Harmony Progression in The Music of Magnus Lindberg [PDF]

Zitiervorschau

HARMONIC PROGRESSION IN THE MUSIC OF MAGNUS LINDBERG

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BY EDWARD PAUL MARTIN

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BM, University of Florida, 1999 MM, University of Texas at Austin, 2001

DISSERTATION

Submitted in partial fulfillment of the requirements for the degree of Doctor of Musical Arts in Music in the Graduate College of the University of Illinois at Urbana-Champaign, 2005

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© 2005 by EDWARD PAUL MARTIN. All rights reserved.

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C e rtif ic a te

of

C o m m ittee

A pproval

University o f Illinois at Urbana-Champaign Graduate C ollege October 10, 2005

We hereby recom m end that the thesis by:

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EDWARD PAUL MARTIN E ntitled:

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HARMONIC PROGRESSION IN THE MUSIC OF MAGNUS LINDBERG

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B e a ccep ted in p a rtia l fu lfillm en t o f the requirem ents fo r the degree of: Doctor of Musical Arts

Signatures:

D irecto r o f R esea rch - Stephen Taylor

H e a d o f D e p a rtm e n t - Karl Kramer

Committee on Final Examination*

C hairperson

C om m ittee M em ber -

Com m ittee M em ber - x om Ward

C om m ittee M em ber -

Commjlfee M em ber -

Zack Browning

yf

W illiam Heiles

C om m ittee M em ber

* Required for doctoral degree but not for master’s degree

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ABSTRACT Magnus Lindberg (b. 1958) developed a sophisticated harmonic system in the 1980s and continues to incorporate and refine this system in more recent works. This dissertation examines the composer’s consistent and methodical harmonic system by exploring his innovative treatment of harmony and harmonic progression in his music composed since 1986. Lindberg’s core harmonic vocabulary consists of 12-tone chords, overtone chords, and composite sonorities that exhibit aspects of both. He applies the chaconne principle, the heart of his system, to create recurring harmonic progressions and large-scale formal structures allowing him to achieve harmonic unity within a work. As I show, however, even in their simplest form, Lindberg’s chaconnes are much more complex than their

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Baroque predecessors. Lindberg’s innovations consist of several specific techniques, recurring from work to work, that expand the idea of the traditional chaconne. These include the insertion of new progressions between the main chords of the chaconne and

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the creation of new progressions by applying the cyclic nature of the chaconne not only to a sequence of chords, but also to properties and characteristics associated with those

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chords. In the course of examining the five works that are discussed in-depth in this dissertation, I will highlight similarities and differences in the manner in which Lindberg implements his system in each, revealing its gradual evolution. Finally, I will discuss the juxtaposition of his harmonic system with elements that are foreign to the system in more recent works and make comparisons with aspects of tonality.

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To my wife Amy and my newborn son Owen

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ACKNOWLEDGEMENTS

I would first like to express my gratitude to my advisor Stephen Taylor; I feel that a significant portion of what I have accomplished at the University of Illinois, as a composer, teacher, and scholar, can be directly attributed to his support and guidance. Our discussions proved to be extremely valuable during my work on this dissertation. His insightful questions coupled with his carefully thought out criticisms helped me to focus my thoughts and refine my arguments. I would especially like to thank him for consistently reading and returning my work in a timely manner. I would also like to thank the other members of my doctoral committee, Zack Browning, William Heiles, and

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Tom Ward for their invaluable insights and comments.

I would especially like to thank Magnus Lindberg who graciously spent two hours with

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me in Los Angeles on October 6th, 2005, the day of the premiere of his orchestral piece Sculpture. Our meeting proved to be extremely helpful to my work, confirming much of my analysis and pointing me toward areas that required further examination. I would like

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to convey my appreciation to my good friends, musicologist Eduardo Herrera and composer Jake Rundall, for willingly (and sometimes unwillingly) subjecting themselves to my repeated inquiries for their thoughts and opinions. I would also like to thank my parents for their constant support. Finally, I can only begin to express my love for and gratitude to my wife Amy. She is my inspiration and I can truly say that I would not be where I am without her. I am forever grateful to her for her unwavering support, patience, understanding, excellent editing skills, and occasional nagging. And to my son Owen, your birth only one month after my dissertation defense inspired me through the final stages of this process.

