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© Chardan Howe, 2019

Sta

sis and Motion Explored in Three of my

Musical Compositions

Mémoire

Chardan Howe

Maîtrise en musique - composition - avec mémoire

Maître en musique (M. Mus.)

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Stasis and Motion Explored in Three of My Musical

Compositions

Mémoire

Chardan T. B. Howe

Sous la direction de :

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RÉSUMÉ

Le but principal de ce mémoire est d’explorer les concepts et les gestes musicaux du statisme et mouvement en musique. Le mémoire va présenter comment ces concepts et gestes peuvent enrichir la compréhension d’une composition, au niveau de sa forme, du rythme, etc.

Les trois œuvres à l’étude sont :

1) Brume, pour quatuor à cordes, où l’atmosphère statique présente très peu de matériaux qui n’évoluent guère, et ce, pendant un long moment.

2) Sous le Sol, pour quintette à vents, où le statisme de la pulsation est dynamisé par les changements métriques, agogiques, et tonaux.

3) Lumière et Couleurs, pour l’orchestre, dans laquelle tous les éléments du discours musicale (harmonie, durée, hauteur) sont prédéterminés à l’aide d’une série de Fibonacci.1

Dans le contexte du mémoire, je vais définir les mots « statisme » et « mouvement », expliquer les sources d’inspiration musicales et littéraires qui me sont dirigées vers cet approche, et, en finale, je vais analyser les trois œuvres mentionnées ci-haut et présenter les concepts de statisme et de mouvement se présentent au niveau de la composition.

1 “Une série des nombres où le calcul d’une terme est déterminé par la sommation des deux termes

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ABSTRACT

This thesis is meant to be an exploration of musical gestures pertaining to the concepts of stasis and motion in music, in three of my original compositions. The intent of this exploration is to demonstrate how looking at musical compositions from the perspective of stasis and motion can help both the composer and the listeners to understand their formal structures, as well as be interesting, inspiring, and can add more depth to a work. The compositions are as follows:

1) Brume, for String Quartet, which details my attempt at creating an overall atmosphere of stasis with little, minutely-detailed motion over a long period of time, using very little musical material.

2) Sous le Sol, for Woodwind Quintet, where changes in metre, rhythmic accent, and key signature (motion) come to the fore to obscure an unchanging (static) rhythmic drive. 3) Lumière et Couleurs, for Orchestra, where all of the elements of stasis and motion, such as harmony, rhythm, and pitch are guided in part by a pre-determined compositional process, namely, the Fibonacci sequence.2

I will first define what is meant by stasis and motion in the context of this essay, then I will explain the musical and literary sources of inspiration that led to my choosing this approach, and, finally, I will

2 A series of numbers a series of numbers where a number is found by adding up the two numbers before it”

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analyze the three-aforementioned works and how I applied stasis and motion throughout their compositional processes.

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TABLE OF CONTENTS

RÉSUMÉ ... ii

ABSTRACT ... iii

TABLE OF CONTENTS ... v

LIST OF TABLES ... vii

LIST OF FIGURES ... viii

LIST OF MUSICAL EXAMPLES ... ix

ACKNOWLEDGEMENTS ... xi

INTRODUCTION ... 1

My Training as a Musician and Composer ... 1

Artistic Inspirations ... 2

Thesis Objectives ... 3

CHAPTER 1 ... 4

1.1 - Definitions, Ideas, and Philosophy ... 4

1.2 - Context in Recent Music History ... 6

1.3 - From perception to application ... 9

CHAPTER 2 ... 10

2.1 - Brume ... 10

2.1.1 – Form of Brume ... 11

2.1.2 – Structural Analysis of Brume ... 12

2.2 - Sous le Sol ... 21

2.2.1 – Form for Sous le Sol ... 22

2.2.2 - Structural analysis of Sous le Sol ... 23

2.3 - Lumière et Couleurs ... 40

2.3.1. – Form for Lumière et Couleurs ... 41

2.3.1.1 - Colours/Harmony ... 41

2.3.1.2 - Rhythmic Repetitions Table ... 41

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CONCLUSION ... 53

BIBLIOGRAPHY ... 55

ANNEX: COMPOSITIONS ... 57

ANNEX 1 – BRUME ... 58

ANNEX 2 – SOUS LE SOL ... 73

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LIST OF TABLES

Table 1: The Form for Brume ... 11

Table 2: The Form for Sous le Sol ... 22

Table 3: The Form for Lumière et Couleurs ... 41

Table 4: The Colour-Harmony Table of Lumière et Couleurs ... 41

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LIST OF FIGURES

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LIST OF MUSICAL EXAMPLES

Example 1: Brume, mm. 6-10 ... 13 Example 2: Brume, mm. 19-20 ... 14 Example 3: Brume, mm. 23-24 ... 15 Example 4: Brume, mm. 27-28 ... 15 Example 5: Brume, mm. 31-33 ... 16 Example 6: Brume, mm. 40-41 ... 17 Example 7: Brume, mm. 53-56 ... 18 Example 8: Brume, mm. 69-71 ... 18 Example 9: Brume, mm. 79-83 ... 19 Example 10: Brume, mm. 96-102 ... 20

Example 11: Sous le Sol, mm. 17-20 ... 24

Example 12: Sous le Sol, mm. 57-59 ... 25

Example 13: Sous le Sol, mm. 78-80 ... 26

Example 14: Sous le Sol, mm. 96-98 ... 27

Example 15: Sous le Sol, mm. 114-116 ... 28

Example 16: Sous le Sol, mm. 120-122 ... 28

Example 17: Sous le Sol, mm. 130-132 ... 29

Example 18: Sous le Sol, mm. 141-143 ... 30

Example 19: Sous le Sol, mm. 156-158 ... 31

Example 20: Sous le Sol, mm. 165-167 ... 31

Example 21: Sous le Sol, mm. 178-180 ... 32

Example 22: Sous le Sol, mm. 192-194 ... 32

Example 23: Sous le Sol, mm. 232-236 ... 33

Example 24: Sous le Sol, mm. 241-244 ... 34

Example 25: Sous le Sol, mm. 252-253 ... 34

Example 26: Sous le Sol, mm. 263-266 ... 35

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Example 28: Sous le Sol, mm. 286-288 ... 36

Example 29: Sous le Sol, mm. 307-309 ... 37

Example 30: Sous le Sol, mm. 316-320 ... 38

Example 31: Sous le Sol, mm. 331-333 ... 39

Example 32: Sous le Sol, mm. 341-343 ... 39

Example 33: Lumière et Couleurs, mm. 1-8 ... 43

Example 34: Lumière et Couleurs, mm. 43-53 ... 44

Example 35: Lumière et Couleurs, mm. 112-126 ... 46

Example 36: Lumière et Couleurs, mm. 163-167 ... 47

Example 37: Lumière et Couleurs, mm. 197-205 ... 49

Example 38: Lumière et Couleurs, mm. 265-271 ... 50

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ACKNOWLEDGEMENTS

“No man is an island”, so I cannot complete this huge compilation without identifying and thanking a few of the people who, in different ways, helped me structure and build my own ‘island’. I would like to thank Professor Éric Morin, for the safe space he created to be criticized constructively, and my research director, Professor Aaron-Liu Rosenbaum, for the knowledge, support, and

countless hours he put into tweaking the little things and making sure this thesis is the best it could be. I’d also like to thank my mother, who despite being tone deaf (she gave me permission to reveal this) listened to chapters 1 and 2 and for her encouragement and input as a non-musical editor, and Liana, for her unwavering support!

