PORTFOLIO OF COMPOSITIONS

PORTFOLIO OF COMPOSITIONS

AN EXPLORATION OF THE MANIPULATION OF MODES

by

HENRY SEVER FLURRY

A thesis submitted to the University of Birmingham for the degree of MASTER OF ARTS IN COMPOSITION

Department of Music School of Humanities College of Arts and Law

University of Birmingham March 2016

University of Birmingham Research Archive

e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.

ABSTRACT

This thesis consists of a portfolio of compositions accompanied by a written

commentary and audio recordings of the works. The commentary discusses each of

the works within the context of how mode is manipulated and treated for neotonal

purposes. Four techniques are presented and illustrated with examples from the

portfolio: the application of added-tone sonorities modelled after the music of Eric

Whitacre; the construction of synthetic modes that conform to the constraints of

Dmitri Tymoczko !’s model of scale networks; the generation and application of

rotational arrays based on a row that is derived from prior material and is a subset

of the octatonic; and the generation of “Russian modes” and derivatives using ideas

inspired by Russian music theorist Boleslav Yavorsky. Particular attention is paid

both to methods of modulation and their musical significance and to the octatonic

implications of the latter two techniques. Each example presented includes detailed

analysis within the context of the applied technique and its relevance to the intended

musical affect.

DEDICATION Thank you, Maria Flurry, for your love, encouragement, and patience. Thank you for your faith in my art. Thank you for inspiring me.

Thank you, Anna and Nathan, for your love, encouragement, and willingness to sacrifice some Dad time this past year.

Thank you, Michael Zev Gordon, for accepting me into your program and for patiently guiding me through my research and growth.

Thank you, Dr. Rinna Saun, for trusting me with a commission for a piano concerto, for your feedback during the composition process, and for your careful preparation for its premiere.

Thank you, Christina Cuda Robertson, for learning, performing, and recording my piano solos. Thank you, Jonathan Best, for the timely birthday gift of a recording session of the piano solos.

Thank you, Dennis Houser and the Prescott Chorale, for learning and performing my choral work. Thank you, Daniel Boyce, for your editing advice on the same work. Thank you, Margaret Houck, for recording the reduction of the choral work.

Thank you, Birmingham Contemporary Music Group, for your reading and commentary on my chamber work.

Thank you to my students for your flexibility in scheduling this past year and for your support of my continued education.

Thank you to my community, Prescott, Arizona, for your support of me as a composer, for the opportunities you provide for public performances of my compositions, and for the local mentors (many already mentioned) I have the pleasure of knowing.

In keeping my acknowledgements confined to this Master’s program, I am aware that I fail to recognize but a fraction of those I might thank. Please know that every day I have the opportunity to invest my heart into music, each of you who has contributed to that opportunity receives a quiet, deeply-felt thank you.

CONTENTS OF PORTFOLIO

Thesis: Portfolio of Compositions

List of Scores:

In the portfolio:

• I Wish I Could Remember That First Day

• The Nightingale and the Rose

• Currents: A Piano Concerto

I. “River”

II. “Breaking”

III. “Still”

In the addendum:

• Song Without Words

• Seguirilla No. 1

• Seguirilla No. 2

• À la manière de la neige

CD Containing Recordings of My Works

CD TRACK LISTING

1. I Wish I Could Remember That First Day Piano reduction performed by Margaret Houck

2. The Nightingale and the Rose Performed by the Birmingham Contemporary Music Group University of Birmingham workshop of 28 April 2015

Currents: A Piano Concerto Sibelius 7.5, NotePerformer 1.50

3. “River”

4. “Breaking”

5. “Still”

Addendum Performed by Christina Cuda Robertson

6. Song without Words

7. Seguirilla No. 1

8. Seguirilla No. 2

9. À la manière de la neige

TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION 1!

Context 1!

Standardizing Names for Synthetic Modes 3!

Background Works 7!

Portfolio Works 9!

CHAPTER 2: I WISH I COULD REMEMBER THAT FIRST DAY 11!

Understanding Added-Tone Sonorities 11!

Context in Added-Tone Sonorities 12!

Clusters as an Outgrowth of Added-Tone Sonorities 15!

Balance in I Wish I Could Remember That First Day 18!

CHAPTER 3: THE NIGHTINGALE AND THE ROSE 20!

Tymoczko’s Constraints in Scale Construction 20!

Intersecting Collections and Modulation 21!

Scale Networks As Preparation for Composing 25!

Harmony in The Nightingale and the Rose 29!

CHAPTER 4: THE MODES OF “RIVER” 35!

Generating the Scales and the Scale Network 35!

Types of Modulation in “River” 39!

Octatonic Hexachord Subsets in “River” 43!

CHAPTER 5: ROTATIONAL ARRAYS AS A DERIVATIVE OF MODE 50!

Introduction 50!

Rotational Array for “Breaking” 51!

Application of the Rows 54!

Stacked Columns in the Arrays 55!

Transposed Stacked Rows in “Breaking” 57!

Octatonic Implications of the Rows 60!

Intentional Clashing With the Prevailing Octatonic 63!

Conclusion 65!

CHAPTER 6: MODES INSPIRED BY YAVORSKY’S THEORIES 66!

Boleslav Yavorsky’s Theories on Mode 66!

The Mode for “Still” 68!

Nearer, My God, to Thee and “Still” 71!

A Second Derivative Mode 75!

Delaying Stability With Modulations 79!

CHAPTER 7: CONCLUSION 83!

APPENDIX: ROTATIONAL ARRAYS FOR “BREAKING” 86!

BIBLIOGRAPHY 89!

LIST OF MUSIC EXAMPLES Example(1:(I"Wish"I"Could"Remember"That"First"Day(bars(1.4,(82.89(..........................(13!Example(2:(I"Wish"I"Could"Remember"That"First"Day,(bars(58.60(.................................(15!Example(3:(I"Wish"I"Could"Remember"That"First"Day,(bars(28.35(.................................(16!Example(4:(I"Wish"I"Could"Remember"That"First"Day,(bars(41.46(.................................(17!Example(5:(I"Wish"I"Could"Remember"That"First"Day,(bars(11.14(.................................(18!Example(6:(“River”,(bars(13.19(................................................................................................(22!Example(7:(The"Nightingale"and"the"Rose,(bars(155.162(.................................................(24!Example(8:(The"Nightingale"and"the"Rose,(bars(193.195(.................................................(28!Example(9:(The"Nightingale"and"the"Rose,(bars(8.15(........................................................(31!Example(10:(The"Nightingale"and"the"Rose,(bar(16.29(.....................................................(32!Example(11:(“River”,(bars(7.18(................................................................................................(39!Example(12:(“River”,(bars(76.84(..............................................................................................(42!Example(13:(“River”,(bars(54.70(..............................................................................................(45!Example(14:(“Breaking”,(bars(1.15(.........................................................................................(54!Example(15:(“Breaking”,(bars(56.63(......................................................................................(56!Example(16:(“Breaking”,(bars(34.38(......................................................................................(59!Example(17:(“Breaking”,(bars(119.132(.................................................................................(61!Example(18:(“Breaking”,(bars(161.173(.................................................................................(64!Example(19:(“Still”,(bars(2.15(...................................................................................................(70!Example(20:(Bethany,(the(setting(for"Nearer,"My"God,"to"Thee(.......................................(71!Example(21:(“Still”,(bars(16.25(.................................................................................................(72!Example(22:(“Still”,(bars(68.79(.................................................................................................(74!Example(23:(“Still”,(bars(92.107(..............................................................................................(78!Example(24:(“Still”,(bars(152.179(............................................................................................(80!

LIST OF FIGURES Figure(1:(Seguirilla(Compás(..........................................................................................................(8!Figure(2:(F(Spanish(Phrygian(.......................................................................................................(8!Figure(3:(Examples(of(Added.Tone(Sonority(Notation(.....................................................(11!Figure(4:(Intersection(of(F♯(wtq(and(E(wtq(...........................................................................(23!Figure(5:(Intersection(of(F♯(wtq(and(B(Melodic(Minor(.....................................................(24!Figure(6:(Initial(Scale(Network(for(The"Nightingale"and"the"Rose(................................(26!Figure(7:(Final(Scale(Network(for(The"Nightingale"and"the"Rose(..................................(27!Figure(8:(Whole.Tone(Quint(and(Scalar(Triads(..................................................................(30!Figure(9:(Maximally(Intersecting(Scales(of(“River”(...........................................................(35!Figure(10:(Blues(Scales(Two(Steps(from(G(wtq(...................................................................(37!Figure(11:(Scale(Network(for(“River”(.....................................................................................(38!Figure(12:(“River”(Theme(Structure(.......................................................................................(40!Figure(13:(Hexachord(and(Whole.Tone(Quint(Comparison(...........................................(43!Figure(14:(Rotational(Array(for(“Breaking”(.........................................................................(52!Figure(15:(Transposing(Stacked(Rows(...................................................................................(57!Figure(16:(Stacked(Rows(of(Flourish"with"Fireworks(........................................................(58!Figure(17:(Building(the(Rising(Water(Figures(in(“Breaking”(..........................................(62!Figure(18:(Tritone(Resolution(Systems(in(Yavorsky's(Theories(...................................(67!Figure(19:(Yavorsky's(Duplex.Major(Mode(..........................................................................(68!Figure(20:(Yavorsky(Pitch(Gravitations(................................................................................(68!Figure(21:(Harmonic(Source(for(“Still”(..................................................................................(69!Figure(22:(Second(Harmonic(Source(for(“Still”(...................................................................(76!

LIST OF TABLES Table(1:(Tetrachord(Names(Used(...............................................................................................(5!Table(2:(Mode(Names(Used,(Part(1(.............................................................................................(6!Table(3:(Mode(Names(Used,(Part(2(.............................................................................................(7!Table(4:(Modulations(in(“River”,(bars(43.70(.......................................................................(46!Table(5:(Collection(Shifts(in(“Still”,(bars(92.104(.................................................................(77!

Introduction 1

Chapter 1: Introduction

Context

Parallel to the twentieth century development of musical styles pushing far from

tonality is a lineage of composers who continued to explore novel ways to assert

tonality. Considering only the United States of America, there is a rich heritage of

composers who embraced and defined styles grounded in tonality: Aaron Copland,

Samuel Barber, David Diamond, Vivian Fine, Leonard Bernstein, and Gian Carlo

Menotti each offered their most significant impact in the middle 50 years of the

century. More recently, Ellen Taaffe Zwilich, John Corigliano, William Bolcom,

Jennifer Higdon, and Lowell Liebermann have enjoyed acclaim for their tonal

works.

Within this vein of tonal writing are a variety of approaches to harmony. Much of

Copland’s music found its voice with the open and quartal harmonies now so

strongly associated with the “American” sound. Fine studied and successfully

applied Henry Cowell’s concepts of dissonant counterpoint.1 Bolcom brazenly

borrows elements of popular music to stretch the boundaries of art music.

Liebermann often writes with 12-tone rows that are harmonized tonally.2

The initial proposal for this master’s program was to explore ways for my

composing to break beyond its strong common practice roots while maintaining a

sense of “tonal” harmonic motion. The list of composers above is in itself evidence

that one can perceive and appreciate tonality in ways well beyond common practice,

yet my steps outside of common practice and modality had never been far.

1 (Spilker 2010, 131) 2 (Barrymore 2000)

Introduction 2

There are practical reasons for my goals. I live in rural America where the

ensembles and audiences for whom I compose are, on average, resistant to the

avant-garde. However, in my experience as a programmer of concerts featuring

contemporary Arizona composers, this same audience has a hunger for new musical

ideas that are grounded in some application of tonal harmonic motion. The variety

of musical approaches this audience has applauded is wide. Bruce Reiprich’s Water

Leaves for solo piano and Moon in Blue Shadows for flute and piano employ ethereal

gestures that paint within modal collections without creating strong harmonic

motion. James DeMars’ Tapestry IX for solo violin begins with a simple germ that

evolves into virtuosic lines while constantly shifting through fragments of modality.

His Colors Fall for flute and saxophone echoes Native American flute motifs but

chromatically avoids pentatonic suggestions. Douglas Gibson’s Awakening Within

patiently layers a web of instrumental voices over an ostinato, using modes

reminiscent of the Near East. Roshanne Etezady’s Glint for saxophone and clarinet

weaves quick counterpoint between two highly chromatic lines, moving between

periods of relative consonance and tight dissonance. Daniel Asia’s Shiru Ladonai

with soprano, flute, marimba, and piano sets the Hebrew text from Psalm 96 in

dance rhythms and complex scales and harmonies reflective of Stravinsky. Rodney

Rogers’ Alleluia, Sing the Stars for choir creates dense and dynamic added-tone

sonorities from multiple independent lines of counterpoint. All of these works

approach tonality very differently, yet my community consistently responded to

concerts featuring these composers with comments such as “a breath of fresh air”

and “water for a parched soul”.

As starting points for my research, I used three composers with whom I was

familiar, whose scores were easily accessible, and who represented different ways of

approaching tonality: Eric Whitacre, Claude Debussy, and Igor Stravinsky. The

Introduction 3

study of Whitacre’s music provided a model of expanding the harmonic colours

available to a style firmly grounded in the tradition of common practice. The works

of and academic papers on Stravinsky and Debussy were the beginnings of multiple

threads of exploration that led to a study of many composers, diverse approaches to

music theory, novel modes, and different ways to manipulate these modes. By the

end of my research period, I was writing music where the execution of harmonic

motion was based more on the progression of pitch class sets and less on the motion

of one harmony to another harmony.

This commentary is not a complete account of how I composed each piece. Instead I

will reveal some of the harmonic-syntax explorations that allowed me to develop my

musical language. Each piece uses techniques and ideas gleaned from specific

academic writings, and I will highlight relevant papers and ideas before discussing

examples from my works. The examples I offer present harmonic relationships

specific to the syntax I’m using and relate the intended affect.

I will discuss four of my explorations in harmony and mode: my application of

added-tone sonorities; the construction of new modes that conform to the

constraints of scale networks; rotational arrays based on short rows created from a

subset of a parent mode; and the generation of modes and their complements using

ideas inspired by Russian music theory.

Standardizing Names for Synthetic Modes

I have not discovered an established or standard way of naming modes or synthetic

scales. There are well-known names for common practice modes (e.g., major or

harmonic minor), the traditional church modes (e.g., Dorian or Phrygian), and a

Introduction 4

handful of synthetic scales (e.g., overtone or Neapolitan minor).3 The most universal

way to define an arbitrary mode might be to use pitch class set notation, yet pitch

class set notation is both cumbersome to use in prose and, by definition, an

“unordered collection”4 that would not imply a tonic.

For the purposes of writing in prose, I have adopted a naming convention for seven-

note modes that combines descriptive names5 (sometimes shortened) for each of the

two tetrachords that comprise the mode. The tetrachord that begins at the first note

of the mode is given first, and the tetrachord that ends at the octave is given second.

A few modes will be referenced by their universal names (e.g., melodic minor) or a

more descriptive name I have assigned.

3 (Persichetti 1961, 31-49) 4 (Roeder) 5 Some of the less common names are derived from the following web page: (Solomon 2005)

Introduction 5

Tetrachords I use in naming my modes are listed below:

Table 1: Tetrachord Names Used

Pitch Classes Name Used Full Descriptive Name, if Different6

0 2 4 5 Major

0 2 3 5 Minor

0 2 4 6 Lydian

0 1 3 5 Phrygian

0 1 4 5 Arabian Arabian Tetramirror

0 2 3 6 Harmonic Harmonic-minor Tetrachord

0 1 4 6 All-1 All-interval Tetrachord.1

0 3 5 6 Blues7 Perfect-fourth Diminished Tetrachord

0 3 5 7 Minor-58 Perfect-fourth Minor Tetrachord

0 1 2 3 Chromatic BACH / Chromatic Tetramirror

6 (Solomon 2005) 7 This tetrachord is the first four notes of a blues scale. I find Blues more descriptive than Perfect-fourth Diminished Tetrachord. 8 I use “5” in the name “Minor-5” to reflect the added interval class of a perfect fourth.

Introduction 6

Below are the names I use for the seven-note modes used in my portfolio:

Table 2: Mode Names Used, Part 1

Pitch Classes9 Derived Name10 Alternate Name

0 2 4 6 7 8 T Lydian Phrygian Whole-Tone Quint (WTQ)11

0 2 4 6 7 8 E Lydian Arabian

0 1 4 5 7 9 E Arabian Major

0 2 4 6 7 9 T Lydian Minor

0 1 4 6 7 8 T All-1 Phrygian

0 3 5 6 7 9 E Blues Major12

0 2 3 6 7 8 T Harmonic Phrygian

0 2 3 5 7 9 E Melodic Minor

0 1 3 5 7 8 E Phrygian Arabian

0 3 5 7 9 T E Minor-5 Chromatic13 Some of the transformations applied to my modes generate blues scales with an

added seventh tone. These scales are named “Blues” with a suffix indicating the

added interval:

9 “T” and “E” represent the pitch classes ten and eleven. 10 Derived names are not offered if there already exists a very common name for the mode. 11 This is the parent mode for the derived modes used in much of the music discussed here. It is constructed from the whole-tone scale with an added tone at the perfect fifth above 1. The name Whole-Tone Quint is given to this mode to reflect this construction. 12 Blues Major is mode two of the All-1 Phrygian. 13 Only once do I use this: the E Minor-5 Chromatic scale [ E G A B C♯ D D♯ E ] in bars 81 and 83 of “River”. While I treat this collection with similar harmonic and melodic figures as other scales in nearby bars, I do not think that this collection analytically stands on its own as a true scale: the listener perceives the notes of the top tetrachord as either mixture or chromatic passing tones within some variant of an E minor scale.

Introduction 7

Table 3: Mode Names Used, Part 2

Pitch Classes Name

0 1 3 5 6 7 T Blues + 1

0 2 3 5 6 7 T Blues + 2

0 3 5 6 7 8 T Blues + 8

0 3 5 6 7 9 T Blues + 9 When a tonal centre is perceived within a given scale (e.g., G Whole-Tone Quint),

that tonal centre is usually the first scale degree (e.g., G).

When convenient, I notate the expected diatonic note spellings within my modes to

help clarify the scale degree of each note. However, a higher priority is given to

readability for the musician, and alternate note spellings are commonly used. For

example, within the A♭ Blues Major mode, a vertical harmony of scale degrees

[ 1 3 6 ] would be spelled diatonically as [ A♭ C♯ F ], but in a piano part I would

spell it as [ A♭ D♭ F ] to ease readability.

Background Works

Prior to beginning my master’s program, my music reflected a strong grounding in

common practice or diatonic modal harmonies. In the addendum of this thesis are

four piano works, written early within my master’s time frame, that reflect this

history.

The piano work Song Without Words is a pastiche work I wrote to demonstrate my

most comfortable style of writing. It is of a mid-romantic and lyrical style

demonstrating traditional harmonic and phrase structures typical of that period.

Introduction 8

Seguirilla No. 1 and Seguirilla No. 2 are two works inspired by the Flamenco

seguirilla14 rhythm and style. The foundation of the Flamenco seguirilla rhythm is its

12 beat compás which, when notated in western style notation, is typically

subdivided and accented thus:

Figure 1: Seguirilla Compás

Seguirilla No. 1 is written over a ~4 ostinato that outlines the compás. While the work

makes use of chromatic harmonic motion near the middle, as a whole the piece

clearly is in B♭ minor.

Seguirilla No. 2 also is written in ~4, but it dispenses with the ostinato and

experiments with ways to imply the compás melodically. The work stays largely

within the Spanish Phrygian mode and briefly visits the octatonic.

Figure 2: F Spanish Phrygian15

The fourth piano work in the addendum is À la manière de la neige, a work modelled

after Debussy’s piano prelude entitled Des pas sur la neige. À la manière de la neige

marks the beginning of my wider experimentation with modes. Like Debussy’s

work, the context of the ostinato within À la manière de la neige continuously shifts as

the colour of the musical layering moves through juxtapositions of one or more

14 Also known as seguiriya. 15 The Spanish Phrygian mode is equivalent to mode 5 of the harmonic minor scale. In the Flamenco treatment of the Spanish Phrygian mode, frequently 7 is raised, which creates a mode with two augmented seconds.

128/

>œ œ œ ™ œ ™ œ

& œ œb œn œb œ œb œb œ

Introduction 9

modes, both traditional (e.g., major and melodic minor) and synthetic (e.g.,

octatonic and acoustic).

Portfolio Works

There are three major works included within this portfolio:

1. I Wish I Could Remember !That First Day – a setting of a Christina Rossetti poem

for SATB divisi. The poem is an untitled sonnet that opens with the words “I

wish I could remember that first day”.16 I will be discussing my use of added-

tone sonorities in this work and its harmonic implications.

2. The Nightingale and the Rose – a chamber work for woodwinds, brass, strings,

piano, and percussion (14 instrumentalists). It is the first work in this set to

explore the idea of scale networks and to make heavy use of the Whole-Tone

Quint mode.

3. Currents – a three movement piano concerto inspired by the complex

relationship between New Orleans, my birthplace, and the waters that

border and cross the city. This is my last and most substantial work of the

portfolio. With this concerto, both my harmonic language and my

orchestration rose to a new level of sophistication. The movements within this

work are:

a. “River” – inspired by the Mississippi River. This movement further

develops the practice of creating synthetic modes from scale networks.

Like The Nightingale and the Rose, “River” uses the Whole-Tone Quint

mode as its parent mode.

16 (Rossetti 1995, 330)

Introduction 10

b. “Breaking” – a reaction to the flooding of New Orleans after

Hurricane Katrina. This movement is almost exclusively written from

material derived from rotational arrays. I will discuss how the initial

row that I chose for this work derives from the material presented in

“River” and how the octatonic implications of the generated arrays are

utilized.

c. “Still” – a statement of hope built upon a reflection on both the beauty

and loss created by standing water. This movement makes use of

complementary pitch class sets generated by techniques derived from

early 20th century Russian music theory. I will introduce Russian

music theorist Boleslav Yavorsky, his concepts of modes, how his

theories inspired my process, and the harmonic implications utilized

within this movement.

I Wish I Could Remember That First Day 11

Chapter 2: I Wish I Could Remember That First Day

Understanding Added-Tone Sonorities

Eric Whitacre is well known for his rich harmonic treatment of tonal music. In her

dissertation “Added-Tone Sonorities in the Choral Music of Eric Whitacre”, Angela

Hall offers theories on how the harmonies of Eric Whitacre are perceived in a tonal

framework. Hall’s theories and her extensive documentation of how Whitacre uses

specific sonorities offered me a strong foundation for understanding how to apply

similar sonorities to I Wish I Could Remember That First Day.

To analyse Whitacre’s vertical sonorities, Hall developed a notation that represents

what she calls the added-tone sonority. I will use this notation in my examples. For a

given vertical sonority, an added-tone sonority marking will indicate the diatonic

triad deduced from the pitch class collection, what non-chord tones are added to

this triad, and the bass note used for this sonority. Figure 3 demonstrates how to

read added-tone sonority notation.

Figure 3: Examples of Added-Tone Sonority Notation

{a) b) c)

&?

