Copyright 2010, Robert DeVet

Flux: for Brass Quintet with Analysis

By

Robert DeVet, B.A.

A Thesis

In

Music Composition

Submitted to the Graduate FacultyOf Texas Tech University in

Partial Fulfillment ofthe Requirements for

the Degree of

Master of Music

Approved

Peter FischerChair

Michael Berry

James T. Decker

Peggy Gordon MillerDean of the Graduate School

December, 2010

Copyright 2010, Robert DeVet

TABLE OF CONTENTS

I. INTRODUCTION_________________________________________________________ 4

II. A SYSTEM OF QUARTAL HARMONY AND ANALYSIS_____________________________ 6

III. AN HISTORICAL CONTEXT FOR THE QUARTAL HIERARCHICAL SYSTEM OF HARMONY__________________________________________________________10

IV. HARMONIC AND STRUCTURAL ANALYSIS_________________________________13

ANALYSIS OF MOVEMENT _________________________________________I 13

ANALYSIS OF MOVEMENT ________________________________________II 20

ANALYSIS OF MOVEMENT ________________________________________III 26

V. CONCLUSION________________________________________________________ 35

WORKS CONSULTED_____________________________________________________ 36

APPENDIX A COMPLETE SCORE OF FLUX: FOR BRASS QUINTET_________________ 37

I “WAITING TO WIN ______________________________________________” 40

II “STRIDES FORWARD ____________________________________________” 47

III “OSTINATO __________________________________________________” 52

Texas Tech University, Robert DeVet, December 2010

ii

CHAPTER IINTRODUCTION

This paper will examine the piece Flux: for Brass Quintet, completed in the

spring of 2010 by Robert DeVet. It will first examine the system of quartal harmony

employed in the piece and define a concise system of analysis. It will then present a

several examples of quartal harmony in the music of other composers and briefly inspect

a similarly rigorous system based on perfect intervals. Each movement will then be

analyzed formally, harmonically, and motivically. The piece consists of three individual

movements, “Waiting to Win,” “Strides Forward,” and “Ostinato.”

Flux: for Brass Quintet had its genesis during the summer of 2004. During that

time I was attending the American Festival for the Arts summer music conservatory in

Houston, Texas. To fultill an assignment, I penned a viola trio that included the much of

the thematic material that would eventually become the second movement of Flux. Upon

revisiting the original viola trio five years later, I was dissatisfied with the former

realization of my thematic ideas and was convinced that I could now, as I could not

previously, fulfill more of the potential that I saw contained within the work. I decided to

expand upon those thematic ideas that I liked, and from them, to draw a harmonic system

that would withstand scrutiny and analysis far beyond the original intent of the piece.

After I had written the bulk of the second movement, I decided that it was the

right time to codify the harmonic system. In this way I let theory follow practice. The

specifics of the system are laid out in the Chapter 1. Armed with this system, I felt ready

to tackle the task of writing the surrounding movements, whose notes flowed with

varying degrees of ease and difficulty from my pen.


1

When I finally had a chance to step back and view the work as a whole, I realized

that the expressive flow of the piece from beginning to end made a remarkable parallel to

the compositional growth that I had experienced during its writing. I heard the

juxtaposition of furious passages and plodding dissonance in “Waiting to Win” and

relived the fever pitch of excitement that I experienced while I was devising the system

along with my own struggle to understand it. In the driving pulse of “Strides Forward,” I

felt a determination to use the language effectively. Finally, in the flowing lines of

“Ostinato,” I began to hear the real ease that comes with familiarity with a language.

In the music of Flux, I have found a mode of expression that I can continue to

explore long after completing the piece. I have always liked quartal harmonies, but have

avoided using them as a compositional tool until now because I believed that I needed

some organizing principle in order to utilize them in a coherent manner. Now that I have

devised such an organizing principle, countless new harmonic possibilities are available.


2

CHAPTER IIA SYSTEM OF QUARTAL HARMONY AND ANALYSIS

The harmonic language employed throughout Flux: for Brass Quintet is quartal.

The relative consonance and dissonance of the sonorities can be ascertained by

examining the quality and distribution of the intervals when arranged so that each

member of the sonority is separated from its neighbors by a fourth, whether perfect or

augmented. Furthermore, while sonorities are often inverted, the inversion does not have

an effect on the analyzed dissonance or consonance.