And lastly, I’d like to thank God, for if He wasn’t a God who loves, directs and sustains, none of this would be possible!!

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INTRODUCTION

My Training as a Musician and Composer

As a young classical musician who has spent most of his life around a piano, and as a composer who has been in academia around the same time, I have had the pleasure of encountering many subgenres of classical music. From the Gregorian chant of the medieval era, to the rubato period of the Romantic era and the various forms of experimentation that took us through the 20th century, there have been many pieces and works from subgenres that pique my interest. Each new subgenre has opened the path for another method of perceiving and listening to music. For example, Debussy’s music was revolutionary for classical music during his time, as he resisted the usual Academy trends of traditional harmony for parallel extended chords (such as 9ths and 11ths) and unprepared modulations, in an attempt to “do something different”.1 He succeeded, and those two treatments of the elements in his music have now become standard harmonies in today’s music. During my own growth as a composer, I admittedly didn’t write a lot of music using extended chords in the same way Debussy did, but I have always admired his spirit as an artist who wished to take the definition of music in another harmonic direction.

Another similar example is the work of Schoenberg, who purposefully sought to expand the expressive capabilities of music through experimentations of free atonality and the invention of the

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twelve-tone system for which he is famously credited. 2 In seeking a method that had no basis in the hierarchal system of tonality and assigning all twelve pitches of the musical scale equal importance, the end result is not only a new tool with which to write music, but a musical output that sounds very far-removed from the tradition of his predecessors, say Beethoven and Chopin. While I don’t seek to deny the connections and inspirations of the composers of the past in my works, Schoenberg’s experimentations in free atonality have pushed me to think of my own music in terms outside of tonality; the third movement of his Five Pieces for Orchestra comes to mind in this regard,3 where the harmonies are secondary to the changes in timbre, both moving very subtly as the movement builds. These innovations of Debussy, Schoenberg, and others have repeatedly proven that music, like any other language, is a living and growing entity.

Artistic Inspirations

Of the many subgenres of classical music that exist, to date the one that has touched me the most deeply is minimalism. It does not matter how many times I listen to works within this subgenre, there always seems to be something new to be gleaned, both intellectually and emotionally. Whether the hypnotic qualities of minimalist music reside in the rhythmic drive of Philip Glass, the textural complexity of Steve Reich or in the harmonic purity of Arvo Pärt, there is one thing all three styles of music have in common: the interplay between stasis and motion, leaning heavily on the side of

2 Woodard, Craig Healey. Stasis in Music and the Formation of Musical States and A Portrait of an Infant

(Coming into Being). New Brunswick, New Jersey. 2012. 15-16.

3Berlin Philharmonic. Fünf Orchesterstücke, Op. 16 - III: Farben. Cond. Sir Simon Rattle. Comp. Arnold

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stasis. The second movement of Arvo Pärt’s Tabula Rasa, for two violins, prepared piano, and chamber orchestra is a quintessential example of this.4 Every single instrument is either playing a D minor scale or outlining a D minor chord, at various rhythmic speeds. This aspect of counterpoint did not seem apparent to me upon first listen, but after listening to it repeatedly, it is now one of my personal favourite examples to cite of music that mostly appears static, but interplays with motion.

Thesis Objectives

It is my contention that, while the terms of stasis and motion are rarely used explicitly as means of analyzing and composing music, the usage of these terms grants access to a new way of appreciating music. To support this contention, I will be defining what stasis and motion mean from a more popular standpoint, then putting that definition into a historical context and alongside the viewpoints of musicians. Recent historical examples are provided to illustrate how stasis and motion played a role in the previous works as well as in the three compositions created for this thesis.

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CHAPTER 1

1.1 - Definitions, Ideas, and Philosophy

When it comes to the description and analysis of music, the terms generally used: “rhythm, melody, harmony, timbre, and texture,”5 can be grouped together as the basic elements of music. Focusing exclusively on these elements of music, however, discounts the many ways each element can be divided, defined, and analyzed. As the American philosopher Eric Hoffer notes, “It is the stretched soul that makes music, and souls are stretched by the pull of opposites [emphasis mine] - opposite bents, tastes, yearnings, loyalties”.6 We can take the element of rhythm, for example, and divide it into opposites such as slow or fast, strict or free, etc. Melody, while not being a central focus for the purpose of my compositions, can be viewed as the conjunct-disjunct opposite pair, among other things. Timbre, as defined by the Merriam-Webster dictionary, is “the quality given to a sound by its overtones, such as […] the quality of tone distinctive of a particular singing voice or musical instrument”.7 For the purposes of this thesis, the definition of timbre will be expanded to include the quality of tone distinctive of particular combinations of musical instruments. These combinations can include brassy vs. reedy in reference to the musical instrument families, or more general words such as smooth vs. sharp. Harmony can be divided into consonant or dissonant and from this division comes the idea of another pair of opposing elements: stasis and motion.

5Schmidt-Jones, Catherine. The Basic Elements of Music. Houston, Texas: Connexions. 2008. 1.

6 ETNI - English Teacher's Network. 1997. Music Quotes. Accessed 2017.

http://www.etni.org/quotes/music.htm.

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Stasis is defined as “the state of equilibrium or inactivity caused by opposing equal forces”.8 In a musical context, one way of interpreting this is to divide musical elements into two main

categories: active or inactive. For example, one can take a rhythmic figure and continually repeat it over a long period of time, as Steve Reich does in both his Music for Mallet Instruments, Voices and Organ9 and Eight Lines (Octet).10 The repetitions can be seen as inactive, as they are unchanging

over a long period of time. To insert active elements into the music, the composer either changes the metre or reduces the texture, among other options. As Tom Johnson wrote of a concert of minimalist music in The Minimal Slow-Motion Approach, “[The minimalist pieces of music] all work on a static dynamic plane [...] if you can flow with [the music], and stop wanting something dramatic to happen, it can be extremely rich”.11 Through this richness that may come with stasis, we can also come to better appreciate the qualities that encompass its opposite: motion.

According to the Merriam-Webster dictionary, motion can be defined as either a “melodic change of pitch”, with respect to music, or “an active or functioning state or condition”. 12 The idea that the perceived motion we hear in music is an aural illusion is a position that Max Wertheimer posits, and one with which I only partially agree:

Though a listener may perceive a movement from the first tone to the second, each tone merely begins and ends at its stationary position on the frequency continuum. Recent

8Collins English Dictionary. n.d. Stasis. Vers. 12. Accessed 2017. https://www.thefreedictionary.com/stasis

9 Reich, Steve. Music for Mallet Instruments, Voices and Organ. 1973. Accessed 2018.

10 Reich, Steve. Eight Lines (Octet). 1979. Accessed 2017.

11 Johnson, Tom. The Minimal Slow-Motion Approach: Alvin Lucier and Others. 1972. 4.

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advances in the modeling of apparent-motion effects in vision provide a starting point for the modeling of the strong apparent-motion effects in music13

I see this position holding ground from a scientific perspective, as Robert O Gjerdingen discusses in his article Apparent Motion in Music?14, and I even use the same position as a bit of indirect

inspiration for Brume.15 However, I also believe that when it comes to the perception of motion within music, the definition of motion cannot simply stop at Wertheimer’s aural illusion, as I believe this difference between “real” and “apparent” motion warrants further exploration of the concepts of motion (and stasis) in music.