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TABLE OF CONTENTS LIST OF EXAMPLES............................................................................................................ vii LIST OF TABLES.....................................................................................................................x 1. INTRODUCTION................................................................................................................. 1 2. HARMONIC VOCABULARY........................................................................................... 7 2 .1 . 1 2 - t o n e C h o r d s ................................................................................................................................................... 7 2 .2 . O v e r t o n e C h o r d s ...........................................................................................................................................1 6 2 .3 . C o m p o s i t e C h o r d s ......................................................................................................................................... 2 3

3. HARMONIC PROGRESSION......................................................................................... 40 3 .1 . C h a c o n n e ....................................................................................

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3 .2 . T h e “F r e e z e ” T e c h n i q u e .......................................................................................................................... 4 2 3 .4 . S e q u e n c e

of of

C h a c o n n e b y I n t e r p o l a t i o n ..............................................................................4 7

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3 .3 . E x p a n s i o n

C h o r d P r o p e r t i e s ......................................................................................................... 5 8

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4. FORM DETERMINED BY HARMONIC PROGRESSION..........................................75 5. HARMONIC PROGRESSION COMBINED WITH FOREIGN MATERIAL

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6. CONCLUSIONS................................................................................................................. 95 APPENDIX A: LIST OF WORKS BY MAGNUS LINDBERG..................................... 101 APPENDIX B: DISCOGRAPHY OF WORKS BY MAGNUS LINDBERG MENTIONED IN THIS DISSERTATION........................................................................ 105 BIBLIOGRAPHY................................................................................................................. 107 AUTHOR’S BIOGRAPHY..................................................................................................109

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LIST OF EXAMPLES

Example 1. The first 12-tone chord from Twine for solo piano..........................................3 Example 2. An overtone chord from Marea, m. 101............................................................3 Example 3. An illustration of Lindberg’s use of interpolation............................................ 5 Example 4. An illustration a sequence of chord properties..................................................5 Example 5. A reproduction of Rae’s reduction of the symmetrical 12-tone chord from Lutoslawski’s Jeux venitiens, mov. 4, letter F ........................................................................8 Example 6. Twine, mm. 1-11...............................................................................................11

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Example 7. The eight main symmetrical 12-tone chords from Twine. The vertical line shows the vertical axis of symmetry...................................................................................... 12 Example 8. The twelve main symmetrical 12-tone chords from Kinetics..........................14

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Example 9. The eight main symmetrical 12-tone chords from Marea................................15

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Example 10. The first overtone chord from Grisey’s Partiels............................................. 17 Example 11. A comparison of the natural overtone series on Ebl (rounded to the nearest quarter-tone) and an overtone chord built on Ebl from Kinetics, mm. 269-279.............. 19 Example 12. A comparison of the natural overtone series on Cl (rounded to the chromatic scale) and an overtone chord built on Cl from Marea, m. 101..........................19 Example 13. Kinetics, mm. 256-257 (notated at concert pitch).........................................21 Example 14. The overtone chord from Kinetics, mm. 256-257..........................................22 Example 15. A reduction of the viola, cello, and bass parts from Marea, mm. 107-114. 22 Example 16. Twine, m. 73 and m. 134................................................................................ 23 Example 17. A 12-tone overtone chord built on C l........................................................... 25 Example 18. Kinetics, mm. 1-4 b.2 (notated at concert pitch)

.................................28

Example 19. The 12-tone and overtone components of composite sonority from Kinetics, mm. 1-4 b. 2............................................................................................................................29 Example 20. The 12-tone and overtone components of the composite sonority from Kinetics, mm. 57-58.....................................................................

