Robert Kelley in his article entitled Tradition, the Avant Garde, and Individuality in the Music of Olivier Messiaen: Musical Influences in Méditations sur la mystère de la Sainte-Trinité writes:
"A glance at any twentieth-century music textbook will give one the impression that serialism, chance music, electronic music, and the post-modern trends of minimalism and neo-romanticism have seemed to dominate the music of the second half of the twentieth century. However, a more detailed look into the music presented in the texts suggests that the work of most individual composers during the period represents a more eclectic collection of influences that include one or more of these major trends among them, sometimes only during a short period of the composer's productive life. This observation shows that a more complete view of late twentieth-century music comes from looking at the influences on individual composers and thus gives the perspective that this music abounds with tradition. Much of this rich sophistication in twentieth-century music was fueled by the explosion of resources that arose from musicological and ethnomusicological research. Only in the twentieth century have musicologists and other researchers successfully begun to construct a complete musical picture of such sources as the Medieval period, non-Western cultures, and the political and philosophical zeitgeists of all of the many times and cultures. Music in the twentieth century, then, does not draw on one central and contemporary tradition to the exclusion of foreign influence, but, rather, makes use of many much more individualistic origins and inspirations as its "tradition". "
This is well illustrated in the case, reported by Michael Ball, of the French composer and teacher Olivier Messiaen.
"In the forties and fifties Messiaen was shunned on the one hand by the new 'avant-garde' as too sweet and sentimental and on the other hand by the more conventional musical public as too austere and discordant. Boulez in particular could not come to terms with and reacted against works like Turangalila with its rich mix of tonal and atonal language saying that he prefers the ones that remain true to one style or the other. However, one gem of a composition was to turn twentieth-century music on its head. This was Mode de valeurs et d'intensites (1949), part of four studies in rhythm for piano. It took Schönberg's theory of serializing pitches a whole leap forward whereby Messiaen effectively serialized all musical parameters i.e. pitches, durations, dynamics and articulations. Thus each note has a character and identity all of its own which is maintained throughout the piece. For example, middle C will always appear as a dotted minim value, forte dynamic and have a tenuto articulation mark. Although this paved the way for the young generation of composers such as Stockhausen, Boulez, Nono etc. to explore previously uncharted territory, Messiaen himself never pursued the idea beyond that study."
In his article about the British composer Edmund Rubbra (1901-1986), Francis Routh considers different kinds of 'progressive'.
" There are two main kinds of progressive, whether in music or in other fields of human activity. The first are those who are entirely disenchanted with the continued relevance of established methods and past traditions; they therefore seek to do away with them, and to replace them with something else; something fresh, untraditional. The second are those who do not discard past traditions, but seek instead to reinterpret them, and to apply them in a fresh context as they see fit.
The first kind, who may be described as the ideological iconoclasts, are far more readily noticeable than the second. It is indeed one of the prime requisites, if you are going to put forward new methods and fresh styles, that your gestures should be both strikingly novel, if possible outrageous, and immediately recognisable. Thus the avant-garde aesthetic is a simple one. But the severe risk run by those who subscribe to it is twofold; partly that means may be mistaken for ends - the striking of a fresh posture, the adoption of an untried process, may be mistaken in itself for an art-work, which it is not; and partly that, by thus shifting the scale of values, the concept of permanent validity in the finished work becomes relative. Your novelty one week may well be made redundant by someone else's more radical novelty the next, if you have no other yardstick by which to measure it than the fact of its 'progressiveness'.
The second kind of progressives run risks as well, though of a different, more subtle, nature. They may be overlooked as merely 'traditional', and their work not understood for what it is. Because they do not sever all links with the past, as the other kind do, but on the contrary accept the past and try to relate it to the present, their relevance for the present may he questioned. In the eyes of the first kind they will probably appear as 'blacklegs', who have, by compromising with tradition, forfeited any right to he called 'progressive' at all.
And yet the self-styled revolutionaries, of whom several adorn the history of music - much as heretics adorn the history of the Christian Church - rarely reach beyond the ephemeral stage. At most they succeed in focusing attention on to a particular idea, which others may then pursue and develop. Art reaches a more than ephemeral validity only when its creator takes a wider view of tradition than the narrowly revolutionary one. "
The American composer Benjamin Lees (1924-2010) wrote: "There are two kinds of composers. One is the intellectual and the other is visceral. I fall into the latter category. If my stomach doesn't tighten at an idea, then it's not the right idea."
Bernard Herrmann (1911-1975), whose musical scores enhance the cinematic content of Psycho, North by Northwest, Vertigo, Citizen Kane and many other fine films, famously said "Musically I count myself an individualist. I believe that only music which springs out of genuine personal emotion is alive and important. I hate all cults, fads, and circles."
Joe Horowitz in his article entitled Bernard Herrmann and Musical Topography observes:
"His [Herrman's] favourite composers - an unfashionable twentieth-century list - included Debussy, Ravel, Elgar, Delius, Holst, and Ives. His distinctive compositional style was a direct suffusion of his morbid Romantic self. Among his musical signatures are nervous ostinatos, irresolute motivic scraps, and lurid colours."
These points are raised also in Musical Borrowings which we paraphrase below:
Those composers who have felt limited by the mainstream avant-garde movement, have turned instead to the music of the East, a tradition which goes back to Debussy and consists mostly of stylistic modeling, to that of the past or to jazz, which brings a popular style to art music. Avant-garde composers too have looked to music of the past, mostly to medieval music. While many use general stylistic references, a few have used direct borrowings. For example, Peter Maxwell Davies's Missa super L'Homme Armé offers his criticism on the material he borrows, demonstrating that the mass has degenerated in modern society; hence, he interrupts the sacred reference with the foxtrot. Donatoni reduces borrowed material to small sound bites, offering no respect for the composer's ego or personality. These and other examples demonstrate that the search for outside inspiration has advantages as well as disadvantages; some composers seem to seek mere novelty or shock value, but fresh developments in the field have been interesting in any case.
William Grant Still's Afro-American Symphony, Florence Price's Symphony in E Minor, and William Dawson's Negro Folk Symphony are examples of American musical nationalism, they also represent the culmination of the Harlem Renaissance, an affirmation of the black cultural heritage in which composers sought to elevate the Negro folk idiom to symphonic form. Still's Afro-American Symphony is based on a theme in the Blues idiom. The second theme of the first movement of Dawson's Negro Folk Symphony is based on the spiritual Oh, M' Littl' Soul Gwine-a Shine, and the two themes of the third movement are based on the spirituals O Le' Me Shine, Lik' a Mornin' Star and Hallelujah, Lord I Been Down into the Sea. In Symphony in E Minor, Price is more subtle in her use of elements from the Afro-American folk tradition: her instrumentation calls for African drums; the principal theme of the first movement and its countermelody are built upon a pentatonic scale (the most frequently used scale in Afro-American folk songs); and the third movement is based on the syncopated rhythms of the Juba, an antebellum folk dance.