‡ All i.c.'s are relative to the root of the chord.* i.c. t = i.c. 10; i.c. e = i.c. 11

Added-Tone Sonority‡

b(2)/0B minor triad

Added tone i.c. 2 (C#)

i.c. 0 is in the bass(i.e., is in root position)


E(5t)/4E major chordAdded tone i.c. 5 & 10* (A, D)i.c. 4 is in the bass

(i.e., a G# is in the bass)


C(26)/2C major triad

Added tones i.c. 2 & 6 (D, F#)

i.c. 2 is in the bass(i.e., a D is in the bass)

wwww#www wwww#

ww#www# www


While using added tones to enrich triadic harmonies is a well-documented

compositional technique,17 Hall’s theories offer six specific factors used to help

determine the perceived triad of the sonority within a tonal framework: 18

1. The root of the triad must be included within the sonority;

2. Major and minor triads are the preferred interpretation;

3. Completeness of a triad within the sonority lends favour towards that

interpretation;

4. If possible, the triad should include the bass note of the sonority;

5. Preference is given to triads where the bass note is the root of the triad;

6. When considering incomplete triads, preference is given to triads that include

the third.

When all of these factors are considered, multiple interpretations of various

confidence levels may arise. Typically the interpretation of the highest confidence

level is chosen, but often the context lends credence to an interpretation of lesser

confidence.19

Context in Added-Tone Sonorities

Hall’s theories on the perception of added-tone sonorities resonate with my aural

interpretations. While writing I Wish I Could Remember That First Day, I remained

17 (Persichetti 1961, 111-18) 18 (Hall 2012, 71) 19 (Hall 2012, 77)


aware of what harmonic context the listener would hear. When I sought a specific

harmonic foundation for a line, I was able to construct sonorities that intentionally

reinforced these harmonies. Hall’s observations occasionally proved useful for

conveying specific affects – e.g., tight and dark, or open and consonant. When I

could not find a sonority to reflect my intention, Hall’s categorization of added-

tones20 offered combinations I might not have considered.

The opening (Example 2a) and closing (Example 2b) cadences of I Wish I Could

Remember !That First Day are typical of this piece:

Example 1: I Wish I Could Remember That First Day bars 1-4, 82-89

20 (Hall 2012, 82-91)

{

{

{

ReductionIp

wish

c#(t)/0b(2)/7

f#(8)/0

I

G(9)/0

could

f#(8)/0

re

b(t)/3

mem-

e(t)/0

ber-

G/7

A(5t)/4

G/7

e(5)/0

that

e(t)/t

first

e(9)/9

b(8)/0

day,

b/0 b(2)/0

mp

Adagio (ca. q=60)1 2 3 4

b:re mem- ber- first

Reduction...

G(2e)/4

Firstp

G(2e)/2

touch

G(26e)/2

of

G(2e)/2

hand

G(29e)/2

in

(w.t.)

hand in hand in hand in

G(26t)/7

hand in hand

G(269t)/7

in

G(26t)/7

hand.

82 83 84

D:

Red.

G(26)/7

fdid one but,

e(25t)/0

but know!

G(29e)/0

D(2e)/7 or

A(5)/0

ritenuto85 86 87 88 89

vione, but know!

54 44

54 44

34 44

34 44

54 44 24 34 44

54 44 24 34 44

&##

a)

?##i v i iv i

&##

b)

nbn

?##IV (w.t.) IV

&## U

?## ∑IV I

U

œœ ˙ œœ ™™ œœj œœ œœ œœ ˙ œœ œœ ˙ ˙ ˙ Ó

Œ Œœœ

œœ ™™ œœJœœ œœ œœ œœ œœ œœ œœ œœ œœ œ œ œ œ ˙ Œ œ

œœ˙ ™

Œ œœœ œœ ™™˙œœ œœ œœ œœ ˙ ™œœ œœb œœ œœ wwwœœJ

œ œ

œœœ Œ œœœ ww˙ ‰ œœJ œœb œœn˙™™œœ œœœ œœ œœ œœ œœn œœ

˙ ™™™™ Œ œ Œœ Œ

˙ ™ ˙ Œ œŒ˙ ™ ˙ wwww

˙™™™™ Œ Œ Œ Œ ˙ Œ ˙

˙www


As modelled in Hall’s paper, I label each vertical sonority and the underlying

harmonic movement. Vertical sonorities can be supportive of the underlying

harmony or reflect decorative harmonies (e.g., bar 1, beat 5).

When determining the actual perceived triad within an added-tone sonority, Hall

mentions multiple times the importance of considering the “tonal context”, “musical

context”, or simply “context”. Example 1 above includes several sonorities that I

analysed as different from the default analysis of the vertical harmony. By a straight

interpretation of Hall’s rules, the harmony of bar 82, beat 3, looks like it should be

based upon a B minor harmony [ b(8t)/0 ] that is an extension of the previous

phrase’s harmonies, yet I clearly hear (and intended) a G major harmony. The

G(2e)/4 interpretation falls neatly into a stacked third harmony (a GM9 harmony in

first inversion) and leads directly into the G harmony area that follows. The

potential ambiguity of interpretation enabled by added-tone sonorities lends both

beauty to the music and support for the underlying theme of misplacement in the

poetry.

The final chord in bar 89 also is ambiguous. It mostly is heard as a D major

harmony, even though the sonority contains the complete A major triad, an A is in

the bass, and there is no third of the D major triad. If a D harmony were to follow

this chord, then bar 89, beat 1, would no doubt be an A major harmony. Instead, its

prominence as a final chord and the emphasis on the D within the sonority favours

the D tonic interpretation.

Hall does not specifically mention melody as a factor to be considered when

determining the interpretation of an added-tone sonority, but melody can play an

important role.


Example 2: I Wish I Could Remember That First Day, bars 58-60

Example 2 presents a melodic sequence reflecting a brief moment of joy that, by bar

60, is slightly coloured by lingering regret. Bar 60 is shown with two possible

interpretations of the sonorities. The ear favours the C minor to D minor

interpretation over the E♭ major to F major interpretation partly because the

melody outlines the chord tones of the C minor and D minor chords, continuing a

pattern of outlining chord tones set forth in the prior two bars. The ambiguity of

major and minor interpretations, with a clear leaning towards the minor, nicely

reflects the poet’s joy tinged with regret.

Clusters as an Outgrowth of Added-Tone Sonorities

Near the middle of I Wish I Could Remember !That First Day are these words from

Christina Rosetti’s poem:

So unrecorded did it slip away,

So blind was I to see and to foresee,

So dull to mark the budding of my tree

That would not blossom yet for many a May.

In setting these words I use note clusters, melodic tritones, and a shifting harmonic

base to paint a sense of blindness and missing details. While much of the middle

section of I Wish I Could Remember !That First Day does not fit neatly within Hall’s

{Reductionsuch A day

f exclamatory

of days! Day of days! Day of days!

(q=60)58 59 60

a(t)/0 Eb(2e)/0 F(69)/0 C(5t)/t Bb(9e)/0 Eb(29)/4

c(5t)/7

F(29)/4

d(5t)/7

44

44

&##

?##Default interpretation:

Considering context:

œœn œœ œœœœbbn ™™™™ œœœj œœœ ™™™ ‰ œœœœnb ™™™

™ œœœœ<n>J

˙n œœœœbnb ™™™™ œœœœn

j˙

œœœœ

œœœbb ™™™ œœœJ

œœœnn ™™™ ‰œœœnb<n> ™™™ œœœJ

˙ œœœbn ™™™ œœœJ

˙


added-tone sonority model, the use of cluster harmonies flows organically from the

complex harmonies generated by added-tone sonorities. Consider the transition into

the text quoted above, where I begin my use of clusters to reflect the elusive nature

of the speaker’s memory:


The four-note clusters that evolve in bars 32 and 34 are clear paraphrases of bar

31’s three-note cluster created by the C♯ within the B minor harmony.

The evolving cluster motif repeats throughout the middle section and leads towards

a large-scale harmonic resolution on the word blossom. Just prior to this resolution,

where the words dull and budding are key, the vocal lines repeatedly try to break out

{

{

{

Reductionaught

A(t)/7

I,

b(5)/0

b(58)/0

b(5t)/t

A(59)/0

aught I,

A(2)/2

A(2)/0

A(2t)/t

G(9e)/0

aught I

G(29)/0

can

G(269)/0

say.

b(2)/0

p

(q=60)28 29 30 31

...

b: i

aught I,

bVII

aught I

bVI

can say.

i

nnnpp

Red.So

b(2)/0

pun re- cord- ed- did

B(2)/0

it slip a

B(2t)/0

way,

[ G+(2)/4 ]

-mp

B(8t)/0

meno mosso (ca. q=50)32 33

B

So un re- cord- ed- did it slip a -

Red.So

G(6)/7

pun re- cord- ed- did it slip

G(69)/7

a way,

f#(5t)/0

-

f#(5t)/7

mp

D(29e)/0 A(29)/7

Sop

34 35

way,

G f#

So un re- cord- ed- did it slip a

F

way,-

44

44

54

54

&## U U

?## U U

&##-

?##

&##

?## -

œœœœ ˙ ™™™™ œœœœ ˙ ™™™™

œœœœ œœœœ ˙˙ ˙ ™™™

™ Œ

œœ Œ œœ œœ œœ Œ œœ œœ ˙ ™™ œœ ˙ ™™ œœ

‰ œj œ ™ œ œ œ œœ# œœ œœœ ™™™ œœœœ wwww#

ww ˙ ™‰ œj œ œ œ œ ‰œ ™ œ œ œœJ

‰ œj œ ™ œ œ œ œœn œœ œœœ ™™™ œœœœ ˙ ™™™™ œœœœ

‰ œnJ

ww ‰ ™ œJ œ œ œ œ œœ ™ œ œ œ œnŒ


of the clusters, and the harmonies devolve into ambiguity as the work enters a brief

whole-tone section:


An important attribute to the text painting here is the blurring of the harmonies. Bar

41’s pitch gravity is towards E, but the clusters in beat 4 obscure this. Likewise bar

43’s harmonic centre of the B tritone is blurred by the sonorities within beat 3. Both

areas create tension that is subsequently released: a fifth movement to the A minor

in bar 42, and a near-fifth movement to the F in bar 43, beat 4. The whole-tone[1]

area of bar 44 reflects a complete sense of being harmonically untethered. Only with

the entrance of the alto’s E♮ on beat 4, bar 44, can analysis of added-tone sonorities

{

{

{

Reduction

mpSo dull to mark the bud ding- of my

[ C(25e)/e ]

tree

a(8)/0 a(28)/0 a(258)/0(q=50)

41 42

So dull

(e area) (a area)

So dull to mark the bud ding- of my treeto

Red.So

(b° area)

mfdull to mark the bud ding- of my tree the

e(5)/343 44

mark,

(b° area) F (w.t.)

So dull to mark the bud ding of my tree

Red.

e(5)/5

bud ding

e(5)/3

-

e(258)/3

G(2e)/2

of

G(9)/0

my

a(9)/0

tree

b(15t)/7

that

G(9e)/7

would

C(9)/4

not

D(2t)/t

blos

f

D(29t)/t

D(259t)/t

-

D(2t)/t

D(t)/t

D(29t)/t

a(29t)

som

45 46

A Dorian: v VII i VII IV i

44

44

54

54

&## (harmonies from p.t.'s)

[ C(2)/0 ]

?##

&## (harmonies from p.t.'s)

[ a(28)/2 ]

[ C(5e)/e ]

F(6e)/0

F(6e)/e

(Whole Tone area) a(2)/0

?##n

&## n n n

?## nn

‰ ‰ œj œ ™ œ œ œ œœ œœ œœœn œœœœnn ˙nn ™™™™ Œ

œJw

‰˙ ™ œJ œœ œœ œœ œœ œœœn œœœn œœœ œœœn œ‰ œj

‰ œœJ œœ ™™ œœ œœn œœœ œœœœ œœœœn œœœœn œœœœn

˙˙# ™™™™ ‰

œœœœj

w™Œ ‰

˙ ™ œJ œœœ<#> œœœ œœœ œœœ œœœ# œœœ œœœ œœœ œœœŒ

œœ ™™ œœ<#>n œœ œœœœ œœ œœ œœ œœ œœ œœ œœœœ œœ œœ œ ˙ ™™œœ œœ œœ œœ œœ œœ ˙n

œœœ ‰ œJ œ œœœ œœœœn œœœœn ˙ ™™œœ œœ œœ œœ œœ œœ ˙


once again be applied. 21 It is at this point in the music that harmonic clarity is

reasserted, and there is a clear, melodically sequential, progression to the plagal

cadence on the word blossom.

Balance in I Wish I Could Remember That First Day

While my study of added-tone sonorities has opened up a new harmonic richness

within diatonic modes, I have come to the conclusion that in I Wish I Could Remember

!That First Day I could have created more balance and contrast by finding more space

for open voicing and less dense harmonies. Within the 89 bars of the work, 61 bars

contain five to eight voices, and 28 bars contain only four or fewer voices. Only 22

bars of the work contain no divided sections. Between bars 24 and 46, every bar

contains five or more voices. From bars 72 to the end, only two bars (both

comprised entirely of a rest and a pickup) have fewer than 5 voices.

There are many choral works written for 8 voices that have a sense of clarity and

balance, so I believe other factors may contribute to the imbalance I sense. Consider

the following bars using 6 independent voices:


21 The entrance of the E♮ very briefly throws this work into the A Whole-Tone Quint mode. The WTQ mode is of significant importance in the other works of this portfolio.

{Reduction

D(6)/0

dim,mp

D(6)/6

D(6)/4

D(26)/2

D(6)/4

A(29)/7

if

E(59)/0

bright

E(59t)/t

E(2t)/2

or

e(2)/3

dim,

e(25)/5

b(58)/0

if

A(2)/2

bright

G(9e)/4

or

A(2)/2

dim

G(9)/0

or

f#/0

bright

G(9)/7

or

A(9)/4

dim

b(25t)/0

the sea

G(9e)/0

mf

A(29t)/0

son.- Itp

(q=60)11 12 13 14

A: IV

If bright or dim, If

I

bright,

V

If bright or dim,

v I(I

bVII I bVII)

vi bVII I ii bVII I

44

44

&##

?## <n>

˙# ™™™™ œœœœ œœœœ# ™™™

™ œœœœjœœœœn ™™™™ œœœœ

j œœ œœœœ œœœœ œœœœ œœœœ œœœœn œœœœ œœœœ ˙ œœœœ

‰ œj

‰ œ#J œ œ œ œœ œ ™ œj ˙œ œ œ œ œ œ œ œœ œ‰Óœj œ œœœœ œœ ˙ œœ Œ


While the added-tone sonorities change on each moving voice, bars 11, 12, and 14

maintain a harmonic rhythm of roughly two structural harmonies per bar. In

contrast bar 13 suddenly jumps to a harmonic rhythm of every quaver. This

combined energy of the harmonic rhythm and the added-tone sonorities contributes

to a complexity that is not well-balanced. Bar 13 might have been better balanced

with slower harmonic rhythms or thinner sonorities.

Compare this to Example 2, page 15, where seven voices are active. The slow

musical rhythm, slower harmonic rhythm, and pseudo-sequential nature offer the

listener a chance to “taste” each sonority, successfully counter-balancing the

complexities of the harmonies.

!

The Nightingale and the Rose 20

Chapter 3: The Nightingale and the Rose

Tymoczko’s Constraints in Scale Construction

In his paper “Scale Networks and Debussy”, Dmitri Tymoczko ! presents concepts of

scale construction and scale networks that I used to create new modes and

relationships for The Nightingale and the Rose and “River”, the first movement of

Currents. Below I define some of Tymoczko’s terminology that I will be using in my

discussions of my works.

Tymoczko notes that, in the early twentieth-century, there was a composition

tradition of composers such as Rimsky-Korsakov, Debussy, and Ravel who wrote

music using new scales and harmonies while retaining a traditional hierarchy among

those harmonies and scales. He labels this composition tradition the scalar tradition.22

I consider my works The Nightingale and the Rose and “River” to be of a similar

tradition.

Within this scalar tradition, Tymoczko observed a number of potential constraints

in how scales are constructed:23

• DS (Diatonic Seconds) – the chromatic interval between two consecutive

notes of a scale are either one or two ascending semitones.

• NCS (No Consecutive Semitones) – scales do not have two or more

consecutive semitones.

• DT (Diatonic Thirds) – the chromatic interval of the “thirds” of a scale (the

outer interval defined by three consecutive notes of a scale) is either three or

22 (Tymoczko 2004, 219-20) 23 (Tymoczko 2004, 222-26)


four semitones. This is a given if the constraints of DS and NCS are satisfied.

However, it is possible to have the DT constraint satisfied while failing DS.

For instance, the harmonic minor scale contains only major and minor thirds,

but it also contains an augmented second, which violates DS.

While much early twentieth-century music uses scales that satisfy all of the above

constraints, few of the modes I use satisfy the NCS or DT constraints, and a few do

not satisfy the DS constraint. I will discuss some of the implications of this further

on.

Intersecting Collections and Modulation

Tymoczko borrows nomenclature from set theory to describe relationships between

scales while cautioning that the “sets” and “collections” being discussed are still

scalar in nature: pitch classes within these objects are ordered, are cyclical at the

octave, and define their own intervallic relationships (e.g., scalar seconds, thirds,

etc.).24

When discussing common-tone modulation between scales, Tymoczko defines a few

more terms. The collection of common tones between two scales is, by definition,

the intersection of the two collections. Two sets maximally intersect when all but one

of the smaller set intersect with the other set. C major and A harmonic minor

maximally intersect; the two scales have 6 tones in common. By design, many of the

scales I use maximally intersect. For example, the C Whole-Tone Quint [024678T]

and the C Lydian Arabian [024678E] maximally intersect.

24 (Tymoczko 2004, 233)


A set class maximally intersects itself when two distinct transpositions of that set class

maximally intersect. 25 Each diatonic collection can maximally intersect itself twice:

C major and G major differ by only one note, as does C major and F major. Each of

my Whole-Tone Quint collections maximally intersects itself five times. The G wtq

and F wtq have in common the six tones of the whole-tone[1] scale, but for the

seventh tone (5) G wtq has a D♮ and F wtq has a C♮. G wtq has similar

intersections with A wtq, B wtq, C♯ wtq, and E♭ wtq. This makes shifting between

related WTQ collections relatively gentle, a trait useful in communicating the quiet

flow of water in the example below from “River”:

Example 6: “River”, bars 13-19

25 A set class, by definition, contains all transpositions and inversions of a set. Tymoczko expressly states in footnote 13 that he is considering only transpositions when speaking of classes. (Tymoczko 2004, 283)

{{

{

{

Piano

Orchestra

p

(q=60)

13 14 15

A

G wtq:

ppA wtq:

Pno.

Orch.

mp dolce

16 17 18 19

F

mf

F wtq: G wtq:

p

4444

44

&3

3

”“

&3 3

? Stgs.

#

& bn b“: ;

3

3 3 3

&3

3 3

& ∑ ∑Cl. solo

3

? nnb b

œ ™œj œ# œœJ ˙ ≈ œRœ

œn œ# œœJœœ œœb œœ œœ ™™ œœJ œœJ œœ# œœ## J

œœbn œœn œœb œœ# œœœJ œ# œJ ˙ ≈ œ œn œ# œJ œ œb œ œ ™ œJ œJ œ œ#J œn œ œ œ œ

˙ ™‰ œœ

jœœ œœ œœ œœ œœ

œ œ wœœ œœ œœ œœ œœ œœ œœ œœ wœœ œœ œœ œœ œœn œœ œœ# œœ

œœ ™™ œœbJ œ œJœ œ œ œœb œœ#n œœ œœbb œœn ˙

™™ œœ œœn œœb œœ# œœ œœJ œœ ™™ Œ œœœ ˙

œ ™ œj œ œ œ œ œ# œ œb œn ˙ ™ œ œ œb œ# œ œj œ ™ Œœœœ ˙

Ó Œ ‰ œJ œ ™ œJ œ ™ ≈ œ œb œn

œœœ œn ˙ ™œœ œœ œœ œœ œœ œœ œJ œ ™ œœœ œœ œœ œœ œœ

j œœœœœj

˙ ™œœ œœ œœ œœ

œ ˙œœ œœ œ

œ œœ˙

œœ œœ œœ œœ œœ œœ œœ œœ


The intersection between two collections is only concerned with common tones and

not with the voice leading between the scales. This is different from the typical

treatment of common-tone modulation in earlier tonal practice. When modulating

from C major to A harmonic minor, the ♯5 of C major becomes the 7 of A harmonic

minor, and the function of each of the scale degrees within C major shifts up by two

scale degrees. 1 in C major becomes 3 in A minor, 2 in C major becomes 4, ♯5

becomes 7, and so forth. This strictly linear shift of scale degree numbers through a

modulation is called maximally-smooth voice leading. Maximally-smooth voice leading

is not a requirement of Tymoczko’s approach, and my music frequently employs

common-tone modulation where scale degrees do not align so neatly. Consider the

relationship between F♯ wtq and E wtq, two scales used in The Nightingale and the

Rose:

Figure 4: Intersection of F♯ wtq and E wtq

The 5 of F♯ wtq is a C♯, and it is substituted with a B to become the 5 of E wtq. The

substituted tone retains its previous scalar functionality. The other scale tones shift

in functionality differently. The [ 6 7 1 2 3 ] of F♯ wtq become [ 7 1 2 3 4 ] of E wtq,

a shift of one scalar degree. However, 4 of F♯ wtq shifts by two scalar degrees to

become 6 of E wtq.

It is possible to have modulations that are ambiguous until more of the destination

scale is revealed. From F♯ wtq, the appearance of a B♮ might indicate the arrival of

the B melodic minor scale. Consider the intersection of these modes:

1 2 3 4 5 6 7 1 1 2 3 4 5 6 7 1

&F# wtq E wtq

œ# œ# œ# œ# œ# œ œ œ#œ œ# œ# œ# œn œn œ œ


Figure 5: Intersection of F♯ wtq and B Melodic Minor

Unlike in Figure 4, this modulation offers maximally-smooth voice leading. When

leaving F♯ wtq, the arrival of pitch class eleven is ambiguous in its destination until

a C♯ indicates B melodic minor or a C♮ indicates E wtq.

Example 7: The Nightingale and the Rose, bars 155-162

In Example 7, the accompaniment figure alternates between 2 bars of F♯ wtq and B

melodic minor. When the B♮ is introduced at bar 157, beat 1, the shift to B melodic

minor and not another mode is only confirmed when the C♯ is played on beat 2. If C

naturals had been used instead of the C sharps, I would have modulated to the

sonically similar E wtq. The harmonic gist would remain, but the modal colour of

1 2 3 4 5 6 7 1 1 2 3 4 5 6 7 1

&F# wtq B melodic minor

œ# œ# œ# œ# œ# œ œ œ#œn œ# œ œ œ# œ# œ# œn

{{

Reduction

f

(q=120)155 156 157 158

mp

F# wtq:

mpBm (melodic):

Red.

mf

159 160 161 162

F# wtq: Bm (melodic):

34

34

34

&Vln. solo

#3

##3

&Muted Brass

?CB pizz.

Cello

& #

&?