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Example 21. The 12-tone and overtone components of the composite sonority from Kinetics, m. 245....................................................................................................................... 30 Example 22. The progression of eight composite sonorities from Marea, mm. 50-66.... 31 Example 23. A reduction of Fresco, mm. 259-260..............................................................33 Example 24. The 12-tone and overtone components of the composite chord from Fresco, mm. 259-260............................................................................................................................ 33 Example 25. A comparison of the overtone series built on Cl (rounded to the chromatic scale) and a combination of chords 1 and 2 from Steamboat Bill Jr..................................35 Example 26. A comparison of the overtone series built on Cl (rounded to the chromatic scale) and a combination of chords 1 and 3 from Steamboat Bill.Jr..................................35

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Example 27. A comparison of the overtone series built on D1 (rounded to the chromatic scale) and a combination of chords 4 and 5 and the top three pitches of chord 6 from Steamboat Bill Jr..................................................................................................................... 36

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Example 28. Steamboat Bill Jr., mm. 61-65 b. 2 (notated at concert pitch)......................37 Example 29. Steamboat Bill Jr., mm. 201-207 (notated at concert pitch).........................38

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Example 30. A comparison of the final chord from Steamboat Bill Jr. (mm. 201-207) to chords 1, 2, and 3.................................................................................................................... 38 Example 31. The harmonic construction of Marea, mm. 67-74.........................................42 Example 32, Marea, mm. 67-74. Dynamics, articulations, pedal marks, and performance instructions have been omitted from this example for clarity. All instruments are notated at concert pitch....................................... 43 Example 33. The harmonies from Twine, mm. 105-110.................................................... 46 Example 34. A comparison of Twine, mm 105 with chord 1 and chord 3........................46 Example 35. A reduction of Kinetics, mm. 165-170 b.l (notated at concert pitch)......... 50 Example 36. An illustration of the harmonic structure of Kinetics, mm. 165-170...........51 Example 37. The harmonies from Kinetics, mm 165-170..................................................51 Example 38. A reduction of Fresco, mm. 209-216 (notated in concert pitch)..................52 Example 39. The harmonies from Fresco, mm. 209-216 (the diamond-shaped note heads are foreign tones played by the cello)................................................................................... 54 Example 40. The harmonies from Fresco, mm. 203-209.....................................................56

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Example 41. Twine, mm. 86-92............................................................................................ 57 Example 42. The harmonies from Twine, mm. 86-91........................................................ 57 Example 43. The 12-tone component of the following progressions from Kinetics: mm. 60 37-56, mm. 57-d.b. 71, mm. 72-84, mm. 85-102.................................. Example 44. The fundamentals from the following progressions of Kinetics: mm. 37-56, 57-d.b. 71,71-84....... 64 Example 45. The construction of Twine, mm. 1-80............................................................65 Example 46. Twine, mm. 60-68............................................................................................70 Example 47. Twine, m. 29.................................................................................................... 71 Example 48. The harmonies from Twine, mm. 50-59........................................................ 72

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Example 49. The imperfect formal symmetry of Twine.....................................................76 Example 50. The formal structure of part 1 of Twine, mm. 1-85...................................... 77

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Example 51. The formal structure of part 2 of Twine, mm. 86-160.................................. 79

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Example 52. The formal structure of Kinetics.....................................................................82 Example 53. The harmonic consistency of the individual progressions that make up the chaconne from Marea, mm. 50-198..................................................................................... 85 Example 54. The formal structure of Steamboat Bill Jr..................................................... 89 Example 55. The overtone chords from Steamboat Bill Jr., mm. 31 and 44.....................90 Example 56. A reduction of Fresco m. 117-118................................................................. 92

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LIST OF TABLES

Table 1. Properties of the eight main symmetrical 12-tone chords from Twine................ 13 Table 2. The register contours of the progressions from mm. 37-56, mm.57- d.b.71, mm. 72-84, and mm. 85-102 from Kinetics...................................................................................61 Table 3. The pitch-class sets of the top hexachord from the harmony in each position of the following progressions from Kinetics: mm. 37-56, mm. 57-d.b. 71, mm. 72-84, mm. 85-102.................................................................................................................................... 623 Table 4. A list of fundamentals associated with each position in the following progressions from Kinetics: mm. 37-56, 57-d.b. 71, 71-84................................................. 63