1.2 - Context in Recent Music History

Before going further, it should be noted that there has been a PhD thesis written by Craig Healey Woodard on the topic of stasis in music.16 However, while Woodard’s focus was strictly on describing stasis, I expand my focus to include motion, and contextualise stasis as a concept to be paired and analyzed in conjunction with motion. Generally speaking, the idea of stasis is explicitly associated with the American school of minimalism of the 1960’s and 1970’s.17 One of the few composers who described his own aesthetic as stasis is Morton Feldman, stating that he was

13 Gjerdingen, Robert O. 1994. "Apparent Motion in Music?" Music Perception: An Interdisciplinary Journal

11 (4): 335-370

14 Gjerdingen, Robert O. 1994. "Apparent Motion in Music?" Music Perception: An Interdisciplinary Journal

11 (4): 335-370

15 This point will be further explained in the analysis of Brume

16 Woodard, Craig Healey. Stasis in Music and the Formation of Musical States and A Portrait of an Infant

(Coming into Being). New Brunswick, New Jersey. 2012.

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“involved in stasis. It’s frozen, at the same time, it’s vibrating”.18 Interestingly enough, both Morton Feldman and the American minimalists position themselves and their music as outside the avant-garde aesthetic being pushed at that time. As Dan Warburton DMA notes:

[T]he minimalists [and Morton Feldman] have shown little interest in wooing this more exclusive market - unlike as was the case with the Darmstadt avant-garde, the emergence of minimal music was not accompanied by a flood of polemical rhetoric - and the academics have accordingly given them little analytical attention19

This initial lack of analytical attention, however, did not deter theorists from applying those concepts or terminology to minimalist music. Indeed, the concept of stasis has been identified in the works of Webern, as the English minimalist composer Michael Nyman notes of La Monte Young’s

observations:

[La Monte Young] noticed Webern’s tendency to repeat pitches at the same octave position throughout a section of a movement, and saw that while on the surface level this was a ‘constant variation’ it could also be heard as ‘stasis, because it uses the same form throughout the length of the piece...the same form over and over again’20

While the use of constant variation is by no means the only form of stasis available as a means of composition, I believe this example to be one of the more straightforward instances in modern music

18 Beaudoin, Paul. 1992. "Morton Feldman's On Time and the Instrumental Factor." American Symphony

Orchestra. December 20. Accessed 2017. http://americansymphony.org/morton-feldmans-on-time-and-the-instrumental-factor/

19 Warburton, Dan. 1988. "A Working Terminology for Minimal Music." Intégral

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history where motion can be heard as stasis. La Monte Young himself takes the history of stasis a step further by referencing the organum works of the Renaissance period:

‘Climax and directionality have been among the most guiding factors [for Western music since the 13th century], whereas music before that time, from the chants, through organum and Machaut, used stasis as a point of structure a little bit more the way Eastern musical systems have. 21

In the context of organum, a particular aspect of stasis comes from having one voice on what’s referred to as a cantus firmus, and the other voice(s) simply moving parallel to the cantus firmus.22

In an interesting example of demonstrating a blend of stasis and motion more recent to the examples above, Australian composer Percy Grainger composed The Immovable Do for an unspecified number of instruments. As he writes:

The Immovable Do (composed 1933-1939) draws its title from one of the two kinds of Tonic Sol-fa notation, one with a “movable Do” (“Do” corresponding to the key-note of whatever key the music is couched in, from moment to moment; so that the note designated by “Do” varies with modulation) and the other with an “immovable Do” (in which “Do” always stands for C). In my composition [The Immovable Do]–which is not based on any folksong or popular tune– the “immovable Do” is a high drone on C which is sounded throughout the whole piece23

21 Nyman, Michael. 1999. Experimental Music: Cage and Beyond. 2nd. 140.

22 “A melodic theme or subject; especially: one for contrapuntal treatment” (Merriam-Webster 2018).

23 Wind Band Literature. 2016. The Immovable Do by Percy Grainger. June 20. Accessed 2017.

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The fact that this piece was composed roughly 30 years ahead of the American minimalist composers is surprising. Although Percy Grainger made no explicit mention of either stasis or motion, his work can still serve as an example of both.

1.3 - From perception to application

Clearly, the concepts of stasis and motion can be applied to the music of past eras.

However, they were not commonly used in the description of compositions. What would it look like to apply them to music in the 21st century? I believe that stasis and motion add extra compositional and analytical perspectives which can expand our understanding of the expressive capabilities of music and enrich the musical listening experience. In the three following compositions: Brume for string quartet, Sous le Sol for woodwind quintet, and Lumière et Couleurs for orchestra, I will apply these concepts in three different ways. Each source of inspiration will be stated at the beginning of the analysis (and occasionally expanded upon later to clarify areas of the analyses) along with an explanation offered on how stasis and/or motion can be applied to the works.

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CHAPTER 2

2.1 - Brume

Brume, written for String Quartet, is heavily inspired by the notion of a fog looming over an urban landscape, as shown in the image below. Part of the nature of fog is that it seeps in and lingers either briefly or for an extended period of time before moving on. This particular piece thus seeks to have the least amount of activity possible (stasis) in a large amount of time. Much like actual fog, the motion in the piece is slow on a macro-level, and each event is marked by a subtle change on the micro-level that grows to be more noticeable as the piece progresses. For the purposes of this analysis, middle C = C4

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11 2.1.1 – Form of Brume Table 1 Form of Brume Section (stasis) A Subsection (motion) 1 2 3 4 5 6 7 8 Duration (motion) 1’ (mm. 1 – 10) 1’ (mm. 11 – 20) (mm. 21 1’ – 30) 1’ (mm. 31 – 40) 1’30” (mm. 41 – 55) (mm. 56 – 71) 1’30” (mm. 72 – 2’ 90) 3’30” (mm. 91 – end) Tempo (stasis) Slow (q = 40) Texture/Pitch (motion)

A5 E5 E5 and A4 A4 and D4 A4 and D4 A4, D4, G3 D4, G3, C3

Short interjections on A5, A4 Short interjections on A4, D4 Interjections on A4, D4, G3 Long Interjections on E5, A4, D4, G3 Long interjections on E5, A4, D4, G3 Long and short interjections on A4, D4, G3 Long interjections on A3, D3, G2, C2 Dynamic Ranges (motion) pp(p) < pp pp < p p < mp mp < mf mf < f f < ff ff < fff (forte possible) Rhythm (motion) Unmeasured (tremolo) 32 nd notes > 16th septuplets 16th septuplets > 16th sextuplets > 16th quintuplets 16th quintuplets > 16th notes 16th notes > 8th note triplets 8 th note triplets > 8th notes Quarter note triplets > Quarter notes > Half note triplets > Half notes > Whole notes

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Brume can be considered one continuous movement, split into eight smaller subsections:  mm. 1-10  mm. 11-20  mm. 21-30  mm. 31-40  mm. 41-55  mm. 56-71  mm. 72-90  mm. 91-end.