˙ ™™œ Œ Œ œœ œœ<n># œœ# œœ## ˙ ™™œ Œ Œœœ œœ# œœ## œœ#

Œ œ# œ# œœœ#j ‰ œ œ œœœ

j ‰ Œ œ# œ# œœœ#j ‰ œ œ œœœ

j ‰ Œ œ œ# œœœ##j ‰ œ œ œœœ


j ‰

œbœb™ Œ ‰ œbŒ œœ ™ œb ‰ ŒŒ œœ

™ Œ ‰œŒ

œbœb™ œ

‰ ŒŒ

˙ ™™œ Œ Œœœ œœ## œœ## œœœ#

# ˙# œœ# ˙

Œ œ# œ# œœœ#j ‰ œ œ œœœ


j ‰ Œ œ œ# œœœ##j ‰ œ œ œœœ


j ‰

œbœb™ œb ‰

œbŒ

œœ ™ œb ‰ ŒŒ œœ™ Œ ‰

œŒ

œbœb™ œ

‰ œŒ


the music would have changed subtly: there would not have been as much contrast

between bars 155-156 and bars 157-158.

Scale Networks As Preparation for Composing

Tymoczko creates what he calls scale networks to help analyse the relationships

between scales used in Debussy’s music. A scale network is a collection of scales

used within a work that are graphed along maximally intersecting relationships.

Optimal modulations between scales can be traced along the graph.

For The Nightingale and the Rose and “River”, I decided to reverse Tymoczko’s

analysis process by defining my scale networks first and then writing music that

used the graph as a map for potential modulations. I opted for these constraints:

• All of the scales in my networks are 7 note collections.

• Each network uses a Whole-Tone Quint as a parent scale.

• Each scale in the network is no more than two steps away from the parent

scale.

• My shifts do not require smooth voice leading between scales.

Figure 6 shows the scale network I initially created for The Nightingale and the Rose:


Figure 6: Initial Scale Network for The Nightingale and the Rose

In this scale network, the parent mode is the F♯ wtq, and all other scales are only

one step away. In the paths between the nodes I mark the notes that need to be

exchanged to modulate from one scale to another. The F# wtq needs to replace its D

with a D♯ to modulate to the C♯ melodic minor. The reverse transformation

modulates back to F♯ wtq.

F# wtq

B♭wtq

F : C#

F# Lyd Harm.

C# : E

F : E

A♭wtq

C# : E♭

F : E♭

C# mel. min.

D : D#

D : C#

E wtq

C# : BB mel. min.

B : B#

C# : C


Figure 7 represents the final set of scales used in the piece:

Figure 7: Final Scale Network for The Nightingale and the Rose

My work did not visit F♯ Lydian Harmonic nor B♭ wtq, but it did visit A♭ acoustic,

a scale not in the original network and the only scale two shifts away from the

parent scale. Most of the work is set in one of the WTQ scales. The visits to the

melodic minor or acoustic scale areas tend to provide one of two important

harmonic functions: alternating harmonic sections of two closely related scales (e.g.,

F♯ wtq to B melodic minor, as in Example 7 above), or mode ambiguity when a

scale degree and its chromatic alteration are present at the same time. Consider the

following example:

F# wtq

E♭mel. min.A♭ acoustic

A♭wtq

C# : E♭

F : F♭

C# mel. min.F# acoustic

D : D#

D : C#

E wtq

C# : B

B mel. min.E acoustic

B : B#

C# : C



Here the music is within A♭ wtq and is entering the climax. The black arrows

indicate the sources of the scale ambiguity between A♭ wtq and A♭ acoustic. For

three bars the viola asserts an F♮ from what would be A♭ acoustic against the E♮ (a

respelled F♭) from A♭ wtq. This is the last and most assertive conflict of modes

within the work. At bar 196, the ambiguity is resolved to leave the music in A♭ wtq.

Shortly after this climax the work ends.

{

°

¢

°

¢

Bassoon

Horn in F

Trumpet in C

Trombone

Glockenspiel

Piano

Violin I

Violin II

Viola

Violoncello

Contrabass

mf

(q=120)193 194 195 196

f

f

f

mp

fcresc.

° *° * simile

f

f

f

f

simile

mf

54

54

54

54

54

54

54

54

54

54

54

54

? ⬇

& ∑

& ∑⬇> > >

? ∑

& ∑ ∑

&

? ⬇

& ≥

& ≥

Barco ⬇≥

? ≥

? ⬇

˙b ™ ˙ ˙b ™ ˙ ˙b ™ ˙ ˙b ™ ˙Œ Œ Œ Œ

œb œb œ œb ˙b ™ œ ˙ ™ ˙

Œ œb œ œb œb œb œ œb œb œn œb œb œn ˙b œ œ ˙ ™ ˙

Œ œ# œ œ# œ# œb œb œb œn wb œ ˙ ™ ˙

Œ ˙bb œœb œœ œœbb ˙ œœbn œœ

Œœœb œœ

Œœœ#

Œœœb œœ

Œœœ#

Œœœb œœ

Œœœ#

Œœœœbb œœœ

Œœœœ#

˙bb ™™

˙ ˙bb ™™

˙ ˙bb ™™

˙ ˙bb ™™

˙

Œ Œ Œ œ œ œb ˙ ™ ˙ ˙ ™ ˙ ˙ ™ ˙ ™ ˙ ˙

Œ Œ Œ œb œb œ ˙ ™ ˙ ˙ ™ ˙˙ ™ ˙ ™ ˙ ˙

Œ œb œ ˙<n> ™ ˙ ™ ˙ ˙ ™ ˙ ˙ ™ ˙b ™ ˙ ˙b

Œ œn œb ˙ ™ ˙ ™ ˙ ˙ ™ ˙ ˙ ™ ˙ ™ ˙ ˙

œb œ œ œ œ œb œ œ œ œ œb œ œ œ œ œb œ œ œ œ


Harmony in The Nightingale and the Rose

I chose the Whole-Tone Quint mode as my primary mode within The Nightingale and

the Rose and “River” for two reasons:

• The Whole-Tone Quint is a peculiar scale that surprises the listener with its

ability to find stable points on the tonic and fifth yet lose its grounding when

its whole-tone heritage is emphasized.

• While the “whole-tone plus one” has been used by various composers (I have

found analyses of Bartok, Reich, and Berg mentioning this scale), I find it a

relatively underexplored scale within the scalar tradition of composition.

It might be reasonable to analyse a WTQ area as fundamentally of the whole-tone

mode, but Tymoczko points out that the “whole-tone plus one” scale is one of

several important twentieth-century scales that, depending upon analytical context,

may need to be analysed on its own merits.26 I believe my treatment of the WTQ,

where 5 (the added tone) plays a prominent role in both colour and in asserting the

tonic, justifies analysing the WTQ as a fundamental scale rather than a superset of

the whole-tone scale.

In his section on scale construction, Tymoczko mentions that scales used by

Debussy typically are DS and NCS compliant. Tymoczko also offers two

observations that are relevant to understanding my modes of choice:

• Any scale satisfying both DS and NCS are locally diatonic, meaning that any

three consecutive notes in this scale can be found in traditional diatonic

26 (Tymoczko 2004, 227)


scales. For example, within the octatonic scale, which satisfies both DS and

NCS, any three consecutive notes could also be found in a major scale.

• Any stack of scalar thirds from a scale satisfying the DT constraint will by

default sound “tertian” – meaning that they will be stacks of either major or

minor thirds.

Consider the Whole-Tone Quint and the harmonies created by stacked scalar

thirds:

Figure 8: Whole-Tone Quint and Scalar Triads

The WTQ is neither NCS nor DT compliant. It is not completely locally diatonic,

nor are all its harmonies tertian in nature. This gives the WTQ its previously

mentioned ability to float between stability and a lack of grounding. It also explains

why it would be difficult to use exclusively the stacked-third harmonies shown in

Figure 8. Using harmonies not based upon stacked thirds unlocked harmonic

options suitable to the affect I was seeking within The Nightingale and the Rose.

Consider the opening theme of The Nightingale and the Rose:

&Whole-Tone Quint

œ œ œ œ# œ œb œb œ œœœ œœœb# œœœb œœœb# œœœb œœœb œœœ#b œœœ



In Oscar Wilde’s The Nightingale and the Rose, a young student seeks to escort a

professor’s daughter to an upcoming ball, and a nightingale decides to help the

student by obtaining a red rose demanded by the woman. A key theme of the story

is the skewed impression of what “true love” is by the three main characters: the

student, the woman, and the nightingale. I relate that skew within my music with

clear but warped references to nineteenth-century waltz clichés. Example 9 states

the A theme in the first introduction of my “waltz”. #4 bars are compressed into %4,

bass movements of fourths and fifths are adjusted to near-fourths and near-fifths,

and the harmonic motion slips in and out of a diatonic centre.

For each harmony outlined by the accompaniment figure I note the component scale

degrees. While the tonic of the section is tertian – [ 1 3 5 ], F♯ major – all of the

other harmonies are non-triadic, and most are a stacked scalar third and second. A

paper analysis of the work might suggest that the stacked thirds and seconds are

{

{

Reduction

mf

(q=120)8 9 10 11

F#wtq: [135]

mp[467] [135] [467] [135] B mel: [123] F#wtq: [467] [235]

Red.

dim. mp

12 13 14 15

[135] [467] [135] [467] [135] B mel: [123] F#wtq: [467] [235]

54

54

64

64

&Cl.>

(brief ambiguity between

F# wtq and B mel. min.)

? Stgs.. . . . . . .

c

.L. . .

&(brief suggestion of Ab wtq.)

F

Ÿ#~~~~~~.>

?. . . . . . . . . . . -

œ# œ# œ# œ œ# œ# œ œ# œn œ œ# œ# œ# œ œ ™ œj œ#J ‰ œ# œ œ# œ# ™ œ# j œ# ˙# Œ œ#

˙# ™Œ œœ## œœ ˙

Œ œœn ˙# ™Œ œœ## œœ ˙

Œ œœn ˙# ™Œ œœ## œœ ˙#

Œ œœ ˙Œ œœn

˙#Œ œœ## œ

Œ

œ# œ# œ# œ œ# œ# œ œ# œ# œ œ# œ# œ# œ# œ œ œ# œ#œj ‰ œ œ# œnJ ‰

œ# œ# œ œ œn œ# œ#J ‰ ‰ œ#j œ# ˙ œj ‰

˙# ™Œ œœ## œœ ˙

Œ œœn ˙# ™Œ œœ## œœ ˙

Œ œœn ˙# ™Œ œœ## œœ ˙#

Œ œœ ˙Œ œœn

˙# ™

Œ œœ## œœ ™™ Œ ‰


incomplete seventh chords that fit within some modal hierarchy of triads,27 but this

is neither the case nor the intention. Instead, I hear only hints of hierarchy from the

movement of the bass underneath voice leading between a stable triad (the F♯ major

triad) and open voicings of stacked major and minor seconds that deviate from

diatonic expectations.

Example 10: The Nightingale and the Rose, bar 16-29

27 Persichetti, for example, proposes a hierarchy of primary and secondary triads within the church modes. (Persichetti 1961, 32)

{{

{

Reduction

f f

(q=120)16 17 18 19 20

mf

(G§ chromatic color tone)

mf

E wtq: [1357]

I7

mf[5724]

V7

[1357]

I7

[5724]

V7

f

(borrow C# from F# wtq)

Red.

f

21 22 23 24 25

p ff mf

I7

[1357]

mf V7

[5724]

I7

[1357] [1256]

Red.

mfmp

26 27 28 29

mp

pp pp mf

I WT I WT I

mp

34 54

34 54

34 54

34 54

34 54

34 54

54

54

54

&Stgs.

.Brass.

& WW. ä. . . . . . . . .

Ÿ# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

? Tbn.

Mostly whole tone area.

Direction from melody and bass.

ä

&Stgs.

.

&Pno.

Ÿ< >~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ##.>

. WW.

. . . . . .. . .

?Stable arrival point at

perfect fifth on beat 4.

&Winds

.

&Pno.

Glock. up 8va

> > > > >∑

? ∑ ∑Cello pizz.

œœœœœœ##

œœœ##œœœ# œœœ###

œœœ œœœ#œœœJ ‰ ‰

œœœJ˙## Œ œœ# œœ

j ‰ ‰ œœ#jœœ# ™™ ‰

Œ œœ# œœ## œœœn

j ‰ œœœ#j ‰ Œ œœœ##

j ‰ œœœj ‰ Œ

œœ# œœ## œœœnj ‰ œœœ#

j ‰ Œ œœœ## œœœ œœœj ‰ ˙# ™ ˙

˙ ‰ œJ ˙ ‰ œj ˙ ‰ œJ ˙ ‰ œj œ ™ ‰ œ# ™ ‰ œ#

œœ# œœj ‰ ‰ œœ#

j œœ ™™ ‰ œœœ#œœœ##

œœœ##œœœ# œœœ###

œœœn œœœ###œœœ##n J ‰ ‰

œœœJœœœ#

œœœn# ™™™

‰

Ó™˙<#> ™

Œ˙ œœ# œœ# œœJ

œj ‰ œœ# œœ## œœœn

j ‰ œœœ#j ‰ Œ œœœ##

j ‰ œœœj ‰ Œ

œœ# œœ## œœœ<#>j ‰ œœœ

j ‰ Œ œœœn# œœœ œœœJ ‰

œ<#> ™ ‰ ˙ œJ ‰ ˙ ‰ œJ ˙ ‰ œj ˙ ‰ œJ ˙ ‰ œj

œœ œœ##J ‰ ‰œ#j ˙#

œ œJ ‰ ‰œ# j œ# œ œ

œ œ# œ# j œœ#jœœ## œœ

j ‰ Œ Œ Ó

Œ˙

œœ œœ# œœ ‰ Œ˙

œœ œœ# œœ ‰ Œœ# ˙

œœ# œœ# œœ ‰ œœœœœœ ‰ Œ˙ ™

œœœœœœ ‰ Œ Œ Œœœ# œœ# œœœ<n>

œ Œ Œ Ó Œ Œ œ œ œ#


The B theme of The Nightingale and the Rose (Example 10) demonstrates a contrasting

approach to harmony within the WTQ. This section is set in the E wtq scale, which

is maximally intersecting with the previous section’s F♯ wtq. The harmonic shift

from F♯ wtq to E wtq is smooth yet distinct in character from a more traditional

diatonic shift. The core harmonic treatment here is between tonic and dominant,

unabashedly emphasized by the portamento trombone. Yet, within the WTQ there

is room to slip into pure whole-tone sections (bars 27 and 28) that offer contrast and

satire.

While “River” is diverse with its modulation techniques, The Nightingale and the Rose’s

modulations, both at local and structural levels, are constrained to the paths defined

by the scale network in Figure 7 above.

The interlude (bars 85-154, not shown) offers a more varied treatment of my modes.

At this point in Wilde’s story, the nightingale is able to create a red rose from a

white rose bud by pressing the rose’s thorn into her heart. The nightingale sings her

most beautiful night song ever while the lifeblood is drained from her and infused

into the rose, which ultimately blossoms beautiful and red. Through this journey,

the modulations between the modes navigate a triangle from my scale network:

E wtq → F♯ wtq → B melodic minor → E wtq → E acoustic → F♯ wtq.

There are mode conflicts representative of the nightingale’s life struggle. In bar 111

the nightingale song in the piccolo begins to assert B melodic minor with a repeated

B♮ that clashes with the B♯ (of F♯ wtq) in the bass line. In bars 126 and 128 the

piccolo firmly holds onto the D♮ of B melodic minor while the bass line clashes with

a D♯ (a chromatic passing tone hinting at B major). In bar 129, at the height of the

nightingale’s song, and just before her death, the harmonic tension is released with a


clear modulation to E wtq and a resolution to an E7 [ 1 3 5 7 ] chord. Bar 138

modulates to E acoustic, the solo violin blossoms into the red rose, and the D theme

returns in F♯ wtq.

With The Nightingale and the Rose I discovered new harmonies and relationships

within the context of the WTQ mode, and I experimented with “mixture” in non-

diatonic modes. Although there are steps outside of tertian territory, harmonic

motion within The Nightingale and the Rose remains defined by clearly delineated

chord movement. In “River” I explore novel synthetic scales and harmonic motion

defined more by modulation and less by chord motion.

The Modes of “River” 35

Chapter 4: The Modes of “River”

Generating the Scales and the Scale Network

In my continued exploration of modes and scale networks, I sought a palette of

diverse colours that would offer me a breadth of character for “River”. Using G wtq

as the parent, I determined what maximally intersecting scales I might use. I

included both well-known scales and previously unfamiliar scales that seemed to

offer potential:

Figure 9: Maximally Intersecting Scales of “River”

°

¢

°

¢

°

¢

&G Whole Tone Quint

&#7 : G Lydian Arabian (Mode 5: D Arabian Major)

&b2: G All-1 Phrygian (Mode 2: Ab Blues Major)

&b3: G Harmonic Phrygian*

&b4: C Melodic Minor (Mode 4: F Acoustic)

&#6: D Melodic Minor (Mode 4: G Acoustic)

&b3: D Phrygian Arabian*

&b7: E minor-5 chromatic‡

&4 → b3: Eb Lydian Arabian (Mode 5: Bb Arabian Major)

&* Not used in the final work.‡ Not on the initial list of scales, but added while composing.

6 → #7: F# Phrygian Arabian

˙ ˙ ˙ ˙# ˙ ˙b ˙ ˙

˙ ˙ ˙ ˙# ˙ ˙b ˙# ˙

˙ ˙b ˙ ˙# ˙ ˙b ˙ ˙

˙ ˙ ˙b ˙# ˙ ˙b ˙ ˙

˙ ˙ ˙b ˙ ˙ ˙ ˙ ˙

˙ ˙ ˙ ˙ ˙ ˙ ˙# ˙

˙ ˙b ˙ ˙ ˙ ˙b ˙# ˙

˙ ˙ ˙ ˙ ˙# ˙n ˙# ˙

˙b ˙ ˙ ˙ ˙b ˙b ˙ ˙b

˙# ˙ ˙ ˙ ˙# ˙ ˙# ˙#


Of this list, only the WTQ and the melodic minor / acoustic scales were previously

familiar to me. The brackets demarcate the parent scale from the two types of

modulations: those that are maximally-smooth voice leading and those that are not.

For maximally-smooth voice leading, the adjustment of the G wtq’s scale degree is

given. To modulate from G wtq to G Lydian Arabian, ♯7 indicates that 7 must be

raised (F → F♯). When a modulation causes a displacement of a scale degree, the

complete transformation is noted. To modulate from G wtq to E♭ Lydian Arabian,

4 → ♭3 indicates that 4 must be substituted with the equivalent of ♭3 (C♯ → B♭). In

some modulations, notes of the scale will need to be respelled. In moving from G

wtq to E♭ Lydian Arabian, the B of G wtq is respelled as a C♭ in E♭ Lydian

Arabian.

Absent from the list above are the maximally intersecting modulations between G

wtq and the five other WTQ scales derived from the same whole-tone[1] scale: A, B,

C♯, E♭, and F wtq. To modulate to any of these scales, 5 of G wtq must be

substituted with the quint from the new scale’s tonic. Modulating from G wtq to B

wtq requires the transformation 5 → ♯7 (D → F♯). None of these modulations offer

maximally-smooth voice leading.

I also wanted to invoke the sound of the blues scale within the movement. To

modulate from G wtq to a blues scale requires a minimum of two steps. A pure blues

scale comprises six notes, but my transformations result in seven-note collections: a

blues scale with an added-tone.28 The extra note adds an unexpected twist to the

blues character and reinforces the connection to the parent scale. The blues scales to

which I could modulate are shown below.

28 See Table 3, page 7 for the nomenclature of the blues scales with an added tone.


Figure 10: Blues Scales Two Steps from G wtq

The brackets again demarcate the G wtq from modulations with maximally-smooth

voice leading and modulations that displace scale degrees. All transformations are

shown in their complete form.

Figure 9 and Figure 10 both mark with an asterisk each scale that was not used in

the final version of “River”. The seven-note scales that were used, including all of

the maximally intersecting WTQ scales, are mapped into this scale network:

°

¢

°

¢

°

¢&G Whole Tone Quint

&2, 3 → #2, #3: G Blues + 8

&1, 2 → b1, b2: Ab Blues + 9

&4, 7 → b4, b7: A Blues + 2*

&1, 6 → b1, #6: B Blues + 2

&4, 3 → b4, #1: D Blues + 1*

&4, 6 → b4, #1: D Blues + 9*

&* Not used in the final work.

6, 4 → #6, #2: E Blues + 1*

˙ ˙ ˙ ˙# ˙ ˙b ˙ ˙

˙ ˙b ˙ ˙# ˙ ˙b ˙ ˙

˙b ˙b ˙b ˙n ˙b ˙ ˙b ˙b

˙ ˙ ˙ ˙ ˙# ˙ ˙ ˙

˙ ˙# ˙ ˙ ˙ ˙# ˙ ˙

˙ ˙b ˙ ˙ ˙# ˙ ˙ ˙

˙ ˙ ˙ ˙# ˙ ˙ ˙ ˙

˙ ˙ ˙ ˙ ˙# ˙ ˙ ˙


Figure 11: Scale Network for “River”

The network summarizes the relationships between the scales. Each line with a

single arrowhead on the ends represents a maximally intersecting relationship. A

double arrowhead means that the modulation requires two steps and results in an

intersection of only five notes. Black arrowheads indicate maximally-smooth voice

leading in the modulation. White arrowheads indicate that a scale degree is

displaced in the modulation. The text on each line indicates the transformation

required to modulate. Modulating from G wtq to A♭ blues major requires the

transformation A → A♭. Modulating back from A♭ blues major to G wtq requires

the inverse transformation: A♭ → A.

G wtq

A wtq

D : E

B wtq

G blues+8

F wtq

F acoustic

D : D♭

G acoustic

D : D

#

F# phryg. arab

F# : E♭

D#

: D

F# : E

D arab. maj.G lyd. arab.

F# : F

E min-5 chrom

F : E

D : FF# : E

C# wtq

G# : D

A♭ blues maj

A : D

A acoustic

F# : F

F# : D

D : E

F : E

A♭ blues+9

B blues+2

E♭ : E

C# : C

D : C

B♭, C : A, B

G : E

F : D

A♭ : A

G : G♭

G harm. arab.

B : B♭

E♭ :

E#

E♭ wtq B♭ : D

F# : D


Types of Modulation in “River”

“River” employs scale modulations mostly of three types: maximally intersecting

modulations; modulations between parallel modes; and modulations involving tonics

related by fifths. A few modulations fall outside of these categories. The following

example demonstrates parallel and maximally intersecting modulations:


{

{

{

Piano

Low Strings

p

(q=60)

7 8 9 10

pp gentle

G wtq:

Piano

Low Stgs.

11 12 13 14

G blue+8:G wtq:

Piano

Low Stgs.