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Table 5. A comparison between the register contours of the main progression of symmetrical 12-tone chords and the individual progressions of the indirect progression from mm. 12-80 of Twine.......................................................................................................66

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Table 6. The register contour of the main progression of symmetrical 12-tone chords and a register contour that is determined by the average high and low pitch from each chord in positions 1 through 8 in the indirect progression from mm. 12-80 of Twine................ 69

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Table 7. A comparison between the register contour of the main progression of symmetrical 12-tone chords and a register contour that is determined by the average high and low pitches from all of the chords in each of the eight progressions from mm. 12-80 of Twine................................................................................................................................... 74 Table 8. The harmonies (shown as chord numbers) from the indirect progression and four direct progressions of Kinetics.......................................................................................93 Table 9. The thirteen distinct hexachords that are the source of the main progressions of symmetrical 12-tone chords in Twine, Kinetics, Marea, Steamboat Bill Jr., and Fresco. 96

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1. INTRODUCTION

In an interview about his recent music published in 1994, Finnish composer Magnus Lindberg (b. 1958) states, “if there’s any theoretic work, it concerns essentially the harmonic structure.”1 Lindberg indeed developed a distinct and sophisticated harmonic system during the late 1980s and continues to incorporate elements of this system into more recent works. While a few authors have described certain aspects of Lindberg’s work with harmony on a surface level, there exists no comprehensive study that examines his music in sufficient enough detail to explain the inner workings of the system and how it has evolved from piece to piece. This dissertation will examine the composer’s innovative approach to harmony and harmonic progression in his music composed since

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1986, with the goal of discovering and describing his consistent and methodical harmonic system. I will provide detailed examples of individual harmonies and progressions from

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several works, showing how these determine aspects of large-scale formal structures. I will also include a discussion of recent works in which Lindberg combines his system

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with other, unrelated material.

Lindberg received his formal training at the Sibelius Academy in Finland under Paavo Heininen. In 1977, he and other fellow students of Heininen, such as Kaija Saariaho and Esa-Pekka Salonen, formed Korvat auki (Ears Open), a group that promoted contemporary music through the organization o f concerts, seminars, and meetings with performers and musicologists.2 It is in the context of this organization that the characteristics defining Lindberg's early music begin to emerge: “a taste for the extreme, the forthright, even the bizarre.”3 While still a student at the Sibelius Academy, Lindberg studied abroad in Siena with Franco Donatoni and came in contact with Brian Femeyhough at Darmstadt. Upon graduation, he moved to Paris where he continued his studies with Vinko Globokar and Gerard Grisey and met several times with Iannis

1 Peter Szendy, liner notes to recording Magnus Lindberg, Ensemble Intercontemporain, directed by Peter Eotvos, trans. by Stefan Rice, (Ades - Paris: IRCAM, 1994): 39. 2 Ibid., 6. 3 Risto Nieminen, “The Calculation of Prosesses is a Source of Inspiration,” Finnish Music Quarterly 2 (1986 issue 3): 32.

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Xenakis.4 These diverse influences, especially those of Globokar and Grisey with whom he studied concurrently, had a significant impact on Lindberg’s development as a young composer. As Julian Anderson writes, “the modernist, radically experimental aesthetic of Globokar could hardly be further removed from Grisey’s explorations of time, perception and acoustics. In fact, Lindberg once remarked that he was given such totally conflicting advice that he felt as if he were ‘living two lives simultaneously’.”5 Lindberg’s music leading up to the composition of Ur leans heavily on Globokar's influence. His early style, which is described in one of the first articles on the composer as “severe, almost harsh,”6 reaches its apex with Lindberg’s first major orchestral work, Kraft (1985), for large orchestra, six soloists, and electronics.