The goal of this piece is to show stasis by creating a sound environment starting with as little melodic material as possible and gradually expanding it over time. All of the pitches used in this piece (with the exception of the natural harmonics) are produced from open strings.

2.1.2 – Structural Analysis of Brume

Brume debuts with a single unmeasured tremolo drone on A5, at an extreme pianissimo level and sul tasto. The drone element is static in the sense that the drone itself is continuously heard, despite the slight modifications made to it as the piece develops. The entire first subsection stays this way, with long sul ponticello punctuations on A4 from the cello, pizzicato punctuations on A5 from the viola, and arco 16th notes in the first violin (when the second violin is playing the drone) (Example 1). This is to set the tone of a static atmosphere starting from the most minimal of “melodic material”.

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Example 1 - Drone passing, with pizzicato punctuations (mm. 1-5)

The drone starts to slow down rhythmically at m. 11, after about a minute of very little activity, changing from A5 to E5 in the first violin playing 32nd notes, marking the start of the second

subsection. There are the occasional pizzicato punctuations on E5 (second violin), A5 (viola), and A4 (cello), while the E5 “drone” is passed from first to second violin (m. 15), also slowing down from 32nd notes to 16th septuplets (Example 2).

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Example 2 - Addition of new pitch, drone slow down (mm. 19-20)

The next set of pizzicato interactions is the viola and cello together, starting with A4 and expanding to include the D4 underneath. At the same time in m. 19, not only does the first violin pick up the drone from the second violin, but the E5 drone slows down to 16th septuplets and starts the third small subsection by expanding to include a perfect fifth underneath in the viola, also playing 16th

septuplets. At m.23, the cello is the one doing the pizzicato punctuation on A4, D4, and eventually G3 (Example 3). Note as well that the drone is simultaneously slowing down rhythmically to 16th sextuplets in the first violin.

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Example 3 - Addition of G, out-of-sync perfect fifth alternation in second violin (mm. 23-24)

In the same measure, the second violin alternates between A4 and E5, the same notes as the drone of the first violin and viola, but on rhythmic values that grow unsynchronized, giving the impression of more motion. The A4 then gets passed from the viola to the second violin, and later by the cello in a similar out-of-sync manner to the second violin above (Example 4). Eventually, the drone slows down to 16th quintuplets and starts to adopt the alternating aspect of the second violin and continues into the next subsection, introduced by pizzicato punctuations from the viola and cello (Example 5).

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Example 5 - Alternating perfect fifth drone (mm. 31-33)

The out-of-sync rhythms in the piece make a return in the viola in m. 35, where they’re spread out for 4 measures. Eventually, the A4 and E5 drones from the previous subsection reduce themselves to just the A4 and start the fifth smaller subsection with a mix between 16th quintuplets and 16th notes (Example 6)

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Example 6 - Drone pitch and rhythmic deceleration (mm. 40-41)

The fifth subsection (mm. 41 – 55) starts with the A4 from the previous subsection being doubled by the violins, but eventually one of them drops out, and in its place the viola plays the D4 underneath in 16th quintuplets, to contrast with the A4 16th notes. The cello does a couple pizzicato punctuations on A4 for timbral contrast, but the real marked difference is the introduction of sustained punctuations from the first violin in m. 46. These more elongated punctuations are seen as both static and in motion; static, as a result of its duration being longer than the previous iterations, and yet, in motion as their dynamic level changes. As the subsection carries on, the drone starts to alternate, but eventually the sustained punctuations do too, between the first violin and cello (Example 7), signifying the landscape being slowly overtaken by the fog and adopting its qualities.

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Example 7 - The drone is exchanging pitches, with more sustained punctuations (mm. 53-56)

Even though the drone stops alternating pitches at measure 55, the viola is still directing it in the process of slowing down to 8th note triplets. As well, from m. 66, the punctuations are much more prolonged than they were before, and the alternations yield new harmonic voicings (Example 8).

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The drone reduces itself in pitch to just a D4 by m. 76, and the viola is reduced rhythmically to regular 8th notes in m. 79. In that same measure, the long punctuations come back in the first violin, but are followed by a pizzicato cello pluck in m. 82 (Example 9), which repeats until the end of that

subsection, representing the little bits of the landscape that can still be seen through the fog. Example 9 - Reduced drone, long punctuations, and short punctuations (mm. 79-83)

At this juncture, as the violin and cello go through their final set of long whole-note and pizzicato punctuations, the drones in the second violin and viola starts to alternate between D4 and G3. To start the final subsection of the piece, the first violin comes in on the same notes as the drone, but in quarter-note triplets as opposed to 8th notes, signalling another rhythmic deceleration. The cello takes the whole-note punctuations from the first violin in the previous subsections and displaces them by a couple of beats, but slowly approaches the first beat of every measure, with the final punctuation point introducing C3 for the first time in the piece (Example 10).

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Example 10 - Cello approaching first beat with whole notes. First appearance of C3 (mm. 96-102)

The drone continues to slow down rhythmically, passing from quarter notes, to half-note triplets, to half notes, and eventually, whole notes at the end (refer to mm. 120 – end in Annex 1). The cello introduces the final note, C2, only a few measures from the end. The last sonority is a chord comprised of almost all of the notes used in the piece, depicting the total encapsulation of the cityscape by the fog.

As detailed in the analysis above, Brume displays little motion via the punctuations and the slow changes in the drone within the span of approximately 13 minutes. Ultimately, the piece can be seen as primarily static, with gradual changes in motion.

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2.2 - Sous le Sol

My second piece, Sous le Sol, is composed for wind quintet (Flute, Oboe, Clarinet, French horn, and Bassoon). For this piece, in contrast to Brume, I have created a sense of stasis starting from a place of intense motion. The piece is built around an ostinato and is occasionally interrupted and phased out by different musical ideas. Sous le Sol, as the name implies, draws inspiration from the concept of soil, which may seem motionless in matter on the surface, but, in effect, pulses underneath, growing and nourishing a variety of plant and animal life. One needs only to till and closely examine a section of soil to see inactivity and activity. This composition seeks to portray the activity that can exist amidst apparent inactivity (stasis) and, in doing so, creates interplay between these opposites that is definitely alive.

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2.2.1 – Form for Sous le Sol

Table 2

Form for Sous le Sol

Section (motion) A B C A’

Tempo (motion > stasis) e.= 156 q = 120 q . = 78 h = 60 Subsection (motion > stasis) 1 2 3 4 5 Duration (motion > stasis) 1’ 2’ 2’ 2’30” 3’ Time Signature (motion > stasis) 12/16 3/4 6/8 3/2 Rhythmic Pulse Division (stasis > motion)

4 4-against-3 3 3-against-2 2 Augmented

3-against-regular 2 4-against-3-against-2

Texture (stasis > motion) Monophony /Heterophony (ostinato only) Polyphony (4 ostinato voices, 1 “sprout”) Polyphony (2-4 ostinato voices, 1-2 “sprouts”) Polyphony (1-2 ostinato voices, 3 “sprouts”) Polyphony (4 to 5 “sprouts”) Pitch Range: Sprouts (stasis > motion)

Low Low to Mid-Low Low to Mid-High Low to High Pitch Range:

Ostinato (stasis > motion)

Low to Mid-High Low to

Mid-High Mostly High Low to High

Articulation (motion > stasis)

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2.2.2 - Structural analysis of Sous le Sol

Sous le Sol, written for woodwind quintet, explores motion through the shifting of agogic accents, tempo changes, key signature changes, and time signature changes as a metaphor for the activity in the soil, in contrast with the stasis of the soil itself, represented by a rhythmically

unchanging ostinato. The piece itself is divided into four main sections:  mm. 1 – 130

 mm. 131 – 217  mm. 218 – 301  mm. 302 – end.