15 16 17 18

A wtq: F wtq: G wtq:

4444

44

&b bb n bb

3 3

3

3

3

”“

&3 3 3

?- - -

&b bb n bb

3

3

3

3 3“: ;

&3 3

3

? bb

-

& bn b“: ;

3

3

3 3 3

&3 3

3 3

? # nnb b-

Œ˙ œœ œœ ˙ ™™ ‰™ œRœ œ# œ œœn ™™ œœnJ œœ œ œœJ œœ œ œ œœbn ˙n ‰

œœbJœJ

Œ ˙ œ œ ˙ ™ ‰™ œ œ# œ œ ™ œnJœb œ œ œ œ œb œb ˙ ‰ œbJ

˙ ™œœ œœ œœ œœ œœ

j œœœ ˙œœ

jœœ œœ œœ œœ œJ œ ™œ

œ œœ œœ œœ œœœJ œ ™ ˙œœ œœ

œ ™œœ œœ œœ œœ œœ œœ œœ œœœJ œJ œb ™ œ

œ œœb

œœ ™™ œœbJœœ œ œJ

œ œn œ ˙n œœœœb œJ œœ œ œ œ ™œ

j œ# œœnJ ˙ ≈ œRœœn œ# œœJ

œœ œœb œœ œœ ™™ œœJœ ™ œbJ œ œb œn œb ˙ œ œb œn œb œ œJ œ# œnJ ˙ ≈ œ œn œ# œJ œ œb œ œ ™ œJ

œœ œœb œœb œœ ˙ œ ™œœ œœ œœb œœb œœbb œœb œœbœbJ ˙ ˙ ™œœb œœ œœ œœb œœ œœn œœ œœn œœn œœ œœ

œ œn wœœ œœ œœ œœ œœ œœ œœ œœ

œœJ œœ# œœ## Jœœbn œœn œœb œœ# œœ œœ ™™ œœbJ œ œJ

œ œ œ œœb œœ#n œœ œœbb œœn ˙ ™™ œœ œœn œœb œœ# œœ œœJ œœ ™™

œJ œ œ#J œn œ œ œ œ œ ™ œj œ œ œ œ œ# œ œb œn ˙ ™ œ œ œb œ# œ œj œ ™

wœœ œœ œœ œœ œœn œœ œœ# œœ œœœ œn ˙ ™œœ œœ œœ œœ œœ œœ œJ œ ™ œœœ œœ œœ œœ œœ

j œœœœœj

˙ ™œœ œœ œœ œœ

œœœ œœ œœ œœ


This first entrance of the soloist is after a gentle G dominant ninth accompaniment

figure that is evocative of the slow and deep rolling of the Mississippi River. The

piano theme was composed with this underlying structure in mind:

Figure 12: “River” Theme Structure29

Despite the decorative chromatic figures, the G wtq scale can be discerned from the

underlying structure. The parallel modulation from G wtq to G blues+8 is a two-

step shift executed by the addition of the B♭ and C♮ and loss of the A♮ and B♮. G

wtq returns in bar 13, and a series of maximally intersecting modulations occur in

bars 15, 16, and 17: to A wtq, then F wtq, and returning to G wtq.

The treatment of modes in Example 11 differs from the treatment of modes in The

Nightingale and the Rose. Rather than create harmonic movement with clearly

delineated chords moving within a single mode, here each mode acts as a single

harmonic wash, and each harmony change is marked with a modulation. Because

the majority of tones within each mode are available to define this harmonic wash, I

can create lines in the accompaniment figure that move easily and independently,

shaping a sense of water currents. The unhurried harmonic rhythm evokes my

impressions of the slowly changing river. The piano solo – chromatic, figurative, and

a bit jazzy in nature – is slightly unpredictable and lazy in its movement. It takes 10

slow bars to traverse an octave and reflects the unhurried pace of life associated

with the Deep South.

29 Elements of this structure are used as the seed for the rotational arrays of “Breaking”.

& œ œ œb œ œ œ œ# œ œ œn œ œ œ œ œ


Example 12 below demonstrates modulation connected by harmonic or tonic

relationships. Here I imagine a typical New Orleans street corner near the

Mississippi River, where incongruent sounds mingle. The pizzicato contrabass,

swooping clarinets, and bright trumpets parody the easy jazz paradigm underneath

a busy triplet piano figuration of questionable industriousness. The cello echoes the

river motion of the opening. The complexity of the scales and their modulations

contribute to the sense of conflicting noises, yet there is a clear connection between

the scales that harmonically unifies the section.

The piano run in bar 76 is an F♯ Phrygian Arabian scale that leads to bar 77’s B

blues+2 mode, the “home scale” for this section. This is the only maximally

intersecting modulation in this example. The rest of the modulations are three-step

modulations whose relative distances in common tones is appropriate to the

incongruent mingling. Outside of this example, there is only one other three-step

modulation in “River”.

Bar 79 modulates to the G Phrygian Arabian scale with a treatment of the scale that

is unique at multiple levels. This modulation is one of the few multiple-step

modulations that are neither parallel nor related by fifth: the G minor tonic is heard

as home within this scale. However, within the G Phrygian Arabian scale is a

respelled F♯ major triad, [ B♭ C♯ F♯ ], that asserts itself. In addition, the E♭ of the

scale (6) is at times clearly heard. The result is a complex mixture – a dominant

triad and four chromatic neighbours (B♭ C♯ E♭ and G♮) to the B minor triad –

striving to resolve to the tonic of the B blues+2 scale in bar 80.



{{ {{ {{

Pia

no

Orc

hes

tra

ppp

legato

( q=60)

76

77

78

mf jazzy

pp F# P

hryg

. Ara

b.:

pp

B b

lues+

2:

Pia

no

Orc

h.

mp

79

80

81

mp

brassy

p

G h

arm

. Ara

b.:

B b

lues+

2:

p E m

in.-

5 c

hro

m.:

p

Pia

no

Orc

h.

mf

82

83

84

mp

mf

B b

lues+

2:

E m

in.-

5 c

hro

m.:

B b

lues+

2:

3 84+3 8

4 4

3 84+3 8

4 4

3 84+3 8

4 4

3 84+3 8

4 4

3 44 4

3 44 4

3 44 4

3 44 4

4+3 8 4+3 8 4+3 8 4+3 8

&7

7

73

33

33

3

33

33

33

3” “

&3

33

33

3

33

33

3

33

&∑

Cl.

#3

3 3

3

?S

tgs.

Cb., T

bn

., T

ub

a

# ##C

b. p

izz.V

c.

&3

3

33

33

33

33

3

33

33

33

33

3

“:; &3

33

33

33

33

33

33

33

33

33

3

&T

pt.

Tp

t.

33

3

? &“:;

33

33

33

3

33

&?

∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏&

∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏

33

33

33

3

&# #

# nnn

∑&

Fl.

, B

sn.

3 33

3

?#

#

œ#œœ

œœ#œœn

œ#œœ

œœ#œœn

œ#œœ

œœ#œœn

œbœnœœœœ#œ

œœ

œnœœ#œœnœ#œœœœb

œœ

œ#œbœœœœœ#œœ#œœ

œœb

œœbœœœbœ

‰‰

‰œœœœœbœœb

œœ

œœœœœbœnœœbœœ

œ#œ

œnœœœbœœbœœœœœ#

œœ

œœœœbœœ#

‰œ œ

œ œ# Jù ùœ œ™™

Œ≈œ#

œnœ œ

œ #jœ œ

œœ

Óœj

œœ n ùùœœ #

œœ#œœn #

œœ

œ œ ™™œ

œœœœœœœœn #

œœœœŒ

œœ#

‰œ#

œœ

œ#œ#

œœn

‰œ J

‰œ

œœ

œœ J

‰œ#

œœ

œn œ# J

œbœ

œ#œn

œœb

œ#œb

œœb

œœ#

œnœ#

œœb

œ#œ

œbœ#

œœ

œbœ

œbœn

œœ

œnœ#

œœ

œnœn

œnœbœ

œœ

œœn

œnœ

œœ

œœ#

œœ#

œnœ#

œœ

œnœ#

œnœ#

œ#œ

œnœ

œœ#

œœb

œ#œ

œbœ

œ#œn

œ#œ

œnœ

œ#œ

œbœ#

œœ

œbœ#

œœb

œnœ

œnœ

œbœn

œbœ

œœb

œœnœ#

œœ

œœ

œœ

œœ

œœn

œœ

œnœ#

œnœn

œœb

œœ

œbœ

œnœ

œ œœ œ#

œ œ#œ œ

œ œœ œb

Óœ œ

œ œ#œ œ

œœn˙# ùù

œ œ#œ œn n

œ œ#˙œj

œ#™œ œ J

‰Œ

œœ

œœn

œ#

œb‰

œ# J‰

œœ

œbœ

œb JŒ

œnœ

œ#œ

œŒ

œœ#

‰œ#

œœ J

œœ#

œnœ

‰œ

œœn

œœ J

œœ#

œœn

œ

œœ

œ#œ

œ#œ

œœ

œbœ

œœ

œnœ

œœ#

œœ

œbœ

œ œ œnœ œ œ#

œ œ œ ™™™ Jœ

œnœ#

œ œœ œ#

œ œnœœ

œbœ

œ œ œ# nœ œ œ

œ œ œ‰

œœ

œœ#

œœ

œ#œ

œœ

œbœ

œœ

œbœn

œnœ#

œœ

œ œ œ œn ™™™™œœœœ nj

˙œœœœœ # ™™™™™

œœœœjœœœœ

‰

‰œ <# >œ

œœ

œ œœ œ

˙œ œ

œ œb bœ œn

˙Ó

‰œœœ#

œœœnœœœ # #

‰œœn J

‰œ J

‰œ

œœn J

‰œ J

œ#œn

œœ#

œ œ Jœ

œ#œ œ J

œŒ

œœ#

œœn

œŒ

œœ

Œ™œ#

œœ

œnœ#


The modulations to and from the E minor-5 chromatic scales30 in bars 81 and 83 are

straightforward reflections of the tonic (B) and subdominant (E) relationship. Even

though the modulations are three-step, the fifth relationship between the tonics

strongly connects the two scales.

Octatonic Hexachord Subsets in “River”

The scale network of Figure 11 contains only seven-note scales, and the majority of

“River” stays within these scales. However, there are three sections of “River”

written with hexachord and octatonic approaches borrowed from my harmonic

explorations for “Still”. Scale networks may contain scales of all sizes, but in these

sections I treat modulation differently than that assumed by a scale network.

Consider the relationships between the G wtq and six specific hexachords:

Figure 13: Hexachord and Whole-Tone Quint Comparison

Below the G wtq scale is a block of hexachords and the resulting hexatonic scales.31

The first column of hexachords comprise stacked major triads a tritone apart (cf.

Petrushka chord). The second column contains hexachords that comprise stacked

minor triads a tritone apart. Each hexachord in the first column is the complement

30 See footnote 13 on page 6 regarding the suitability of calling this a true scale. 31 I use hexatonic in its generic sense to mean any six-tone scale, not in the specific sense of a scale of alternating semitones and minor thirds. (Wilson)

°

¢

°

¢

&G Whole Tone Quint

&G Major + C# Major A minor + Eb minor

& B Major + F Major C# minor + G minor

&Eb Major + A Major F minor + B minor

˙ ˙ ˙ ˙# ˙ ˙b ˙ ˙

˙ ˙### ˙ ˙b ˙ ˙# ˙ ˙ ˙ ˙bbb ˙ ˙b ˙ ˙# ˙n ˙#

˙## ˙n ˙ ˙ ˙# ˙# ˙# ˙ ˙##˙bn ˙# ˙ ˙ ˙n ˙b ˙b

˙bb ˙# ˙b ˙b ˙ ˙n ˙b ˙b ˙b ˙# ˙n ˙b ˙b ˙ ˙ ˙


of the hexachord in the second column. The hexatonic scales in Figure 13 above are

the only six hexatonic scales used in “River”.

The hexatonic scale derived from the stacked G and C♯ major triads (called G/C♯)

maximally intersects both G wtq and C♯ wtq: five tones are in common. The A and

E♭ minor hexachord (called Am/E♭m) is a complement to G/C♯; the two

hexachords have zero intersection. Each of these hexachords is a subset of a distinct

octatonic collection. The hexachords in the subsequent staves have similar

relationships to WTQ scales and each other.

Example 13 below represents about half of the hexatonic bars within “River”. Here

I make a clear reference to the jazz heritage of New Orleans. The contrabass and

tuba present a walking bass, and the piano offers an improvisatory treatment of the

octatonic scale over syncopated seventh chords. In jazz nomenclature, the octatonic

scale is called the diminished scale, and the left-hand voicings of diminished triads

plus major sevenths pulled from the diminished scale is a common jazz

accompaniment to this scale.32

32 In jazz, these chords are sometimes considered to have dominant function, but I do not treat them as dominants. (Levine 1989, 76-81)



{{ {{ {{

Pia

no

Orc

hes

tra

pO

ct 1

,2:

e=q (q

=12

0)54

55

56

57

58

59

60

Oct 0

,2:

Oct 0

,1:

pp

B/F

:C#m

/Gm

:

Pia

no

Orc

h.

mp

f

61

62

63

64

65

Oct 0

,2:

Oct 0

,1:

mf

mf

Eb/

A:

pF

m/B

m:

Pia

no

Orc

h.

q=e

(q=

60)

66

67

68

69

70

°

mf

p C#

wtq

:

4 43 4

4 4

4 43 4

4 4

4 43 4

4 44 4

3 44 4

2 44 4

3 4

2 44 4

3 4

2 44 4

3 4

2 44 4

3 4

3 44 4

2 44 4

3 44 4

2 44 4

3 44 4

2 44 4

3 44 4

2 44 4

&.

..

33

33

33

33

33

33

33

33

33

33

33

33

&.

..

33

33

33

3

&∑

∑∑

Tp

t. h

arm

. m

ute

∑∑

∑3

3

?C

b. p

izz.

, Tb

a.

&.

” “

33

33

33

33

33

33

3

&.

. 3.

-3

33

33

3

3

&T

pt.

harm

. m

ute

Cl.

?3

33

33

33

33

3

33

33

?H

ns.

, Tb

ns.

bb

3 3

3 3

3 3

&3

33

33

33

33

3

36

63

3

&. 3

. 3

3

3

3

3

3

?B

sn.

Tp

ts.

&3

33

33

33

33

33

?#

n b#

n bn b

#n b

#n

#n b

Tb

ns.

, Tb

a.

3 3

3 3

œœbœœ

œœbœb™œ œb

œœbœ J

œb œœœb

œ Jœb œœbœ

œb œœb œ

œb œ‰‰

œb Jœœ œ

œ œ#œ

œ J‰Œ

œ œ œ œb # JŒ

Œœ# Jœ#œ#œn

œnœœœ

™ œœ# œ

œ#œ# JŒœ J œ#

œœœœb

œbœ™ œ

œ#œnœ#œ#œ#œn

œ#œ#œ

Œ˙b nb

œœœœœœœœb nbj

œœœœ˙n bb

œœœœœœœœb nj

˙˙b nb

œœœœn ##nj ‰

Œœœœ# njŒ

œœœœb nb bŒ

œœœœn ##j ˙

˙n #nœœœœ

œœœœb nbj œœœœœœœœn #nj

˙œœœœn ##

œœœœœœœœb nbj

‰œœ œj

‰ œ#œ œ#

œœ

œb™œ

œœb

œ ™œbœ

œœ ™

œb œœ

œbœ

œ#œ

œb™œœb

œœ

œ#œ

œ™œœb

œbœ#

œœb

ÓŒ

‰‰

œn Jœb

œ œœ#

œ J‰

œ Jœb

œœ

œœ

œ#œ

œ#œnœ

œbœ

œœ#

œœ#

œ#œ#

œ#œn

œbœ

œœ

œœ

œbœn

œœ

œœb

œ

˙ œœœœ

œ œ œ œb nbb J‰

‰œb J

œbœbœbœ

œb J‰

‰œ œ œ œb nbb

œ œ œ œœ œ œ œb bb J

œ œ œ œb bbœ œ œ œ

œ œ œ œ# bnJ

œ œ œ œœ œ œ œ# b J

œ œ œ œœœœœb b

œœœœœœœœ# #j

œœœœn nb bŒ

Ó

œœb

œ#œ#

œœ

œb™œ œ

œ#œj

‰Œ

Œœj

œbœ

œœ

œœ#

œœ#œnœ

œbœ

œœ#

œœ#

œœ#

œœn

œbœ

œœ

œœ

œbœn

œœ

œœb

œ

œnœb

œ#œ#™

œœ

œ#™œ#œ

œbœ

œ#œ#™

œœb

œœ

œœ œœœ œ

œjœœ

œ œ Jœ

œjœœ

œ œ Jœ

œj œ œ J

œbœn

œbœ

œœ

œnœb

œbœ

œbœ

œœ

œœb

œœb

œœb

œœ

œœn

œbœb

œœb

œœ

œœn

œbœb

œœ#œ#œ œ

œ œœ œ

œ œœ œ

œœ

œœ

œœ

‰‰

œ œ œ œ# b J‰

œ œ œ œn # J‰

œœœœn #j ‰œœœœ b bj

œœœœŒ

Ó‰

‰œ œ œ œ# b J

‰œ œ œ œn # J

‰œœœœn ##j ‰

œœœœ b bj ‰œœœœb nbj ‰

˙n #wwww b n

œ#œn

œbœ

œœ

œnœ#

œ#œn

œbœ

œœ

œœb

œnœ#

œnœb

œœ

œœn

œ#œ#

œnœb

œœ

œœ

œ#œ#

œ#œn

‰œœbj

œœœ# nœœœb#

œœœ n #œœœ# #

œœœ#œœœ

œœ œœ œ œ

œœ œœœ œ

œ œ œœœ œ

œjœœ

œ œ Jœ

œjœœ

œ œ Jœ

œ œ œœœ œ

œ œ œœœ œ

œ œ œww# #


The 10 bars prior to this example are unambiguous in their hexatonic assertions, but

the octatonics in Example 13 supplement the hexatonic foundations. The walking

bass stays within each of the hexatonic scales labelled in the example: B/F →

C♯m/Gm → E♭/A → Fm/Bm. The piano and other instruments playing over the

walking bass use the octatonic scale that is a superset of the active hexatonic. For

example, in bar 54, with the walking bass in B/F, the piano makes use of all eight

notes within Oct0,2, a superset of B/F. When the walking bass shifts to C♯m/Gm, the

piano right hand shifts to Oct1,2, a superset of C♯m/Gm, however the left hand

borrows notes from Oct0,1, creating tension that is resolved in bar 61. All remaining

octatonics in Example 13 are supersets to the active hexatonics.

The walking bass and improvisatory piano in bars 54-64 are stylistically convincing

as jazz. Yet, to the best of my knowledge, the hexatonic nature of the bass line

against the piano’s octatonic has not previously been explored this way.

Table 4: Modulations in “River”, bars 43-70

Only Hexatonic Scales All Active Scales Bar Transformation33 Scale Transformation34 Scale 43 A wtq A wtq 45 A, D♯, (E) → G♯, D G/C♯ A, D♯, (E) → G♯, D G/C♯ 49 complement Am/E♭m complement Am/E♭m 54 B♭, E → B, F B/F E♮, B♭ → (2)5(8)E Oct0,2 58 complement C♯m/Gm 0369 → 147T Oct1,2 61 G♯, D → A, E♭ E♭/A 258E → 0369 Oct0,1 65 complement Fm/Bm 147T → 258E Oct0,2 70 F♯, C, D → F𝄪, C♯, D♯, (A) C♯ wtq 0(2)6 → C♯, F𝄪 C♯ wtq

33 Notes in parentheses indicate extra scale degrees that are removed (left side of the arrow) or are added (right side of the arrow). 34 Transformations into and out of the octatonic are represented by pitch class numbers. “T” represents pitch class ten, and “E” is pitch class eleven.


Unique to bars 45 to 69 are modulations that do not follow the conventions

previously discussed. In Table 4, the first major column relates the modulations into,

through, and out of the hexatonic scales used in “River”: The second major column

adds consideration of the octatonic scales.

The modulation from A wtq into G/C♯ is a relatively short two-step, maximally-

smooth transformation that involves the loss of one extra tone (E). The modulation

is further facilitated by the developmental nature of the music here: earlier musical

gestures are reinterpreted within the G/C♯ hexatonic scale.

In contrast, the modulation to Am/E♭m is antithetical to the common tone approach

of all previous modulations presented in this paper. The modulation from G/C♯ to

the complement Am/E♭m is both dramatic – the ear recognizes the complete shift

between hexachords with no common tones – and maximally-smooth: each tone

from one hexachord shifts chromatically up or down to a tone of the next

hexachord.35 With this modulation is a sense of stepping forward.

To return to G/C# would be a musical step backwards. Instead, bar 54 makes a two-

step shift to the B/F major hexachord. This is an optimal shift between scales of

these two hexachord classes: there are no more than four common tones possible

between any of the potential pairs. The transformation (B♭, E → B, F) is a Leading-

tone exchange36 for each of the triads involved: E♭ minor → B major and A minor

35 In “Still”, some of my Russian inspired modes are closely related to these hexachord complements. Chapter 6: Modes Inspired by Yavorsky’s Theories examines the voice leading that generates these modes and how this voice leading is closely related to the modulations between complements. 36 A Leading-tone exchange is a transformation mapping a major triad onto a minor triad (and vice versa), where the two tones of the minor third are kept and the third


→ F major. The effect is a subtle shift in colour between the two closely related

hexachords that does not disturb the forward motion of the previous modulation.

The series of hexachord modulations from bar 45 to bar 65 is sequential in nature:

G/C♯ → Am/E♭m →

B/F → C♯m/Gm →

E♭/A → Fm/Bm

This three-cycle sequence creates a sense of harmonically stepping forward three

times – once for each of the complement modulations – and a triad root movement

that walks the whole-tone scale from which the entire movement is derived: G A B

C♯ E♭ F.

The net result is an intentional climb to a localized climax that begins at bar 70.

However, the modulation from Fm/Bm hexatonic to the C♯ wtq in bar 71 would be

a three-step transformation: only half of the hexatonic is comprised of tones

common to C♯ wtq. This is far from optimal, and there is no potential claim of a

parallel or fifth relationship that would smooth the transition.

The smoothness of this modulation is explained by the role of the octatonic scale at

play. In bars 54 to 65, the octatonic scales are subservient to the hexachords

emphasized melodically and harmonically by the bass and piano, and we hear the

hexatonic modulations as primary. However, starting in bar 65, the piano and

clarinet increasingly give equal time to all tones within the octatonic so that a full

octatonic sound is prominent by the time bar 70’s transition to C♯ wtq occurs. The

tone moves by step. For example, the transformation between F major and A minor is a Leading-tone exchange. (Berry)


effect is a smooth modulation involving five common tones between Oct0,2 and C♯

wtq, and the heightened energy of the previous 25 bars is undisturbed upon exiting

this extended hexatonic area.

I have examined how Tymoczko’s approach to scale networks has influenced my

choice and design of the modes I used in both The Nightingale and the Rose and

“River”. I showed how the Whole-Tone Quint scale can alternate between a strong

grounding in tonality and floating through the whole-tone. I created for “River” a

sizeable and diverse network of closely related scales. Considerable discussion has

focused on the modulation between my modes, and I have used some of Tymoczko’s

metrics (the size of the intersection and the smoothness of the voice leading) to

discuss how the modulations support the intended affect of my music. I expanded

Tymoczko’s approach to modulation to include discussion of parallel modulation

and modulation by tonic relationships, and I used these as justifications for the

success of many multiple-step modulations.