The employed sonorities are arranged into three classes: sonorities with no

tritones, sonorities with one tritone, and sonorities with two tritones. Members of the first

class are the most stable, members of the second class are less stable, and members of the

third class are the least stable. If the number of included pitches in the sonorities is five,

the second and third classes can be further divided into four and three subclasses

respectively. The second class is divided into four different sonorities dependent on

where the included tritone occurs. The third class is divided into three different sonorities

in the same manner based on the positions of the two tritones.

While relative dissonance within each class of sonorities is more difficult to

perceive, for the purposes of analysis, a hierarchy of stability may be constructed based

on how the tritone relates to the bottom interval in the sonority. Dissonance increases as

the tritone or tritones approach the bottom of the chord. Each different sonority can then

be given a number from zero to seven, zero being the most stable with no tritones and

seven the most unstable with the intervals, from bottom to top, tritone, perfect fourth,

tritone, perfect fourth. This hierarchy of stability is illustrated in Example 2.1.


3

If sonorities with fewer than five pitches are to be analyzed, the numbering system

becomes confusing because four- and three-pitch sonorities contain fewer intervals and

consequently fewer of the numbered sonorities. When the number of pitches is decreased

to four, sonorities 1, 5, and 6 are no longer possible because a tritone in those sonorities is

between the fourth and fifth pitches from the bottom and the resulting sonority exists

earlier in the hierarchy. When the number of pitches is decreased to three, in addition to

the three impossibilities shared with four-note sonorities, sonorities 2 and 7 become

impossible. Naturally, three-note sonorities cannot include two tritones without repetition

of pitch, placing a natural limit on how much dissonance can occur when only three

pitches are present. Despite the confusion inherent in this system, sonorities having the

same number will be considered of equivalent stability regardless of the number of

pitches. The complete hierarchy of stability is illustrated in Example 2.2.

&&&

44

44

44

!!!

!!!

!!!

!!!

!!!

&&&

wwwwwbbbwwwwbbwwwb0

Stable

wwwwwbb

1

wwwwwbwwwwb

2

wwwwwwwwwwww3

wwwww#wwww#www#4

wwwww#

5

wwwww##

6

wwwww###wwww##

7Unstable- - - - - - - - - - -

& wwwwwbbb

0Stable

wwwwwbb1

wwwwwb2

wwwww3

wwwww#4

wwwww#

5

wwwww##

6

wwwww###

Unstable7

- - - - - - - - - - -

[Title][Composer]

Full Score[Subtitle]

[Arranger]

No Tritones One Tritone Two Tritones

Example 2.1: Five-pitch sonorities, hierarchy of stability.


4

For the sake of brevity, each sonority in the hierarchy will be referenced by a

string of symbols. First, the letter ‘H’ indicating a member of the hierarchy. Second, an

arabic numeral signifying the number of the sonority within the hierarchy. Finally, an

arabic numeral within parentheses denoting the number of pitches of the hierarchy. For

instance, a number 4 sonority containing five pitches would be notated as “H4(5)” or,

more generally, any 4 sonority can be notated as “H4.” See Example 2.3 for analysis of

several sonorities using this system.

As was previously noted, the differences in stability are more easily perceptible

when moving between sonorities that contain different numbers of tritones. While the

different sounds of an H1 and an H4 can be easily discerned if they are sounded near

enough to each other and given enough duration, over the course of a movement the

relationship between them can be obscured. Because the relationship between the larger

&&&

44

44

44

!!!

!!!

!!!

!!!

!!!

&&&

wwwwwbbbwwwwbbwwwb0

Stable

wwwwwbb

1

wwwwwbwwwwb

2

wwwwwwwwwwww3

wwwww#wwww#www#4

wwwww#

5

wwwww##

6

wwwww###wwww##

7Unstable- - - - - - - - - - -

& wwwwwbbb

0Stable

wwwwwbb1

wwwwwb2

wwwww3

wwwww#4

wwwww#

5

wwwww##

6

wwwww###

Unstable7

- - - - - - - - - - -

[Title][Composer]


[Arranger]

No Tritones One Tritone Two TritonesExample 2.2: Complete hierarchy of stability.

& c ! ! !

& wwwwbbSpecific:!H0(4)

General:!H0

wwwwwbbH1(5)

H1

www##H4(3)

H4

wwww#H7(4)

H7

wwwwwbbH5(5)

H5

& !

& ! ! !

& ! ! !