2.2.2.1 – First Section – 12/16, F Major, mm. 1 – 130

Section one starts out in 12/16 with the bassoon and French horn trading one note of the soon to be established ostinato, back and forth. The ostinato is marked by the addition of the clarinet,

contributing the second and third notes to the ostinato as well as building up the general texture of the piece (Example 11). The oboe and, later, the flute, join the ostinato one and two octaves higher, respectively. Everything at this point is staccato, to start the gradual articulation of stasis.

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Example 11 - Building up the ostinato (mm. 17-20)

Eventually, all of the voices grow in gradual crescendo before the clarinet introduces the first “seed” being planted in the soil in m. 56. Significantly, I use the pitch G to represent the seed being planted, because in French, the word “soil” translates to “Sol” – the same as the solfège syllable. The long notes at the end of the interjection represent the plant slowly trying to push its way out of the soil to grow. As well, each attempt that the plant makes to break through the soil is placed on an off-beat displaying the interaction between the moving (plant) and the static (soil) (Example 12).

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Example 12 - The first “plant” in the clarinet (mm. 57-59)

Eventually, the clarinet finishes “blooming” and rejoins the static material, and it is the bassoon that takes up the motion, expanding on it by adding another pitch, in a way not too dissimilar to how the soil was musically depicted. The effect here is that the plants and soil are both elements from nature, and musically, I wanted to show their similarity while still noting subtle, yet noticeable, differences. The orchestration is eventually reduced to just the low end in the clarinet and French horn, yet it maintains the same life-giving energy it has had throughout (Example 13).

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Example 13 - The bassoon as a blooming plant, soil ostinato reduced to low frequencies (mm. 78-80)

At m. 91, the clarinet inserts more motion and effectively begins a cycle of uninterrupted motion starting at m. 95. At the same time, the flute and oboe start outlining a rhythmic pattern in 3/4 time, though still working within the confines of 12/16 (Example 14). The bassoon, after a while, ceases to play staccato, but isn’t necessarily playing legato. From this point, the piece is gradually moving from a clear delineation of stasis and motion, to an intermediary stage, where aspects of both are

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Example 14 - Blooming clarinet, shifting rhythmic accents in soil (mm. 96-98)

The clarinet moves again, being joined by the French horn at the unison, adding grace notes and trills (Example 15). Eventually, the bassoon drops out temporarily, leaving the flute and oboe to subtly enforce the triple feel that’s soon to come in the next section, with the oboe dropping the staccato articulation. The French horn goes back into the soil, in counterpoint with the bassoon. The clarinet repeats a bloom cycle and is soon joined by the flute at the octave (Example 16). Note that this particular plant motif is almost entirely constructed in intervals of a second that grow larger, akin to the growth of a plant. The section ends with each instrument building up to a crescendo in

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Example 15 - Clarinet and French horn “bloom” (mm. 114-116)

Example 16 - Flute joins the clarinet in becoming a part of this plant’s growth (mm. 120-122)

2.2.2.2 – Second Section – 3/4, G Major, mm. 131 – 217

At this point, to convey the fact that plants do not grow at a consistent pace, the section changes to 3/4 time, but the soil ostinato still continues. The flute and oboe are now playing the soil motif in rhythmic groups according to the time signature, but it is the other instruments that remain on the 12/16 accentuation from the previous section (Example 17).

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Example 17 - Same soil motif, different rhythmic accent (mm. 130-132)

The key change in m. 137 has the soil itself modulating in terms of key, but its rhythmic figures and phrasing are unchanged. The soil motif appears in the old key by the bassoon, but “blooms” in the new key. To maintain a balance between motion and stasis in the piece, I not only decided to prolong the plant motif, but I also increased the interval around which it is structured (a third, as opposed to a second). As this is happening, the French horn prepares the land to welcome another plant, though it gets interrupted by the regularity of the ostinato (Example 18)

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Example 18 - New key, larger plant (mm. 141-143)

The “blooming” material is in the bassoon once again, meeting the French horn at the octave, grace notes included. The end of the French horn’s motif marks the appearance of the oboe which is preparing the soil, and later joins the bassoon two octaves above, although the grace notes in this case are not synchronized (Example 19). Note that even though the French horn does return to the soil, the rhythmic pattern it uses to outline the soil is slightly modified, though it keeps the energetic nature. The plant itself, as it blooms, begins to adopt more “natural” qualities by slowly adding rhythms and accentuations that would be considered irregular in the context of the time signature in that section, as shown in the bassoon and flute (Example 20).

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Example 19 - Bassoon and Oboe, differently placed grace notes (mm. 156-158)

Example 20 - Bassoon and Flute - irregular rhythms (mm. 165-167)

Gradually, the flute and oboe make their way back into the soil, and the French horn prepares the soil once again to start to bloom. The rhythms add more motion as the motif develops. The bassoon is

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also in bloom, but actually takes the motif of the plant from the first section and uses it almost like a cantus firmus beneath the other instruments (Example 21). Eventually, the flute and oboe follow suit, with the flute taking the role of cantus firmus and the oboe becoming the blooming plant (Example 22).

Example 21 - Horn blooms, while Bassoon serves as cantus firmus (mm. 178-180)

Example 22 - Flute as cantus firmus above “blooming” oboe (mm. 192-194)

Measure 204 introduces the last blooming cycle in this section. There, I intersperse both plant motifs from the current and previous sections, but rather than just combine them, I make them compete with each other a bit before ending the section on a large crescendo with trills in the low instruments while the high winds continue with the soil motif into the next section (refer to mm 215-218 in Annex 2), representing a brief period of simultaneous stasis and motion. The intent here is to create a more powerful result than if only one of the two elements were used.

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2.2.2.3 - Third Section – 6/8, A (minor), mm. 218 – 301

This third section has the flute and oboe representing soil. Occasionally, the soil is interrupted by tremolos in the plant voices, representing various weeds that can sprout from seemingly out of nowhere. The weeds, represented by dissonant tremolos, end up overtaking the soil, to the point where the soil is reduced to only one voice. There are still plants that do their best to bloom, and the interval of the blooming motif is increased to a fourth, but every instance is interrupted by one or many weeds taking their places as shown in m. 232 (Example 23).

Example 23 - Plants trying to grow, too many weeds (mm. 232-236)

At m. 241, the clarinet takes over the role of the soil from the oboe, but since there are weeds popping up on occasion in the clarinet and bassoon, it starts to adopt some of the accidentals from the weeds. This is the contamination of the musical material, shifting again into The oboe tries to sprout up as a plant on the interval of a perfect fourth, but eventually the weeds infect it, expanding it to a tritone, in both augmented fourth and diminished fifth form, expressing nature’s variety (Example 24). The flute later attempts to bloom as a plant and is successful, but the more complex rhythms represent the struggle to do so (Example 25). The tremolos, representing the weeds, are expanding.

