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 (D. Min.)--Western Seminary, Portland, OR, 2008. / Abstract. Includes bibliographical references (leaves 318-329).

Thesis (M.A.)--Bowling Green State University, 2008. / Document formatted into pages; contains v, 96 p. Includes bibliographical references.

Thesis (D. Min.)--Western Seminary, Portland, OR, 2008. / Abstract. Typescript. Description based on print version record. Includes bibliographical references (leaves 318-329).

Thesis (S.T.M.)--Concordia Seminary, 1992. / This is an electronic reproduction of TREN, #020-0088. Includes bibliographical references (leaves 124-129).

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 (D. Min.)--Concordia Seminary, St. Louis, 1993. / Abstract. Includes bibliographical references (leaves 181-186).

Thesis (D. Min.)--Trinity Evangelical Divinity School, Deerfield, Ill., 1999. / Abstract. Includes bibliographical references (leaves 318-326).

Thesis (S.T.M.)--Concordia Seminary, 1992. / Includes bibliographical references (leaves 124-129).