In some senses, the Romantic era in music never ended. Although many composers reacted against the Romantic aesthetic, others, including Elgar, Delius, Rachmaninoff and Sibelius, continued to write such music during the twentieth century.
Dr. Frank La Rocca writes: "Aaron Copland (1900-1990), taking stock of the changes in the musical landscape of the late 1930s wrought by the spread of the radio and phonograph, made his decision to 'see if I couldn't say what I wanted to say in the simplest possible terms' (subsequently earning universal public acclaim and a Pulitzer Prize for Appalachian Spring). What he would not have known then was that he was, at the same time, earning himself the scorn of the coming generation of post-war, university-trained composers in the United States. Copland's populist orientation and clearly stated intent to reach out to the broadest possible audience violated the prime directive of mid-century musical aesthetics. Copland's disarmingly honest statement would be held up as evidence that he had 'sold out' ".
As Frank LaRocca observes: "this post-war generation, led by such figures as Babbitt and Boulez was, after all, the one that made 'popular' the opposite of 'serious' in music, as if popular appeal and intellectual and structural interest had suddenly become incompatible qualities."
Various forms of "Neo-Romanticism" have since restored the ideals of melody, traditional harmonies, emotional expression, and narrative among many younger composers. The result is that "contemporary" music by composers like Philip Glass and Arvo Pärt is often more appealing to a broad audience than earlier works by composers who claimed to be the authentic voice of the twentieth century in stressing dissonance and fragmentation in their music. The benefits of 'Neo-Romanticism' came also to Alan Hovhaness who had continued to do what he had done for over seventy years: composing in a colourful expressive style. His works enjoy today a popularity they lacked during most of his long life. In essence, neo-romantic music is characterised by an extended tonality which is freely chromatic within an overall harmonic-tonal structure. The music of Richard Strauss, Mahler, Puccini, Ravel, Rimsky-Korsakov and early Schönberg is representative of this style.
It is generally agreed that the breakdown of tonality commenced in 1857 with Wagner's Tristan & Isolde. It pushed chromaticism into a new sound world where the boundaries of tonality could be barely contained as, for example, in Richard Strauss' opera Elektra. It was in 1909 that the German theorist and composer, Arnold Schönberg (1874-1951), wrote the opera Erwartung, which clearly abandoned tonality completely. In his youth, Schönberg had pursued the post-Tristan & Isolde path of intense lyricism in composition, warmly encouraged by Gustav Mahler.
Schönberg revolutionized modern music by establishing the 12-tone technique of serial music as an important organizational device. His early works, e.g., Verklärte Nacht (1899), expanded Wagner's and Mahler's use of the chromatic scale. His later works are highly contrapuntal. In 1908 he completely abandoned tonality in a set of piano pieces and a song cycle. He first employed the 12-tone technique in a work in his Suite for Piano (1924). He was also a teacher; his students included Alban Berg and Anton von Webern and for this reason his famous 12-tone system, for a long time dominated twentieth-century music, both directly and through Anton Webern's serial and atomistic works. Schönberg, Berg and Webern are sometimes called the 'Schoenberg trinity' or the 'Second Viennese School', where the 'First Viennese School' embraces Haydn, Mozart and Beethoven.
Ruth Crawford Seeger's String Quartet (1931) was one of the first works to employ extended serialism, a systematic organization of pitch, rhythm, dynamics, and articulation. Milton Babbitt's Three Compositions for Piano (1947) and Structures, Book Ia, one of Pierre Boulez' earliest attempts at employing a small amount of musical material, called cells (whether for use as pitches, durations, dynamics, or attack points), both employed highly serialized structures.
Debussy was more a Symbolist than an Impressionist who might have followed Mallarmé's dictum, "To name an object sacrifices three-quarters of the enjoyment. To suggest it - that is our dream". Certainly, he never considered himself an "Impressionist", describing his approach to composition in the following terms.
"There is no theory. You have only to listen. Pleasure is the law. I love music passionately. And because l love it, I try to free it from barren traditions that stifle it. It is a free art gushing forth, an open-air art boundless as the elements, the wind, the sky, the sea. It must never be shut in and become an academic art."
"Historically viewed", Virgil Thomson wrote, "Debussy is the summit toward which during the two centuries since Rameau's death, French music has risen... Internationally viewed he is to the musicians of our century everywhere what Beethoven was to those of the nineteenth - our blinding light, our sun, our central luminary." In 1971, the year of Stravinsky's death, the great Russian-born innovator declared, "Debussy is in all senses the century's first musician".
David Dubal has written, "Debussy's pianism contains layers of exquisite 'chording', harmonies hovering unresolved in the most rarefied, intoxicating air. New concepts in pedalling and minute rhythms governing microspacing and a range of atmospheric tonal problems necessitate the highest sensitivity and elasticity that a pianist may possess. Unfortunately, as the most exportable of French piano composers, he has been subjected to many untenable performances. He may indeed be the most poorly played composer, generally speaking, after Chopin."
Impressionism released the chord from its function in regard to the movement and goal of the music. Chords could be freely altered. Chords no longer required preparation or resolution in conventional harmonic patterns. Writers describe this as the "emancipation of sound." Harmonic patterns were free to move in non-traditional manners. This blurring of traditional tonal progressions may be analogous to the Impressionist painters' technique of avoiding hard edges and sudden, sharp contrasts.
Paul Brians' writes, in Post-Romantic Music Before World War I:
"There are some similarities between Impressionist painting and Impressionist music.
Impressionist art often tries to capture fleeting moments in which a certain kind of light transforms the objects it shines on. It is more about color and light than it is about the actual objects being painted and tends increasingly toward abstraction. Impressionist music often lacks the sort of strong forward drive characteristic of earlier music. Time seems suspended. The sense of key is sometimes highly ambiguous, and there is a preference for whole-tone keys which cannot provide the sense of resolution traditional in Classical and Romantic music.
Impressionist artists deliberately rejected the large historical and mythical subjects for simple, everyday ones like horse races, ballet dancers, gardens in bloom, working people enjoying Sunday in the park. Their techniques rejected ornateness and polish for sponteneity and naturalness. Impressionist composers specialized in small-scale works using smaller, simpler orchestras than their predecessors and simpler, more transparent textures.
Impressionist painters were powerfully influenced by Japanese prints. Impressionist composers were influenced by Asian scales.