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Example 24 - Plant expanding to include the tritone (mm. 241-244)

Example 25 - Flute successful in blooming against growing weeds (mm. 252-253)

Despite the weeds, at least one plant will creatively try and find a way to bloom. At measure 261, the oboe and French horn attempt to slowly bloom as a plant, although the soil infected by weeds (tritone) causes this plant to bloom without the proper nutrients of the soil (Example 26). There are

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various references to the bloom motif in the clarinet, horn, and bassoon after that, but all of them are infected by weeds, represented by the tritone intervals (Example 27).

Example 26 - Horn finds a creative way to bloom (mm. 263-266)

Example 27 - Tritone plants (mm. 274-277)

At m. 280, the oboe foreshadows the next section by accentuating the 3/2 pattern in the context of the 6/8 section, though both of these patterns are passed around the high woodwinds. The weeds are still persisting in their tremolos, but they slow down to regular 16th notes, and eventually, 8th notes and quarter notes (Example 28). The horn and bassoon try one last time to “bloom” together as one plant, and while they manage to bloom past all of the weeds, the descending tritone represents their

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struggle to survive. This interplay between weeds and soil grows and grows via a crescendo right into the final section of the piece (refer to mm. 297-300 in Annex 2).

Example 28 - The soil returns with different rhythmic accentuation (mm. 286-288)

2.2.2.4 - Final Section – 3/2, F major, mm. 302 – end

The final section of Sous le Sol has the soil ostinato repeating in the key of F major, but the transition from the previous section hides the key change through the tremolos (refer to mm. 302-303). When the tremolos start to slow down, the soil does so as well, not only by reducing its texture to two voices, but also having one of the voices slow down to 4:3 quarter notes, as opposed to implied 12 eighth notes. The soil motif returns in the clarinet, horn, and bassoon, but at different octaves, and it takes a while before the plants bloom (Example 29).

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Example 29 - Longer preparation of the soil; plants yet to come (mm. 307-309)

Eventually, the soil gets temporarily reduced texturally and rhythmically to a homophonic texture and gets passed around in all instruments. Rhythmically, I decide to reduce the original soil motif from the first section down to irregular quarter notes against the implied quarter note pulse, to represent that the soil has adapted to the new environment, but it is still made of the same components from the first section. The flute gets ready to be planted by not only playing its “preparatory” note (G) in its high range, but also to extend the motif by trilling. Soon after, all of the voices representing plants end up trilling their notes (Example 30). Here is yet another musical portrayal of contrasting concepts – nature seeming still even while she is preparing herself to reproduce.

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Example 30 - Flute and Horn are trilling to prepare more soil; Soil has become 4:3 quarter notes (mm. 316-320)

These new plants then start to take form at m. 325, with the horn and the clarinet stating the same plant motif as in the beginning of the piece, (see Example 15) but the clarinet plays the motif in a disjunct manner from the horn, both melodically and rhythmically (refer to mm 323-325 in Annex 2). In addition, rather than having the plants stay in the same instrument for the entire section, I

transform the motif by transposing certain parts of it to other instruments, changing and expanding on the rhythms or even, in the case of the bassoon, turning it into a cantus firmus (Example 31). The dovetailing of instruments could be interpreted as another type of motion, in contrast with the rhythmic consistency of the plant motif in the same instrument.

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Example 31 - Bassoon as plant motif cantus firmus, while other plants are blooming (mm. 331-333)

At this point, the soil rhythmically starts to adopt some of the qualities of the plants, by adding a voice in regular quarter notes against the 4:3 already previously established. On top of that, the voice also starts to gradually ascend and descend in pitch material as it is being passed around the ensemble, though it keeps its general shape (Example 32). The plants seem to have fully bloomed, represented by the various trills, but eventually, as in their cycle in nature when plants die, their musical presence is reduced to nothing but the richness of the soil.

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At m. 349, the last semblance of a plant appears in the French horn, via repeated dotted quarter notes, surrounded by nothing but soil. Eventually, the clarinet takes over the dotted quarter notes, and the soil starts to slow down, gradually going from quarter notes to a dotted whole note, depending on the instrument. Everyone is in constant crescendo and trills with some dovetailing going on between the bassoon and the French horn until the last two measures, with accentuated quarter note punctuations and long note trills until the end, except for the bassoon (refer to mm. 359 – end in Annex 2). At the end of the process, there may have been lots of beautiful plants that sprouted up in nature, but it is the soil that gives the plants nutrients to grow.

2.3 - Lumière et Couleurs

My third piece, Lumière et Couleurs, is for orchestra. This piece takes inspiration from Newton’s theory on the nature of light and colour, which suggests that (white) light as an entity is actually composed of a spectrum of colours. The original experiment had a source of white light being shone through a prism and diffusing to produce the entire colour spectrum. If another prism is placed after the colour spectrum, the colours revert back to their original form of light. This

experiment can be understood in five stages: 1 - The presentation of light, 2 – Light diffracting in a prism, 3 – The resulting colour spectrum, 4 – Colours collecting in another prism, and 5 – The return to the original light source. Formally, this translates to the piece having three overarching sections: the original light source, the light in the process of diffusion or collection, and the colour spectrum in its entirety. The Fibonacci sequence is integral to the compositional process of this work, as it is the generative process from which all forms of stasis and motion are derived.

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2.3.1. – Form for Lumière et Couleurs

Table 3

Form for Lumière et Couleurs Section (movement > stasis) A B C C’/B’ A’ Duration (movement > stasis > movement) 1’30” 2’30” 3’ 2’ 1’30” Tempo (stasis >

movement > stasis) Larghetto q = 53 - 56

Accel to... Vivace

q = 149 - 155 Rit to... Larghetto q = 53 - 56

Light Discourse White light Diffusion of white light to the prism colours

All colours of the spectrum Diffraction of all

colours back to white light

White light

Rhythm/Orchestration (movement)

Sparse > Dense Sparse > Dense Dense > Sparse >

Dense Dense > Sparse

Pitch/Harmony (stasis > movement > stasis)

C Dissonances,

non-traditional pitch classes

Arpeggio Colours (see below) Colours mixed with

dissonances Colour chords against C drone

Harmonic Texture (stasis > movement >

stasis)

One note > dyads

(including octaves) Dyads > Clusters 1 triad 1 triad 2 triads 3 triads 5 triads Triads > clusters 5 notes, with triads (bitonality) > One note (including octaves)

Timbre (movement) Separate > Blended Separate Separate Blended

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2.3.1.1 - Colours/Harmony

These are the chosen associations for the harmonies depicted in the third section of the piece. Note that all harmonic implications centred around pitch class C are what represent white light, as musically it is the only key center without a single accidental. Any accidentals can be seen as a new “colour”.

Table 4

The Colour-Harmony Table for Lumière et Couleurs

Colour Harmony

White light C (major)

Red F# minor Red-Orange D major Orange G minor Orange-Yellow E minor Yellow A minor Yellow-Green G major Green A major Blue-Green D minor Blue Bb major Blue-Violet Ab major Violet Db major Red-Violet Gb major White C (major)

2.3.1.2 - Rhythmic Repetitions Table

Table 5 below represents the construction process of each rhythmic cycle, as directed by the Fibonacci sequence. Each rhythmic cycle and the following repetitions are defined by the note value it starts on.

