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題名:十二音列樂曲的方陣與模型研究--以魏木和荀白克的樂曲為例
書刊名:中國統計學報
作者:郭美惠王琛瑤應廣儀 引用關係
作者(外文):Guo, Mei-HuiWang, Chen-YaoYing, Guang-Yi
出版日期:2007
卷期:45:2
頁次:頁170-188
主題關鍵詞:十二音列馬可夫模型自我相關係數時間序列模型AutocorrelationMarkov modelTime series modelTwelve-tone series
原始連結:連回原系統網址new window
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本文介紹十二音列音樂所使用的十二音列方陣,並對魏本及荀白克的十二音列樂曲建立統計模型。本文所分析的樂曲色括魏本的第二十號到第三十一號作品和荀白克的第二十五號、第三十三a號以及第三十七號作品的第一樂章。樂曲資料的型態分為僅考慮、十二音列序列的四個基本形式的四型資料以及將每個基本類型再分別細分為十二個子類型的四十八子型資料。在第一部份我們先介紹十二音列及十二音列方陣的建構方法以及樂曲資料的型式。在第二部份我們對樂曲的四型資料建立馬可夫模型及時間序列模型,藉此探討樂曲中十二音列四型資料的序列相關性及樂曲中所使用四型資料的實證分佈與模型平穩分佈的關係。最後我們對四十八子型資料建立自我迴歸及移動平均的時間序列模型,探討不同樂曲對十二音列序列安排的相關性。
In this study, we introduce the twelve-tone matrices of twelve-tone compositions and build statistical models for the twelve-tone musics of Webern and Schönberg. The music pieces analyzed here includes opus No.20,21, ...,31of Webern and opus No. 25,33a and first movement of No.37 of Schönberg. Two types of data are considered in each music piece, the first type is the four-form data which contains the basic four row series and the other type is the forty-eight sub-form data which are the respective twelve sub-forms evolved from the four basic row forms. In this paper, we will first introduce the twelve-tone series, the methodology of building twelve-tone matrices and data forms of music pieces. Next, we will establish Markov models and time series models for the four-form data, based on the models we will study the autocorrelations of the twelve-tone four-form series data and the relation between the four-form frequencies used by the composers and the stationary distributions of models. Finally, we will build the autoregressive and moving average time series models for the forty-eight sub-form data, and discuss the autocorrelation structures of different twelve-tone music pleces.
期刊論文
1.Beran, J.、Mazzola, G.(1999)。Analyzing Musical Structure and Performance-A Statistical Approach。Statistical Science,14,47-49。  new window
2.Repp, B.(1992)。Diversity and Communality in Music Performance: an Analysis of Timing Microstructure in Schumann’s ”Tr¨aumerei”。J. Acoust. Soc. Am.,92,2546-2568。  new window
3.Waugh, W. A.(1996)。Music, Probability, and Statistics。Encyclopedia of Statistical Sciences,6,134-137。  new window
會議論文
1.Conklin, S.(2003)。Music Generation from Statistical Models。AISB 2003 Symposium on Artifical Intelligence and Creativity in Arts and Sciences。Aberystwyth, Wales。30-35。  new window
圖書
1.Bailey, K.(1996)。Webern Studies。Cambridge:Cambridge University Press。  new window
2.Bailey, K.(2004)。The Twelve-Note Music of Anton Webern: Old Forms in a New Languange。Cambridge:Cambridge University Press。  new window
3.Lester, J.(1989)。Analytic Approaches to Twentieth-Century Music。USA:R.S. Means Company。  new window
4.Milstein, S.(1992)。Arnold Schoenberg: Notes, Sets, Forms。Cambridge:Cambridge University Press。  new window
5.Perle, G.(1991)。Serial Composition and Atonality - An Introduction to the Music of Schoenberg, Berg, and Webern。USA:University of California Press。  new window
6.Stewart, I.、Golubitsksky, M.(1992)。Fearful Symmetry: Is God a Geometer?。USA:Blackwell。  new window
7.Stewart, Ian(1998)。Life's Other Secret: The New Mathematics of the Living World。John Wiley & Sons Inc.。  new window
8.Steinberg, R.(1995)。Music and the Mind Machine。New York:Springer。  new window
9.Yaglom, A. M.、Yaglom, I. M.(1967)。Wahrscheinlichkeit und Information。Berlin:Deutscher Verlagder Wissenschaften。  new window
10.Brockwell, P. J.、Davis, R. A.(1996)。Introduction to Time Series and Forecasting。New York:Springer-Verlag。  new window
11.De La Motte-Haber, H.(1996)。Handbuch der Musikpsychologie。Laaber:Laaber-Verlag。  new window
12.MacDonald, I. L.、Zucchini, W.(1997)。Hidden Markov and Other Models for Discrete-valued Time Series。London:Chapman and Hall。  new window
其他
1.Mazzloa, G.,Zahorka, O.(1996)。RUBATO on the Internet,http://www.unizh.ch/groups/mml/musicmedia。  new window
 
 
 
 
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