Although Schoenberg viewed his twelve-tone method as an extension of the Germanic musical evolution from Bach to Brahms, one group of writers in America identified twelve-tone antecedents with Medieval and Renaissance polyphony. Such a correlation of Schoenberg's practice with this textural orientation of the past was part of a larger movement (what I term "neopolyphony") recognizing twentieth-century musical developments as the genesis of a polyphonic epoch reviving both the technical and aesthetic concerns of the former era. With Schoenberg's practice applied to this analogical context, other writers (Hill, Krenek, Perle) advanced certain modal theories based in various degrees on the internal organization and functional role of the Church modes.

Twelve-tone music illustrates many characteristics relative with those of conventional tonal form, though works are based on a different composition method. The fundamental question of twelve-tone music arises in debate on terminology between tonal and atonal as well as methodology of musical analysis. Certain theorists try to approach twelve-tone music by traditional harmonic views rather than by pitch-class set theory. Conventional harmonic aspects arise from the fact that both tonal and twelve-tone music share similar narrative strategies. This point is explored in examining Anton Webern's Quartet for Violin, Clarinet, Tenor-Saxophone and Piano, Op. 22, which displays connection to tonal music. The present study seeks to examine certain features of the composer's working in pitch materials; i.e., the dispositions of pitch classes and the characteristics of the matching dyads, and thereby to disclose the connection between twelve-tone methods and conventional harmony.

Composition for Arnold Schoenberg is a comprehensible presentation of a musical idea (musikalische Gedanke); the totality of a piece represents the idea. For tonal works, he defines Gedanke as a process of resolving the "tonal relation" or "tonal problem." Contrary to the numerous tonal examples illustrating the notion of Gedanke, Schoenberg hardly expounds on the Gedanke principle for his atonal and twelve-tone repertoires. This study reevaluates Schoenberg's compositional philosophy and aesthetics including Gedanke, comprehensibility, Grundgestalt, and developing variation in light of his compositional practices in Begleitungsmusik zu einer Lichtspielszene, Op. 34. Although Schoenberg denies the existence of a tonal problem and hierarchy among pitches in twelve-tone compositions, the registral placement found in Op. 34 indicates certain functionality assigned to each pitch-class, producing a sense of "departure and return." The approach here elucidates the "idea" of Op. 34, in which the large-scale formal organization unfolds through contextually emphasized tonal relations. This study also explores Schoenberg's concept of the multi-dimensional presentation of a musical idea. Even though Schoenberg's discussion of musical coherence is usually limited to the immediate musical surface, I believe that he was also aware of an extended realization of foreground motives in the sense of Heinrich Schenker's "concealed motivic repetition." This analysis of Op. 34 demonstrates how the enlargement of a surface motive facilitates an understanding of the relation between the parts and the whole, which is perceived as the totality of Gedanke.

This thesis centers around a certain twentieth-century compositionaI device, the method of composition with twelve tones. There are many terms to designate this device, for example: "basic set," "tone-row," "note-series," "serialism," "serial technique," "twelve-note series," "twelve-tone technique" or "twelve-tone method." TI is thesis is a methodical research demonstrating the contemporary conventional way of scientifically and artfully manipulating twelve equal tempered degrees of the chromatic scale to produce a desirable system. In order to arrive at any substantial conclusions, it is necessary to make a critical examination and evaluation of known twelve-tone compositional procedures from as many angles as possible, so as virtually to exhaust every practical and speculative potentiality included in the technique, that is, within the range and limits of our present needs. This examination and evaluation will also involve a comparative investigation of various uses of the device, in order to produce and suggest ideas for further theoretical insights. The ultimate purpose of this thesis is to pinpoint the "hows" and "whys" of Rochberg's use of the twelve equal tones in Sonata-Fantasia.

