which quickly achieved worldwide currency. The symphony’s stylistic roots were numerous; the influence of composers as diverse as Pyotr Ilyich Tchaikovsky and Paul Hindemith (and, avowedly, Shostakovich’s contemporary Sergey Prokofiev) is clearly discernible. In the music Shostakovich wrote in the next…

Ellen Taaffe Zwilich: In 1983 her Symphony No. 1 (1982; originally titled Three Movements for Orchestra) was awarded the Pulitzer Prize for music, making her the first woman to be so honoured. The Peanuts® Gallery (1996), for piano and orchestra, consists of sketches of Charles M. Schulz’s comic-strip characters and was…

Symphony No. 1 in B-flat Major, Op. 38, symphony by German composer Robert Schumann that premiered on March 31, 1841, in Leipzig and was conducted by Schumann’s friend Felix Mendelssohn. It is an intensely optimistic work and is the most frequently performed of Schumann’s four symphonies.

harmony: Modulation: …in the first movement of Symphony No. 1 in C Major, Opus 21 (1800), of Beethoven, there is considerable emphasis on the chords of D, both major and minor, establishing D as a dominant leading to a cadence on G, the point of arrival. Much of the dissonance in music…

Symphony No. 1 in C Minor, Op. 68, orchestral work by German composer Johannes Brahms that, with its lyricism and thematic unity, is widely regarded as one of the greatest symphonies of the Austro-German tradition. Nearly 20 years in the making, the composition premiered on November 4, 1876, in

Symphony No. 1 in D Major, symphony by composer Gustav Mahler, also known as Titan. Begun in Leipzig while Mahler was serving as second conductor of the Stadttheater and drafted in about six weeks, it premiered in Budapest November 20, 1889, after Mahler assumed the post of musical director of the

Aleksandr Borodin: …his first major work, the Symphony No. 1 in E-flat Major (1862–67), written as a result of his acquaintance with Mily Balakirev, of whose circle (The Five) he was a member, along with Nikolay Rimsky-Korsakov, Modest Mussorgsky, and César Cui. Borodin began his Symphony No. 2 in B Minor in…

Dmitri Shostakovich: Later life and works: His Symphony No. 10, composed in 1953, the year of Stalin’s death, flew in the face of Zhdanovism, yet, like his Symphony No. 5 of 16 years earlier, compelled acceptance by sheer quality and directness. His Symphony No. 11 (1957), a paean to revolution, earned him…

Gustav Mahler: Musical works: last period: 9 (1910), and Symphony No. 10 in F Sharp Major, left unfinished in the form of a comprehensive full-length sketch (though a full-length performing version has been made posthumously). The first of the three again revealed Mahler’s superstition: beginning as a song cycle (to Chinese poems in German…

Alan Hovhaness: His Symphony No. 16 for strings and Korean percussion (first performed 1963) shows his use of unusual instrumental groupings, as does his Sextet for violin, timpani, drums, tam-tam, marimba, and glockenspiel (1966).

Samuel Barber: In the Symphony No. 2 (1944; rev. 1947), commissioned by the U.S. Army Air Forces (which he had joined in 1943), Barber introduced an electronic instrument imitating radio signals for air navigation, an effect replaced in the revised version by an E-flat clarinet.

Symphony No. 2, flowing three-movement symphony by American neo-Romantic composer Howard Hanson, written as a counter to such musical trends of the day as formalism and serialism. The symphony was commissioned by the Boston Symphony Orchestra for the occasion of its 50th anniversary, and the work

John Corigliano: …Prize in Music for his Symphony No. 2 for String Orchestra.

