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History and Application of Dualism and Inverse Harmony

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History and Application of Dualism and Inverse Harmony HISTORY AND APPLICATION OF DUALISM AND INVERSE HARMONY A thesis submitted to the College of the Arts of Kent State University in partial fulfillment of the requirements for the degree of Master of Arts by Ross Downing May, 2020 Thesis written by Ross Downing B.M.E., Kent State University, 2017 M.A., Kent State University, 2020 Approved by _______________________________________ Joshua Albrecht, Ph.D., Advisor _______________________________________ Kent McWilliams, D.M.A., Director, School of Music _______________________________________ John R. Crawford-Spinelli, Ed.D., Dean, College of the Arts ii TABLE OF CONTENTS FIGURES AND TABLES………………………………………………………………………..iv MUSICAL EXAMPLES…………………………………………………………………………vi ACKNOWLEDGEMENTS……………………………………………………………………...vii INTRODUCTION i. Preface……………………………………………………………………………..1 ii. Synopsis on Dualism……………………………………………………………...5 iii. Synopsis on Inverse Harmony…………………………………………………….8 iv. Comparison/Contrast Between Dualism and Inverse Harmony…………………12 PART I: HISTORY OF DUALISM A. Gioseffo Zarlino……………………………………………………………………...15 B. Jean-Philippe Rameau………………………………………………………………..17 C. Moritz Hauptmann…………………………………………………………………...21 D. Arthur von Öttingen………………………………………………………………….25 E. Dr. Hugo Riemann…………………………………………………………………...30 F. Siegmund Levarie and Ernst Lévy…………………………………………………...33 PART II: DEVELOPMENT OF INVERSE HARMONY A. Jacob Collier…………………………………………………………………………40 B. Ernst Lévy……………………………………………………………………………49 C. Contextual Inversion…………………………………………………………………54 D. Inverse Harmonic Properties and Progressions……………………………………...57 E. Margaret Notley……………………………………………………………………...62 PART III: INVERSE HARMONIC ANALYSIS………………………………………………..67 CONCLUSION…………………………………………………………………………………..98 BIBLIOGRAPHY……………………………………………………………………………....100 iii FIGURES AND TABLES FIGURES Figure 1 – The Harmonic Series……………………………………………………………...3 Figure 2 – Intervallic Inversion of a Major Triad…………………………………………….5 Figure 3 – Pitch Class Clock Face…………………………………………………………..10 Figure 4 – Harmonic and Arithmetical Division of the Perfect Octave…………………….16 Figure 5 – Harmonic and Arithmetical Division of the Perfect Fifth……………………….16 Figure 6 – Hauptmann’s Two Explanations of the Major and Minor Triads……………….24 Figure 7 – Von Öttingen’s Diagram of Tonal Space………………………………………..27 Figure 8 – C Major Tonic Fundamental and Phonic Overtone……………………………..28 Figure 9 – F Minor Tonic Fundamental and Phonic Overtone……………………………...29 Figure 10 – Riemann’s Depiction of von Öttingen’s Phonic Overtones/Undertone Series...31 Figure 11 – Secondary Perfect Fourth in Harmonic Series…………………………………38 Figure 12 – Secondary Minor Third in Harmonic Series…………………………………...38 Figure 13 – Lévy’s Inversion of C Ascending Major to Generate C Descending Phrygian..39 Figure 14 – Minor Plagal Cadence Substitutes for a Major Perfect Cadence………………41 Figure 15 – Collier’s Facebook Post Mentioning Negative Harmony……………………...42 Figure 16 – Collier’s Inversion of a Dominant Chord About an Axis of Symmetry……….43 Figure 17 – Collier’s Inverted Circle of Fifths Chord Progression…………………………45 Figure 18 –Collier’s Undertone Series……………………………………………………...46 Figure 19 – Levy’s Diagram on Primary and Secondary Dominants and Subdominants…..49 Figure 20 – Harmonic Motion of Major and Minor Centripetal Chords……………………53 Figure 21 – Contextual Inversion of a Dominant Chord About a Tonic Triad……………..56 iv Figure 22 – Inversional Symmetry at Index 7………………………………………………58 Figure 23 a. Inverse Progression #1 – Simple Diatonic Triads……………………………………60 b. Inverse Progression #2 – Simple Diatonic Triads with Circle of Fifths Motion…….60 c. Inverse Progression #3 – Inverted French Augmented Sixth Chord………………...61 d. Inverse Progression #4 – Inverted Secondary Dominant…………………………….61 Figure 24 a. Hauptmann’s Triadic Construction of the Minor-Major Scale………………………64 b. Hauptmann’s Moll-Dur (Minor-Major) Scale……………………………………….64 Figure 25 – Inversional Symmetry at Index 3………………………………………………71 Figure 26 – Inverse Harmony with Chord Extensions…………………………………...