There are many exceptions to these statements. The relationship of Impressionism to Romanticism is not entirely rebellious. For example, Debussy's only opera, Pelléas et Mélisande (1902), can be regarded as a reaction against the heavy, over-emphatic music of Wagner's operas; yet many modern scholars see a logical link between the two, and Debussy much admired the great Romantic. Many of the people who loved Debussy's opera when it was first performed were fervent Wagnerites, like the famous novelist Marcel Proust.
Whatever the exact definition of Impressionism may be, one other comparison is clear: both artistic and musical Impressionism are very popular with a broad public.
All that said, Clair de lune ("Moonlight") is not a particularly Impressionist piece. There are Romantic works with a similar feel, but its emphasis on delicacy is especially characteristic of Debussy. The melody is based on a popular folk song. Note how light the harmonies are, with no huge, crashing chords of the kind common in the music of Liszt, for instance. The rippling figures starting at about 1:45 are supposed to suggest the shining of moonlight on rippling water. Debussy was often inspired by art and artistic ideas.
It is worth noting that there are many lesser composers often associated with musical Impressionism including Frederick Delius (England), John Tomlinson Griffes and Charles Martin Loeffler (U.S.). Some of the works by Italian composer Ottorino Respighi also have an Impressionist feel to them."
Neo-Classicism is a twentieth-century style of composing characterised by the reintroduction of balanced forms and clearly perceived thematic processes of earlier styles to replace the over-exaggerated gesticulation and absence of form of the late Romanticism. The term may be considered misleading when applied to the anti-Romantic style of composers working in the 1920s because the retrospective model was the music of Bach's rather than Mozart's period. It has been suggested that the better label would be neo-baroque.
A neo-classicist is prone to reject the structural tonal system found in true classical music and instead uses expanded tonality, modality, or atonality. Just the term "neo" itself implies a deviation from the traits of true classical music. The whole idea of neo-classicism was a direct result of anti-romanticism in an attempt to refine and control expressionism. Neo-Classicism is less known for its reinstitution of the technique of composers like Mozart and Haydn, but known more-so for its power in the manipulation of earlier elements.
The three schools of neo-classicism are those of Stravinsky, Schönberg, and Hindemith. Richard Strauss' Ariadne auf Naxos, Prokofiev's Classical Symphony, Stravinsky’s Oedipus Rex, Pulcinella, Symphony in C, Capriccio for piano and wind and Piano Concerto, Britten’s Billy Budd, Tippet's Concerto for Double String Orchestra, Vaughan William's Violin Concerto and Hindemith’s song cycle Das Marienleben and opera Cardillac are works composed in the neo-classical style.
A variety of Western European movements appeared at the beginning of the early twentieth century, associated with extreme statements and political stances. In his 1901 book The Gothic Renaissance Johannes V. Jensen adumbrates some of the ideas associated with the Futurist movement. He identifies a Germanic and Southern-European concept of 'life according to ideas', these ideas often expressed through Symbolism, a manifestation of Romantic mysticism, which we have met when considering nationalism in music - (see above). He contrasts this with, in his view, a more praiseworthy Anglo-American society full of 'invention and action'. Futurism was a reaction to Symbolism which, by the early twentieth century, had run its course.
The range of national, collective as well as individual manifestations of futurism have led some critics to speak of "futurisms" in the plural. While genuinely international in scope, futurism is generally associated with the two countries where it was most evident, Italy and Russia.
The Italian Futurist movement was founded by the painter Luigi Russolo (1885-1947) and the poet Fillipo Tommaso Marinetti (1876-1944). Marinetti said that "a speeding automobile is more beautiful than the Victory of Samothrace" and wrote the manifesto, Musica Futurista. As it related to music, the movement sought "to present the musical soul of the masses, of the great factories, of the railways, of the transatlantic liners, of the battleships, of the automobiles and airplanes. To add to the great central themes of the musical poem the domain of the machines and the victorious kingdom of Electricity."
The Futurist movement in Russia included Larionov, Goncharova, and Malevich. In France, Marcel Duchamp and Robert Delaunay among others developed, in their own ways, the Futurist ideas about the representation of movement.
Futurists adopted the Cubism of Picasso and Braque and went on to inspire the Vorticists, the Dadaists, the Rayonists and the Constructivists. The Dada movement (1910s and 1920s) defied artistic conventions and what they stood for; it placed its faith in progress and rationality. Dadaists combined pieces of everyday objects into montages. The Surrealist movement (1920s and 1930s) followed Dada in its rejection of conventions, but did so for a "higher" purpose; to unite the conscious and subconscious.
While mechanical musical instruments go back thousands of year, the musical capabilities of early computers were demonstrated in the early 1950s with CSIRAC, Australia's first digital computer, which "stunned" audiences with a rendition of Colonel Bogey (but of which there is no known recording), a Ferranti Mark 1 computer which was recorded performing Baa Baa Black Sheep and a truncated version of In the Mood, and an IBM mainframe computer at Bell Labs in the US in 1957 (again, where recordings have survived).
The practicality of linking the art of composition, as opposed to that of performance to mechanical, electromechanical or purely electronic machines has been a mainly twentieth-century preoccupation. The twentieth century saw its crop of mechanical performers. In 1944 Percy Grainger and Burnett Cross patented a machine that 'freed' music from the constraints of conventional tuning systems and rhythmic inadequacies of human performers and a mechanical invention for composing "Free Music" used eight oscillators and synchronizing equipment in conjunction with photo-sensitive graph paper with the intention that the projected notation could be converted into sound. Four years later John Scott Trotter built a composition machine for popular music.
Computer-generated music arrived in 1953/4 with the work of Lejaren Hiller (1924-92) and Leonard Isaacson, from the University of Illinois. They 'composed' the Illiac String Quartet the first piece of computer-generated music. The piece was so named because it used a Univac computer and was composed at the University of Illinois. In 1956 Martin Klein and Douglas Bolitho used a Datatron computer called 'Push-Button Bertha' to compose music. This computer was used to compose popular tunes; the tunes were derived from random numerical data that was sieved, or mapped, into a preset tonal scheme.
In 1958, while working at Bell Laboratories, Max Mathews first generated music by computers. This rather ad hoc work was soon systematised with the establishment, also in 1958, of The Studio for Experimental Music at the University of Illinois, directed by Lejaren Hiller. In the same year Max Mathews and Joan Miller, also at Bell Labs, wrote MUSIC4, the first wide-spread computer sound synthesis program. Versions 1 through 3 were experimental versions written in assembly language while MUSIC4 and MUSIC5 were written in FORTRAN. MUSIC4 did not allow reentrant instruments (same instrument becoming active again when it is already active); MUSIC5 added this. MUSIC4 required as many different instruments as the thickest chord, while MUSIC5 allowed a score to refer to an instrument as a template, which could then be called upon as many times as was necessary.
