수열, 음열 : 그 패턴의 음악적 응용 = Musical application of the patterns of set, tone-row, and numerical progression

다국어 초록 (Multilingual Abstract)

Between 1923 and 1933 many composers in Europe became aware of H. Cowell's works. Schoenberg invited him to a master class in Berlin in 1932. This contact may account for the forearm piano clusters that figure prominently in Berg's 'Lulu.' Even Bartok wrote for permission to use his clusters. Cowell's big interest in expanding sound resources even led to the sponsorship of Ives and Varese. The latter is linked with Electronic sound texture. At the beginning of the electronic age, the vision of the Futurists had not been forgotten. Moreover, the "new vocalism" of the 1960s saw composers also linked with Electronic sound texture: Berio, Crumb, Penderecki etc.
Other phenomena to be mentioned is an increasing need to simplify creative stance as a reaction against Expressionism. It was acted in ways since 1920. Some have heard, in the 'Carmina Burana' by C. Orff, the aggressive and repetitious figurations, ostinatos. Orff identified some of the most basic elements of music, thereby endorsing many of the simplifying procedures. P. Hindemith also with Schoenberg may be mentioned in this vain of Simplicity. Meanwhile Schoenberg and Stravinsky had demonstrated the capacity to admire each other's music in the early teens. In recent years Boulez judged that "Stravinsky's and Schoenberg's paths to Neo-classicism differ basically only in one being diatonic and the other chromatic. Both composers adopt dead forms. And because they are so obsessed with them they allow them to transform their musical ideas until these too are dead." C. Rosen concluded that Serialism appeared to attempt the realization of the classical dream of a reconciliation between unity and diversity. Webern's path to new music is different though. Together with Schoenberg's concept of Klangfarbenmelodie, his rhythmic-contrapuntal conjunction provided the basis of his personal style - a style to increasing conciseness of expression and economy of motivic content. Much of the fascination of Webern analysis has turned on the observation of the interaction of micro- and macro- formal elements; of color, motif, and rhythm in the service of canon, variation, rondo, scherzo, and sonata forms. Messiaen's interest in the irrational values of Chopin and in Debussy's rhythms no longer dependent on tonality and pulse contributed to a metricality. The rhythmic structures of Greek and Hindu music complemented his investigation into the question of rhythmic and pich modes. The latter was given a explication in his 'Technique de mon langage musical(1944).' Nontheless, Messianen's example led to similarly systematic and serial explorations in the works of his pupils: Boulez proceeded to tackle a larger Beethoven-like four-movement form in the appearance, guise of his 'Second Piano Sonata(1947-48).' Here nonrepetitive, nonhierarchical rhythms achieve a stream of polyphonies and relationships that no ear could be expected to hear. The opening of 'Structures 1a' by Boulez reveals his adaptation of one of Messiaen's pitch modes from 'Mode de valeurs.' Having promoted an all-encompassion order in 'Structures 1a, Book I' Boulez realized that he had written something that was "total." This led to loosening of the technique in 'Le Marteau sans maitre(1952-54),' where the serial orders are undecipherable by the analyst. Stockhausen, by this time, was from Series to Formula. His 'Zeitmasse' for woodwind quintet uses a scale of tempi related to the longest and shortest note values. E. Carter was a special case: metrical modulation and layered forms. His concept of metrical modulation, which followed from Indian talas, Arabic and Balinese systems, Cowell's 'New Musical Resources,' 15th-century music, Skriabin, and Ives, has proven to be identifiable traits to "extension." It means manipulation of timbral and temporal groupings as an aspect of form. Messiaen,, Carter and Cowell, still more minimalist music were from Eastern backgrounds in sonorities and rhythmic structures. Cowell's turn to non-European musics led to the idea of "elastic form." It remained for Cage to translate these impulses not so much into compositions as into divergent aesthetic orientations.
Chance may be involved in the process of composition, in performance, or in both. In the composition process pitches, durations, intensities, and their distribution in time may be chosen by dice throwing, interpretations of abstract designs(Cage), or according to certain mathematical laws of chance(Xenakis). In performance, chance is allowed to operate by leaving some elements and/or their order of appearance to the performer's discretion(Boulez, Stockhausen, Pousseur), thus introducing the idea of choice. The first well-known example of 20th-century aleatory composition was Cage's 'Music of Changes for piano(1951).' Stockhausen had already explored ideas of redundancy in randomly created texts and the aleatoric manipulation of electronic controls, resulting in "an aleatoric layer of individual pulses which speeded up statistically."
In the main portion of this thesis, there mentions two different kinds of computer programs showing Mathematica's matrix operation and designing program modules for repetitive processing and random number production. These are for the applications of such aspects to real composing environments. The latter, random pitch program is in the spirit of the Xenakis' approach to musical structure.
Fractal designs have recently gained attention in the computer music field. They are applicable to musical materials, as demonstrated by Program FRACDEC. Fractals are an example of what is called one-over-f fractional noise. This means that integer patterns generated by the fractal routine will exhibit self-similarity. Many composers consider fractals to be more useful than other types of randomly generated sequences, because they closely relate to and resemble the melodic patterns found in traditional music. Mathematical models derived from the field of Chaos Science have been applied to electronic music or any instrumental/vocal music. One of those is Lorenz's model of fluid behaviour. And one example of composition which shows central idea of order within chaos; various swings between the poles - regular/irregular, loud/soft, atonal/harmonic ancient instrumental timbre/sampled one of ancient instrumental - are manipulated in David Clark's.

목차 (Table of Contents)

• Ⅰ. 서 론
• Ⅱ. 연구의 배경
• Ⅲ. 본론
• 1. 12음열주의에서의 옴고 리듬 사용기법
• 2. 음열의 분석도구 - 집합이론
• 3. 음열 산출 및 변환 - 그 프로그램 또는 악곡 예
• Ⅳ. 요 약
• 참고문헌
• Abstract