Harmonically speaking, “River” represents some new areas of growth. Working

with new synthetic modes has opened a variety of new colours. For much of the

work, the harmonic motion is defined not by individual chords but by modulations

between different scales. Still, my modes frequently functioned more as colourful

variations of traditional harmonic relationships instead of radical breakthroughs in

how I approach harmony.

To break beyond my traditional approach to harmony, I needed completely

different tools. Below I discuss the first of these tools I explored – rotational arrays

– and how it relates to my use of modes.

Rotational Arrays as a Derivative of Mode 50

Chapter 5: Rotational Arrays as a Derivative of Mode

Introduction

“Breaking” is likely the most emotional work I have written, and understanding the

context of the movement is useful in my discussion of rotational arrays. The

program notes I wrote for the “Breaking” explain:

As Hurricane Katrina passed by New Orleans, storm surges pushed water from the river

and lake into the canals that cross the city. While the rising water overtopped some

levees, it was the seven catastrophic levee failures within the city that overwhelmed the

city’s pumping stations and prevented New Orleans from completely draining the

floodwaters for nearly a month. Although the levees were designed to resist water at levels

much higher than those Katrina pushed into the city, the Army Corps of Engineers

eventually conceded that the levees were never built nor maintained to those design

specifications. Tests that demonstrated the appropriate design strength were either

misinterpreted or ignored, money was pinched, and many fingers were pointed in the

flooding’s aftermath. As it turns out, the 2005 New Orleans flood was not a natural

disaster: it was a man-made disaster that killed a thousand or more New Orleans

residents and cost over $100 billion.

The second movement is not about the tragedy and pain of the flood, as originally

intended. It is more an expression of the anger that grows with awareness of the extent

that human decisions — whether by error, apathy, or intentional malfeasance — played

a role in this disaster.

The arc of the work is inspired by the timeline of events associated with Hurricane

Katrina. On 28 August 2005, at 12.40 a.m. (Central Daylight Time), Katrina was

far offshore and declared a category 4 hurricane. On 30 August, around noon,


martial law was declared in New Orleans. These two events were mapped onto a

musical time period of five minutes – the originally intended length of “Breaking” –

at a tempo of q= 120.

On 29 August, between 6.30 a.m. and 9.00 a.m., there were seven catastrophic

failures in the levees protecting New Orleans.37 This maps to near the 2’30” mark in

my music. Up to this point, “Breaking” has been climbing in intensity. At bar 77

(rehearsal J), which exactly correlates to the moment (6.00 a.m.) when water first

topped some of the levees in New Orleans East, the music dramatically changes

character. Following shortly are seven full orchestral fortissimo hits symbolizing the

seven levee failures, the last hit falling on the 9.00 a.m. mark. The coordination of

the levee failures to my music is the only place where I carefully matched the time

frames. The music that follows symbolizes the rising waters and the chaos within

the city. The ending is a raw expression of anger.

Rotational Array for “Breaking”

To generate material for “Breaking”, I used rotational array techniques modelled

after those applied by Oliver Knussen for Flourish with Fireworks.38 In Flourish with

Fireworks, Knussen’s treatment of the material generated by his five-note row and

the resulting rotational arrays is deeply engaging, yet it has enough transparency

that the listener can immediately connect to the motivic elements involved and hear

the harmonic language at work. My goal was to match that same level of

transparency and engagement.

37 These times are estimates deduced from a combination of first-person accounts and stopped clocks of flooded houses. (Nelson 2015, 37) 38 (Anderson 2002)


I connect the material for movement 2’s rotational arrays with the material from

movement 1. The row I chose and its generated array are shown in Figure 14

below.39

Figure 14: Rotational Array for “Breaking”

The prime row has five notes: F D E♭ B A. A few key characteristics of this row’s

derivation stand out:

a) The entire row is of the G wtq scale.

b) There are no duplicate notes.

c) When arranged in order of pitch, the resulting ordered collection is NCS

compliant. (Including a C♯ would have created two consecutive semitones.)

39 The staff labeled Sf is explained in “Stacked Columns in the Arrays” on page 55.

°

¢

Af

Bf

Cf

Df

Ef

Sf

Oct0,2

Oct1,2

Oct0,2

Oct1,2

either way

&Stacked Row Harmonies and Inversions

&Oct0,2

&

&

&

&Stacked Column Harmonies revoiced as incomplete M7 chords w/ added tone

˙ ˙ ˙b ˙ ˙ ˙˙#n

˙˙#n

˙˙#n

˙˙n#

˙˙n#

˙ ˙b ˙ ˙ ˙b ˙˙#nb

˙˙#nb ˙

˙n#b˙˙n#

b ˙˙n#

b

˙ ˙# ˙ ˙ ˙ ˙˙b ˙

˙b ˙˙b

˙˙b

˙˙b

˙ ˙b ˙ ˙# ˙ ˙˙bb

nb ˙˙bbnb ˙

˙bbbn

˙˙bn

bb˙˙bnbb

˙ ˙# ˙# ˙ ˙˙˙bb

n˙˙nbb

˙˙nbb

˙˙nb

b˙˙bnb

˙ ˙###b ˙#b ˙bnn ˙nn#n‹ ˙ ˙œb##

Y

Yn##Y

Ynbn˙œ#nnn


d) Sequentially, it is the first five notes of the opening melodic structure within

“River” (Figure 12) that collectively meet the above criteria.

e) The entire row is of the Oct0,2 scale.

Constraining this row to the G wtq scale and deriving its sequence from the opening

theme of “River” connect “Breaking” to the previous movement. Other rows I tried

also had connections to “River”, although not always in the same way. That this row

has no duplicate notes and is NCS compliant is largely a byproduct of my

experimentation: of the nineteen rows that I explored, this one best offered an

interesting melodic shape and an appropriate balance of consonance and dissonance

in the resulting harmonies. Limiting the row to the octatonic scale was not a

requirement I predefined, but it is a characteristic that is heavily utilized in

“Breaking” and discussed further below.

As illustrated in Figure 14, the row is rotated in the traditional manner. I label each

of the rows generated by the rotation Af through Ef. The letters A to E indicate a

specific rotation of the row, and the f indicates that each of the rows is transposed to

start on pitch class F. The second bar of each row shows the stacked row harmonies

for that row. The initial chord, comprised of the row’s five notes, is an open voicing

spanning roughly a twelfth. Each successive chord is a different inversion of the

first chord. The voicing and inversions shown here are the same voicings used by

almost all of the piano’s vertical harmonies.


Application of the Rows

Example 14: “Breaking”, bars 1-15

Like Knussen, I use the generative cell as a loose map of pitch centres for the entire

movement. At the local level I employ a more flexible application of the rows: row

statements may begin anywhere within the cell, cycle in sequence, end anywhere,

and temporarily be interrupted by restatements of prior material. This enables more

control of melodic lines and, perhaps of greater importance, the ability to develop

the work’s energy with rhythmic repetitions of musical fragments. In the opening of

“Breaking” (Example 14), partial row repetition is key to the character of the

rhythmic brass. The piano’s melodic gesture in bar 13 restates notes from both Af

and Bf and is used to close the phrase.

{{

{

{

{

{

Piano

Orchestra

pp

Af, Oct0,2

q=120 2 3 4 5 6 7

pp

pp

Af, Oct0,2

Piano

Orch.

espress.

8 9 10 11

ppp

p

BfR, Oct0,2

pp

Cf, Oct1,2

Piano

Orch.

Bf, Oct0,2

A12 13 14 15

p

Cf, Oct1,2

p

44 4+38 4444 4+38 44

44 4+38 44

44 4+38 44

5454

5454

54 4454 44

54 4454 44

& ∑ ∑ ∑ ∑ ∑

& ∑ ∑ ∑ ∑ ∑

? ∑ ∑Timp.

> > > > >? Tbns., Tba., Low Stgs. accents. . . . . . -> . . . -> . . -> . . -> . .

. . . >∑ . . . . . . -> . .

& ∑ ∑ ∑

& ∑ ∑ ∑

? ∑ ∑ &Vln.

? . -> . -> . .. . . . > . . . . . . . . . . . > . . . n##. >

. . . . .

& ∑ ∑

& ∑ ∑

& ?Cls., Hns.. . > . . . . > . . > >

? #<#>. . . . . . . . . . .

#. . . . . . . . . . . .

##. .

.> >

˙#n œœœJœœœ œœœ#J

˙ œœœ ™™™

˙ œœœjœœœ œœœn#

j˙ œœœ ™™

™

Œ Œ Œ œ œœ œ œ œ œ œ œ œœœ œ œ œ œ œ œ œ œ œ œœœœœ œ œ œ œ Œ Ó

œœ œœ œœ œœ œœ œœ œœœbb œœ œœ œœ œœœbb œœ œœ œœœb œœ œœ œœœb œœb œœ œœœœœœ œœj œœ ™™ ww ww œœ œœ œœ œœ œœ œœ œœœ#b œœn œœ

Ó ˙

Ó ˙#

Ó˙# w

œœ œœœ#b œœn œœœ#b œœn œœ œœ# œœ œœ œœ# œœ œœ œœ œœ œœ œœ œœ œœ œœb œœ œœ œœ œœ œœn# œœ œœ œœ œœb œœ œœ# œœ œœ œœ œœ œœ œœ

œœœJœœœ# ™™™ œœœb ˙#bn œœœn# ˙nb ˙#bn

œœœ<#>j œœœn ™™

™œœœb ˙b œœœn ˙b ˙b

w<#> œ w œ œœn# œœ œœ œœ œœ œœ œœ œœ# œœ œœ œœ œœb œœ

wœœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœœ œœ wœœ œœn œœ œœ œœ œœ œœ œœ œœ œœ œœœ œœ œJœœj ‰ Œ Ó Ó œ œ


To create cohesion and facilitate the soloist’s performance, most piano voicing

comes directly from the voicing of the stacked harmonies already discussed. The

piano chords in Example 14 can be found within the generated arrays shown in

Figure 14. Bar 5, beat 1, is voiced the same as Af, stacked row 3. Bar 6 is voiced as

Af, stacked row 1. The row gives the melody, and the stacked row gives the

harmony that fits underneath a particular note.

Tension is created when the octatonics of two rows clash. In bar 11, the trombones

begin a rhythmic pattern using the first two notes of Cf, which belongs to the Oct1,2.

At the same time, the tuba and violin hold the F♯ from BfR, and the piano continues

unfolding its statement of Af and Bf. Af and Bf belong to the Oct0,2, and the tension

between the clashing octatonics foreshadows the nature of this movement. At bar

14, the piano pauses, ending the Oct0,2 clash, and the Cf statement in the horns and

clarinet continues without tension.

Stacked Columns in the Arrays

In Figure 14’s rotational array, the first bar of the last staff (labelled Sf) shows the

stacked column harmonies from the array. These harmonies are generated the

standard way: all of the first notes of each row are collected into the first chord, all

of the second notes of each row into the second chord, and so forth. Duplicate notes

are removed.

In the second bar of Sf, I have revoiced each chord as an incomplete major 7th chord

with an added-tone placed above or below the chord. The closed noteheads indicate

the added tone, and the open noteheads indicate the tones that are from the major

7th chord. Noteheads with a cross indicate that the note can be considered the added

tone or part of the major 7th chord.


This entire rotational array is used in five different transpositions: one for each note

of the original row (F D E♭ B A). The suffix note name for each label (Af – Ef, Sf) is

changed to match the transposition (e.g., Af, Ad, Aes, Ab, and Aa). The complete set

of rotational arrays is contained within the appendix on page 86.

The stacked rows, which are not subsets of octatonics or WTQs, are used only

occasionally within “Breaking”. In the following example, the piano and brass

unfold the Sd harmonies as articulation for the neoromantic treatment of the rows Af

- Df in the violins and accompaniment.


The bottom staff in Example 15 uses the harmonies of Sd. I label the source of each

harmony with Sd.1 to Sd.4 to indicate which of the four Sd harmonies is being used.

Each of the Sd harmonies has four voices, and I separate them into two separate

lines of music. The bass line is played sequentially by the octaves in the piano and

{

{

Orchestra

f

Af, Oct0,2

Bf, Oct0,2

(q=120)

G

56 57 58 59

ff mf

from Dd, Oct0,2

f mf

mfmf simile

f

Orch.

Cf, Oct1,2

Df, Oct0,2

60 61 62 63

from Ed, Oct1,2

f

from Dd, Oct0,2

simile

f

44

44

44

44

34

34

34

34

&Vlns.

&WW

>Cls.

?Low Stgs.

b>

> .- .-

' ' '

.-

' ' ' ' 'b. .

' ' '> ' ' ' 'b

' ' ' ' ' '

. .

? ∑Piano and brass

Sd.1

Sd.4

Sd.2

> . >∑

Sd.2

Sd.3

Sd.3

Sd.2

>.

>.

& ∑

&

? b'> ' ' ' '

b' ' ' ' ' ' '> ' ' ' ' '

b' ' ' ' '

? ∑ ∑

Sd.1

Sd.4

Sd.2

> .Sd.3

Sd.3

>.

Sd.2

Sd.4

>.

Sd.1

>.

œœ#j œœ ™

™ œœœœbb œœJ

œœnn ™™ ˙ œœ

œœ œœ ™™ œœ##Jœœ œœ

˙## Œœœœœ##J ‰

˙nb œœnb œœnn œœ œœb œœn œœn ˙b œœ ˙b Ó

œœœj œœ œœœ œ œ œœ œœ

jœ œ œœ

œj œœb œ œœ œ œœ œœ œœœ œ œœœj œœ œœœ œ œ œœ œ œœ

jœœj

œœ œœœ œ œ œ œ œœ œ œœ œœ

Óœœ œœœn## œœ##

Óœœ##

œœœ#œœ

œœœn

œœ œœ## œœœœnn œœ œœ œœ

œœ œœœœ

œœ œœœœ œœbb ˙

˙bn ˙n ˙ ˙ œœ ˙b ™™ ˙ ™™

œœœj œœ œ œœ œ œœ œœ

jœ œ œœ

jœœœ œ œ œœ œœœ œ œ œœ

jœœœj œœb œœœ œ œœœ œ œ œœ

jœœj

œœœ œ œ œœ œœj

œ œ

Ó Œœœ œœœn## œœ##

œœœ#œœnn

œœœnnœœ

œœœnbb


brass. The top three voices are played in reverse order, from the fourth chord to the

first chord. These two separate threads of music are alternated to create the figures

seen in the piano and brass. Rehearsal G is the beginning of a lengthy crescendo in

energy that culminates just before the point marking the levee breaks. The long arcs

of the violin lines bring imagery of strengthening winds. The stacked columns of Sd

do not share a scale with any other material, and the accents offer a harsh

independence evocative of the violence of the storm.

Transposed Stacked Rows in “Breaking”

One final transformation is used to generate potential harmonies. For each set of

stacked rows within a given row rotation and transposition, the inversions are all

transposed to the first note of that iteration of the row. Figure 15 demonstrates the

transposition for the row Af.

Figure 15: Transposing Stacked Rows

In Figure 15, Tf shows each inversion of the stacked rows transposed to bass note F.

For convenience in reading the collection, the second bar in Tf shows the same

harmonies of the first bar revoiced into closed position.40 There are five distinct sets

of stacked-row transpositions (Tf – Ta), one for each note of the original row. All

five are included at the end of the appendix on page 86.

40 The specific voicing of the closed position has no relevance to how “Breaking” was composed.

°

¢

°

¢Af

Tf

Oct0,2

Oct1,2 Oct0,2 Oct0,2 Oct0,2 Oct1,2 Oct1,2 Oct0,2 Oct0,2 Oct0,2 Oct1,2


&Transposed Stacked Rows Closed Position

˙ ˙ ˙b ˙ ˙ ˙˙#n

˙˙#n

˙˙#n

˙˙n#

˙˙n#

˙˙bb

n ˙˙nbb

˙˙bn

nn ˙˙bn

bb ˙˙nbnn ˙bbb ˙nbnb ˙bnn ˙## ˙nn#


Within “Breaking”, the process of generating rotational arrays and harmonies

parallels my understanding of Knussen’s process for Flourish with Fireworks with one

exception. When Knussen generated his stacked-row harmonies, he maintained the

same relative registers for each note of the row. Thus, his five-note row generated

stacked-row harmonies that look like this:

Figure 16: Stacked Rows of Flourish with Fireworks

Compare this with Figure 15, where my stacked rows are voiced differently from

the original registers of the row’s notes. Consider the implications of the differences:

• Voicing: In my analysis of Flourish with Fireworks, I did not note any harmonic

moments where Knussen intentionally maintains the same voicings as shown

above. In contrast, my choice of voicing plays a large role in the piano part of

“Breaking” (see the discussion about Example 14 starting on page 54).

• Order of Transpositions: The choice of voicing for the stacked rows affects

the order of the bass notes in the sequence of inversions, and the order of the

bass notes directly defines the order of transpositions of each harmony. Thus

the order of the transposed stacked harmonies in Flourish with Fireworks is

determined by the register of each note in the original row, and the order in

“Breaking” is determined by the voicing I chose for the stacked rows.

°

¢

°

¢Row I

Transposed

I II III IV V

&Original Row for Flourish with Fireworks Stacked Row Harmonies and Inversions

&Transposed Stacked Rows Knussen's Closed Positions

˙ ˙b ˙ ˙n ˙˙˙# ˙

˙ ˙˙# ˙

˙n ˙

˙

˙˙# ˙

˙bbb ˙

˙#˙˙##

#˙˙n# ˙

˙# ˙bbb ˙#nn ˙#n## ˙nn


If the order of the transposed stacked-rows were not significant in either work, than

this difference of process would be of no consequence. However, both works do

utilize the harmonic progression generated by this order. In Flourish with Fireworks,

shortly after rehearsal E, Knussen treats the sequence of chords above (labelled I –

V) as a chorale to accompany the melody.41 Likewise, there are a couple of areas in

“Breaking” where the transposed stacked-rows are iterated in their original

sequence. Example 16 below offers one such spot.


This is a local climax of a musical line of thought initiated in bar 1. For some time,

the piano has dominated the scene, and this is the last climactic exclamation before

the piano moves to an accompaniment role. In bar 35, the piano articulates with

chords from the Tf sequence: Tf.2, Tf.3, and, after a few reiterations of those two,

Tf.4.

41 (Anderson 2002, 4)

{

{Piano

Orchestra

f

Af, Oct0,2 Tf.2

ff

Tf.3 Tf.4

f

Af, Oct0,2

(q=120)

D E

34 35 36 37 38

fffff

f

Dd, Oct0,2

f

f

f fp

24 44 34 44

24 44 34 44

24 44 34 44

24 44 34 44

24 44 34 4424 44 34 4424 44 34 44

&> . > . > > . . > . .”“

?. . . . . . > . .

&> . > . > > . . > . .

?. . . . . . > . .‘“

&Fls, Obs, Cls., Stgs.

bbFls, Obs, Cls. . . . . . .

+Tpts.

. . . . >? Hns.

& > . . . . . . > . . . > . . > . . -> . . . . . >? Tbns., Tba. -> . . . . . . -> . . . -> . . -> . . -> . . . . . >

? ∑Bsns.

. . . . >? Timp.

> > > > > >

œœœ# œœœ#n œœœ# œœœ#n ˙#n ‰œœœ#n ™™™ œœœ#n œœœ Œ ‰

œœœ#n ™™™ œœœ#n œœœ Œ œœœ##

œœnn œœ œœ œœ œœ œœ œœœbb œœ œœœœœ#n œœœn œœœ#n œœœn ˙b ‰ œœ ™™ œœb œœ Œ ‰ œœ ™™ œœb œœ Œ œœn

œœ œœ œœ œœ œœ œœ œœœbb œœ œœ

œœ˙˙ œœbb wœb œ œ ˙

wœb œ œ œj œ œj ˙b ™

œJ ‰ œœb œœ œœ œœ œœœœbbJ ‰ Œ Ó

œ œ# œœ# œ# œ œ œ œ œ œœ œ œ# œ œœ# œ œ œœ# œ œ œœ# œ œ œ œ œ œ œ# j ‰ Œ Ó

˙b œœœb œœb œœ œœ œœ œœ œœ œœœn œœb œœb œœ œœœnb œœb œœ œœœnb œœb œœ œœœnb œœ œœ œœ œœ œœ œœ œœbJ ‰ Œ Ó

wwb ww œœj ‰ œœ œœ œœ œœ œœ œœ

j ‰ Œ Óœb œ Œ œ œ# œ œ œ œ œ œn œ œ# œ œn œ œ œ œ œ œ œ# œ œ œ œ œn æææw#


Octatonic Implications of the Rows

As mentioned before, row Af is contained within Oct0,2. By extension, each

transposition, rotation, and stacked-row is also contained within an octatonic.

Because the octatonic is a mode of (very) limited transposition, there is significant

overlap of the containing octatonics. Of the 25 iterations of the row, thirteen

iterations are of Oct0,2, six are of Oct1,2, and six are of Oct0,1. The 25 chords of the

stacked-row transpositions share an identical distribution of octatonics. Within each

transposition of an array (e.g., Af – Aa, or Cf – Ca), there are three rows of one

octatonic and two of the octatonic two semitones higher. Each set of transposed

stacked-row harmonies shares a similar distribution. Using a generative cell that is a

subset of a mode of limited transposition enables the application of a cohesive

harmonic idiom based upon that mode.

Example 14 on page 54 demonstrated layering rows and harmonies of incompatible

octatonics to create increased dissonance and tension. Example 17 below shows the

climax of “Breaking”, just before the piano cadenza, and demonstrates other ways

the octatonic relationship is utilized. At this point in the music, the levees are long

breached, and prominent is the rising water figure in the strings, first introduced in

bar 102. With each reiteration of this extended strings gesture, more voices are

added, the range is increased, and the dynamic level is raised. The brass accents

impart the violence and danger of the tragedy, and the piano is expressing panic

with its arpeggios and block chords over the entire range of the instrument.



° ¢{

° ¢{ ° ¢Pia

no

Bra

ss

Str

ings

WW

Acc

ents

Ces O

ct 0

,2

ff

Oct 0

,1( q=120)

N

119

120

121

122

123

124 °

Da

Oct 0

,1

ff

Bb

Oct 0

,2D

a O

ct 0

,1

CesR

Oct 0

,2D

aR

Oct 0

,1A

aR

Oct 0

,1

EesR

Oct 0

,2B

a O

ct 0

,1

mp

Ces O

ct 0

,2A

a O

ct 0

,1

mf

Pia

no

Bra

ss

Stg

s.W

W

Tim

p.

O

125

126

127

128

129

130

131

132

ff ff

fpf

ffff

4 4 4 4 4 4 4 4 4 4 4 4 4 4&>

>>

>” “

>>

>>

>>

∑3

33

œ œ#> œ œ#

> œ œ œ# #

> œ œ œ#> œ œ œ#

?∑

∑∑

∑œœ#

œœ#œœ

œœ#œœ

>œœ#>œœ #

>œœ #>œœ

>œœœ# #

&∑

∑.

..

..

..>

.>

..>

..

.

