Title page for etd-0606102-183622


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URN etd-0606102-183622
Author Chen-Yao Wang
Author's Email Address wangcy@math.nsysu.edu.tw
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Department Applied Mathematics
Year 2001
Semester 2
Degree Master
Type of Document
Language zh-TW.Big5 Chinese
Title Statistical Analysis and Modeling of Twelve-Tone Music-Pieces from Webern and Schoenberg
Date of Defense 2001-06-04
Page Count 57
Keyword
  • Markov property
  • Extended autocorrelation
  • AICC
  • Autocorrelation function
  • Partial autocorrelation
  • Twelve-Tone music
  • Abstract 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、partial 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.
    Advisory Committee
  • Mong-Na Lo Huang - chair
  • Kwang-I Ying - advisor
  • Mei-Hui Guo - advisor
  • Files
  • etd-0606102-183622.pdf
  • indicate access worldwide
    Date of Submission 2002-06-06

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