The Columbia-Princeton Electronic Music Center was formally established in 1959. The group had applied through the Rockefeller Foundation, and suggested the creation of a University Council for Electronic Music. They asked for technical assistants, electronic equipment, space and materials available to other composers free of charge. A grant of $175,000 over five years was made to Columbia and Princeton Universities. In January, 1959, under the direction of Luening and Ussachevsky of Columbia, and Milton Babbitt and Roger Sessions of Princeton, the Center was formally established. PLF 2 was developed in 1962 by James Tenney. This computer program was used to write Four Stochastic Studies, Ergodos and others and in 1963 Lejaren Hiller and Robert Baker composed the Computer Cantata. In 1964, Gottfried Michael Koenig used PR-1 (Project 1), a computer program that was written in Fortran and implemented on an IBM 7090 computer. The purpose of the program was to provide data to calculate structure in musical composition; written to perform algorithmic serial operations on incoming data. The second version of PR-1 completed, 1965.
Improvisation too was a topic that received a lot of attention. Jam Factory, written by programmer David Zicarelli, was designed to listen to MIDI input and 'improvise' immediately at some level of proficiency, while allowing (Zicarelli) to improve its ability. Joel Chadabe, Offenhartz, Widoff, and Zicarelli began work in 1986 on an algorithmic program that could be used as an improvisation environment. The performer could be seated at the computer and shape data in real time by "a set of scroll bars that changed the parameters of this algorithm, such as the size of the jump from one note to another, the lowest and highest note, etc." The original version was to be named "Maestro," then "RMan" (Random Manager), and finally, "M."
One might say that computer music reached full maturity once the computer itself could be considered a 'musical instrument'. Music Mouse, written by Laurie Speigel, was designed to be a stand-alone performance system. It may be used as a MIDI controller or as a performance station using the Macintosh internal sound. Unlike other programs for the Macintosh environment, Music Mouse was not intended to be used as a recorder/player program. Instead, the program enables the programmer to "play" the computer.
Serial music is constructed according to the principle, described independently by Hauer and Schönberg in the early 1920s, of 12-note composition. According to the Schönbergian principle, the 12 notes of the equal-tempered scale are arranged in a particular order, a series or row, that serves as the basis of the composition. Serial technique requires that the succession of notes be ordered as they are in the row, but simultaneities--chords--have no succession within them, so the principle of order relations does not apply to them. In Schönberg's Method of Composing with Twelve Notes Which are Related Only to One Another, the note-row may be used in its original form, or inverted, or retrograde, or retrograde inverted; in each of these forms it may be transposed to any pitch (each note-row may thus have forty-eight possible forms). All the music of the composition is constructed from this basic material; any particular note may be repeated, but the order must be maintained. Octave transpositions are permitted. Notes may occur in any voice, may be used either melodically (horizontally) or harmonically (vertically) but the entire sequence must be employed before the row may be repeated. The row is normally designed to avoid outlining the triads or patterns associated with tonality. Berg's Lulu (1937) and Schönberg's Moses und Aaron (1957), both written entirely in serial technique, are considered the two masterpieces of the serial repertoire. Both employ the same arduous vocal style as Wozzeck and are significant undertakings for performers and audience alike. Later developments of 12-note theory introduced the idea of using six-, four- or three-note segments of a row as compositional elements. As originally designed by Schönberg, the method was intended to preclude tonality, though later composers, notably Berg, found ways of using the technique in a tonal context - as indeed did Schönberg himself.
Princeton's Michael Wood, the prominent literary and film critic, describes how jazz has affected his own work:
"Jazz for me is not just a taste and a pleasure and a memory. It is also a way of thinking and working, a secret analogy behind much of what I do when I read and write....I have often thought that most readers and writers, and certainly most critics, have a governing analogy for what they are doing, something that literature, or the act of reading or writing is most like. It is a likeness, not an identity."
John Maurer's excellent article entitled A Comparison of Free Jazz to 20th-Century Classical Music:similar precepts and musical innovations clarifies the relationship between modern jazz and twentieth-century music. In many ways the relationship is coincidental rather than functional. What interested and inspired twentieth-century jazz musicians also interested and inspired twentieth-century composers and it is no surprise that common themes and variations run through both art forms.
From the investigations of folk music, world music and other non-western artistic traditions came the realisation that western culture was but one way of looking at culture and art, even high art. Rhythms, harmonies, structures and musical scales, foreign to late nineteenth-century European experience, inspired composers bored with the past and hungry for new ideas. Non-western scales were a particularly rich area although somewhat held back by the absence of instruments made to play these extended scales. Of course, little is really new and the ancient Greeks and their concept of scale and interval are the true fathers and mothers of many ideas in this field including that of 'just' intonation. The term 'mictrotone' was invented by the Mexican violinist and composer Julián Carrillo (1875-1965) although he was neither the first nor the only composer-performer to explore this sound world. Carrillo demonstrated his instruments in New York in 1926. They included an Octavina for eighth tones and an Arpa Citera for sixteenth tones. There are several recordings of Carillo's music, especially the string quartets.
Ferruccio Busoni (1866-1924) described microtones in his book Sketch of a New Aesthetic of Music and Ivan Alexandrovich Vïshnegradsky (1893-1979) and Alois Hàba (1893-1973) both wrote music with microtonal elements. The most remarkable figure thought was Harry Partch (1901-1974), an American composer, musical theorist and musical instrument inventor, who devised the first working system and built many special musical instruments to allow his ideas to be realised.
[You may wish to read Bitter Music by Harry Partch, Collected Journals, Essays, Introductions, and Librettos (edited with an Introduction by Thomas McGeary) which includes journals of Partch's hobo period, sprinkled with fragments of speech set in staff notation, and his research trip to Europe, during which he met Yeats and Dolmetsch; an account of a solo backpacking trip along California's "Lost Coast"; and librettos from all of his major theatrical works.]
His system divided the octave into 43 divisions, an idea postulated by Hermann von Helmholtz (1821-1894). Other systems too were explored. The division of a 12 semitones scale into 24 quarter tones has been the most popular. Joseph Yasser promoted the dividing of the scale into 19 divisions, Hàba used sixth-tones, quarter-tones and fifth tones, while Vïshnegradsky worked with a scale having 31 divisions. The scope to alternatives in this area is limitless and you are recommended to use the links below to learn more of the theory and practice of microtonal music.
In his essay entitled The revolution in sound: electronic music (1960), Milton Babbitt writes:
"all factors militate against the composition of complex contemporary music: the uncompensated time involved in its composition, the crushing costs of preparing materials, the inadequate number of rehearsals, and the consequent, unusually unsatisfactory, always ephemeral performance. The electronic medium discriminates not at all against such complexity; rather, it is most appropriate to it. Such music can now remove itself entirely from the inapposite milieu of the public concert hall; it exists, in any case, only in recorded form, and is so available to anyone who is interested, to be played and replayed at the listener's convenience"
As well as providing simple and reliable ways of recording and making music, electronic devices were soon to provide a completely new and rich sound world. Compositions that utilize the capacities of electronic media for creating and altering sounds may be called electronic music or electro-acoustic music.