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Lindberg’s compositional approach takes a marked turn in the direction of Grisey’s style beginning with Twine: the often unabashedly brutal language of his music from the early

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1980’s gives way to a relatively softer and more refrained style. This new sound is due in large part to Lindberg’s newfound interest in harmony and harmonic progression. In an interview with Tony Lundman, Lindberg states, “Up to the [orchestral] trilogy Kinetics-

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Marea-Joy (1988-90) I had avoided working with harmony. Harmony was a ‘by­ product’ of the work with timbre and rhythm.”7 While this statement is not entirely accurate (he did begin to work out some harmonic ideas in the early 1980s), it is true that Lindberg did not begin to methodically develop his own harmonic system until the composition of Twine. Twine, which itself is a substantial and effective work, can be described as a transitional piece in which Lindberg tested his new harmonic system that was next applied in the orchestral trilogy.

This dissertation will provide an in-depth discussion of Lindberg's use of harmony and harmonic progression starting with Twine for solo piano (1988) and including the following additional works: Kinetics for orchestra (1989), Marea for orchestra (1990), Steamboat Bill Jr. for clarinet and cello (1990), and Fresco for orchestra (1998). I

4 Ibid., 32-33. 5 Julian Anderson, “The Spectral Sounds of Magnus Lindberg,” Musical Times 133 (November 1992): 565. 6 Nieminen, “The Calculation of Prosesses is a Source of Inspiration,” 32. 7 Tony Lundman, “Music with Muscle,” Nordic Sounds 4 (December 2002): 18.

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strongly encourage the reader to supplement the information found in this text with recordings of Lindberg’s music; a discography of the composer’s works mentioned in this dissertation is found in Appendix B.

Lindberg’s innovative harmonic system includes a core harmonic vocabulary and a systematic means by which he arranges individual harmonies into progressions.8 This harmonic vocabulary consists of two distinct components: 12-tone chords (in which the intervals are often arranged symmetrically with respect to their vertical axis) and overtone chords which are modeled on the natural harmonic series. Examples 1 and 2 show a typical instance o f each type of chord. Chapter 2 will analyze the construction of these two categories individually and then show the ways in which Lindberg combines

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them to form composite sonorities that exhibit aspects of both.

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Example 1. The first 12-tone chord from Twine for solo piano.

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Example 2. An overtone chord from Marea, m. 101.

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xr 8 In this dissertation, the term harmonic progression is simply used to refer to a succession o f harmonies. It is not meant to allude to any aspect of harmonic progressions or harmonic function in tonal music, though as will be discussed in chapter 6, however, several similarities do exist between Lindberg’s harmonic progressions and those found in tonal music.

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All of Lindberg’s recent music that is built on harmonic progressions shares the following feature: a main progression of symmetrical 12-tone chords can be identified for each work. Lindberg consistently employs several techniques to create an intricate network of relationships between the main progression and all secondary progressions in a piece. At the heart of each of these techniques lies the chaconne principle. A chaconne, which is very similar to and has become virtually synonymous with a passacaglia, is a Baroque form consisting of a continuous variation of material built on a bass / harmonic ostinato.9 While several authors, including Julian Anderson, Lauri Otonkoski, and John Wamaby, have described Lindberg’s harmonic progressions with this term, this dissertation will examine these progressions in greater depth, citing examples from several pieces. As Wamaby points out, Lindberg occasionally applied the

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chaconne technique to earlier works, such as Ground (1983) for harpsichord, but he did not begin to consistently develop it until the composition of the second movement of

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Kraft (1985).10

When asked how he applies the principle of chaconne to his music, Lindberg replied: “I

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built a series of chords that comprised somehow the skeleton of the whole work. They are omnipresent, they give the work form and identity.” 11 The “skeleton” that Lindberg is referring to is each work’s main progression of symmetrical 12-tone chords. Notice that Lindberg does not describe his use of chaconne simply as being an ostinato built on the main harmonic progression, as would result from a strict application of the Baroque technique. While the Baroque meaning of the term is a fairly accurate description of the harmonic progressions in some of Lindberg’s music, such as Marea, it is misleading when applied to other works, such as Twine or Kinetics. In the latter, as I will show in chapter 3, the main harmonic progression of symmetrical 12-tone chords is not literally repeated as an ostinato, as occurs in its Baroque predecessor. Lindberg consistently applies two techniques (only one of which has been discussed, though incompletely, in the existing literature) that expand the idea of the chaconne from its Baroque definition. The first o f these is described as interpolation, defined as the insertion of a new element 9 The Harvard Dictionary o f Music, 4* ed., s.v. “Chaconne,” by Elaine Sisman. 10 John Wamaby, “The Music of Magnus Lindberg,” Tempo 181 (June 1992): 25-26.