Johannes Brahms: Maturity and fame of Johannes Brahms: …next year he produced his Symphony No. 2 in D Major (1877). This is a serene and idyllic work, avoiding the heroic pathos of Symphony No. 1. He let six years elapse before his Symphony No. 3 in F Major (1883). In its first three movements this work too appears…

Symphony No. 2: The Age of Anxiety, programmatic symphony for piano and orchestra by American composer Leonard Bernstein. It was inspired by the long poem The Age of Anxiety (1947) by English-born poet W.H. Auden. Bernstein’s symphony premiered April 8, 1949, with the Boston Symphony Orchestra,

Ilya Of Murom: …was the basis of the Symphony No. 3 (1909–11; Ilya Muromets) by Reinhold Glière.

symphony: Mendelssohn: 3 (Scottish) and Symphony No. 4 (Italian), both in A major–minor. The Scottish (also called Scotch), completed in 1842, although not programmatic, is expressive of Mendelssohn’s poetic nature. Its beginning was sketched during a visit to Scotland in 1829. In structure the work consists of four…

Symphony No. 3, symphony for orchestra and choruses by Austrian composer Gustav Mahler that purports to encapsulate everything the composer had learned about life to date. Although performances of the incomplete symphony occurred earlier, the entire piece was first presented in Krefeld, Germany, on

Symphony No. 3, symphony for orchestra by American composer Aaron Copland that premiered in Boston on October 18, 1946, with the Boston Symphony Orchestra and its conductor, Serge Koussevitzky, who had commissioned the work. The first movement begins with a gentle theme from the woodwinds and

Aleksandr Scriabin: In Switzerland he completed his Symphony No. 3, first performed under Arthur Nikisch in Paris in 1905. The literary “program” of this work, devised by Tatiana Schloezer, with whom he had formed a relationship after abandoning his wife, was said to represent “the evolution of the human spirit from pantheism…

Jean Sibelius: …composer Granville Bantock commissioned his Symphony No. 3 in C Major (1907). With this work Sibelius turned his back on the national romanticism of the second symphony and the Violin Concerto in D Minor (1903) and moved toward the more searching and uncompromising mode of utterance of En Saga and…

Organ Symphony, orchestral work by French composer Camille Saint-Saëns, notable especially for its grand use of an organ in the final movement. The work premiered on May 19, 1886, in London, where Saint-Saëns was engaged in a concert tour, and it became one of the first widely praised symphonies by

Pyotr Ilyich Tchaikovsky: Middle years: …summer of 1875, Tchaikovsky composed Symphony No. 3 in D Major, which gained almost immediate acclaim in Russia.

symphony: Schumann: 3 in E-flat Major (1850; Rhenish) and Symphony No. 4 in D Minor (1841, rev. 1851). The five-movement Rhenish is less “classical” than the Symphony No. 2. Inspired by a ceremony at Cologne Cathedral as well as by the appearance of the cathedral itself, the polyphonic grandeur and harmonic richness,…

Eroica Symphony, symphony by Ludwig van Beethoven, known as the Eroica Symphony for its supposed heroic nature. The work premiered in Vienna on April 7, 1805, and was grander and more dramatic than customary for symphonies at the time. It was Beethoven’s largest solely instrumental work. It has

Johannes Brahms: Maturity and fame of Johannes Brahms: …six years elapse before his Symphony No. 3 in F Major (1883). In its first three movements this work too appears to be a comparatively calm and serene composition—until the finale, which presents a gigantic conflict of elemental forces. Again after only one year, Brahms’s last symphony, No. 4 in…

Prague: …Mozart lived there, and his Prague Symphony and Don Giovanni were first performed in the city. In addition, the lyric music of the great Czech composers Bedřich Smetana, Antonín Dvořák, and Leoš Janáček is commemorated each year in a spring music festival. The

Wolfgang Amadeus Mozart: The last travels of Wolfgang Amadeus Mozart: …series of three symphonies, in E-flat Major (K 543), G Minor (K 550), and C Major (the Jupiter, K 551), usually numbered 39, 40, and 41; these, with the work written for Prague (K 504), represent the summa of his orchestral output. It is not known why they were composed;…