The invention of electronic devices came before composers could exploit their unusual sound characeristics. The first significant instrument, the Theremin, was invented in 1920 by the Russian Leon Theremin (1896-1993) and manufactured by the Radio Corporation of America (RCA). It used interference beats from two oscillators to produce pure sine-wave notes. Australian composer Percy Grainger (1882-1961) and Bohuslav Martinu (1890-1959) both composed for the Theremin. The Ondes-Martinot, invented in 1928 by Maurice Martenot, and the Trautonium, invented in 1930 by Dr. Friedrich Trautwein, were of a similar design. Grainger and his wife Ella worked with Burnett Cross to produce in 1948 their own electronic instrument, the Free Music Machine, as part of Grainger's search for music free from traditional tonal and rhythmic constraints. This work continued until 1960 when the Electric Eye Tone Tool appeared. It now forms part of the Percy Grainger Museum in Australia.
The earliest electronic musical works used recorded sounds that were electronically altered. The invention in 1940 of the tape recorder increased the possibilities for modifying recorded sounds, by cutting the tape to create new juxtapositions of sound (called splicing), by varying the speed to change the pitch of the recorded sound, and by mixing together two or more different recordings which could then be played back simultaneously. Les Paul, a pioneer of electronic music, inventing the first solid-body electric guitar in 1946 and recorded music in the 1950s in an eight-track recording studio which he designed.
Pierre Schaeffer (b. 1910), a sound technician working at Radio-diffusion-Television Française (RTF) in Paris, produced several short studies in what he called Musique concrete. In October 1948, Schaeffer's early studies were broadcast in a "concert of noises". possibly echoing the first concert of Futurist music in 1914 entitled "art of noises", presented by Marinetti and Russolo in Milan, Italy. Schaeffer and Henry (1927-96), along with engineer Jacques Poullin composed Symphonie pour un homme seul (Symphony for a Man Alone); the work actually premiered on March 18, 1950. Pierre Schaeffer developed a technique similar to the later tape loop, the sillon fermé, and patented his Phonogène in the 1950s.
Voltage regulation led to the invention of the synthesizer, a device that could produce and modify sound. Milton Babbitt used the earliest RCA synthesizer developed in the late 1950s. In the 1950s studios specializing in electro-acoustic music production were established including the West German Radio Studio in Cologne, associated with composer Karlheinz Stockhausen, the Italian Radio Studio in Milan, associated with Luciano Berio and Bruno Maderna, and the Columbia-Princeton Electronic Music Center, associated with Otto Luening, Vladimir Ussachevsky, Mario Davidovsky, and Babbitt.
Michael Ball in his essay Licht aus Stockhausen writes:
"From 1955 electronic technology began to develop from monophonic sound reproduction to stereophonic (2 track) and then 4 track output. This was very exciting for Stockhausen because for the first time he could move the sound around directionally in space. This led to the composition Gesang der Jünglinge (1955/6) a landmark 'classic' in twentieth-century music. The piece is actually for 5 groups of loudspeakers and at the first performance the 5th track was played back via a mono tape recorder started synchronously by hand with the 4 track tape. It is also the first piece to combine vocal (non electronic) sounds with electronically produced sounds. This preoccupation with movement in space together with the concept of the 'time spectrum' where temporal layers were sub divided, is relatively easy to produce in the electronic studio but to transfer the same idea to live musicians proved incredibly difficult, so in his composition Gruppen 1955/7 Stockhausen divided a huge symphony orchestra into three smaller groups and used three conductors to synchronise the whole event. In 1959 Carré (Squares) was composed for 4 orchestras and 4 choirs again using techniques discovered in Gruppen but with the introduction of 'moment form' a new way of shaping time. Stockhausen had spent many hours in aeroplanes flying between destinations in America and the time perspectives one experiences when flying led to experiments with 'moments' and the concentration of the 'Now'. Moments can be an instant or indeed an eternity, metronomic time becomes only one kind of time.
This was developed in Kontakte (1959/60) for piano and percussion with electronic tape, perhaps the most seminal work of the twentieth century to combine live musicians with electronic tape. Here Stockhausen was producing sounds of complete originality, sounds that lie somewhere between wood and metal, skin and wood etc. Through electronics he was able to analyse the acoustical microstructure of a sound which led to the synthesising of sounds as well as the 'decomposition' of sound where for example, a sound begins as a continuous timbre then gradually slows right down until it becomes a pulsed rhythm. He created a special 'rotation table' to record these sounds moving intricately around the 4 channel speaker system. One of the most important aspects of Kontakte is where one timbre is transformed into another and during these transformations completely new sound colours are heard."
In 1964, the first successful 'sampler' based on magnetic tape technology, the Mellotron, was marketed.
By the second half of the 1980s digital sampling technology had become a standard part of every electronic piano, organ, or synthesizer. Musicians have explored extensively the possibilities of the manipulation of recorded sound. The phonograph has been used for works like John Cage's Imaginary Landscape No. 5 as well as "scratching" by DJs in the popular music tradition. Other works have used this technology to manipulate pre-existing recorded works by other artists, generating conflict with copyright law. Among these works are James Tenney's Collage No. 1 (Blue Suede) and John Oswald's Plunderphonics.
Daphne Oram (1925-2002) wrote the first piece to manipulate elecronic sounds in real-time as opposed to presenting pre-recorded sounds as an adjunct to live performance. In 1957/8, with Oram, the composer Desmond Briscoe (1925-2007) founded the BBC Radiophonic Workshop, the department of the BBC that supplied sound effects, emotive cues, incidental music and programme themes for radio and television. Initially the workshop mostly consisted of outdated equipment and was confined to two rooms at the BBC's Maida Vale Studios (formerly a roller-skating venue). Briscoe became Senior Studio Manager. Oram left the workshop after a year to pursue her own compositions. Throughout the existence of the workshop, and even before its official founding, Briscoe and other composers, engineers and sound designers created the distinctive sound of BBC programmes. The Radiophonic Workshop was a division of the drama rather than the music department. Oram went on to become a major figure in the field of electronic music developing 'Oramics', a notational technique utilizing marks made on 35mm film stock which could be read by photo-electric cells. 'Oramics', which appeared contemporaneously with Cornelius Cardew's graphic score Treatise (1964-67), became the most successful graphic-based composition machine-system available until it was superceded by touch-sensitive digital machines such as Iannis Xenakis's UPIC. Oram wrote an important study on electronic music entitled An Individual Note of Music, Sound and Electronics. The live manipulations of prerecorded magnetic tape material also forms the basis of Laurie Anderson's Tape Bow Violin.
