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Trans-Diatonic Theory and the Harmonic Analysis of Nineteenth-Century Music De Andrade Negri, Alexandre Jorge Jr De Andrade Negri, A

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Trans-Diatonic Theory and the Harmonic Analysis of Nineteenth-Century Music De Andrade Negri, Alexandre Jorge Jr De Andrade Negri, A University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2018-04-25 Trans-Diatonic Theory and the Harmonic Analysis of Nineteenth-Century Music de Andrade Negri, Alexandre Jorge Jr de Andrade Negri, A. J. (2018). Trans-Diatonic Theory and the Harmonic Analysis of Nineteenth-Century Music (Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/31872 http://hdl.handle.net/1880/106586 master thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY Trans-Diatonic Theory and the Harmonic Analysis of Nineteenth-Century Music by Alexandre Jorge de Andrade Negri Júnior A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS GRADUATE PROGRAM IN MUSIC CALGARY, ALBERTA APRIL, 2018 © Alexandre Jorge de Andrade Negri Júnior 2018 ii Abstract A hallmark of nineteenth-century music is the conscious and systematic exploration of ‘non- normative’ harmonic relations especially by composers such as Liszt, Brahms, Wagner, and others. Non-normative in this context is taken to refer to any harmonic relation that fulfills the following two conditions: (1) at least one, but normally both chords (or harmonic regions) are chromatic to each other and/or to their context; and (2) the intervallic relationship between their roots is derived from a symmetrical division of the octave (i.e., they must be either a semitone, a whole-tone, a minor third, a major third, or a tritone apart). By their nature, diatonic-based analytical systems do not have the necessary tools or flexibility to explain Romantic non- normative harmonic relations, as defined above. This thesis proposes a new approach to analysis of later nineteenth-century harmony. In chapter 1, this thesis considers four modern theories of harmony that were developed to address the issues raised above. The theories examined are by Gregory Proctor (1978), Harald Krebs (1980), David Kopp (2002), and Richard Cohn (1996, 2000, 2012). Because all of these theories are ultimately rooted in an adaptation of conventional diatonic analytical practices or concentrate upon very limited aspects of non-normative harmonic relations (mainly, chromatic mediant relations), they are found to be inadequate to deal with characteristically difficult passages of nineteenth-century harmony. In chapter 2, this thesis proposes a new theory of harmony, entitled ‘trans-diatonic theory.’ The key concept of trans-diatonic theory is the ‘diptych principle,’ which fuses parallel keys (and chords) into a new, greater unit. The diptych principle generates a trans-diatonic scale, which provides richer, more complex harmonic relations that, in turn, allows for a more logical understanding of non-normative harmonic relations. The final chapter shows the practical advantages of the trans-diatonic system through the analysis of a variety of harmonically challenging passages from different works. These analyses demonstrate the use and effectiveness of the trans-diatonic theory. iii Preface This thesis is original, unpublished, independent work by the author, Alexandre Negri. iv Acknowledgements My first debt is to my advisor, Dr. Kenneth DeLong, whose never-ending support and steady guidance have been of the utmost importance to me during these last two years. Without his invaluable advices, this thesis would not have been possible. To my exam committee members, Drs. Joelle Welling, Allan Bell, Leonard Manzara and Adam Bell, my deepest gratitude for their engagement with my work and invaluable insights and contributions. My heartfelt thanks to the music faculty as well, specially to Drs. Friedemann Sallis and Laurie Radford for their comments on earlier stages of my research. To my friends and colleagues, Dr. J. Orlando Alves and Lauro Pecktor, my sincere thanks for their candid observations during various stages of my work. My sincere gratitude to the School of Creative and Performing Arts staff members, especially to Alison Schmal, for their constant help and support. I would like to extend my gratitude to my dear friends, Júlio and Andrea, Paulo and Ana Amélia, and Giselle whose sincere friendship and sense of community have made the absence and distance from home less daunting. To my dear wife, Taciana, to whom this work is dedicated, there are no words to express my deepest regard and admiration for her unconditional support and motivation. The greatest gratitude to my family. To my grandmother, Martha, for the first lessons in music and theory. To my sister, Camila, for always believing in me. To my parents, Alexandre and Fátima, for the precious gift of life and unwavering, enthusiastic support. None of this would have been possible without them. v For Taciana vi Table of Contents Abstract............................................................................................................................................ii Preface.............................................................................................................................................iii Acknowledgments...........................................................................................................................iv Dedication........................................................................................................................................v Table of Contents............................................................................................................................vi List of Tables..................................................................................................................................vii List of Figures...............................................................................................................................viii List of Musical Examples................................................................................................................ix Introduction: The Need for a New Harmonic System..................................................................1 1. Chapter 1: Modern Theories of Harmony................................................................................8 1.1 Gregory Proctor..................................................................................................................8 1.2 Harald Krebs.....................................................................................................................11 1.3 David Kopp......................................................................................................................13 1.4 Richard Cohn....................................................................................................................20 2. Chapter 2: The Trans-Diatonic Theory..................................................................................35 2.1 The Diptych Principle.......................................................................................................35 2.1.1 Towards Mode Fusion...............................................................................................36 2.1.2 The Trans-Diatonic Scale..........................................................................................38 2.2 Orders of Complexity and Tonnetzing..............................................................................46 2.2.1 Third Order of Complexity........................................................................................48 2.2.2 Second Order of Complexity.....................................................................................54 2.2.3 First Order of Complexity..........................................................................................57 2.3 Trans-Diatonic Transformational System........................................................................60 3. Chapter 3: Trans-Diatonic Analyses.......................................................................................67 3.1 Franz Schubert..................................................................................................................67 3.1.1 Mass in Eb Major, Sanctus, mm. 1-13........................................................................67 3.1.2 Piano Sonata in D Major, I, mm. 1-16........................................................................69 3.1.3 Die Zauberharfe, Overture, mm. 1-47.......................................................................71 3.1.4 Die Sterne..................................................................................................................72 3.1.5 String Quartet in G Major, I, three excerpts...............................................................73 3.2 Johannes Brahms, Ein deutsches Requiem, II, mm. 261-273............................................77 3.3 Franz Liszt........................................................................................................................79 3.3.1 Polonaise I from Die legend vom heiligen Stanislaus, two excerpts...........................79 3.3.2 Lélio Fantasy, mm. 195-198......................................................................................82 3.4 Cesar
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