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A Model of the Tonal-Chromatic System and Its Application To Louisiana State University LSU Digital Commons LSU Doctoral Dissertations Graduate School 2015 A Model of the Tonal-Chromatic System and Its Application to Selected Works of Gustav Mahler Andrew David Nicolette Louisiana State University and Agricultural and Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_dissertations Part of the Music Commons Recommended Citation Nicolette, Andrew David, "A Model of the Tonal-Chromatic System and Its Application to Selected Works of Gustav Mahler" (2015). LSU Doctoral Dissertations. 695. https://digitalcommons.lsu.edu/gradschool_dissertations/695 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Digital Commons. For more information, please [email protected]. A MODEL OF THE TONAL-CHROMATIC SYSTEM AND ITS APPLICATION TO SELECTED WORKS OF GUSTAV MAHLER A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The School of Music by Andrew David Nicolette B.A., Shepherd University, 2009 M.A., The Catholic University of America, 2011 May 2015 ©Copyright 2015 Andrew David Nicolette All Rights Reserved ! ii ACKNOWLEDGEMENTS I am grateful to all of the people who made this project possible. First, I would like to thank my committee members: to Dr. Robert Peck, my advisor, for his role in the conception and development of this project, his encouragement, and his enthusiasm about my success; to Dr. Jeffrey Perry, for his unbelievable attention to detail, and his insightful comments and writing critiques; to Dr. Dinos Constantinedes, for serving as my minor professor and his seemingly unlimited depth of knowledge; to Dr. Andrew King for his willingness to step in the day before my general exam and remain flexible throughout the dissertation process. Next, I extend thanks to the entire music theory faculty at LSU for their commitment to the program and to the students. It has been an honor and a pleasure to work as a teaching assistant and instructor. I also want to thank my family and friends: to my parents, Alan and Anne Nicolette, for their unending love, support, and encouragement; to Jeff Yunek, Zach Hazelwood, Sam Stokes, Adam Hudlow, Wesley Bradford, and Jacob Gran, my fellow Ph.D. students for their friendship, support, and for all of the memories we made while at LSU; to Dr. Joshua Carver, for his friendship and all of the hours of conversation about life and music. I especially want to thank my beautiful and loving wife, Margaux, without whom none of this would be possible. Throughout all of these years, she has been a source of comfort and confidence. I thank her for picking up and moving to another part of the country so that I could pursue my degree, for working unbelievably hard for us all of these years, and enduring the financial hardship of graduate school. Above all, I am grateful to God, for who He is and the effect He has had on my life; for the grace and wisdom to complete this project, and the strength to endure ten years of schooling; I am unbelievably grateful for the gift of music that He has bestowed upon me. ! iii TABLE OF CONTENTS ! ACKNOWLEDGEMENTS . iii LIST OF EXAMPLES . vi . ABSTRACT . xi CHAPTER 1. LITERATURE REVIEW . 1 INTRODUCTION . 1 EARLY THEORETICAL LITERATURE . 3 NEO-RIEMANNIAN THEORY . 16 HARRISON, HARMONIC FUNCTION IN CHROMATIC MUSIC . 22 KOPP, CHROMATIC TRANSFORMATIONS IN NINETEENTH-CENTURY MUSIC . 29 SUMMARY . 33 2. ANALYTICAL METHODOLOGY . 35 THE TRANSFORMATIONAL PERSPECTIVE . 35 PITCH SPACE AND THE TONAL-CHROMATIC SCALE . 38 ENHARMONIC RESPELLING . 48 MAPPINGS, TRANSFORMATIONS, AND OPERATIONS . 49 INTERVALS . 50 SETS . 61 PIVOT INTERVALS AND SETS . 64 TRANSPOSITION . .65 INVERSION . 70 VOICE-LEADING SPACES . 74 3. ANALYSIS 1: GUSTAV MAHLER, PIANO QUARTET IN A MINOR . 77 HISTORY AND BACKGROUND . 77 FORMAL AND HARMONIC OVERVIEW . 79 THE EXPOSITION . 83 THE DEVELOPMENT . 88 CONCLUSION . 95 4. ANALYSIS 2: GUSTAV MAHLER, SYMPHONY NO. 5, IV, ADAGIETTO . 97 INTRODUCTION AND BACKGROUND STRUCTURE . , . 97 THE MOTIVE AND ITS HARMONIC FUNCTION . 100 MODULATION ZONES . 111 ! iv 5. ANALYSIS 3: GUSTAV MAHLER, KINDERTOTENLIEDER, NO. 2, NUN SEH’ ICH WOHL, WARUM SO DUNKLE FLAMMEN . 118 MUSICAL FORM AND TEXT . 118 BACKGROUND HARMONIC STRUCTURE . 120 MOTIVIC PROCESS . 122 FOREGROUND HARMONIC STRUCTURES . 124 6. CONCLUDING REMARKS . 138 BIBLIOGRAPHY . 142 VITA . 153 ! v LIST OF EXAMPLES 1.1. From Mitchell (1985), graphic reduction of the essential features of the Prelude from Wagner’s opera, Tristan und Isolde . 6 1.2. Reduction of Wolf, “In der Frühe,” originally by Felix Salzer . 10 1.3. Figure 2 from Marra (1986), four spellings of the chromatic scale . 11 1.4. Marra, tonal chromatic scale . 13 1.5. Inversional symmetry between major and minor triads, E = inversional axis . 17 1.6. Riemannian triadic transformations . 18 1.7. Neo-Riemannian operations . 20 1.8. (a) The generation of the hexatonic relationship using L and P; (b) the four hexatonic systems as labeled by Cohn: north, south, east, west; (c) the hexatonic scale formed by the composite pitches in the northern hexatonic system HEX3,4 . 22 1.9. Gustav Mahler, Piano Quartet in A minor, mm. 147-151 . 26 1.10. Harmonic cycles and scale-degree agents; (a) authentic cycle; (b) plagal cycle . 27 1.11. Kopp’s common-tone transformations . 32 2.1. (a) Helix representation of pitch-class space; (b) spiral representation of pitch-class quotient space . 39 2.2. Cyclic representation of the quotient map (Q12) represented by the integers (ℤ12) of chromatic pitch-class space (pcs) . 40 2.3. (a) Discrete pitch-class space generated by a series of semitones; (b) discrete pitch-class space generated by a series of perfect fifths . 41 2.4. Generic pitch-class space; integers mod 7 (ℤ7) . 42 2.5. (a) Linear representation of chromatic pitch-class space generated by fifths, each box represents the scale-degree collection of the keys of C (box 1) and A (box 2); (b) cyclic representation of the key of C; (c) cyclic representation of the key of A . 44 ! vi 2.6. (a) Linear representation of generic pitch-class space generated by fifths, each box represents the scale-degree collection of the keys of C (box 1) and A (box 2); (b) cyclic representation of the generic scale-degree space of C; (c) cyclic representation of the generic scale-degree space of A . 46 2.7. Tonal-chromatic scale with PC space, CSD space, and GSD space notated . 46 2.8. Schenker, scale degrees of the tonal system when combining major and minor, as well as the Phrygian II . 47 2.9. Mapping tables; (a) cross-domain mapping between pitch-class space and a space of twelve instruments; (b) many-to-one mapping between pitch-class space and a C major triad; (b) one-to-one mapping of pitch-class space into pitch-class space . 50 2.10. (a) Linear representation of the chromatic universe; (b) interval motion on the infinite line; (c) interval motion represented as integer values on the infinite chromatic line . ..
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