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The Rhythmic Repetitions Table for Lumière et Couleurs

Number of rhythmic repetitions 1 1 2 3 5 8 13 Number of measures of rest between repetitions 0 0 1 1 2 3 2

2.3.2 - Structural analysis of Lumière et Couleurs

Written for orchestra, Lumière et Couleurs was created to explore the impact a generative compositional process can have on the appearance of stasis and motion. I decided to use the Fibonacci sequence as the formula for generating and managing all of the elements of music, as the ever-increasing resulting mathematical sums of the process suggest a form of motion. Since the Fibonacci sequence goes on ad infinitum, I only use the following numbers in the sequence as the basis for the vast majority of the material: (0,) 1, 1, 2, 3, 5, 8, and 13. The numbers used in lesser capacity are 21, 34, 55, 89 and 144, as attempts at using them on the micro-level of the piece proved to render the piece too long, in my estimation. The piece is divided into three sections overall:

 mm. 1 – 84

 mm. 85 – 323 (which is itself divided into 5 subsections, each based on a set of colours in the colour wheel)

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2.3.2.1 – First Section – MM. 1 – 84: White Light (stasis) and its Diffusion (stasis > movement)

Lumière et Couleurs begins with the bass drum starting a rhythmic cycle based on the Fibonacci sequence in quarter notes, joined a bar later in rhythmic canon by the triangle in half notes (Example 33). To mark the first appearance of the light, the violas and 2nd violins entering on pizzicato middle C’s in eighth notes, with the viola articulating a new cycle using arco dotted half notes (refer to mm. 1-9 in Annex 3). The clarinets also join in to add a new timbre to the pizzicato string cycle but still keep the sparse texture, while the contrabasses come in on a C two octaves below. This change in orchestrations, notably the violas and contrabasses, represents the expansion of the light spectrum. At measure 14, the flutes and oboe add another octave, this time, above, in order to expand the spectrum further. The stasis is represented in this section by the use of a single pitch class, C, until the light begins to diffract.

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To represent the process of diffusion, not only does the tempo slowly accelerate, but the instruments depart from the initial C by chromatic motion, forming combinations of dyads that gradually begin to exclude the initial light source (pitch C). This is the tipping point for the motion in this section, representing the change from light to colours. For example, the clarinets diffract away from the C by two semitones in measure 26, joined by the bassoons two measures later, forming a major third between the pairs of voices (refer to mm 33-37 in Annex 3). The brass instruments (except the tuba) expand the light to an augmented 5th, trading entries between the original pitch of C in the trumpets. The end of the diffusion is signalled initially in the French horns and then finally in a combination of all brass (Example 34). The diffusion process comes to a gradual end when the whole orchestra is holding the interval they diffracted to (a large tutti F# minor chord), while crescendoing and accelerating into the next section.

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2.3.2.2 – Second Section - MM. 86 – 324: The Colour Spectrum (movement) and its Dispersion (movement > stasis)

As noted above, the subsections in this piece are tied to both a number in the Fibonacci sequence and a specific chord progression and further tied to a colour for symbolic representation. Even though the colours that are derived from pure light are based on a subtractive system, I opted to use the colours that would be produced in an additive colour system, as the Fibonacci sequence itself is additive mathematically. The section as a whole is focused on motion, as indicated by the faster tempo.

“1” - Red (F# minor)

This sub-section focuses on the aspect of 1, with red being the first colour depicted in the additive colour system. As such, each rhythmic cycle begins with one repetition, and this cycle begins with the timpani playing on a Fibonacci cycle of what appears to be eighth notes on F#, which is in sharp contrast with the white light pitch class C. In actuality, the cycle is at the half note level. The bassoons enter on whole notes, although these appear as tied half notes because of the meter, while the clarinets enter in quarter notes (refer to mm 108-116 in Annex 3). The cellos spell out the full F# minor arpeggio in eighth-note triplets, while the violins play the same arpeggio an octave higher at the eight-note level (Example 35). This sequence continues, until the contrabass starts a series of successive entries at measure 113, on a reverse cycle of the Fibonacci sequence; that is, starting with rhythmic groups of 13 and working back towards 1, with the instruments that participated in this colour coming in at points in relation to the sequence.

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Example 35 - Strings with rhythmic counterpoint (mm. 112-126)

“1” – Red-Orange (D major)

I decided to change the colour to red-orange for this sub section, because, according to the Fibonacci sequence, even though the number “1” is repeated, it is considered a new integer sequentially. Musically, this is expressed through the fact that every rhythm is linked to only one instrument family, even if there is a mix of timbres within said family. The motion in this subsection is a subtle one, shifting from the “stasis” created in the separation of instruments in the last subsection, to timbres in motion, creating different colour combinations. In m. 86, the contrabass begins on a rhythmic cycle of quarter notes, the glockenspiel and vibraphone starting a cycle of half notes, with the trumpets entering a bar later on half notes that evolve into whole notes. The trombones start their cycle on quarter note triplets five measures after the beginning of the section (refer to mm.133-142 in Annex 3). The violins start their cycle of eighth-note triplets eight measures after the start of the section, while the clarinets being their eighth note cycles thirteen measures after the start of the section. As in the previous section, the contrabass counts back from thirteen to start their successive entries, spelling out the whole chord.

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“2” – Orange (G minor) and Orange-Yellow (E minor)

In this subsection, in order to focus on the next term in the Fibonacci sequence, 2, every rhythmic cycle starts with two repetitions, as opposed to just one. Also, this subsection is based around two chords (G minor and E minor), and by extension two colours, as opposed to just one. The motion is starting to grow more pronounced in the orchestration, as the texture becomes increasing polyphonic at the start of each subsection. The French horns take the lead by outlining both the G minor and E minor chords, but eventually this figure gets divided between the trumpets and trombones (refer to mm. 163-178 in Annex 3). The flutes and keyboard instruments follow the French horns by starting a whole note cycle in the third measure, while the oboe and first clarinet alternate on an eighth note triplet cycle (Example 36). The eighth-note cycle is given to the viola, second violins, and trumpets, while the tuba is alternating the bass notes of each chord. For these successive entries at the end of the subsection, the violas and celli are the ones that hold the pitch G into it, as G is the common note between G minor and E minor, and the last two measures before the change in harmony restate the chord progression in full.

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“3” – Yellow (A minor), Yellow-Green (G major), and Green (A major)

The number “3” is the key in this subsection: three chords, three colours, three repetitions. In order to increase the rhythmic density and the general feeling of motion, the violins and cellos are given a rhythmic cycle on 16th notes, but instead of having them play the notes altogether, I divide the figure between them, with the cello emphasizing the first note of each group. I felt the division of the figure was necessary to keep the gesture’s intended motion feel intact as it progressed through its rhythmic cycle without tiring out the performers. The violas pick up two measures later on an eighth note cycle, outlining the arpeggios of each chord as the progression moves, joined by the vibraphone (Example 37) and, much later, by the French horns. The quarter note triplets are then taken up by the trumpets, joined by the 2nd clarinet on the G major chord, and the oboe on the A major chords. The flutes had previously started quarter note cycles in the second measure, but are joined much later by the glockenspiel, providing motion at the timbral level. At this point, the bassoons start a half note cycle, changing whenever the harmony changes, but are joined by the trombones (refer to mm 213-220 in Annex 3). The successive entries at the end of the section starts by carrying over the G major chord. All of the entries follow the reverse Fibonacci cycle as with the other subsections and finishes with a reiteration of the last two chords, G major and A major, before heading into the next sub-section.