& ! ! !

& ! ! !

& ! ! !

[Title][Composer]


[Arranger]

Example 2.3: Examples of specific and general analyses of sonorities.


5

classes is much more perceptible, a parallel system of analysis may be employed for

passages that simply move from one larger class to another. Since the only numbered

sonority to be a member of the first class is H0, this can be used to designate that class.

The other two classes can be designated as A, for sonorities H1 through H4, and B, for

sonorities H5, H6, and H7. In this way the move between more generalized stability and

instability can be notated, with or without the specific sonorities notated with the

appropriate alpha-numerical strings. This is especially useful when analyzing passages

that contain similar rhythmic, textural, and/or contrapuntal material and move through the

larger classes of sonorities in the same manner, but utilize different specific sonorities. In

these cases, the more general analysis reveals that, in fact, the harmonic motion is

essentially equivalent.

This system of harmonic composition and analysis will, from now on, be referred

to as the Quartal Hierarchical System of Harmony.


6

CHAPTER IIIAN HISTORICAL CONTEXT FOR THE

QUARTAL HIERARCHICAL SYSTEM OF HARMONY

In his book Techniques of Twentieth Century Composition, Leon Dallin states that

quartal chords are rarely used as the only harmonic material in a piece of music. Among

the reasons that he gives that they are often eschewed except to add coloristic variation is

that the sonorities is that they “lack the resonance of tertian sonorities.” 1 Another reason

that they are often overlooked may be that they often do not contain the sonic complexity

that many contemporary composers look for. While they have not always been treated as

a complete harmonic palette, composers have been using quartal sonorities as ways to

extend their harmonic landscape for at least a century.

Quartal harmonies were well suited to the impressionists’ goal to obscure and

minimize the functionality of their harmonies. Along with extended tertian harmonies,

many impressionistic pieces included passages colored with quartal harmonies. Claude

Debussy’s “La Cathédrale engloutie” contains passages full of quartal harmonies as can

be seen in Example 3.1.2 While quartal harmonies are present in the piece, so are tertian

&?23

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!!

!!

!!

&?

5 !!

&?

" " "....wwwwŒ œœœœ œœœœœœœœ œœœœ œœœœ

Œ œœœ œœœ œœœ œœœ œœœwww& ?

˙˙˙ wwww-

˙˙˙ wwww! ˙

˙˙˙ wwww-

˙˙˙ wwww! ˙

....wwww

....wwww

œœœœ Œ Ó Óœœœœ Œ Ó Ó

&?

11 !!&

!!

!!

!!

!!

!!

!!

&&

18 !!

!!

!!

!!

[Title][Composer]

Full Score[Subtitle] [Arranger]

Example 3.1: “La Cathédrale engloutie,” mm. 85-89.


7

1 Leon Dallin, Techniques of Twentieth Century Composition, 2nd ed. (Dubuque, IA: Wm. C. Brown, 1964), 77.

2 Claude Debussy, Preludes (Book I.) (London: United Music Publishers Ltd., 1910)

and quintal.

In his Theory of Harmony, Arnold Schoenberg describes a hypothetical quartal

system as “no less defensible on natural grounds” as a quintal system.3 When the third

edition of the book was published in 1922, he had already written several pieces that

included quartal harmonies, and was not above referencing both Pelleas und Melisande

(1902-03) and Kammersymphonie (1906).4 In the Kammersymphonie, the arpeggiated

six-pitch sonority in the horn in mm. 5-6 is structurally significant through the entire

piece, see Example 3.2. However, the harmony of the piece is, again, not strictly quartal

and includes a variety of other harmonic structures.

The difference between the above examples and the quartal hierarchical system is

that the system seeks to treat quartal sonorities with enough organization and variety so

that, by themselves, they can create a harmonic environment that is sufficiently

interesting to hold an audience’s attention for the entirety of large works. The rigor of the

system is reminiscent of Peter Fischer’s treatment of quintal structures.5 In his system, as

in the quartal hierarchical, the primary consonant sonority is based on a structure of

perfect intervals, in this case fifths. All of the basic sonorities contain three pitches, and

& C 44Horn in F œƒœ œ œ .œ œb œb Œ ˙## ƒ

&4 ! ! ! ! ! ! !

&11 ! ! ! ! ! ! ! ! !

&20 ! ! ! ! ! ! ! ! !

&29 ! ! !