During the 1960s Moog and Buchla made synthesizers more widely available and pop groups like the Beach Boys and the Beatles used these and Les Paul's invention of multi-track recording to great effect. Eventually synthesizers switched from voltage control to digital control and in 1983 the MIDI (Musical Instrument Digital Interface) standard was agreed on by synthesizer manufacturers. Commercial digital samplers are also used in a variety of contemporary composers' works, for example, Michel Waisvisz 's The Archaic Symphony and Nicolas Collins's Devil's Music
Why did musical improvisation die in the eighteenth century, to be fully reborn only in jazz? Until the late eighteenth century, musicians were trained to improvise and embellish, and even to create entire compositions spontaneously. But by the Romantic period, improvisation had almost become a lost art. Although organists and opera singers continued to learn how to improvise, for most instrumentalists the art of spontaneous improvisation survived only in the solo cadenza. From a modern perspective, the decline of improvisation seems paradoxical, because modern listeners think of spontaneity as a characteristic of Romanticism. Improvisation is most often associated with jazz. But there are other forms- international and very old forms, long pre-dating jazz- which are associated with it as well. There is flamenco, in which improvisation is an integral part of the form, with master players being able to perform for hours at a time without stopping. And then of course there's raga. The rules for improvisation here are much more strict than with jazz, but once again it's not unusual for performers to go for hours. And despite the rules, the performers do have a lot of leeway. In each of these cases, the music and the expectations place upon it by the audience all tie in to the music's social function. Flamenco is viewed as a way of life; raga is steeped in philosophical and religious precepts. In these cultures, improvisation is not only acknowledged as valid, it's fully expected as part of the proceedings. Perhaps one cause of the loss of improvisation was the loss of a system of musical shorthand that made instant composition easy: figured bass notation. The modern jazz improviser uses "fake books" which contain chord symbols - the standard modern shorthand for harmonies. The standard musical shorthand in the eighteenth century was figured bass, or thorough-bass. Instead of using chord names, it indicated harmonic patterns by means of numerical notations above a written bass line. Three- and four-part harmonic accompaniment to the bass line was worked out instantaneously. The most important eighteenth-century text on thorough-bass notation was Der Generalbass in der Composition (Dresden, 1728), by Johann David Heinichen. For music students who do not read German, Heinichen's work is clearly explained (and partially translated) by George J. Buelow, in his Thorough-Bass Accompaniment According to Johann David Heinichen, rev. ed., Studies in Musicology, No. 84 (Lincoln: U of Nebraska P, 1986).
The music critic and composer Kyle Gann has argued that John Cage (1912-1992) 'was part of a generation - one could mention Milton Babbitt and Conlon Nancarrow, close contemporaries of Cage, and others - for whom music was simply a pattern of sounds, incapable of expressing or eliciting emotion except by some willing self-delusion on the part of the listener'. Cage began experimenting with indeterminacy in 1939. In his composition, Imaginary Landscape No. 1, multiple performers are asked to perform on multiple record players, changing the variable speed settings. Composers have also experimented with "aleatoric" music, in which form and structure are determined by chance. For some however, the meaning of aleatory is different from chance. Aleatory, which was a European adoption of American chance, implies chance with selected aspects of control; for this reason, aleatory was considered, by Cage, to be a corruption of his idea of 'pure' chance. The correspondence of Cage and Boulez throws a sharp light on their differences. Alea, a term from Latin signifying 'a game of dice', was the original term used by Boulez in an essay he wrote which criticizing the use of chance in musical composition, referring to, but without naming him, John Cage's experiments in determining pitch, rhythm, structure, and dynamics by the use of the I Ching. This was not a new idea - Mozart composed works where the order of pre-composed sections was determined by the throw of dice. Boulez, Stockhausen and others have experimented with aleatory music and, more recently, computers have been used to generate music of this description.
Aleatory is also often mistakenly confused with indeterminacy, which refers to performance practice, rather than to composition. It is sometimes confused with improvisation, as well.
Minimalism has also been called repetitive music, mediative music and process music. It was developed in the 1960s primarily in America and during the 1970s became successful in Europe as well. However, minimalism can be traced back to medieval times with the repeated phrases of choral liturgy. It can also be heard in Bach fugues, Ravel's Bolero and Stravinsky's Rite of Spring (heavily reliant on rhythm). It has been argued by Torsten Ekbom that, "Satie was the first composer who affected with monotony, "tediousness", the stationary in music" and should be considered the true father of twentieth-century minimalism. In the opinion of John Cage (see Cage’s Place In the Reception of Satie), Satie was as great a pioneer as Anton von Webern. Of course the real pioneers are those who have a profound influence on the figures we generally associate with twentieth-century minimalism and there is little doubt that the recordings made by Coltrane were significant.
John Coltrane died on July 17, 1967, at the age of forty. His revolutionary use of a single mode throughout Africa, the piece that takes up all of side one of an album, with the astonishing variety Coltrane superimposed on a single F was, according to the composer Steve Reich, a significant, if ostensibly an unlikely, influence on the development of minimalism. The originator of minimalism, La Monte Young, acknowledges the influence of Coltrane's My Favorite Things on his use of rapid permutations and combinations of pitches on sopranino sax to simulate chords as sustained tones. The minimalism that grew in the 1960s was distinct in many ways.
The first composers to develop minimalism, La Monte Young, Terry Riley, Steve Reich and Philip Glass, are all American. Riley's composition In C is thought to be the first to suggest minimalism. It is a piece of overwhelming simplicity.
"You know there is a maverick tradition in American music that is very strong. It's in Ives, Ruggles. Cage, Partch, Moondog, all of these weird guys. That's my tradition."
Thus Philip Glass traced his artistic lineage in an interview with the composer Robert Ashley. Glass, born in Baltimore on January 31, 1937, began his musical career in a conventional enough manner: study at the University of Chicago and Juilliard; a summer at the Aspen Music Festival with Milhaud; lessons with Nadia Boulanger in France on a Fulbright scholarship; many compositions, several of them published, in a neoclassical style indebted to Copland and Hindemith. In 1965. however, Glass worked with the Indian sitarist Ravi Shankar in Paris on the score for a film titled Chappaqua, and that exposure to non-Western music was the turning point in forming Glass' mature style.