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between existing elements. When applied to Lindberg’s chaconne technique, it refers to the insertion of a progression of new harmonies between two of the main symmetrical 12tone chords that usually, but not always, functions as a gradual transformation between those two chords. In the interpolating progressions that do function as transformations, the properties exhibited by each individual chord gradually shift from resembling the proceeding main symmetrical 12-tone chord to resembling the one that follows.

The second method Lindberg uses to expand the chaconne principle, which has not been discussed in the existing literature, is to apply the cyclic nature of the technique not only to the actual chords o f the main harmonic progression, but also to certain properties associated with those chords. This process results in a repeating sequence of chord

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properties that Lindberg uses to build progressions of new harmonies that resemble the work’s main progression and each other. Lindberg applies each of these techniques,

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illustrated below in examples 3 and 4, to achieve harmonic unity throughout a work. On a large scale, the cyclic nature of the chaconne allows Lindberg to create balanced formal structures that, in a very general sense, exhibit classical traits. Chapter 4 will describe

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these formal structures and discuss instances when the composer deviates from them over the course of a work and what affect this has on the overall scheme.

Example 3. An illustration of Lindberg’s use of interpolation.

' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Y- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1

Main progression of eight symmetrical 12-tone chords

etc.

' - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - »- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Interpolating progression between chords 1 and 2

Example 4. An illustration of a sequence of chord properties.

v__________________________.._________________________ / ^

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Main progression of eight symmetrical 12-tone chords

Secondary progression in which each chord exhibits properties of the corresponding chord from the main progression

11 Szendy, liner notes to recording Magnus Lindberg, 40.

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I was fortunate to have the opportunity to talk with Magnus Lindberg on October 5, 2005, the day his orchestra piece Sculpture was premiered by the Los Angeles Philharmonic. From the moment our discussion began, his dynamic conversation and animated gestures revealed a genuine passion for composing and a love of music. It was immediately apparent to me that Lindberg is truly excited about the work he is doing and is by no means close to slowing down (he has composed at least one major orchestra work in each of the past fifteen years). My meeting with Lindberg proved to be extremely valuable to this dissertation; it confirmed much of my analysis and pointed me toward areas requiring further examination. During our discussion, Lindberg revealed to me that he considers his system to be a work-in-progress: while its fundamental components remain intact,

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Lindberg constantly tweaks, expands, and refines the system from piece to piece. I found it fascinating that after nearly twenty years Lindberg continues to build his compositions,

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such as Sculpture, around the same core harmonic system. In the course of examining the five works that are discussed in-depth in this dissertation, I will highlight similarities and differences in the manner in which Lindberg implements his system in each,

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revealing its gradual evolution. Chapter 5 in particular will discuss the juxtaposition of his harmonic system with elements that are foreign to the system in Steamboat Bill Jr. (1990) and Fresco (1998) and show how this process alters the function of the chaconne. I hope that by providing a clear and thorough discussion, this dissertation will spark the interest of others to examine more recent compositions (and revisit earlier works) to further study the evolution of Lindberg's harmonic system.

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2. HARMONIC VOCABULARY 2.1. 12- t o n e C h o r d s

Magnus Lindberg’s innovative harmonic system is built on a vocabulary that consists of two distinct components: 12-tone chords (often referred to as serial chords by Lindberg) and overtone chords. The manner in which Lindberg uses 12-tone aggregates as harmonic entities that will be described in this chapter can definitely be labeled a signature of his style. Lindberg constructs 12-tone chords in early works, such as Twine for solo piano (1988), the same way that he does in later pieces, such as Fresco for orchestra (1998). The method of building 12-tone chords that will be illustrated in this chapter applies to all of Lindberg’s recent music composed using these types of

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sonorities. In my discussion with the composer, I inquired about his reason for focusing on 12-tone harmonies. Lindberg stated that he has experimented with chords consisting

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of less than twelve tones, but found them to be unsatisfactory. He went on to say that he

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enjoys the freedom that 12-tone chords allow him: he is able to call upon any pitch at any 10 moment and it is always a component of the present harmony.