[Title][Composer]


Example 3.2: Kammersymphonie, mm. 4 (partial)-6 in the horns.


8

3 Arnold Schoenberg, Theory of Harmony, trans. Roy E. Carter (Berkeley, CA: University of California Press, 1978), 399.

4 Ibid, 403.

5 Peter Fischer, “Formal presentation on my compositional technique to student composers and faculty,” Presentation text for

presentation given as part of the Visiting Composers Seminar at the University of Arizona, Tucson, AZ. 24 March 2005.

are illustrated in Example 3.4. However, instead of changing only one interval at a time,

the inner pitch is displaced by varying intervals while the outer interval of a major ninth

remains constant in a similar way to the perfect fifth in major and minor triads. This

treatment of the inner pitch as a movable entity results in intervals other than fifths in the

uninverted basic forms of the sonorities.

Historically, very few composers have attempted to systematically treat harmony

based on perfect intervals. Perhaps it is because the sonorities created lie somewhere

between the functional consonance of tertian harmony and the complex dissonance of

many post tonal harmonic languages. Straddling the divide, they do not present

themselves as ready tools with which composers can answer their compositional

questions.

? 44 ! ! ! ! !

? wwwprimary

consonant

wwwless stable

intense

wwwbunstable

dissonant

wwwunstable

dissonant

www#stable

consonant

wwwstable

consonant

www#stable

consonant

?13 ! ! !

?16 ! ! !

?19 ! ! !

?22 ! ! !

[Title][Composer]


Example 3.4: Primary three-pitch sonorities with relative dissonance in Peter Fischer’s quintal system.


9

CHAPTER IVHARMONIC AND STRUCTURAL ANALYSIS

Analysis of Movement I

Movement I, “Waiting to Win,” begins with a downward apreggiation of H0(5),

with a root pitch of F#. See example 4.1 for the opening measures with analysis. In

measure 3, the trumpets and horn intone an H3(3) sonority on C, followed by an H4(3) on

B, and then returning to the original sonority. The harmonic motion is accomplished by

the first trumpet and the horn moving in parallel major sevenths, while the second

trumpet remains stationary with the common tone. Beneath this motion, the trombone and

tuba play a tritone that, when added to the H3 sonority in the other instruments, creates an

H6(5) sonority, and also provides a context against which the H3-H4-H3 harmonic

motion in the top three voices can be considered neighboring motion in the first trumpet

and horn. This motion is followed, in measure 4, by an H4(5) sonority with an F root.

Interestingly, there is only a one-pitch difference between this sonority and that which

opened the movement. Measure 5 is an exact repetition of measure 3 but is followed by

an H3 sonority, again rooted on F. In these five measures the music has moved from H0

&

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42

42

42

42

42

Trumpet in Bb 1

Trumpet in Bb 2

Horn in F

Trombone

Tuba

˙

‰ jœ œŒ œŒ ‰ Jœ

!

˙

˙

˙˙

˙#H0(5)

œ œ " œb œ " œn œ

œ œ " œ œ " œ œ

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‰ rœ# " " rœ ‰H6(5)

˙

˙

˙˙

˙H4(5)

œ œ " œb œ " œn œ


œ œ " œ œ " œ œ‰ Rœ " " Rœ ‰

‰ rœ# " " rœ ‰

˙

˙

˙˙b

˙H3(5)

&

&

&?

?

83

83

83

83

83

42

42

42

42

42

85

85

85

85

85

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

!

!

œPœ" œœ"œœ!

!

!

!

œb . œ œ œ!

!

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œbPœ"œœ"œœrœb "‰ Œ

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!

œb .œœb œb!

!

!

œbFœ"œœ"œœ

œbFœ"œœ"œœ!

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!

œn .œ œb œb

œn .œb œb œb

!

!

!

!

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!

œnfœ œb œb

œn fœ# œ# œ

!

!

œnpœ# œ# œ!

!

œfœb œb œb œ.œ.

œbfœb œb œœ.œ.!

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!

œ œb œb œb œ.œ.œb œb œb œœ.œ.

!

!

!

!

!

!œbpœb œœœœ. œb . œb .

œpœb œb œœœ. œ. œb .

&

&

&?

?

85

85

85

85

85

42

42

42

42

42

85

85

85

85

85

165

165

165

165

165

85

85

85

85

85

42

42

42

42

42

85

85

85

85

85

165

165

165

165

165

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

Œ . ‰ JœfŒ . œfŒ jœf œ‰ œf œ

.œf œ

!