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Example 37 - Strings dovetailing 16th notes (mm. 197-205)

“5” – Blue-Green (D minor), Blue (Bb major), Blue-Violet (Ab major), Violet (Db major), and Red-Violet (Gb major)

In this subsection, the basis of the next number in the Fibonacci sequence, 5, is tied to the number of chords used in the chord progression, and that every rhythmic cycle starts on 5 repetitions. Being the last term in the Fibonacci sequence used for the section as a whole, this is the subsection that provides the most motion. The contrabass provides the bass voice of the chord progression in half notes, later to be joined by the tuba and timpani. The violas and cellos alternate on an eighth note rhythmic cycle, later joined by the glockenspiel. The first violins start a cycle on quarter-note triplets in m. 247, which later gets passed onto the trumpets and oboe. Conversely, the second violins and French horns begin a cycle on quarter notes in m. 249, and then m. 252 starts with a cycle on eighth-note triplets with the vibraphone playing the whole line and the bassoons blending in alternation. The flutes and clarinets start a 16th note cycle in m. 265 (Example 38). The end-of-section cascading entries into the Dispersion process is a bit different in that the rhythmic cycles switch to long, held-over notes in contrast to the changing harmonies in the bass, providing a musical moment with stasis and motion simultaneously. The whole orchestra crescendoes on the final chord

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in either tremolo or flutter-tongued fashion, with the exception of the flutes and clarinets, who continue their 16th note pattern past the climax at measure 291, the climax representing a high point of rhythmic motion. The orchestra then does a large and gradual decrescendo alongside a

deceleration, with the rhythm in the flutes and clarinets slowing down, as well as gradually removing one note at a time from the chord in the progression, focusing it down to a single note (refer to mm 294-301 in Annex 3).

Example 38 - Flute and Clarinet 16th notes; the fastest rhythmic value creating a rhythmic climax of motion (mm. 265-271)

Diffraction – mm. 304 – 324 (movement > stasis)

Finally, the diffraction process is similar to the diffusion process in that the instruments are diverting themselves away from the colours by moving in semitone motions, creating dyads that do not point directly to any of the colours of the previous sections. Rhythmically, all of the cycles repeat themselves in reverse, before going back through the cycle, in a similar method to the diffusion process. As the orchestra is winding down from the previous section, the violin starts the Dispersion

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process on a rhythmic cycle of 16th notes, which the oboe repeats a measure later as a trill, indicating that, even in this process of trying to find stasis, motion can sometimes be an oppositional factor in establishing stasis. The oboe and violin gestures are followed by the trumpets on eighth notes and eighth note triplets, later repeated by the French horns, trombones, and the bassoon, albeit at an interval of a tritone (Example 39). The violas begin to play quarter note triplets and is joined by the first clarinet, with the second clarinet playing regular quarter notes in syncopated counterpoint. Simultaneously, the vibraphone is playing eighth note quintuplets against the viola rhythms, followed a bar later by the second violins. The flutes and glockenspiel add themselves to the mix in quarter notes, doubling the second clarinet, but at an augmented sixth (refer to mm 314-316 in Annex 3). All of these rhythms gradually fill in the space rhythmically while decelerating, culminating into a large crescendo in the 6/4 measure before 325, in which all of the dissonances resolves to the pure stasis of C.

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2.3.2.3 - Third Section: MM. 325 – end – Back to White Light (stasis)

In summary, the large crescendo into the orchestral tutti C’s is the tool that sparks the beginning of this section, fully returning to the pitch stasis that was established in the beginning of the piece. Stasis in dynamics is also achieved in a gradual manner, with all the instruments playing a decrescendo until the end of the piece. The triangle begins to re-establish the qualities of the original white light by playing a fading rhythmic cycle of 13 on quarter notes, followed a bar later by the bass drum and timpani. In the third measure, the first violins, vibraphone, and tubular bells are playing the whole chord progression of the previous section in its entirety (refer to bars 325-332 in Annex 3). While this is happening, the oboe, first bassoon, first trumpet, and first trombone are playing C’s on a rhythmic cycle of dotted quarter notes. At the eighth measure from the start, we have the second bassoon, all of the French horns, the second trumpet, and the second trombone doing a rhythmic cycle on dotted eighth notes, repeating them eight times. All of the rhythmic cycles gradually fade out by finishing at 1, thinning the orchestral texture until the only thing left is the bass drum, which signals tapering stasis as the end of the piece and the refraction of all colour components back into white light (refer to measures 330-end in Annex 3). The flurry of motion of different instruments joining in at different measures and on different notes provides a strong contrast leading to the ending of stasis.

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CONCLUSION

In conclusion, my major goal for this thesis was to expand the expressive capabilities of my music by exploring stasis and motion as effective conceptual tools for both the analysis and

composition of new music. I have attempted to prove my proposition by composing and analyzing three new compositions. For Brume, the music cannot be analyzed using methods of Romantic-era harmony, as the piece itself was not constructed using that kind of harmonic language. Contrast this with Sous le Sol, where the harmonies are explicitly borrowed from that harmonic language but analyzing the piece from that perspective alone neglects the aspects of rhythmic motion offered in the piece. Lumière et Couleurs takes both elements a step further, in order to demonstrate that stasis and motion can also function as simultaneously conflicting elements to the point where the line that delineates them as opposites may not be as clear cut within the same section of a piece. In any case, there is no question that these concepts will serve me well as I continue to compose and study music in the future.

These past three years of research and compositional work put into this study of stasis and motion at the Master’s level have not only allowed me to consider stasis and motion seriously and clinically, but they have also shaped my own personal compositional process in terms of how I now arrange the parameters of a composition. As noted in the introduction, my musical journey has exposed me to numerous ways to use and change the perceptions of the more common elements of music, such as melody, harmony, timbre, rhythm, and texture. As much as those elements

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and vigour that have come with my own “discovery” of stasis and motion as one of the many pairs of opposites within the language of music.

It is worth noting that an added benefit of my years of composition study at the Master’s level is that I learned the importance of thoroughly planning a composition out on paper. This method of planning has certainly been eye-opening, allowing me to simultaneously see multiple possibilities for the direction of a musical idea before committing them to staff paper. I also recognize that my final compositional output has resulted in Brume, Sous le Sol, and Lumière et Couleurs which lean more towards the style of the American minimalists, but despite occasional criticisms of minimalist music as somehow less academic, I do not view this as a negative. On the contrary, I do not believe I would have been able to appreciate, as I now do, the depth of the contribution these composers and their works have brought to “younger” composers such as myself, without having gone through the research and compilation process for this thesis. In fact, the work involved in this thesis has resulted in my being more comfortable listening to, analyzing, and composing one-movement works that expand well beyond the 5-minute point – a former barrier in my work. Finally, I believe it is important to realize that although music is expressed within time, the concept of time does not have to be limited to actual duration; time can be expressed through the use of stasis and motion.

Figure

Figure 1.  Hazy CN Tower, courtesy of (weheart.it 2010)

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