In 1965-1966, Glass spent six months traveling in India, North Africa, and Central Asia. and he returned to New York in the spring of 1966 with a new musical vision (and a new religion - he has been a Tibetan Buddhist for years). Glass rejected his earlier works, formed an ensemble of amplified flutes and saxophones, electric organs and synthesizers, and began writing what is commonly known as "Minimalist" music (though Glass loathes the term; Debussy likewise insisted that he was not an "Impressionist.") "Minimalist" music is based upon the repetition of slowly changing common chords in steady rhythms, often overlaid with a lyrical melody in long, arching phrases. Glass views this style, which contrasts starkly with the fragmented, ametric, harshly dissonant post-Schönberg music that had been the dominant style for the twenty-five years after the Second World War, as hypnotic and trance-like, lifting the spirit out of the mundane and freeing the mind. Minimalist music is meant, quite simply, to sound beautiful and to be immediately accessible to all listeners. Indeed, Glass represents the epitome of the modern "cross-over" artist, whose music appeals equally to classical, rock and jazz audiences.Such an extraordinary, new style was not quickly accepted, but Glass was determined to continue on the path he had chosen. He kept composing and honing the skills and performances of his ensemble, but supported himself for some time as a taxi driver and plumber.
Young studied Indian music with Pandit Pran Nath although he came to Indian music more by thinking through his own musical ideas. Reich studied African drumming in Ghana, and also Balinese gamelan music and the cantillation (chanting) of the Hebrew Scriptures.
Other motivating forces for minimalism have come from the tape studio e.g the use of loops and multiple tracks.
Minimalism has wide appeal. Minimal composers have by far the largest public in contemporary music today. The appreciation of these composers can be said to be due to the simplicity and nature of their works. Terry Riley's recordings are sometimes brought out simultaneously on the pop and classical markets. Philip Glass has composed music for the advertising of the Orange phone company. This popularity has startled many a supporter of experimental music who believed minimalism to be doomed to live a brief life.
Interviewer: Is it possible to say where you get your musical influences from?
It is fashionable and convenient to polarise contemporary music by introducing terms such as 'uptown' (for the avant-garde and modernist) and 'downtown' (for the experimental and minimalist) although one is left having to acknowledge that the most successful 'genres' lie more in what might be called 'midtown' (post-minimalist, modern-classic, but definitely neither atonal nor serial) represented by the idiom of composers like John Adams.
The work, or some substantial part of it, of the composers that appear in this section defies any classification other than that their name is 'maverick'.
There is a passage in the Preface to the second edition of Genesis of a Music in which Partch talks about the path-breaking step taken by the individualist creative artist, and he says that the individual's "path cannot be retraced, for each of us is an original being". And so it was for each of our composers listed below who, through force of will, ploughed new and often lonely furrows in the landscape of twentieth-century composition.
Charles Ives (1874-1954) pursued what is perhaps one of the most extraordinary and paradoxical careers in American music history. Businessman by day and composer by night, Ives' vast output has gradually brought him recognition as the most original and significant American composer of the late 19th and early 20th centuries. Inspired by transcendentalist philosophy, Ives sought a highly personalized musical expression through the most innovative and radical technical means possible. A fascination with bi-tonal forms, polyrhythms, and quotation was nurtured by his father who Ives would later acknowledge as the primary creative influence on his musical style. Studies at Yale with Horatio Parker guided an expert control over large-scale forms.
Ironically, much of Ives's work would not be heard until his virtual retirement from music and business in 1930 due to severe health problems. The conductor Nicolas Slonimsky, music critic Henry Bellamann, pianist John Kirkpatrick (who performed the Concord Sonata at its triumphant premiere in New York in 1939), and the composer Lou Harrison (who conducted the premiere of the Symphony No. 3) played a key role in introducing Ives's music to a wider audience. Henry Cowell was perhaps the most significant figure in fostering public and critical attention for Ives's music, publishing several of the composer's works in his New Music Quarterly.
In 1947, Ives was awarded the Pulitzer Prize for his Symphony No. 3, according him a much deserved modicum of international renown. Soon after, his works were taken up and championed by such leading conductors as Leonard Bernstein and, at his death in 1954, he had witnessed a rise from obscurity to a position of unsurpassed eminence among the world's leading performers and musical institutions.
Charles Sprague Ruggles, the New England composer, teutonized his name to Carl when a youth. Carl's music is sometimes (somewhat incorrectly) associated with that of his friend, fellow composer and sometimes financial backer Charles Ives (1874-1954), for its rugged American individuality. Ruggles, an incorrigible reviser given to working at a snail's pace, produced precious few musical works over his long career, but they are darn good ones! He devoted much of his life to painting, which could partially explain his low musical output. He developed a highly dissonant, contrapuntal style somewhat akin to the atonal styles of Arnold Schönberg (1874-1951) and his pupils.
To a heckler of Ruggles's music, Charles Ives is said to have said: "When you hear strong masculine music like this, get up and use your ears like a man!"
The German music critic and sociologist, Theodor Adorno (1903-1969), expressed Ives' frustration in a more formal manner: he developed the concept of 'negative dialectic', which, as far as music was concerned, meant that music must be difficult because the undemanding acted as a mass sedative, encouraging people not to think. This avant-garde leftist philosophy decried amateurism, 'soft'-music by composer who dared not challenge their audiences, and the Stalinist line that one of music's 'tasks' should be engender nationalistic feelings.
Edgard Varese spent the majority of his life waiting for technology to catch up with him. Varese was simply born too early. Of course if he had been born later, his mentor Busoni would probably not have been around to prepare him for his role in the coming age.
Varese prepared for a career as an engineer by studying mathematics and science. He studied the notebooks of da Vinci. Pulled towards music, he used his learned scientific principles to study the science of sound. He was an unhappy student at the Schola Cantorium and Paris Conservatoire. His friends were a list of who's-who of the time: Satie, Romain Rolland (an author who used Varese as the inspiration of his great novel Jean-Christophe), Russolo, Villa-Lobos, Duchamp, Russolo, Cowell, Luening, Lenin Trotsky, Picasso and countless others.
While at the conservatoire, he began shaking things up, announcing, "I refuse to submit to sounds that have already been heard." His inspirations were Busoni and Debussy. Debussy encouraged him to become a composer telling him, "Rules do not make a work of art; you have the right to compose what you want to, the way you want to." Debussy also encouraged Varese to look at non-western music for inspiration.
After serving in the French army during the first world war, Varese moved to America in 1915 at the age of 33 with $32 in his pocket. Settling down in Greenwich Village, New York, he fell in love with the sounds of the city. The roar of the city became his inspiration. In America he found a musical frontier as yet undeveloped, "American music must speak its own language, and not be the result of a certain mummified European music."
In 1917 he wrote "I long for instruments obedient to my thought and whim, with their contribution of a whole new world of unsuspected sounds, which will lend themselves to the exigencies of my inner rhythm."