Œ ‰ jœpŒ œp‰ .œp˙bp

Œ . ‰ JœfŒ . œfŒ jœf œ‰ œf œ

.œf œ

œ œb œb œb . œ.!

!

!

!

.œNp œ‰ œbp œŒ jœbp œŒ ‰ œ

pŒ ‰ ‰ Jœp

˙#P‰ .œPŒ œPŒ ‰ Jœ#

P!

.œF

œ‰ œF œŒ jœF œŒ ‰ œ

FŒ ‰ ‰ JœF

3I

Robert DeVet

Copyright © 2010 Robert DeVet, ASCAP

ScoreWaiting to Win

Example 4.1: Movement I, opening sonorities, mm. 1-6.


10

to H4 to H3 by changing only one pitch at a time. After the initial statement of H0,

another H0(5) is not sounded until measure 173 at which point the initial spelling of H0 is

stated and repeated to the end of the movement at measure 178.

The rhythmic material developed in the A section is made up of two small motives

illustrated in Example 4.2. First, the sixteenth-note figure in the three upper voices in

measure 3, rhythmic motive 1 or RM 1. This motive sometimes includes a melodic

component; the third and fourth notes in the figure often appear as lower neighbor-tones

to the other notes. However, this melodic aspect is not as important as the rhythmic

aspect, and many instances of this first motive appear on a single pitch. The second

motive, rhythmic motive 2 or RM 2, is first sounded in the horn in measure 8. Unlike the

first motive, this second motive has an important melodic and intervallic component. It is

made up of four eighth notes and first leaps up by a tritone and then steps down. Every

statement of RM 2 follows the same basic contour, if not the same intervals.

After the introductory material, which is characterized by short rhythmic cells

separated by sixteenth-note rests, a development of RM 2 occurs beginning in m. 36. This

melody is in the horn and is accompanied by a complete change of texture; the other

instruments take turns playing longer slurred durations. The horn phrase is followed by

an even starker statement of the same melody, now in the second trumpet and a perfect

fourth higher beginning in m. 48. The accompaniment during this repeated phrase is now

& c ! ! !

& 42wwwwbbSpecific:!H0(4)

General:!H0

wwwwwbbH1(5)

H1

www##H4(3)

H4

wwww#H7(4)

H7

wwwwwbbH5(5)

H5

& 42 !

& œ œ " œ œ " œ œRhythmic!Motive!1

œ œ œ œRhythmic!Motive!2

& ! ! ! !

& ! ! ! ! ! ! ! ! !

& ! ! ! ! ! ! !

[Title][Composer]


[Arranger]

Example 4.2: Rhythmic motives developed in the A section of Movement I.


11

only three staccato eighth notes in two simultaneous voices, first the first trumpet and

horn, next the trombone and tuba, and finally the horn and tuba. These two phrases are

separated and bookended by material from the introduction.

A transitional passage begins at m. 58, and juxtaposes the two trumpets with the

three other instruments. See Example 4.3 for the passage with analysis. The lower three

instruments begin by stating RM 1 on an H3(3). The outer notes of the sonority are

echoed in the trumpets, this time played as a minor second instead of a major seventh.

The other three then state an H4(3). The motion is accomplished by the trombone rising a

&

&

&?

?

42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

!

!

œb œ " œ œ " œ œœ œ " œ œ " œ œ

œ œ " œ œ " œ œH(3)3


œb œ " œ œ " œ œm2

!

!

!

!

!

œb œ " œ œ " œ œœb œ " œ œ " œ œ

œ œ " œ œ " œ œH4(3)



!

!

!

Œ ‰ " Rœb

Œ ‰ " rœm2

œN œ " œ œ " œ œœb œ " œ œ " œ œ

œb œ " œ œ " œ œH3(3)

œb " œ œ " œ œ œ

œ " œ œ " œ œ œ!

!

!

&

&

&??

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba


œ " œ œ " œ œ œ

œ œ " œ œ " œ œœN œ " œ œ " œ œ

œb œ " œ œ " œ œH4(3)




œN œ " œ œ " œ œH3(3)




œ œ " œ œ " œ œH4(3)

Rœ " ‰ Œ

Rœb " ‰ Œ

œn œ œ œ œ œ3 3

œ œ œ œb œ œ3 3

œ œ œ œ œ œ3 3

H3(3) H4(3)

!