&∑

∑>

>>

>

&>

>∑

∑>

>>

>>

>

?>

>>

>>

>>

>>

>>

>>

?>

>>

>>

>>

>>

>>

>cresc.

&∑

>>

>>

>>

>>

>>

>” “

33

33

?>

>>

>>

>>

>>>

>” “

33

33

&..

..

>..

..

>.

...

..

..

...

>>

>>

>>

>>

>>

>

&>

>>

>>

>>

>>

>>

>>>

>

&>

>>

>>

>>

>>

>>

>>

>>

>>

>

?>

>>

>>

>>

>>

>>

>>

>>

>>

>>

>

?>

>>

>>

>>

cresc.

>>

>>

>>>

>

?>

>>

>>

>>>

>

œ œ#œ œ

œ œ#œ œ#

œ œ œ#œ œ œ ™™™

œ œ œn n#œ œ œ

œ œ œ##œ œ œ#

œ œ œ##œ œ œ# #

œœœ ™™™œ œ œ#

œ œ œ˙

www

œœb bœœn n

œœ# #œœ

œœœœb b

œœœœb b

Ó‰

œœœœœb bœœœœœ

œœœœœj‰

Óœœœœœb b

œœœœœ‰

Œ‰


œœœœb #œœœœœ n

Ó‰

œœœœb #jœœœœœb b n

œœœœœœœœœ #

œœœœœ nœœœœœ

œœœœœŒ

æœ œ#æœ œ

æœ œ# næœ œ# #

æœ œnæœ œ#

æœ œn J‰

ÓŒ

‰æœ œb J

æœ œnæœ œb b

æœ œnæœ œ#

æœ œb bæœ œ#

æœ œnæœ œb b

æœ œnæœ œn

æœ œ#æœ œb b

æœ œn næœ œb

æœ œæœ œb b

æ œœ #æ œœ #

æ œœ# #æ œœ# n

æ œœ #æ œœ# #

æ œœ#j‰

æ œœ#æ œœ# #

æ œœ næ œœ# #

æ œœ bæ œœn n

æ œœnæ œœb b

æœ œb bæœ œb

æœ œnæœ œb b

æ œœn bæ œœ n

æ œœb bæ œœ n

æœ œ#æœ œ# #

æœ œn næœ œb b

æœ œnæœ œn b

æœ œ# #æœ œn n

æœ œbæœ œ#


æœ œ#æœ œn

æœ œb b J‰

Ó‰

æ œœb bjæ œœ n

æ œœ# næ œœ# #

æ œœ næ œœ# #

æ œœ næ œœb b

æ œœb næ œœn

æ œœ# #æœ œb


æœ œnnæœ œb b

æœ œæœ œb b

æœ œnæœ œ#

æœ œb bæœ œnn

æœ œ#æœ œ##

æœ œ# #æœ œn n

æœ œ# #æœ œn b

æœ œn næœ œn

æœ œb bæœ œn n

æœ œb bæœ œ

æœ œn b

æ œœ#æ œœ# #

æ œœ# næ œœ# #

æ œœ# #æ œœ #

æ œœb bæ œœ

æ œœb næ œœ #

æ œœbæ œœn #

æ œœ# #æ œœ

æ œœ# #æ œœ #

æ œœb næ œœ# #

æ œœ næ œœ #

æ œœbæ œœn

æ œœb bæ œœ #

æ œœbæ œœ

æ œœb bæ œœ

æ œœbæ œœb b

æ œœæ œœ n

æœ œ# #æœ œ#

æœ œb næœ œ# #

æ œœn #æ œœb n

æ œœb bæ œœ

æ œœbæ œœ #

æ œœbæ œœ

æ œœb bæ œœ# #

æ œœ næ œœ #

œœb bœœn n

œœ# #œœ

œœœœb b

œœœœb b

œ œb bœ œn n

œ œ# #œ œ

œ œœ œbb

œ œœ œbb

œ œbbœ œnn

œ œ##œ œ

œ œœ œbb

œ œœ œ##

œ œbbœ œnn

œ œœ œ

œ œ J‰

˙ b™™™™

˙ ™™™™œ œ œ œb

œ œ œ œœ œ œ œb

œ œ œ œœ œ œ œ



w w w wb

œbœn

œ#œ

œœb bœœn n

œœ# #œœ

œœœœb b

œœœœ bb

œœb bœœn n

œœ# #œœ

œœœœb b

œœœœb b

œœb bœœn n

œœ# #œœ

œ œœ œb b

œ œœ œbb

œ œbbœ œnn

œ œ##œ œ

œ œœ œb b

œ œœ œ##

œ œbbœ œnn

œ œœ œ

œ œ J‰

˙ b b™™™™

˙ ™™™™œ œ œ œb b

œ œ œ œœ œ œ œb b




w w w wb bœ

œbœ

œb

Œ‰

œœœœœ# nbœœœœœ

œœœœb #œœœœ

ŒŒ

œœœœb #œœœœœb b nœœœœœœœœœœj

‰Œ

‰œœœœb #j

‰œœœœj

œœœœœb b nœœœœœœœœœœœœœœœj

‰‰


œœœœb #œœœœ

‰œœœœj

‰œœœœœ nœœœœœ

œœœœœb bj‰

œœœœœ˙˙

˙˙ ™™™™™œœœœœb b

œœœœœœœœœœb b

œœœœœœœœœœ



wwwwwb b

æœ œnæœ œ œbbb

æœ œ œnnæœ œ œ##

æœ œ œb bæœ œ œn n

æœ œ œ# ##æœ œ œn nb

æœ œ œ# ##æœ œ œn nn

æœ œ œb bæœ œ œn

æœ œ œ# ##æœ œ œb n

æœ œ œn #næœ œ œb bb

æœ œ œn nnæœ œ œb bb

æœ œ œb #æœ œ œn n

æœ œ œb bbæœ œ œn #

æœ œ œb bbæœ œ œn nb

æœ œ œn #æœ œ œb nb

æœ œ œn næœ œ œ# ##

æœ œ œb næœ œ œn #n

æœ œ œb bbæœ œ œn nn

w w wb bb˙ ™™™

œ œ œb bbœ œ œ

œ œ œb bbœ œ œ

œ œ œœ œ œ

œ œ œœ œ œœ œ œ

w w wb bb

æœ œ# #æœ œ# n

æœ œ# #æœ œn

æœ œ# #æœ œ œ# n#

æœ œ œn #æœ œ œ# #

æœ œ œb næœ œ œ# #

æœ œ œbæœ œ œn #n

æœ œ œb næœ œ œ##

æœ œ œ#næœ œ œnb b

æœ œ œn #næœ œ œb nb

æœ œ œn #æœ œ œ# n#

æœ œ œn n#æœ œ œ# #

æœ œ œn #æœ œ œ# b

æ œœœ# #æ œœœ# #

æ œœœ n #æ œœœb nb

æœ œ œn bæœ œ œ#b

æœ œ œ#næœ œ œ#b

w w wnb b˙ ™™™

œ œ œnb bœ œ œ

œ œ œnb bœ œ œ

œ œ œœ œ œ


w w wnb b

æœ œ# #æœ œb

æœ œnæœ œb b

æœ œnnæœ œ#

æœ œ##æœ œ œnnn

æœ œ œ# #æœ œ œn ##

æœ œ œnæœ œ œ##

æœ œ œ# #æœ œ œnn

æœ œ œ#æœ œ œb bb

æœ œ œn #æœ œ œn nb

æœ œ œ###æœ œ œnnn

æœ œ œb bæœ œ œ##

æœ œ œn næœ œ œ# #

æœ œ œn ##æœ œ œnn

æœ œ œ##æœ œ œ# #

æœ œ œnnæœ œ œ###

æœ œ œb næœ œ œn #n

w w wb ##˙ ™™™

œ œ œb ##œ œ œ

œ œ œb ##œ œ œ

œ œ œœ œ œ


w w wb ##

æ œœbæ œœ

æ œœ# #æ œœ #

æ œœ# #æ œœ #

æ œœ# #æ œœ

æ œœ #æ œœb

æ œœnæ œœb b

æ œœæ œœb

æ œœœ # #æ œœœb #

æ œœœn #æ œœœb b

æ œœœb #æ œœœn #

æ œœœ# #æ œœœ #

æ œœœb #næ œœœ n #

æ œœœ# n#æ œœœ #

æ œœœ# ##æ œœœ #

æœ œ œ# #æœ œ œ#

æœ œ œn ##æœ œ œb #

w w w#n˙ ™™™

œ œ œ#œ œ œ

œ œ œ#œ œ œ

œ œ œœ œ œ


w w w#

æ æ æ wæ æ æ w


œj‰

æ æ æ œæ æ æ

æ æ æ ™œ

œæ æ æ œ

æ æ æ œœ

œœ

œœ

æ æ æ w


In this section, each of the rows that are being used at any moment shares the same

octatonic superset. Just before rehearsal N, Oct0,2 is the active collection. Starting

at N and continuing to the end of the climax, Oct0,1 is the active collection. The

coordinated shifts of the octatonic supersets offer clear harmonic direction to the

rising water, even while the simultaneous melodic and accented iterations of

multiple rows create complexity and excitement.

Both the brass and piano pull their harmonies from stacked rows. A more complex

process, where notes from the active octatonic are added to supplement or thicken

the music from the active rows, creates the string figures. Figure 17 below

demonstrates the process.

Figure 17: Building the Rising Water Figures in “Breaking”

In Example 17 (page 61), bar 122, a new rising water figure starts in the second

staff shown in the “Strings” section. It is marked as using notes from Da retrograde

(DaR) and Aa retrograde (AaR). Figure 17 demonstrates how these four bars were

created. From the source rows (Figure 17a and Figure 17b) the notes for the rising

Da - Oct0,1 Aa - Oct0,1

DaR AaR

DaR Oct0,1 AaR Oct0,1

DaR Oct0,1 AaR Oct0,1

44

44

&a) b)

&c)

&d)

&e)

> >>

>> > > >

w wn wb wn wb w w# wn wb wb

œ# œn œb œ œ# œ œ# œ#

˙# œ# œn œ# œ œ ˙n œb ˙b œb œ œb ˙ œ œ œ œ# ˙# œn œb ˙ œ œ œn œ# ˙# œ œ œ# ˙<#> œ œ

æœœ#æ

œœ##æœœn æœœ##

æœœb æœœnn æœœn æœœbbæ

œœbbæ

œœbæ

œœnæ

œœb æœœnb æœœn æœœb æœœnæ

œœ#æ

œœ#æ

œœnnæ

œœbbæ

œœnæ

œœnbæ

œœ#æ

œœnnæ

œœ##æ

œœ#næ

œœ#æ

œœnæ

œœ##æ

œœœnæ

œœœn#æ

œœœ#


water line are chosen (Figure 17c). Figure 17d shows the melodic gaps filled in with

scalar material from the prevailing octatonic, Oct0,1. At each note originating from

the rows, the melodic line reverses direction to emphasize that note.

This phrase is from the third statement of the rising water gesture, which requires a

thicker texture than the previous gestures. Each melodic line is thickened with one

or two parallel lines. To double the line, a scalar fourth is added underneath each

note in the original rising water line. In the octatonic, a scalar fourth is either an i.c.

4 or i.c. 5, so a scalar run of the rising water line generates dyads alternating

between i.c. 4 and i.c. 5. Using scalar thirds or fifths would have created a run of

identical intervals, and the flowing imagery would have been diminished. The first

three bars of Figure 17e show the parallel scalar fourths and their alternating sizes.

To generate the third line, a scalar eighth underneath the original melody is added.

This creates an alternating i.c. 10 and i.c. 11 pattern, as shown in the last three notes

of Figure 17e. In “Breaking”, the original notes of the row are accented in the

strings and doubled by the woodwinds. Accenting the notes of the row so that they

are clearly audible helps maintain cohesiveness and adds energy to the rising water

figure. Constraining the added notes to the same octatonic maintains the harmonic

motion of the rising water gestures.

Intentional Clashing With the Prevailing Octatonic

“Breaking” ends with a full expression of anger that begins with a very rhythmic

solo piano section climbing in energy and register. Percussion emphasizes the

rhythmic anger with a three-part canon, and long tone octatonic clusters in the high

strings (foreshadowing the clusters of movement three) add to the tension by

straying out of the prevailing octatonic scale.



{ { ° ¢ ° ¢ { { ° ¢ ° ¢

Pia

no

Hig

h S

trin

gs

Tim

pan

i

Sn

are

Dru

m

Tom

-tom

fffEa

Oct 0

,2

Ees m

elo

dy O

ct 0

,2

Ces M

elo

dy O

ct 0

,2

( q=120)

S

161

162

163

164

165

166

Ha

rm

. Oct 0

,2

°°

Ces O

ct 0

,2

f

+C#

f+

E+

G,E

+A#

+E

+G

,

E,C

#

f f ffp

fffp

ff

Pia

no

Stg

s.

Tim

p.

S. D

.

Per

c.

Ees s

4 O

ct 0

,2E

a O

ct 0

,2

Ces s

5 O

ct 0

,2

167

168

169

170

171

172

173

°°

fpfp

o

+E

+G

,

E,C

#+

EO

ct 1

,2:

+E

+C#

+G

,E+

A#

+Db,

Bb

fp+

Gfp

+G

oO

ct 0

,2:

ppfp

o

ppf

ffpp

f

4 43 4

4 43 4

4 43 4

4 43 4

4 43 4

4 43 4

4 43 4

4 43 4

4 43 4

4 43 4

4 43 4

4 43 4

4 43 4

4 43 4

3 44 4

3 44 4

3 44 4

3 44 4

3 44 4

3 44 4

3 44 4

&#> >” “

bb n nb> >>

∑” “

bb bn> >>

33

33

œ œ œœ œ œ

?C

es O

ct 0

,2

>n bn b#> >

>b #n #>

>>

> >

3

3

33

3

3

3

3

> œ œ œ œb bnœœœ

&.>

.>

>>

>>

>>

>

&O

ct 0

,2:

.>.

>>

>>

>>

>>

?>

>>

3

33

3

33

/>

>>

>>

>>

>>

>>

33

33

33

3

/>

>>

>3

33

3

33

3

3

&b nn bb> >

” “# n#

bn # n# n> >

” “

nbn n” “

# nn# b>>

>∑

∑∑U

∑U

?∑

∑A

ll O

ct 0

,2# nbn b>

n bn bn b>

# n> u>U u

‘ “

&.>.

>.>.

>.>.

.>.

.>.

.>.

.>.

>U

∑U

&.>.

>.>.

>.>.

.>.

.>.

.>.

.>.

>U

∑U

?U

∑U3

3

33

3

3

3

/>

U∑U

/>

U∑U

œœœ œ œ œœœœœ œ œ œ œ

œœœœn nb bœ œ#œ#œ œ#œ œ œb

œ œ œ# #œ œ œb

œ œ œnœœœœ œ œ œ œ

œœœœn #nœ œ#œœ œ#

œ œ œnœ œ œ#œ œ œ

œœœœœœ b

˙™™™™ ˙ ™™™™

œ#œœn

œ œ# #œnœ œ

˙ ™™™™œ#œœn

˙ ™™™™œbœn

œnœœbœnœœ

œ œ œnnnœ œ œœ œ œ

œbœn

œn

œ œœ œ

‰œ œ# J

‰œ œ## J

‰œ œ J

æææw wbæææw w

‰œ œ# J

‰œ œn J

‰œ œb J

æææw wæææw w

œ œ œ œb ##œ œ œ œb ##

‰œ œ œ œb n J

‰œ œ œ œ# bJ

‰œ œ œ œb nb J

æææw w w w#æææw w w w

‰œ œ œ œb J

‰œ œ œ œ# n#J

‰œ œ œ œnn J

æææw w w w#æææw w w w

œbœœ

œ ‰œœ

œ‰œœ

œ‰æææwb

œbŒ

Óœœ

œ ‰œœ

œ‰œœ

œ‰æææwb

œbŒ

Óæ æ æ ™

œœ

œœœ

æ æ æ œœœ

œæ æ æ œ

œœœœ

œœœœ

œœœ

œœœ

œœœœ

œœœ

œœæ æ æ ™

œœœ

æ æ æ ™œ

œ

œœr œr œ

œ œœ

œr œrœ

æ æ æ wœ œ

œœœœ

œœœ

œ œœ

œœœ

œ œœ

œœœ

æ æ æ ™œ

œœ œ

œœ œ

œ œœ œ

œ œœ

œ œ œ˙

œœœ œ œ œ˙

œœœ œ œ œœœœœ œ œ œ œ

œ œ œ œb bœœœœb

œ œ œ œ#œ œ œ œ# #

œœœœ œ œ œ œ˙

™™™™ ˙ ™™™™wwww w w w w

www w w wwww w w w

‰œ œ#œ œ

æææ˙‰

œ œ#œ œ

æææ˙ n‰

œ œ#œ œ ‰

œ œ##œ œ ‰

œ œœ œ‰

œ œbœ œ

‰œ œbbœ œ Œ

æææ˙æææw w

æææw w

‰œ œ œ œbœ œ œ œ

æææ˙ # n#‰

œ œ œ œb nœ œ œ œ

æææ˙ # n‰

œ œ œ œbœ œ œ œ‰

œ œ œ œ# bœ œ œ œ‰

œ œ œ œb nbœ œ œ œ‰

œ œ œ œ# nœ œ œ œ

‰œ œ œ œn bn #œ œ œ œŒ

æææ˙ b næææw w w wb

æææw w w wb

œbœœ

‰æ æ æ

œœœ‰

æææœœ

œ ‰œbœœ

‰œœ

œ‰œœ

œ ‰œœ

œ‰æ æ æ ™


œj œæ æ æ

œj œæ æ æ

œœœ

œœœ

œœœ

œœœ

œœœ

œœæ æ æ ™

æ æ æ wœ

Ó™

æææœ œj œ

œæ æ æ œ

æææœ œj œ

œœæ æ æ œ

œ œœ

œ œœ

œœœ

œ œœ

œœœ

œœæ æ æ ™

æ æ æ wœ

Ó™

All

Oct 0

,2A

ll O

ct 1

,2

attacca


Example 18 shows the final outburst of anger within “Breaking”, where the piano

traverses the complete range of the piano five times before crashing into the lowest

two octaves. The notes of the strings’ high tremolos and accents that are outside the

prevalent octatonic are labelled with a “+”. These extra tones create a strong

dissonance and grating that exceeds anything prior in the movement and prepares

for the stark contrast of the attacca entrance to “Still”.

Conclusion

Fundamentally, “Breaking” is a rhythmic work, which I believe is appropriate for

the subject of the movement. This was the first time I had worked with rotational

arrays, and I will use this tool again in future compositions. The freedom from

functional harmony enabled me to focus on rhythmic development, large-scale

motion of energy, and the expression of deeply felt emotions. Working with a row

that fits within the octatonic offered many unexpected opportunities in the design of

my piece, and the implications of using rows within modes of limited transposition is

worthy of future exploration.

In the next section I discuss my final manipulation of modes: processes inspired by

early twentieth-century Russian music theory. The modes I discuss below share

many similarities with the hexachords discussed in “River”, but the process used to

generate the modes within “Still” suggests a different underlying structure of the

modes, and hence a different treatment in the music. “Still”, the third movement of

Currents, fully embraces the practice of harmonic movement by shifts in modes or

collections and represents to me the full achievement of my goal to break my

reliance on principles grounded in common practice.

Modes Inspired by Yavorsky’s Theories 66

Chapter 6: Modes Inspired by Yavorsky’s Theories

Boleslav Yavorsky’s Theories on Mode

Roughly 50 years after some of Stravinsky’s most influential works, Arthur Berger

published his paper “Problems of Pitch Organization in Stravinsky !”.42 There he

attempted to define a new theory about Stravinsky’s music and, in the process,

coined the term “octatonic”. In contrast, in as early as 1906 Russian music theorist

Boleslav Yavorsky (1877–1942) was documenting theories that would influence

modern Russian music theory and would be applicable to the music of Rimsky-

Korsakov, Scriabin, Stravinsky, and Prokofiev.43

Yavorsky developed a complex theory that was further refined by his student Sergei

Protopopov (1893 – 1954) and late twentieth-century Russian music theorist Yuri

Kholopov (1932–2003).44 The concept of “mode” (lad) in Russia was expanded

beyond the traditional Western definition to incorporate ideas from these theories,45

and lad now roughly translates to tonality.46 In the context of Russian music theory, I

only will be discussing pitch classes, and my use of the term “mode” will refer to

pitch class collections and the relationships between the included pitch classes.

In his theories, Yavorsky came to the conclusion that voice leading, as in the context

of note tendencies dependent upon vertical and horizontal intervals, was to be

replaced with pitch leading and pitch gravitation. The “resolution” of the tritone would

become the predominant force of defining pitch gravitation within a “mode”, and 42 (Berger 1963) 43 (Ewell 2012, sec. 2.7) 44 I have found relatively few sources about Russian music theory written in English. A complex yet comprehensive source is Gordon McQuere’s translation of Protopopov’s text The Elements of the Structure of Musical Speech. (McQuere 1978) 45 (Ewell 2012, sec. 2.1-2.3) 46 Philip Ewell, e-mail message to author, 29 February 2016.


pitch leading is how pitches move, typically along these gravitation paths. Some

explanation is in order.

In Yavorsky’s theories, the resolution of the tritone is the primary cell used to create

his modes.47 He defines the two systems shown in Figure 18: one where a tritone

resolves to an i.c. 4 or i.c. 8, and one where a perfect fifth resolves through a perfect

fourth to an i.c. 3, or the inverse of the intervals resolve to an i.c. 9:48

Figure 18: Tritone Resolution Systems in Yavorsky's Theories

Open noteheads represent stability; closed represent instability. The two or three-

note path from an unstable tone to a stable tone is called a conjunction and is marked

with a slur. Pitch gravitation follows conjunction paths from instability to stability.

These systems are the building blocks for Yavorsky’s modes. They can be combined

in as many ways the octave will allow to create collections where a pitch class is

either stable or unstable. The stable pitch classes within a mode are collectively

known as the tonic, and the unstable pitch classes are collectively known as the

47 I do not detail Yavorsky’s derivations and classifications related to this process. Philip Ewell offers a succinct yet more comprehensive introduction. (Ewell 2012) 48 Yavorsky argues that the tritone cross-relationship in the movement between the two perfect intervals supports his theory of the tritone being the predominant force. The cross-relationship is marked with lines in the diagram. Ewell does not see musical justification in this argument. (Ewell 2012, sec. 2.8, 2.15)

&Converging

Each slur represents a conjunction

Single Symmetrical System

Diverging Converging

Double Symmetrical System

Divergingœœ ˙ œœ ˙ œœ œœb# ˙ œœ œœ#b ˙


connecting moment. Consider the mode that Yavorsky calls the Duplex-Major Mode, the

manifestation of the Petrushka chord:

Figure 19: Yavorsky's Duplex-Major Mode

When the mode is laid out as a scale, the conjunctions can be graphed to show the

pitch gravitations moving from the closed noteheads to the open noteheads:

Figure 20: Yavorsky Pitch Gravitations

Pitch gravitations are an expanded concept of the 7 and 4 pitch tendencies within

diatonic scales, and their function underlies the perception of stability in the lad’s

tonic. When design of the mode and pitch gravitations are considered, an analysis of

music such as Stravinsky’s can be more nuanced than an octatonic-based analysis.49

Inversely, Yavorsky’s theories offer an alternate approach to harmonic and melodic

thinking in composition.