…78 Figure 27 – Imperfect Authentic vs. True Inverse Dominant Cadence in Strauss………….91 TABLES Table 1 – Pythagorean Intervals……………………………………………………………...4 Table 2 – Pitch Class Integer Notation……………………………………………………….9 Table 3 – Dominant Chord Inversion Operation……………………………………………11 Table 4 – Centripetal and Centrifugal Motion in Major and Minor Zones…………………52 Table 5 – Triadic Transformations………………………………………………………….55 Table 6 – C Major Diatonic Triad Inversion………………………………………………..59 Table 7 – E Major Inverse Progression Decoded…………………………………………...71 Table 8 – E♭ Major Dominant Chord Inversion…………………………………………….83 v MUSICAL EXAMPLES Example 1 – Brahms, Fourth Symphony, Second Movement, mm. 1-9………………………...67 Example 2 – Schubert, Piano Sonata in C Minor, D. 958, mvt. 1, mm. 85-98…………………..73 Example 3 – Chopin, Mazurka in B♭ Minor, Opus 24, no. 4, mm. 131-46……………………...75 Example 4 – Schubert, Piano Sonata in A Minor, D. 537, I, mm. 28-57………………………..79 Example 5 – Brahms, Drei Quartette, Op. 31, mvt. III, Der Gang zum Liebchen, mm. 38-51….82 Example 6 – Chopin, Fantasie in F Minor, Op. 49, mm. 326-32………………………………..86 Example 7 – Liszt, Transcendental Etude No. 4, mm. 196-202…………………………………87 Example 8 – Schubert, Mass no. 6 in E♭ Major, D. 950, mvt. 1, mm. 158-64…………………..89 Example 9 – Strauss, Allerseelen, mm. 36-43…………………………………………………...88 Example 10 – Christina Perri, Jar of Hearts, Chorus…………………………………………….93 Example 11 – The Beatles, In My Life, Chorus…………………………………………………94 Example 12 – Post Malone, Stay, Chorus………………………………………………………..95 Example 13 – Radiohead, Creep, Outro…………………………………………………………96 vi ACKNOWLEDGEMENTS I wish to express sincere gratitude to my advisor, Dr. Joshua Albrecht for his consistent flexibility and dedication to helping me to prepare this thesis. Despite my unfavorable schedule, he always made time to meet with me to ensure that everything was coming together appropriately and in a timely manner. In what will undoubtedly be an unforgettable academic year for both of us, to complete this accomplishment is an incredible feat, and I could not have done it without him. I would like to pay special regards to the Kent State University School of Music faculty; particularly my committee, for their dedication to their students’ academic success. Without the contributions of Dr. Christopher Venesile, Dr. Adam Roberts, Dr. Richard Devore, Dr. Scott MacPherson, Dr. Sebastian Birch, Professor Laurel Seeds, Dr. Jennifer Johnstone, Dr. H. Gerrey Noh, Dr. Jane Dressler, and many others, I would not have the knowledge, nor the capacity to produce such a document as this. All of the individuals listed above are in relentless pursuit of educational excellence, both in their own respects, as well as for their students. I wish to thank my parents, Doug and Carol Downing, my three brothers, Kyle, Ian, and Cameron, and my lovely wife, Mackenzie. Whether it be physical, emotional, financial, spiritual, etc., these are the individuals who have provided me with the unwavering love, support, and encouragement that is so imperative when pursuing higher education. Additionally, these six individuals are some of the most intelligent, well-educated, and successful people I know. Their successes have provided me with the motivation and inspiration to continue my education and, as a teacher, enhance my own knowledge so that I may offer it to the next generation of scholars and musicians alike. vii INTRODUCTION i. Preface The term “inverse harmony” is not consistent throughout this compilation of sources. I have chosen the term “inverse harmony” to represent the inversion of a triad either about an axis of symmetry, or using the post-tonal method of inversion introduced by Allen Forte. The earlier theorists discussed in this thesis were concerned more with providing a scientific foundation for the minor triad than with the concept of inversion itself. These works are relevant to the topic of inverse harmony more for the conceptual lineage of inversion rather than directly. Some theorists may even avoid the word “inversion” altogether. In order to maintain uniformity, the terms “inversion” and “inverse” may be used to clarify or replace concepts discussed by other theorists. The term “dualism” has its own definition outside the world of music theory. The terms “dualism” and “harmonic dualism” are used interchangeably throughout writings by theorists and scholars from the early Renaissance through to the modern era. For the sake of brevity, it should always be assumed that “dualism” refers to the music theoretical concept of harmonic dualism. This thesis begins with an exploration of dualism from a historical standpoint. The opening section of the paper will focus on the genesis of dualism when theorists attempted to justify the origin of the minor triad by natural means such as string division and the harmonic overtone series. This synopsis on the history of dualism will imperatively include perspectives from theorists such as Zarlino, Rameau, Hauptmann, von Öttingen, and Riemann. Also included within this section will be the challenges faced by these theorists, as well as the criticisms they received by their colleagues. Naturally, original and unique thoughts on this matter will be included as well. 1 The second section will shift this focus to contextual inversion and inverse harmony. While harmonic dualism and contextual inversion have been historically unrelated, they are linked in one significant way; that they both are relevant in the present-day discussion of
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