!


œb œ œ œn œ œb3 3

œb œ œ œ œ œb3 3

H3(3) H4(3) H3(4)

&

&

&??

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

˙

Œ œ!

!!

˙

˙

˙Œ œ

!

˙

˙

˙˙

˙H4

˙

˙

˙˙

˙

!

!

!

!!

!

Œ œb

˙Œ œ

!

˙

˙

˙˙

˙#H6

!

!

!

!!

˙

Œ œ!

!!

˙

˙

˙bŒ œb

!

˙

˙

˙˙

˙H2

˙

˙

˙˙

˙

!

!

!

!!

œ œ>

>œb œ>˙b>

œ œ>H2

U "

u "

u "U "U "

I6

Example 4.3: Transitional Passage in Movement I, mm. 58-68. Dashed lines indicate doublings.


12

semitone. The next sonority is an H3(3), with the horn and tuba rising a semitone. This

alternating inner-note/outer-note semitone ascending motion is continued until the last

note in m. 68. Meanwhile the trumpets, which were initially offset from the other three

instruments by a measure, shift one sixteenth-duration earlier. Their pitch material

continues to be the outer two notes of the sonorities played by the other instruments in

minor seconds (see first two measures of Example 3.3). At m. 67 the trumpets cease to

play and the other instruments change their rhythm to eighth-note triplets, leading

eventually to the cadential figure that begins in m. 69. The harmonic rhythm is

accelerating from changing every two measures, to every measure, and finally twice and

three times per measure in mm. 67 and 68 respectively. It should be noted that in mm.

64-67 there are five pitches present but, because the trumpets are doubling the horn and

tuba, their notes do not affect the analysis of the sonorities.

One way to analyze the harmonic motion of much of the movement is as an

attempt to regain the H0 sonority. This concept is especially perceptible in mm. 69-74.

See Example 4.4 for the complete analysis of the passage. As the members of the H5

sonority are arpeggiated from top to bottom, first a three- and then a four-pitch H0

sonority are sounded. Finally, at the entrance of the tuba, the H5(5) sonority is completed.

The next sonority, an H6, is arpeggiated from the center in the horn. The tuba plays the

pitch that would have made the previous sonority an H0, but other pitches have changed,

as if a few too many corrections kept the sonority from returning to the H0. Finally an H2

sonority is arpeggiated from top to bottom. Although this sonority is the most stable in

the passage, the fact that the more dissonant sonorities that preceded it seem to be


13

pointing towards the H0 imbue the H2 with heightened tension. A second way to analyze

the material is to view the movement as an exploration of the harmonic possibilities of

the quartal hierarchical system with extremely minimal use of the H0 sonority except as a

harmonic frame.

The B section, which spans mm. 84-146, does not create much harmonic drive.

Rather, it creates linear drive in the contrapuntal lines. The sonorities created by these

lines function less as means to move from harmonic instability to stability, or the

converse, and more as a means to create an unstable harmonic background that is

generally static. The planing of the H3(3) sonority within the accompanimental figure in

the horn, trombone, and tuba in mm. 84-86 encapsulates this static instability. There is

also, in passages within this section, a more consistent delineation between melody and

accompaniment. All the sonorities in this section are H3’s, H4’s, or very brief H0(3)’s

which are approached by passing or neighboring motion. While H0(3) sonorities appear

in this section, the H0(5) is not sounded until the very end of the movement. Example 4.5

illustrates several instances of the H0(3) in the B section.

&

&

&?

?

42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

!

!


œ œ " œ œ " œ œH(3)3



!

!

!

!

!

œb œ " œ œ " œ œœb œ " œ œ " œ œ

œ œ " œ œ " œ œH4(3)



!

!

!

Œ ‰ " Rœb

Œ ‰ " rœm2

œN œ " œ œ " œ œœb œ " œ œ " œ œ

œb œ " œ œ " œ œH3(3)


œ " œ œ " œ œ œ!

!

!

&

&

&??

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba



œ œ " œ œ " œ œœN œ " œ œ " œ œ

œb œ " œ œ " œ œH4(3)




œN œ " œ œ " œ œH3(3)




œ œ " œ œ " œ œH4(3)

Rœ " ‰ Œ

Rœb " ‰ Œ

œn œ œ œ œ œ3 3

œ œ œ œb œ œ3 3


H3(3) H4(3)

!