The Mode for “Still”

This introduction to Yavorsky’s theories is necessarily brief and extremely

incomplete, yet it is sufficient to demonstrate the influence within “Still”. The

49 (Ewell 2012, sec. 5.6-5.9)

{ tonic connecting moment

& n#n#n#

&œœ# ˙## œœ## œœn‹ ˙## wwwwww œ œ# œ œ œ œ#

œœ ˙ œœ œœb# ˙n

& œ ˙ ˙# œ œ# ˙ œ# ˙# ˙ œ# œ‹ ˙# œ


predominant source of harmonies within “Still” comes from a Yavorsky inspired

mode derived from the C wtq scale:

Figure 21: Harmonic Source for “Still”

Figure 21a shows three generating systems which resolve to five notes from the C

wtq scale. The results are organized sequentially in Figure 21b, with pitch

gravitations marked with slurs. Figure 21c and Figure 21d separate the tonic and

connecting moment, and they are respectively given descriptive labels C7(♯4) (the

pentachord resembles a C7 with an added ♯4) and Dm/G♯m (the hexachord can be

constructed from a D minor and a G♯ minor triad). A few observations relevant to

“Still” follow:

• Dm/G♯m is also the connecting moment to F♯7(♯4).

• The pentachords C7(♯4) and F♯7(♯4) are maximally intersecting.

• The hexachord C/F♯ (constructed from the major triads C and F♯ and

shown in Figure 21e) is a superset of C7(♯4) and F♯7(♯4).

&Generating the mode

a) b)

Complete mode with pitch gravitations

&c)

Tonic: C7(#4) - subset of C wtq & Oct0,1

d)

Connecting Moment: Dm/G#m - subset of Oct0,2

&e)

C/F# hexachord

- superset of C7(#4) and of F##7(#4) - subset of Oct0,1

œœ œœb# ˙n œœ# ˙## œœn ˙n˙ œn œ# ˙n œn ˙# ˙ œb œn ˙b œn ˙

˙ ˙ ˙# ˙ ˙b ˙ œ œb œn œ# œ œn œ

˙ ˙b ˙n ˙# ˙n ˙b ˙


• C/F♯ and Dm/G♯m are complements and are subsets of distinct octatonics.

The 7(♯4) pentachord and its connecting moment are the primary classes of

harmony used within “Still”. The 7(#4) pentachord is treated as a stable arrival

point when following its connecting moment. Consider the notes used in the

opening to “Still”.

Example 19: “Still”, bars 2-15

After an introductory lament by the waterphone,50 the glockenspiel and string

harmonics enter and evoke incessant time with a glassy progression of dyads (and

eventually triads) from the Dm/G♯m hexachord. The muted trumpets and oboes

50 The waterphone is a percussion instrument with a tined, metal resonating chamber attached to a tube. A small amount of water is placed inside the resonating chamber to allow modulation of the tone through movement of the instrument. The instrument may be tapped on the resonator and scraped or bowed on the tines. The tines have pitch but are not tuned.

{

{Orchestra pp

Lento (h=50)

A

2 3 4 5 6 7 8

Dm/G#m:pp fade in and out

Orch.

9 10 11 12 13 14 15

pp pp

pp fade in and out

C7(#4):

22 32 22 32 2222 32 22 32 22

32 2232 22

32 2232 22

&Glock., Stg. Harm.

# #nÿ◊

& ∑ ∑ ∑Tpt. sord.

& # b b nb #n #nn # # ##bn nb bb◊: ;

∑(G.P.)

&Cl., Fl.

3

”“∑

& ∑Ob.

∑

& <#> ∑

˙bb ˙n ˙bb ˙# ˙n ˙bb ˙ ˙bb ˙n ˙bb ˙#˙# ˙n ˙# ˙ ˙

Œ ˙ ™ Œ ™ ˙ ™ œœ# www ™™™ www

˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙

Œ ˙##œœ ww## œœ œœ œœ

œœ##˙ œœ œœ##

œœ œœ œœ ww œœ Œ Ó

Ó Œ œb œ œ ww ww w ™ Œ ˙ ™ Œ

œww Œ Ó œœŒ œ w Œ Ó Œw ˙ ™ ww œw Œ Ó w


fade in and out of clusters of the same hexachord, underneath a slow clarinet and

flute line. The thin tone colours, the quiet and sustained dissonances, and the slow

walk of the dyads – all within the dark harmonic implications of the Dm/G♯m

hexachord – impart a sense of stillness, loneliness, and hopelessness. In bar 13, the

glassy triads shift to the slightly more hopeful tonic (C7(♯4)) and reach into the

emptiness of the grand pause before the piano solo entrance. The fading tones from

the connecting moment linger into this shift, intentionally softening the sense of

resolution.

Nearer, My God, to Thee and “Still”

“Still” is constructed from distorted fragments of the hymn Nearer, My God, to Thee,

as sung to the tune “Bethany”.51 Nearer, My God, to Thee is a traditional feature of the

New Orleans jazz funeral and is played as a slow $4 dirge prior to the burial. It is

fitting to base “Still” upon this hymn: the standing water that remained after the

levee failures was filled with literal death, and the discourse that followed was

predicting the metaphorical death of the city itself. I chose Nearer, My God, to Thee

over other jazz funeral tunes because it is nearly pure pentatonic and thus highly

receptive to alternate harmonizations. When I do present Nearer, My God, to Thee in

its entirety, I base it upon the less common setting in 4 so that the affect is more of

hope than of tragedy.

Example 20: Bethany, the setting for Nearer, My God, to Thee

51 “Bethany”, by Lowell Mason (1792-1872), is the customary setting of Nearer, My God, to Thee in the United States.

2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

64&b

&b

˙ ™ ˙ œ ˙ œ ˙ ™ ˙ ™ ˙ œ ˙ ™ ˙ Œ ˙ ™ ˙ œ ˙ œ ˙ ™ ˙ œ ˙ œ ˙ ™ ˙ Œ

˙ ™ ˙ œ ˙ œ ˙ ™ ˙ ™ ˙ œ ˙ œ ˙ ™ ˙ ™ ˙ œ ˙ œ ˙ ™ ˙ œ ˙ œ ˙ ™ ˙ Œ


The recurring motif of clusters that fade in and out has been foreshadowed by both

of the previous movements, and it is significant that the first clusters of “Still”

(Example 19) offer the first distorted fragments from the hymn Nearer, My God, to

Thee. The attack points of the muted trumpets in bars 5-6 outline the descending

third in the first bar of the hymn. The attack points starting with the oboes in bar 10

and continuing to the trumpets in bar 11 outline the hymn’s contour of Example 20,

bars 11-12.

Frequently the fragments of the hymn unfold slowly or are hidden in inner voices:


{

{

{{

Piano

Orchestra

p

(h=50)

B16 17 18 19 20

Dm/G#m:

p espress.

Gm/C#m:

Piano

Orch.

mp

C21 22 23 24 25

mp

mp pp

Fm/Bm:

p fade in and out

2222

22

&b

3 3 3 3

b3 3

”“

&

&Picc.

&3 3 3 3 3

nnb“: ;

&

& ∑ ∑ ∑Glock., Stg. Harm. # n #

ÿ◊

&+ Fl.b

& ∑ ∑ ∑Tpt. sord.>

wœœ œ œ# œ w œ œ œ# œ ˙b ™ œ œ œ# œœ œ œ œ# ˙ œ œ ˙# ˙ œ œ#

˙bb ˙n ˙bb ˙ ˙# ˙#n ˙n ˙# ˙## ˙nn

wb w œ ˙b ™ œ ˙ ™ œ ˙# œ

œ<#>w<#> ˙ œ œ œb œ œb œ œ œb wœ œ œb œ œ œ œww ˙ ™ ˙nn ™™™ Œ˙## ˙# ˙# ˙#n ˙# ˙b ww# ˙ ™™ Œ

˙ ˙ ˙ ˙

w<#> œ ˙b ™ w ww ˙ ™˙ ™ Œ

Œ Œ ™ Ó wŒ ˙ œœ


Starting at bar 18, the piccolo and top line of the piano take nine bars to outline just

over two bars of the beginning of Bethany’s contour, complete with repeated notes.

In the piano, the right hand’s lower voice (D G♯ B A) outlines the contour of the

hymn’s bars 3-4 and continues through the G in bar 22 to unfold (with some

ornamentation) the contour of bars 5-8 in the hymn.

The hexachord shifts in Example 21 do not follow the connecting moment and tonic

model discussed earlier. Moving the collection from Dm/G♯m to Gm/C♯m can be

interpreted two ways: either as a transposition of a semitone, or as a transposition of

a perfect fifth – both transformations give the same hexachord. This type of

“modulation” is used multiple times within “Still”. At bar 20 this shift seems to step

downwards without releasing any tension, as if one is carefully navigating the

physical aftermath of the tragedy. The shift to Fm/Bm in bar 24 is a play on the

tonic and connecting moment relationship: the tonic of Gm/C♯m, F7(♯4), shares three

common tones (those that make the F’s fifth and tritone) and the same octatonic

superset with Fm/Bm, so the shift from Gm/C♯m to Fm/Bm bears some

resemblance to an arrival on the tonic. However, the end result is different. There is

an additional edge to the shift at bar 24 that helps propel the music into an increased

level of tension on the return of the clusters and walking triads.



{ {{ {{

Pia

no

F/B

:

h = h. M

en

o m

oss

o (h.h.=

45)

G68

69

70

71

F7(#

4) :

°ø

øø

Pia

no

Orc

h.

72

73

74

75

Gm

/C#m

:

øø

F7(#

4) :

ø mf

F#m

/Cm

:

Pia

no

Orc

h.

mp

H

76

77

78

79

mf

F#m

/Cm

:

øø E

7(#

4) :

p

6 4 6 4& ? &

” “” “

?(p

.t.)

(p.t

.)

(p.t

.)

&∑

∑F

ls., V

lns.

&“:; ? &(u

nre

solv

ed s

usp

ensi

on

)

?∑

∑∑

Hn

s., B

sns.

w w w wb™™™™

˙ ™™™™œ œ œ œ

œ œ œ œ#™™™™

œ œ œ œ# J˙ ™™™™

˙œ œ œ œ

œ œ œ œ## #w w w w## #™™™™

œœœœœb

œ œœbœ œ

œ œœœ

œœbœœ

œ œbœ œ

œœ œ

œœœœb

œ œœbœ œ

œ œœœ

œbœœ

œ œœ œ

œœœœ

œœbœ œ

œbœ œ

œ œœœ

œœbœœ

œ œbœœ

œœ œ

œœœœb

œ œœbœ œ

œ œœœ

œœbœœ

œ œbœ œ

w w w wnbn™™™™

œ œ œ œ˙ ##™™™™

˙b bb bw w w w# nn n™™™™

˙ ™™™™œ œ œ œ™™™™

‰≈œ œ# ™™ J

œœ#œ#œœn

œn œœ œ#

œ œbœnœb

œbœ#œœ

œn œœ œ#

œbœnœœb

œ#œœb

œ œ#œb œb

œbœbœ œ#

œb œnœ#œœb

œ#œ

œnœnœn

œnœbœnœbœ œ

œ œnœnœ

œœœbœœn

œbœ œ

œ œœ œ

œbœ œ

œœ œœbœ œ

œœœœœb

œ œbœ œ

œ

Œ™œ œ œ ™™™

œ œ œ ™™™œ œ œ™™™

œ œ œ# ## ™™™œ œ œb bb ™™™

œ œ œ™™™œ œ œb bb ™™™

œ œ™™œ œ# #™™

œ œ# ™™œ œ##™™

œ œn ™™œ œ#™™

œ œn ™™œ œ# #™™

œ œ# ™™œ œ##™™

œ œn ™™œ œ#™™

œ œn ™™œ œ# #™™

œ œ# ™™œ œ# #™™

œ œn b™™œ œn ™™

œ œn #™™

œ œ ™™œ œnb™™

œ œ# n™™

œ œb™™œ œn ™™

œ œ# ™™œ œ ™™

œ œb ™™œ œ# ™™

œ œb™™œ œn™™

œ œ#™™œ œ™™

œbœ#œ

œœbœbœb œ

œ œœ#œbœ#œ

œœbœbœ#œ

œœbœbœ

œœœœb

œbœ#œbœb œ

œ œœ#œ#œ#œ

œœnœbœbœb œ

œ œœnœ#œ#œ

œnœ# œ

œ œ#œ# œn

œnœ#œ#œ

œœ#œœ#

œœnœœ#

œœ#œœ

œœ#œ œ#

œ œœ œ#

œ#œ#œ

œœœ# œ

œ œœ#œ#

w w w™™™˙ ˙b bb ™™™

œ œ œœ œ œb bb ™™™

œ œ œ J˙ ˙™™™

˙ ˙œ œ œ

œ œ œbbbw w wbbb™™™ Ó

Œ˙ b ™™


Example 22 above demonstrates a few harmonic and motivic variations on the

patterns already seen. From bar 68 to bar 75, a left hand piano figure evocative of

water is introduced while the right hand slowly paraphrases bars 1-4 of the hymn.

While the core harmonic movement is between connecting moments and their

tonics, superset and conflicting collections are used to augment the harmonies.

Within this phrase, the collections shift from F7(♯4) to the connecting moment

Gm/C♯m and back to the tonic F7(♯4). However, at the end of bar 70, the right hand

introduces an F♯, expanding the collection by one tone to the F/B hexachord, a

superset to F7(♯4) and complement to Gm/C#m. At bar 74, with the piano again

firmly grounded within F7(♯4), the flutes and violins prepare for their melodic role by

descending through much of the F♯m/Cm hexachord, the connecting moment to a

later arrival of the E7(♯4) tonic. The three common tones between F♯m/Cm and F7(♯4)

strike a balance between tension and fluidity.

At rehearsal H (bar 76) the piano shifts to F♯m/Cm with a reference to the opening

dyads, and the tension is released. The flutes and violins pick up bars 5-6 of the

hymn, but the contour is inverted for the only time within “Still”. This middle

section of “Still”, which continues through bar 104, slowly paraphrases nearly the

entire hymn. This particular hymn fragment is inverted to initiate a slow energy rise

that peaks at bar 102 and gently releases through bar 106. The imagery in my mind

is of a slow draining of standing water, not unlike what New Orleans experienced

as the levee breaches were closed and one by one the pumping stations were

restored to operation.

A Second Derivative Mode

In using Yavorsky’s methods to create tonics and the corresponding connecting

moments, I wanted to limit my tonics to subsets of the WTQ scale. Figure 21 (page


69) demonstrates the creation of the primary mode for “Still”, one whose tonic is

comprised of five-notes from the WTQ. While Yavorsky’s methods can generate a

mode with a six-note whole-tone tonic, another subset of the WTQ scale, this tonic

would not contain 5 of the WTQ, and the reference to WTQ would not be evident.

There is one other Yavorsky mode that has a tonic comprised of five notes,

including 5, from WTQ. Figure 22 shows this mode using notes from E wtq.

Figure 22: Second Harmonic Source for “Still”

This mode shares some symmetry with the mode of Figure 21: the roles of the major

and minor triads are reversed so that the tonic is an added-tone minor triad and the

connecting moment comprises two stacked major triads. In this mode, the tonic I

call Bm6(♭2) is equivalent to a Bm6 (in jazz terms) with an added ♭2. The Bm/Fm

hexachord (Figure 22e) is a superset to both tonics of A/E♭. Two more derivative

hexachords are shown in Figure 22. Figure 22f borrows an E♭ from the connecting

&Generating the mode

a) b)

Complete mode with pitch gravitations

&c)

Tonic: Bm6(bb2) - subset of E wtq & Oct0,2

d)

Connecting Moment: A/Ebb - subset of Oct0,1

&e)

Bm/Fm hexachord

- superset of Bm6(bb2) and of Fm6(bb2) - subset of Oct0,2

&Abb/Bm hexachord

- superset of Bm6(bb2) - subset of Oct0,2

f)

Abb+/Bm hexachord

- superset of Bm6(bb2) - subset of E wtq

g)

œœ œœb# ˙ œœb ˙b œœ# ˙#n ˙b œn œb ˙n ˙n œ# ˙ œb œn ˙# œ ˙b

˙ ˙n ˙ ˙# ˙# ˙œ œb œ# œb œn œn œ

˙n ˙n ˙ ˙ ˙b ˙b ˙n

˙b ˙ ˙ ˙ œb ˙# ˙b ˙b ˙ ˙ ˙ œn ˙# ˙b


moment to create what I call the A♭/Bm hexachord; Figure 22g borrows an E♮ from

the connecting moment to create the A♭+/Bm hexachord.52 The Bm/Fm, A♭/Bm, and

A♭+/Bm hexachords are all supersets of Bm6(♭2), and all maximally intersect each

other. A♭+/Bm also maximally intersects with any of the WTQ scales that share the

same whole-tone scale as E wtq.

These hexachord tonic variations are used in the lead up to the climax of Example

23 (page 78). At this climactic point, the active collections tend to be built upon

major triads, the shifts happen more quickly than usual, and there are more

maximally intersecting modulations here than anywhere else. These quick, relatively

consonant, and smooth modulations (detailed in Table 5), combined with the

flowing piano patterns and growing clusters, evoke for the last time the sense of

water flowing. The semitone / fifth relationship in the last shift creates a sense of

arrival to the closing of the climax.

Table 5: Collection Shifts in “Still”, bars 92-104

Bar Collection How Modulated Here 92 F7(♯4) 94 Dm/G♯m Maximally intersecting; four common tones 96 F/B Four common tones; double Relative transformation53 97 A♭/Bm Four common tones 98 A♭+/Bm Maximally intersecting 102 C wtq Maximally intersecting 102 C/F♯ Maximally intersecting 104 F/B Semitone or fifth relationship (cf. bar 72, Example 22)

52 Compare the A♭+/Bm hexachord to Scriabin’s mystic chord. 53 A Relative transformation is a mapping of a major triad onto a minor triad (and vice versa) where the notes of the major third are kept and the third note moves by step. For example, the transformation between F major and D minor is a Relative transformation. (Berry) Compare to page 47’s discussion of the double Leading-tone exchange in bar 54 of “River”.



{{

{{ {{

Pian

o

Orch

estra

(h.=

45)

L

92

93

94

95

96

mf

øø

øø

mp

ppp

mp

ppp

mp

F

7(

#

4)

:

mp

Dm

/G#m

:F

/B

:

Pian

o

Orch

..

ff

M

97

98

99

100

øø

mp

f

ppp

mp

ppp

Abb/B

m:

Abb

++

/B

m:

f

Pian

o

Orch

..

p

Più

m

osso

N

101

102

103

104

105

106

107

øø

ø

p

C w

tq

:C

/F##:

F/B

:

6 4 6 4 6 4 6 4

3 2 3 2 3 2 3 2 3 2

& ?

>

>

>

>

>

&

Vln

., T

bn

., T

ba., B

sn

. d

ou

bled

at 8ve b

elow

?

Hn

s., low

S

tgs.

&

”“

?

&

&

∑

Up

per S

tgs., W

W.

+ T

pts.

&

∑

?

Low

B

rass, B

sn

., L

ow

S

tgs.

&

“:;

ÿ◊

∑

8

8

&

”“

?

‘“

∑

4:5

8

8

&

Bow

ed

V

ib

es.

U

&

∑∑

∑∑

∑∑

∑

?

∑

w ww

w

b

™™™™w w w w

#

˙ ˙ ˙ ˙

#

#

œ œ œ œ

˙ ˙˙

˙

nb

™™™™˙ ˙ ˙˙b

w ww

w

b

™™™™œ œœ

œ

b

™™™™˙ ˙ ˙ ˙

#

™™™™œ œœ

œ

nb

™™™™

œ

œ

œb

œœ#

œ

œ

œn

œ#

œœ

œ#

œn

œœœ

œb

œb

œ

œ

œb

œn

œ

œ

œ#

œœœ

œb

œœœ

œ#

œ

œn

œ

œb

œn

œ#

œ

œ#

œn

œb

œ

œ#

œ

œœb

œn

œ

œ

œ#

œœ#

œ

œn

œ#

œ#

œœ

œ

œ

œ#

œ

œ#

œœ#

œn

œb

œ

œb

œ

œ

œœb

œœb

œ

œ#

œ

œ#

œ

œn

œ

œ#

œ

œ#

œ

œ#

œœ#

œn

œ

œ#

œ#

œœœ

œn

œ#

œœ

œb

œn

œn

œ

œ#

œœ#

œ

œ

ww

™™

˙˙

™™

Ó™

ww

b™™

˙˙

™™

Ó™

ww

n™™

˙ ˙™™

˙ ˙

#

™™˙ ˙™™

˙ ˙b

™™˙ ˙#

™™˙ ˙™™

˙ ˙#

™™˙ ˙#

n

™™˙ ˙™™

˙ ˙

#

™™

œ œœ

œ

##

™™™™˙ ˙˙

˙

#b

™™™™œ œœ

œ

##

™™™™

œ œ œ œ

n

#

™™™™˙ ˙ ˙ ˙

#

™™™™œ œœ

œ

##

™™™™

œ œœ

œ#

#

™™™™œœ

œ œ#

##

™™™™œ œ œ œ

#

™™™™œ œ œœ

#


#

™™™™œ œ œ œ

#


#

™™™™œ œœ

œ

##

™™™™

œb

œb

œœœn

œ#

œb

œœœb

œ#

œ

œ

œb

œb

œb

œ

œn

œb

œb

œœœ

œ#

œn

œ#

œœœ

œ#

œ#

œœœœ#

œœœ

œ#

œ#

œœœ

œ#

œœœ

œ#

œ#

œ#

œœœœœ

œœ#

œ#

œ

œœœœœ

œ#

œ#

œ#

œœœœ#

œœœ

œ#

œ#

œœœ

œ#

œœœ

œ#

œœ

œ#

œ#

œœœ

œ#

œœœ

œ#

˙™

˙˙

™™˙˙˙™™™

˙ ˙˙˙

#

™™™™˙˙

˙˙˙

#

™™™™™˙˙˙˙˙˙

™™™™™™

˙˙

™™

Ó™

ww

#™™

˙˙

™™

Ó™

˙ ˙##

™™˙ ˙

n

™™˙ ˙#

™™

˙ ˙b

™™˙ ˙™™

˙ ˙#

™™˙ ˙™™

˙ ˙

#

™™

œ œ œœ

#

™™™™œ œœ

œ

#


#

™™™™œ œ œ œ

#

™™™™œœ

œ œ

b

b

™™™™œœœ œb

b

bb

™™™™œ œ œ œ

b b

b

™™™™œ œœ

œ

n#

™™™™

œ œn

œb

œ œ

œ#

œ œ#

œœ œ

#

#

œn

œ œ

b

œœ œ

#

#œn

œ œ#

œ#

œ œ

n

œ#

œ œ#

n

œ œ

#

n

œ œ

n

nœ œ

#

n

œ œn

œ œ#

œœ

#™™

œœ#

n™™

œœn

n™™

œœ#

n™™

ww

n™™

ww

™™

≈œ

œœ#

œ#

œ

≈

œ

œ#

œœ

œ#

≈œ

œœ#

œ#

œ

≈

œ

œ#

œœ

œ#

≈œ

œb

œb

œb

œ

≈

œ

œb

œb

œ

œ#

≈œ

œ#

œn

œb

œ#

≈

œœœ

œœ#

œ œ

nœb

œ œn

œ#

œ œ#

œœ œ

#

#

œn

œ œ

#œ

œ œ

#

#œn

œ œ#

œ#

œ œ

n

n

œb

œn

œb

œn

œnœn

œb

œn

œb

œnœnœn

œb

œœb

œœœœb

œn

œb

œn

œn

œn

w™

w™

wwwwww

<#>

<#>

™™™™™™˙˙˙˙˙˙b

™™™™™™˙˙˙˙˙˙

#

b

™™™™™™wwwwww

™™™™™™ww

wwww

b n

#

n

™™™™™™ww

wwww

™™™™™™w w

™™w

™

˙ ˙™™

˙ ˙

#™™

˙ ˙

b

™™

˙˙#

™™˙ ˙

b

b™™

˙ ˙

#

™™˙ ˙™™

˙ ˙

n

#™™

wwb

™™w

™


Delaying Stability With Modulations

Example 24 below shows rehearsal R to the end. Prior to this section, “Still” offers a

strong statement of hope and community that begins with rehearsal N’s entrance of

the pure-tone bowed vibraphone, a contrast to the microtonal bowed waterphone

that evokes hopelessness at the beginning of “Still”. This leads to an unabashedly

American harmonic and orchestral chorale treatment of the full hymn in its original

form. However, in the last 35 bars of “Still” I remind the listener that, once the

larger community dissipates, only those closest to the tragedy are left to continue the

healing and rebuilding. While hope may remain, the sense of being alone in

continuing the effort may return, the wounds may seem fresh again, and the search

for healing and closure continues. The chorale ends ambiguously, the octatonic

reasserts its colour, and soon the music enters a final section (Example 24, below) of

distorted hymn fragments, broken dyads, and feathered clusters within a series of

rapidly changing hexachords.