What differentiates Lindberg’s 12-tone chords from one another is that each chord is register-specific: each of the twelve tones that make up a chord always resides in a particular octave. This makes register the single defining characteristic distinguishing one chord from another and results in each chord containing a distinct vertical interval structure. Many of Lindberg's 12-tone chords are symmetrical with respect to their vertical arrangement of intervals and constructed around an axis of an “odd-numbered” interval: a minor second, a minor third, a perfect fourth, etc. The interval structure of the top hexachord of a symmetrical 12-tone chord is identical to the interval structure of the bottom hexachord. In each piece that will be examined, the main structural harmonies those that govern important aspects of the piece - are always symmetrical 12-tone chords, while other secondary 12-tone harmonies may or may not be symmetrical.

12 Magnus Lindberg, interview with author and Mandy Fang, October 6,2005, Los Angeles, California.

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Lindberg’s incorporation of symmetrical 12-tone chords into his harmonic vocabulary is a continuing homage to an earlier composer who used similar harmonies: Witold Lutoslawski. Lindberg’s admiration for the Polish composer is clearly evident in the title of his large orchestral work Aura: In Memoriam Witold Lutoslawski, his only piece to include such a dedication. Lutoslawski’s use of 12-tone chords and symmetrical 12-tone chords, which began in 1956, marked what biographer Charles Bodman Rae calls, “the 11 most significant turning point in his career.” Rae goes on to describe the two ways in which Lutoslawski builds 12-tone harmonies: “those that can be classified according to the number and types of intervals they contain; and those that can be classified as chordaggregates (or chord complexes), according to the combination of complementary chords they contain.”14 Regarding the first type, it is common for Lutoslawski to use only one or

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two particular intervals when stacking notes to form 12-tone chords. The composer states that, “the fewer different intervals between neighbor [i.e. Adjacent] notes the chord

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contains, the more characteristic the result is.” He goes on to state that 12-tone chords constructed with all of the intervals result in a color that is “grey.”15 Example 3:1b from Rae’s book, reproduced in example 5 below, shows a symmetrical 12-tone chord built

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only on m2nds and m9ths from the fourth movement of Jeux venitiens at letter F. Example 5. A reproduction of Rae’s reduction of the symmetrical 12-tone chord from Lutoslawski’s Jeux venitiens, mov. 4, letter F16

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When compared to one another, Lindberg’s and Lutoslawski’s 12-tone harmonies are similar only to the extent that they are 12-tone and often incorporate symmetry. The

13 Witold Lutoslawski quoted in Charles Bodman Rae, The Music o f Lutoslawski (London: Faber and Faber Limited, 1994), 49. 14 Ibid. 15 Witold Lutoslawski quoted in Rae, 50. 16 Rae, 51.

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method of construction and the structure of each composer’s harmonies is actually quite different. One possible criticism of Lindberg's 12-tone chords, especially in his early works, is that they tend to exhibit the “grey” quality that Lutoslawski avoids: they do not 17 focus on a limited number of intervals and they are not designed as “chord complexes.” Instead, Lindberg builds his harmonies by applying aspects of Allen Forte’s set theory in a process that, as he states, is based on the “classification of chords and their relations [to one another].”18 Lindberg applies the principles of set theory to construct intricate relationships between the harmonies of a work’s main harmonic progression and those found in the secondary harmonic progressions.