He supported himself doing odd musical jobs, conducting choirs as well as conducting. In 1919 he founded the New Symphony Orchestra which was devoted to modern music. Later he founded, with Carlos Salzedo, the International Composers Guild, which exposed Americans to Debussy, Stravinsky, Bartok and Schönberg. In his prospectus for the guild he wrote, "The International Composers Guild disapproves of all 'isms'; denies the existence of schools; recognizes only the individual."
If minimalism shows what one can do with small ideas, John Cage showed what one could do with silence.
Stanislaw Hansel writes:
"John Cage did most to open silence up as a musical need, despite the paradox. However, musicologists may find many interesting uses of silence throughout history both in "serious" music as well as "ethnic" folk music. Nevertheless, not much has happened in terms of developing silence for nearly half a century since Cage composed his silent piece 4'33" in 1952. Could this be due to the apparent difficulty of articulating musical energies and structures in silence? Actually, Cage's intention was quite different. The composer was trying to liberate the performer and the composer from having to make any conscious decisions, therefore, the only sounds in this piece are those produce by the audience."
There are now developments whereby it may soon be possible to "project" sounds to individual members of an audience without others hearing it. One day we may aspire to create music in someone's mind alone by some form of electronic radio device. These ways may show a future application of silent music.
Even so, inventiveness in modern musical composition and performance has neither diminished nor demanded less attention now, as we enter the twenty-first century, than it did in the last.
Dr. James Sobaskie, at the University of Wisconsin, set out his program entitled A Strategy for Musical Analysis
The main goals in most tonal pieces are usually signaled by cadences, and cadences play critical roles in sectionalizing music. Identify all important cadences, and determine the relative weight or value of each cadence's corresponding goal. Changes in dynamics, texture, tonal center, or mode, strong thematic returns, and even elements of notation may be helpful in determining the individual nature and weight of each goal. Is there a logical relation or sequence which links them?
MeansIt is important to understand the means by which a piece's goals are achieved. Identify the harmonic and contrapuntal elements which are directly involved in creating the cadences you've identified, the cadential chords, essential chromatic elements (if any), and any distinctive voice-leading features. Are there any similarities in the ways the cadences are achieved, or any pattern in the degrees of closure they imply?
ThemesA composition's character, expressiveness, and unity all depend on its thematic material. Identify all statements of the main theme or themes. Are there any other special transformations or striking variations of the theme? How are the themes developed? Are there any special relations among the themes?
MotivesThemes are typically composed of smaller components called motives, and a motive may consist of a collection of pitches, rhythmic cell, harmonic unit, textural feature, or some other distinctive musical idea. Identify the smaller components of the main theme(s) which appear elsewhere, perhaps in the episodes or accompanying counterpoint. How are the motives varied and developed?
Unique FeaturesEvery good piece boasts something specialÑfeatures which distinguish it, make it novel, or represent original technical developments. Identify several musical features which seem particularly unique in the composition. What particularly interests, impresses, or inspires you about the composition and why?
FormMost pieces of music may be subdivided into smaller sections, each of which contributes something special to the whole. Identify the main parts of the composition's musical form and provide a concise statement which summarizes its function. What does each section do in the context of the whole piece?
Tonal StructureTonal compositions typically feature arpeggiations, step progressions, and other pitch structures which elaborate the tonic triad or other structural harmonies, often covering considerable spans of music. Identify any large-scale structural elements you can. How do their components relate to the goals you identified earlier?
ImplicationsDecide how you might use what you've learned about the piece's structure . How can you improve your performance of the music? Is there something you can emulate in your own creative work?
These then are the kind of questions we ask in 'musical analysis'. How the questions are answered depends very much on the tools used to examine them. We consider two below.
Heinrich Schenker (1868-1935), an Austrian music theorist, applied a formal system to tonal musical works.
The following extract comes from A Guide to Schenker's Theory of Tonal Music:
Schenker's theory of tonal music evolved over a period that spanned most of his career. During this time he wrote many other essays which discussed a wide range of topics from close analyses of rhythm and texture to studies of improvisation. Like many musicians then (and now), he felt that the key to understanding the structure of tonal music lay in the pitch organisation. Although his analyses discuss all the various parameters of a musical work, it is nevertheless pitch that his theory concentrates on.
Traditional theory and teaching concentrates on two aspects of pitch - harmony and counterpoint. Schenker felt that both were widely misunderstood and therefore concentrated first on clarifying and correcting what he saw as the mistakes of previous theorists.
His study of harmony is mostly theoretical, while his study of counterpoint is largely based on a teaching method called Species Counterpoint that had been in existence for several centuries. His aim was ultimately to bring these two disciplines together in a study of what Schenker called 'free composition' (i.e. real music!). Towards the end of his career, he formulated the most controversial part of his theory - the fundamental structure.
The part of his theory that initially had the most impact in the English-speaking world was his ideas on what he called parallelism. Motivic analysis had traditionally looked for how themes and motives were related to one another on the surface. Schenker suggested that what was more significant was the way in which musical ideas had hidden similarities. The idea of parallelism is intimately connected with his understanding of the structure of music and is therefore dealt with last.
You may wish to read the article entitled Schenkerian Analysis: Valuable Asset for Music Critics which suggests that Schenkerian analysis can be extended from tonal music, on which Schenker himself applied his method, to non-tonal music which Schenker thought was not 'music' at all. In the latter part of his life Schenker tried but failed to extend his analytical methods to 'musical performance'.
Set theory forms the basis of an analytical method that can be applied to music, whether tonal or not, and from any period.
The following extract introduces an excellent on-line resource explaining set theory as applied to music.
"After Brahms, tonality in Western music began to break down. Whereas before composers had relied upon a specific key area to organize the notes they wrote (e.g. a concerto in C-Sharp Minor), the idea of having such a tonal "home-base" had grown stale by the turn of the twentieth century.
Composers needed a new system to organize their pitches. Arnold Schönberg spearheaded the move away from tonality and began writing atonal music around 1908. By 1923, he had fully developed a "12-tone" system of pitch organization, in which the composer arranges all twelve unique pitch classes into an ordered row and performs various manipulations on that row to generate pitch content for a composition. This system is usually referred to as 'serialism.'
Set theory is not the same as serialism, but the two share many of the same methods and ideas. Set theory encompasses the notion of defining sets of pitches and organizing music around those sets and their various manipulations. Set class analysis refers to the efforts of music theorists to reveal the systems that composers like Schönberg and his followers used to organize the pitch content of their works. Keep in mind that sets and set classes determined pitch content only; the composers remained free to fashion all other aspects of the music according to their artistic desires (at least until super-serialism, a philosophy of subjecting every aspect of the music to serial techniques, came into fashion in the 1950s)."
Mathematical methods applied to musical analysis lend themselves to the use of computers and computational techniques.
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