The piano at rehearsal R is a variation of its first entrance in “Still” (see rehearsal B,

Example 21). The distorted opening fragment of the hymn is heard twice in the

bowed vibraphone and piano top voice: once starting at bar 153, and again at bar

157. Bar 161 begins the last clearly stated fragment of the hymn (bars 3-4), and that

is motivically varied and deconstructed in the final phrases to the end. While the

piano’s inner voice at R is similar to that of rehearsal B, the left hand at rehearsal R

paraphrases the opening’s walking dyads as broken intervals at the crotchet, a

quaver out of phase from the right hand.


The hexachords shift quickly, there are few common tones between adjacent

collections, and the connecting moment and tonic relationship is largely abandoned.


{{

{{ {{

Pian

o

Orch

estra

cantabile

mp

(q=100)

R

152

153

154

155

156

157

158

159

160

161

162

163

mf

pp

pp

pp

Oct

0,2

:Oct

1,2

:Oct

0,2

:

Oct

0,2

:Oct

1,2

:Oct

0,2

:

Pian

o

Orch

.

S

164

165

166

167

168

169

170

Pian

o

Orch

.

ppp

ppp

171

172

173

174

175

176

177

178

179

pp quiet hope

ppp

o

4 4

2 4

4 4

2 4

4 4

2 4

4 4

4 4

2 4

4 4

2 4

4 4

2 4

4 4

4 4

2 4

4 4

2 4

4 4

2 4

4 4

4 4

2 4

4 4

2 4

4 4

2 4

4 4

4 4

2 4

4 4

2 4

4 4

2 4

4 4

4 4

2 4

4 4

2 4

4 4

2 4

4 4

4 4

3 4

4 4

4 4

3 4

4 4

4 4

3 4

4 4

4 4

3 4

4 4

4 4

3 4

4 4

4 4

3 4

4 4

&

∑

b

b

n

b

b#

bb

b

n

n

?

∑

Fm/Bm:

Em/Bbm:

Dm/Abm:

&

D/Ab:

Em/Bbm:

Fm/Bm:

&

Vib

es b

ow

ed

∑

¿¿

¿¿

¿

¿

¿¿

¿

&

WW

fad

e in

/ou

t, feath

ered

overlap

&

Up

per S

tgs., B

rass

Tp

ts., H

ns.

>

?

Tb

ns, T

ba., L

ow

S

tgs.

&

#

n

#

n

b

b

n

#

#

n

b

&

Gm/C#m:

Fm/Bm:

Gm/C#m:

Fm/Bm:

Dm/G#m:

Em/Bbm:

&

¿

¿

¿

¿¿

& &

∑∑

∑∑

∑

?

Oct

1,2

:Oct

0,2

:Oct

1,2

:Oct

0,2

:Oct

0,2

:Oct

1,2

:

&

U

”“

&

U

&

l.v.

∑∑

/

Waterp

hon

e b

ow

ed

∑

low

to h

igh

∑

&

∑∑

∑

?

U

wœ

œ

œœb

œ œ

˙™

œœn

œb

œ™

œœ

œb

j

œ œ

œb

œ˙ œ

œ

wœ

œb

œb

œn

œ œ˙

™

œœ

œ

œœ

j

œb

™

œn

œ œ

œ œ

˙ œ

œ#

w œ

œ

œn

œb

œœ

j

œn

™œ

œœ

j

œ™

œ#

œ œœ œ

‰

œ

œb

œ

œ

j

œ

jœb

œœ

œ J

œ J

œb

œœ

œb

J

œ J

œb

œ J

œ J

œb

œb

œn

œn

j

œ

jœ

œb

œ

œb

j

œ

j

œb

œ#

œb

œn

j

œ

jœn

œb

j

œ

j

œb

œœn

œn

j

œ

j

œb

œœ

œ

j

œ

j

œ#

œ

j

wœ

˙™

œ™

œ#

˙˙#

wœ

˙™

œ J

œb

™˙

˙b

wœ J

œ™

œ J

œ™

œ

œ

ww

wbb

ww

w

˙˙˙

˙˙˙n#

ww

w

˙˙˙

ww

w

#ww

w

ww

w#

#˙˙˙

ww

wn

n#

˙˙˙

˙˙˙

#˙˙˙

www

n

wwn

˙˙

˙˙

#ww

œ ˙

œb

wwb

bww

ww

n˙˙

wwb

b˙˙

˙˙n

n˙˙

wwb

wwb

˙˙

˙˙

ww

˙˙

wwb

ww

ww

b˙˙

ww

n˙˙

˙˙

b˙˙

w œœ

œ

œb

œ œ

˙ œœn

˙ œ

œ

œ

œœ

œœ

œœœ

˙™

œ

œn

œ#

˙ œ

œ

˙ œ

œ#

w œœ

œ

œ

˙ œ

œb

œÓ

œ

œ

j

œ

œ#

œb

œ

j

œ

j

œ#

œœn

j

œ

j

œœ

œ

œn

j

œ

j

œ

œ

œ#

œ

j

œ

jœ

œ#

œœ J

œ J

œ

œb

œ

œb

j

œ

j

œn

œœ

œb

J

wœ

˙

˙œ

™

œ J

œ˙

™w

w#

w

www

#

#

˙˙˙

n

™™™˙ ˙˙#

˙˙˙

n

ww

w

bw

w

w

ww

w

n

#

ww

w

w˙

™

ww

n˙˙

b™™

w˙

˙b

ww

bw˙

Ó

w#

w

œ

œn

œb

œb

œœ

œ

œ

œœ

œ

œ

˙˙

ww

w˙

œ

œb

˙ ˙ ˙

w w w

œ

J

œ

œb

œn

œ

j

œ

j

œ

œb

œ

œb

j

œ

j

œ

œb

œ

œb

j

œ

j

œ

œb

œ

œb

j

œ

j

œ

œb

J

œ™

œ

j

œ

œb

˙w

ww

w<#>

˙

ÓÓ

˙w

œ

ŒÓ

ww

w<#>

ww

w

ww

w

ww

w

ww

w

˙˙

˙Ó

w<#>

ww

ww

ww

ww


The piano’s out of phase figures and lack of local points of stability evoke the search

for grounding. Initially, residuals from the chorale (G♮ and A♮) conflict with the

implied octatonic scales, emphasizing the contrast between this unstable section and

the earlier chorale. To me, this reflects a desire to avoid the realities of the healing

process.

The final hexachord transitions of bars 167 and 169 break the pattern of instability

and almost create a stable arrival point. Bar 167’s transition to Dm/G♯m is a

noticeably subtle shift with four common tones. The transformation is sweetened by

the resolution of the prominent E♮ suspension in the bass, through the octatonic-

compatible E♭, to the D♮ doubling of the soprano line. The final arrival at the

Em/B♭m hexachord in bar 169 hints at stability in several ways:

• The soprano and bass move in parallel to the C♯. Parallel voice leading of this

nature is unusual in this movement, and here it strongly signifies an arrival

point.

• The Em/B♭m hexachord shares three common tones and a parent octatonic

to what would be the tonic of the Dm/G♯m connecting moment (C7(♯4)).

(Compare this to bar 24, Example 21.)

• Only tones from the Em/B♭m hexachord are used in the harmonies, so there

is no pull away from the hexachord’s stability.

• Repeating patterns in the piano accompaniment emphasize the stability

desired at this point.


This almost stable moment represents a tentative arrival at some grounding, and

hope for healing is offered. However, “Still” clearly ends more as a question than a

statement. The movement opened with a Dm/G♯m connecting moment and C7(♯4)

tonic relationship constructed from the C wtq scale, yet closes with a Dm/G♯m to

Em/B♭m shift. Much of the work was constructed around the connecting moment

and tonic relationship, yet the ending only hints at a connecting moment to tonic

resolution. The C♮ and F♯ that would reinforce a sense of the Russian tonic are

never stated, and the movement ends with an emphasis on a first-inversion B♭

minor harmony. Even the final upward gestures by the waterphone and the piano

are feminine in nature: expressing hope, but not making a definitive statement. Ten

years after the levee failures in New Orleans there is hope, but much uncertainty

about New Orleans still remains.

!

Conclusion 83

Chapter 7: Conclusion

The goal of my Master’s program was to learn how to compose in a harmonic

language not tethered to common practice. I did this through the study of

theoretical papers, analysis of scores, and composing with the tools I gathered.

In this commentary, I have presented three significant works for my composition

portfolio. While The Nightingale and the Rose and I Wish I Could Remember That First

Day are formative pieces, I feel that it is the twenty-five minute, three-movement

piano concerto Currents that most fully demonstrates my growth as a composer and

the fulfilment of my goals.

I have used my exploration of mode as a common theme in discussing my works. In

four separate areas of exploration, I have presented my findings from research and

analysis, and I have demonstrated how I have applied these findings to my music.

I discussed the expansion of the diatonic harmonic language through added-tone

sonorities. I used the music of Eric Whitacre as my model and the writings of

Angela Hall as the basis for my theoretical understanding. In I Wish I Could

Remember That First Day, I explored how context affects the interpretation of a

complex chord, gave examples of where the sonorities in my music can not be

analysed as an added-tone sonority, and showed how the use of clusters is a natural

outgrowth of added-tone sonorities.

I explained Dmitri Tymoczko’s theories of scale construction and scale networks

and showed how I used them to map potential scales and modulations for two

works: The Nightingale and the Rose and “River”. For The Nightingale and the Rose I

designed a relatively straightforward scale network based upon my Whole-Tone

Conclusion 84

Quint scale. I showed how my choice of scales affected my harmonic options and

led me towards a use of harmony less connected to common practice but in many

ways still functional.

For “River” I designed synthetic scales new to me using the constraints of maximal

intersection. I created a scale network much more ambitious in scope than that I

used for The Nightingale and the Rose, and I demonstrated the three main types of

modulation I used within “River”: maximally intersecting modulations (the

modulation primarily discussed by Tymoczko); modulations between parallel

modes; and modulations involving tonics related by fifths. I also discussed how and

why I used hexachord complements in “River”, how these related to the WTQ scale,

and my approach to modulation between these hexatonics.

With a row derived from the G wtq and melodic material from movement one, I

modelled the rotational array process for “Breaking” after Oliver Knussen with one

deviation from his method. I offered examples of using every aspect of the array that

was generated. I demonstrated how using a row that is a subset of a mode of limited

transposition opened up opportunities to consider the containing collections

(octatonics, in my case) integral to the harmonic language.

For “Still”, the third movement to Currents, I briefly presented how the Russian

music theorists view and construct modes, and I demonstrated how I constructed

my “Russian mode” as a derivative of the WTQ. I used the connecting moment to

tonic relationship as a means of generating stable arrival points. I explored

hexachords that are supersets to my tonics and the implications of shifting between

complements and shifting by transposition. I discussed how I distorted fragments of

Conclusion 85

the hymn Nearer, My God, to Thee to fit notes from my collections, and I pointed out

where this creates both cohesion and symbolism within the work.

“Still” is a fitting close to my Master’s study. I feel that it represents the culmination

of a year of research, analysis, and composing. Like “Still”, my Master’s ends with

hope and a sense of more work to be done. What I am able to demonstrate today as

my growth as a composer is significant, but undoubtedly the most important skill I

have acquired through this Master’s by Research is the confidence and experience

of exploring new ideas, synthesizing them, and applying them to my own art.

Rotational Arrays for “Breaking” 86

APPENDIX: Rotational Arrays for “Breaking”

°

¢

°

¢

Af

Bf

Cf

Df

Ef

Sf

Ad

Bd

Cd

Dd

Ed

Sd

Oct0,2

Oct0,2

Oct1,2

Oct0,2

Oct1,2

either way

Oct0,2

Oct0,2

Oct1,2

Oct0,2

Oct1,2

either way


&

&

&

&



&

&

&

&


˙ ˙ ˙b ˙ ˙ ˙˙#n

˙˙#n

˙˙#n

˙˙n#

˙˙n#

˙ ˙b ˙ ˙ ˙b ˙˙#nb

˙˙#nb ˙

˙n#b˙˙n#

b ˙˙n#

b

˙ ˙# ˙ ˙ ˙ ˙˙b ˙

˙b ˙˙b

˙˙b

˙˙b

˙ ˙b ˙ ˙# ˙ ˙˙bb

nb ˙˙bbnb ˙

˙bbbn

˙˙bn

bb˙˙bnbb

˙ ˙# ˙# ˙ ˙˙˙bb

n˙˙nbb

˙˙nbb

˙˙nb

b˙˙bnb

˙ ˙###b ˙#b ˙bnn ˙nn#n‹ ˙ ˙œb##

Y

Yn##Y

Ynbn˙œ#nnn

˙ ˙ ˙n ˙b ˙b˙˙n###

˙˙##n#

˙˙###

n ˙˙###

n˙˙###n

˙ ˙b ˙ ˙ ˙n˙˙#n

˙˙#n

˙˙#n

˙˙n#

˙˙n#

˙ ˙b ˙b ˙ ˙#˙˙#b#

n˙˙##nb

˙˙n#b# ˙

˙#b#n

˙˙#nb#

˙ ˙n ˙b ˙n ˙b˙˙#nb

˙˙#nb ˙

˙n#b˙˙n#

b ˙˙n#

b

˙ ˙b ˙n ˙b ˙ ˙˙#nb

˙˙bn# ˙

˙n#b˙˙#n

b ˙˙#n

b

˙ ˙###n ˙bbnn ˙##nnn ˙bbbnn ˙n œ˙## Y

Ybn Y

Y

#n ˙œbb


°

¢

°

¢

Aes

Bes

Ces

Des

Ees

Ses

Ab

Bb

Cb

Db

Eb

Sb

Oct0,1

Oct0,1

Oct0,2

Oct0,1

Oct0,2

either way

Oct0,2

Oct0,2

Oct1,2

Oct0,2

Oct1,2

either way


&

&

&

&

&Stacked Column Harmonies

revoiced as incomplete M7 chords w/ added tone


&

&

&

&


˙b ˙ ˙b ˙ ˙˙˙bn

#˙˙#nb

˙˙#nb ˙

˙b#n˙˙b#n

˙b ˙b ˙ ˙b ˙b ˙˙nbbb

˙˙nb

bb ˙

˙bbbn ˙

˙bnbb˙˙bnb

b

˙b ˙n ˙ ˙ ˙ ˙˙#nn

˙˙#nn

˙˙#nn ˙

˙nn#

˙˙n#n

˙b ˙b ˙ ˙# ˙ ˙˙n#b#n

˙˙b#

nn#

˙˙#bnn

# ˙˙#bn

n#˙˙b#n

n#

˙b ˙n ˙# ˙ ˙˙˙bb

nb ˙˙bbnb ˙

˙bbbn

˙˙bn

bb˙˙bnbb

˙b ˙nnnb ˙### ˙bb ˙nn#n# ˙b ˙œbnnn

Y˙Y#n# Y

Ynbb ˙œ#nnn

˙ ˙# ˙n ˙ ˙#˙˙n#n#

˙˙n#n#

˙˙#nn#

˙˙#n

#n ˙˙n#n#

˙ ˙n ˙# ˙# ˙n ˙˙#bn

˙˙#nnb

˙˙#b

nn˙˙#b

nn ˙˙nnb#

˙ ˙n ˙ ˙# ˙#˙˙bnb

n˙˙nbnb

˙˙nb

bn˙˙nbnb ˙

˙bnnb

˙ ˙n ˙ ˙n ˙b˙˙#n

˙˙#n

˙˙#n

˙˙n#

˙˙n#

˙ ˙n ˙n ˙ ˙b˙˙nb ˙

˙nnb ˙˙nnb

˙˙nbn

˙˙nnb

˙ ˙nnnb∫ ˙n#n ˙###n# ˙bbnbn# ˙n œnbnn Y

Y

#nnn Y

Y### œ˙b#b


°

¢

°

¢

Aa

Ba

Ca

Da

Ea

Sa

Tf

Td

Tes

Tb

Ta

Oct0,1

Oct0,1

Oct0,2

Oct0,1

Oct0,2

either way







&

&

&

&


&Transposed Stacked Rows Closed Position.

&

&

&

&

˙ ˙# ˙n ˙b ˙b ˙˙n#b#

˙˙b#

n#˙˙#bn#

˙˙#bn#

˙˙#nb#

˙ ˙b ˙b ˙ ˙n ˙˙#n# ˙

˙#n# ˙˙#n#

˙˙#n# ˙

˙##n

˙ ˙n ˙b ˙ ˙#˙˙#n#

˙˙#n#

˙˙#n#

˙˙#n# ˙

˙#n#

˙ ˙n ˙b ˙n ˙b ˙˙bn

#˙˙#nb

˙˙#nb ˙

˙b#n˙˙b#n

˙ ˙n ˙n ˙b ˙˙˙n# ˙

˙#n˙˙#n

˙˙n#

˙˙n#

˙ ˙###bn ˙bb#nn ˙##nnn ˙˙b#n# ˙ œbbnn Y

Y

#bnn Y

Y#nnn œ

˙bnb

˙˙bb

n ˙˙nbb

˙˙bn

nn ˙˙bn

bb ˙˙nbnn ˙bnbb ˙nbnb ˙bnnn ˙bbb∫ ˙nn#n

˙˙#nb

˙˙bnn

˙˙##n

n ˙˙n#

bn ˙˙n#

b# ˙bn#n ˙nbnn ˙n#n# ˙nnbb ˙#n##˙˙nn##

˙˙nb

bnb˙˙#nnbn

˙˙#bn

n# ˙˙n#n

nn ˙n#nn# ˙n#n## ˙bbnnn ˙#bn#n ˙n#nnn

˙˙#n#n ˙

˙#nnb ˙˙#nn# ˙

˙n#nn ˙˙nnn

bb ˙n##n ˙#n#n ˙n##n ˙n#nn ˙##nn

˙˙#nn ˙

˙bnb ˙˙#bn# ˙

˙bn#n ˙˙n##n

˙nn# ˙bbnn ˙n### ˙nnbb ˙#nn#

Bibliography 89

Bibliography

Anderson, Julian. 2002. “Harmonic Practices in Oliver Knussen’s Music Since

1988: Part I”. Tempo (221): 2-14.

Barrymore, Laurence Scherer. 2000. “A Composer Balances Tradition, Invention”.

Wall Street Journal, 15 June. Accessed 11 February 2016.

http://search.proquest.com/docview/398773707

Berger, Arthur. 1963. “Problems of Pitch Organization in Stravinsky”. Perspectives of

New Music 2 (1): 11-42.

Berry, David Carson and Sherman Van Solkema. “Theory”. Grove Music Online.

Edited by Root, Deane. Accessed 15 March 2016.

http://www.oxfordmusiconline.com

Ewell, Philip A. 2012. “Rethinking Octatonicism: Views From Stravinsky’s

Homeland”. Music Theory Online 18 (4). Accessed 7 September 2015.

http://www.mtosmt.org/issues/mto.12.18.4/mto.12.18.4.ewell.php

Hall, Angela. 2012. “Added-Tone Sonorities in the Choral Music of Eric Whitacre”.

MA diss., Washington University. All Theses and Dissertations (ETDs)

(Paper 737). doi: 10.7936/K77M061J.

Levine, Mark. 1989. The Jazz Piano Book. Petaluma, CA: Sher Music Co.

McQuere, Gordon D. 1978. “The Elements of the Structure of Musical Speech By

S. V. Protopopov: A Translation and Commentary”. PhD diss., University of

Iowa. ProQuest Dissertations & Theses Global (302883188).

http://search.proquest.com/docview/302883188

Bibliography 90

Nelson, Stephen. “Hurricane Katrina - What Happened? The Geology of the

Katrina Disaster in New Orleans: Field Trip Guide”. (2015): Accessed 25

February 2016.

http://www.tulane.edu/~sanelson/Katrina/Hurricane%20Katrina%20Field%2

0Trip.pdf

Persichetti, Vincent. 1961. Twentieth-Century Harmony: Creative Aspects and Practice.

New York: W. W. Norton.

Roeder, John. “Set (ii)”. Grove Music Online. Edited by Root, Deane. Accessed 4

February 2016. http://www.oxfordmusiconline.com

Rossetti, Christina. 1995. The Works of Christina Rossetti With an Introduction By Martin

Corner, and Bibliography. Herfordshire: Wordsworth Editions, Ltd.

Solomon, Larry. “The Table of Pitch Class Sets”. (2005): Accessed 4 February

2016. http://solomonsmusic.net/pcsets.htm

Spilker, John D. 2010. “‘Substituting a New Order’: Dissonant Counterpoint,

Henry Cowell, and the Network of Ultra-Modern Composers”. PhD diss.,

Florida State University. Electronic Theses, Treatises and Dissertations

(Paper 1605). http://purl.flvc.org/fsu/fd/FSU_migr_etd-1605

Tymoczko, Dmitri. 2004. “Scale Networks and Debussy”. Journal of Music Theory 48

(2): 219.

Wilson, Charles. “Hexatonic”. Grove Music Online. Edited by Root, Deane. Accessed

22 February 2016. http://www.oxfordmusiconline.com

Documents

PORTFOLIO OF COMPOSITIONS