The computer is an important compositional tool for Lindberg. When generating

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harmonies, Lindberg uses the IRC AM computer software Patchwork (which has evolved into OpenMusic) to simulate aspects of Forte’s set theory providing him with, as Julian

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Anderson writes, “large reservoirs of distinct but related harmonic fields.”19 It is obvious that if all of Lindberg's 12-tone chords are taken as a whole, they can each be analyzed as the same set: [0,1,2,3,4,5,6,7,8,9,10,11]. In actuality, Lindberg first applies Forte’s set

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theory to build relationships between progressions of hexachords, which then become the source for his progressions of symmetrical 12-tone chords. After creating a network of related hexachord progressions, Lindberg generates progressions of symmetrical 12-tone chords: the original hexachord is stacked with another hexachord whose interval collection is related by vertical, mirror symmetry to form a 12-tone aggregate. As a result, relationships between progressions of symmetrical 12-tone chords can be observed by isolating either the top or the bottom hexachord of a symmetrical collection and analyzing its pitch-class set (these result in the same set due to the symmetrical property of the chords). In my discussion with Lindberg, he stated that the reason he focuses on building 12-tone chords from two hexachords, rather than three tetra-chords or four tri­ 17 In my discussion with Lindberg (10/6/2005, Los Angeles, California) however, he claims that he sometimes arranges his 12-tone chords in such a way that they do emphasize a particular interval (similar to Lutoslawski’s chords as discussed above). While my analysis did not reveal any such chords, it is possible that Lindberg does construct chords in this manner in his very recent works. Unfortunately, I was unable to obtain scores for any works composed after 1998. An examination of the 12-tone harmonies in Lindberg’s music composed after 1998 may be necessary to highlight more similarities between Lindberg’s and Lutoslawski’s 12-tone chords. 18 Szendy, liner notes to recording Magnus Lindberg, 39. 19 Anderson, “The Spectral Sounds of Magnus Lindberg,” 566.

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chords, is that the hexachord provides him with the greatest number of distinct pitch-class sets to choose from.

There are fifty distinct 6-note sets, thirty-eight 5-note and 7-note

sets, twenty-nine 4-note and 8-note sets, and so on. In general, Lindberg does not incorporate hexachords that have Z-relationships (those related by sharing the same interval vector) with other hexachords. The main progressions of symmetrical 12-tone chords from each work examined in this dissertation do not include any chords that are generated from hexachords that have Z-relationships with one another. This is significant because of the fifty possible hexachords, thirty have Z-relationships. Lindberg’s reason for not including these chords may be that he wishes to make each of a work’s main symmetrical 12-tone chords as distinct as possible. It is important to observe the register, interval content, and pitch-class set associated with each of the main structural chords in

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a piece. These qualities play an important role in determining the characteristics of the

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various secondary harmonic progressions throughout a work.

Twine for solo piano is based on a main progression of eight symmetrical 12-tone chords (labeled chords 1-8) and as will be seen in chapters 3 and 4, these eight chords govern the

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pitch and formal aspects of the entire piece. The work opens with a progression through the eight main chords in mm. 1-11 (shown in example 6). Example 7 shows each of the eight main chords out of context. Chord 1 resides, more or less, in the middle register of the piano, its axis is the perfect fifth of C4-G4, the lowest and highest pitches are D2 and F6 respectively, and the hexachord on either side of the axis contains the pitch-class set (0,1,2,3,4,6). Lindberg applies some or all of these properties to other particular chords throughout the piece, creating harmonic links with chord 1. Table 1 describes each of the eight structural chords from Twine in the terms used above.

20 Magnus Lindberg, interview with author and Mandy Fang, October 6, 2005, Los Angeles, California.

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Example 6. Twine, mm. 1-11.

Chord 2 9 :8 —

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\—9

0:8

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*9>

Chord 4

....

1

Chord 3

Chord 5

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1—s.

Chord 6

Chord 7

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Chord 8

8—i

— Otfpocof

v v8*

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Example 7. The eight main symmetrical 12-tone chords from Twine. The vertical line shows the vertical axis of symmetry. (0,1,2,3,4,6)

Chord 1

(0,1,2,3,6,7)

Chord 2 W—J

(0,1,3,4,6,9)

Chord 3

(0,1,2,5,7,8) Chord 4

Chord 8

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Chord 7

(0,1,2,4,5,8)

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Chord 6

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Chord 5

(0, 1,2,4,6,8)

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