此論文旨在探究對稱技巧在十二音創作概念與實踐之間的關係。前者抽象、後者具體。我先在第一章指出十二音系統内的對稱潛質，再在其後兩章分析對稱技巧在荀白克的《摩西與亞倫》及魏本的交響曲作品21第二樂章内的展現。荀白克“音樂意念及“發展變奏這兩個概念，在《摩西與亞倫》扮演着重要的角式，大大影響了作品内對稱的處理；而魏本對音樂的“一體性“及“可瞭解性“的堅持，亦決定了交響曲第二樂章中對稱的演譯。最後一章總括十二音作曲概念及實踐的關係，並展望日後的研究方向。 / Through an analytical study of Schoenberg’s Moses und Aron and Webern’s Symphony Op.21, second movement, my thesis aims at exploring a central issue in interpreting symmetry in twelve-tone music: the relationship between abstract conception and concrete realization. / In Chapter one, I endeavour to contextualize the uses of symmetry in twelve-tone music within contemporary theoretical perspectives. After defining my methodology, subsequent chapters are analytical examinations of two pieces. Chapter two explores how Schoenberg’s uses of symmetry in the opening of Moses und Aron might be closely associated with his conception of “idea and “developing variation. Chapter three considers the ways in which the symmetrical manifestations in Webern’s variation movement demonstrate his concern for “unity and “comprehensibility. After studying the two composers’ different symmetrical treatments Chapter 4 revisits the relationship between abstract conception and concrete realization in twelve-tone composition, and suggests implications for further research. / Detailed summary in vernacular field only. / Liu, Man Yee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Abstract --- p.i / Abstract (Chinese) --- p.ii / Acknowledgements --- p.iii / List of Figures --- p.vi / List of Music Examples --- p.viii / Chapter Chapter 1 --- Abstract Conception versus Concrete Realization in Twelve-Tone Music --- p.1 / The Twelve-Tone System and its Symmetrical Potentials --- p.5 / Methodology, Selection of Pieces and Overview of Chapters --- p.8 / Chapter Chapter 2 --- Schoenberg’s "Idea" and Twelve-Tone Symmetry --- p.11 / Compositional Concerns / Row Design, Motive, Developing Variation and "Idea" --- p.14 / Moses und Aron: The Idea of God and the Twelve-Tone System --- p.20 / Pre-Compositional Plan / Schoenberg’s Divine Order --- p.28 / Compositional Practice / Realization of Unimaginable God --- p.33 / Realizations of Basic Set (P₉) and its Inversion (I₀) --- p.38 / Implications: Manifestation of Divine Order --- p.44 / First "Image": Musical Representation of the Row by Aron --- p.47 / Second "Image": Musical Representation of God by Aron in the Golden Calf scene --- p.53 / Schoenberg’s Allegory: Irreconcilability in Realizing "Idea" --- p.58 / Chapter Chapter 3 --- Webern’s Variationen and Twelve-Tone Symmetry --- p.64 / Compositional Concerns / Webern and Symmetry --- p.69 / Analytical Perspectives on Symphony Op.21, Second movement --- p.70 / Pre-Compositional Plan / Webern’s Statement on Symphony Op.21, Second movement --- p.73 / Compositional Practice / Thema --- p.77 / Variation I --- p.81 / Variation II --- p.85 / Variation III --- p.92 / Variation IV --- p.96 / Variation V --- p.101 / Variation VI --- p.105 / Variation VII --- p.107 / Coda --- p.110 / Summary --- p.112 / Chapter Chapter 4 --- Epilogue --- p.115 / Pre-Compositional Row Designs --- p.116 / Presentations of Rows in Their Music --- p.116 / Implications for Further Research --- p.119 / Select Bibliography --- p.121

In the thesis, we study the data collected from twelve-note music of Webern and Schoenberg, including opus 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 and opus 31 of Webern and opus 25, 33a and opus 37 of Schoenberg. The data consists of the following two kinds. The data of the first kind consists of the four basic forms of the twelve-tone music. And the data of the second kind consists of the twelve-tone derived from the matrix of the twelve-note music. We will introduce the twelve-note music first and then study two main topics about twelve-note music in this thesis. In the first part, we consider the Markov properties of the first kind data. We compare the sample autocorrelation function and autocorrelation function of the fitted model to determine the fitness of the Markovian model. In the second part, we build the time series model for the second kind data. Sample autocorrelation function¡Bpartial autocorrelation function and extended autocorrelation function are used to determine the orders of the models. The best model is selected based on the AICC. Finally, we check the fitness of the models using sample autocorrelation function and partial autocorrelation function of the residuals.

Roberto Gerhard was a twentieth-century Spanish composer known for his unique treatment of the twelve-tone system. A student of the Spanish nationalist composer, Felipe Pedrell in Barcelona and also a pupil of Arnold Schoenberg in both Vienna and in Berlin, Gerhard's musical trajectory led to a synthesis of these disparate compositional traditions. In this dissertation I will explore the development of Gerhard's compositional procedures. Here, his first string quartet, composed between 1950 and 1955, becomes a useful tool to illustrate how he made the transition from one musical style to another. Gerhard's first string quartet, composed between 1950 and 1955 exhibits various experimental formal procedures but is governed by a single twelve-tone row. The work is composed in the twelve-tone idiom, but nationalist elements decorate the musical surface. The first movement follows the classical model of sonata-allegro form, while mathematical proportions govern durations and formal elements in later movements. I will first investigate Gerhard's musical language and pitch material and then consider the challenges raised by implementing sonata form outside of a tonal idiom. I will then examine his unique mathematical approach to formal design in the third movement. In addition to the string quartet, I will explore Gerhard's treatment of form in such works as his Wind Quintet (1928) and Metamorphoses--Symphony no. 2 (1957-59). / text

Thesis (Ph. D)--University of Rochester, 2008. / Includes abstract and vita. Includes bibliographical references. Digitized version available online via the Sibley Music Library, Eastman School of Music http://hdl.handle.net/1802/7669

Thesis (Ph. D.)--Princeton University, 1981. / Typescript. "This essay and the Chamber concerto together constitute the dissertation but are otherwise inrelated." Includes the author's Chamber concerto, for flute, clarinet, violin, violoncello, and piano (1 ms. score (73 p.)). Includes bibliographical references (leaf 114).

Thesis (D.M.A.)--Ohio State University, 2007. / Title from first page of PDF file. Appendix B (p. 103) includes embedded audio file. Appendix C (p. 104) refers to accompanying PDF files. Includes bibliographical references (p. 105-107).