!




H3(3) H4(3) H3(4)

&

&

&??

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

˙

Œ œ!

!!

˙

˙

˙Œ œ

!

˙

˙

˙˙

˙H4

˙

˙

˙˙

˙

!

!

!

!!

!

Œ œb

˙Œ œ

!

˙

˙

˙˙

˙#H6

!

!

!

!!

˙

Œ œ!

!!

˙

˙

˙bŒ œb

!

˙

˙

˙˙

˙H2

˙

˙

˙˙

˙

!

!

!

!!

œ œ>

>œb œ>˙b>

œ œ>H2

U "

u "

u "U "U "

I6

Example 4.4: End of the A section of movement I, mm. 69-74.


14

The first six measures of the recapitulation, mm. 145-151, are an exact repetition

of the first six measures of the piece except that, rather than an H0 arpeggiating down

through the instruments, the sonority in the first two measures is an H7(5). This H7 can

be thought of as a transformation of the H2 that ended the A section. This transformation

turns one of the more stable sonorities in the quartal hierarchical system into the most

dissonant. The rest of the recapitulation is very brief; the entire section only lasts from

m. 146 to measure 178. In mm. 158-164 the transitional material borrowed from mm.

58-68 is juxtaposed against RM 2. During this passage, the motive is fragmented and

sequenced to follow the rising transitional material. Finally, after another transitional

passage spanning mm. 165-173 that culminates in the first statement of an H0(5) sonority

since m. 2, the coda of the movement begins in m. 174. From this point on all sonorities

are H0(5)’s. This passage begins with the rhythm and texture that was first stated in

measure three. The texture is inverted in m. 175 and returns to the original texture in m.

176. For the final two measures of the piece, the texture is completely homophonic. See

Example 4.6 for analysis of the final passage of the coda.

&&

&

??

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

42

42

42

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42

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

Slower, calmer q = 92!!

"œ#pœ

˙"

!!

˙œœ#˙b

!!

.pœPœb œ

.˙bp

œF

Harmon muteœb˙p

mute

"œ#pœ

˙"

œb œ˙

˙œœ#˙b

œœœ.˙

.pœPœb œ

.˙bp

˙pœFœb

"œ#pœ

˙"

˙œb œ

˙œœ#˙b

.˙œœœ.pœPœb œ

.˙bp

œFœb˙p"œ#pœ

˙"

œb œœb œ˙

˙œœ#˙b

œœb œœ.˙

.pœPœb œ

.˙bp

˙!

"œ#pœ

˙"

!!

˙œœ#˙b

!!

pœPœb

˙bp

!œbfœœ

Pœb œn

˙bP

!œ# œ# œ

˙œœN

˙b

!œœœœ

.fœfœb œ

.˙bf

œbfœœœN˙b

PœbPœn

˙bP

œ# œ# œ!

˙œœN

˙b

œœœ!

fœfœb

˙bf

!!

œ."ŒœbPœœœNœb ."Œ

!!

œ.Œ

œb œœœœb .Œ

!!

!

œ# œ# œ!

!!

œPœœ

!!

!!

œ# œœœbœ."Œœb ."Œ

!œPœœœ#œPœœœbœ.Œ

œb .Œ

&&&?

?

43

43

43

43

43

42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

!œ œ#

œ œ#˙#H4 H0

!

!jœ œn jœjœ œn jœ˙#H4 H0

!

!

œb œ

œb œ˙H4 H0

!

!

œ ˙b

œ ˙b.˙

H0 H4

!

œb œ!

˙bœb œ

˙H4 H1

œb œ!

˙bœb œ

˙H4 H1

!!!

œ œ œ# œœ œ œ# œ#

&&&??

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

!!

˙bœ œb

œ œb

!!

˙bJœ œn Jœbjœ œn jœb

!!

˙bœ œ

œ œ

!!

.˙œ ˙#

œ ˙#

œPœ#!

˙bPP!

œN œ#!

˙b˙

!

œN œ!

˙b˙

!

!!

"œ#pœ

˙"

!!

˙œ œ#

˙b

!!

.pœPœb œ

.˙bp

!!

"œ#pœ

˙"

!!

˙œ œ#

˙b

!!

.pœPœb œ

.˙bp

!!œFœb

œ#pœ

˙"

!!œb œœ œ#

˙b

!!œ œ œœPœb œ

.˙bp

I 7

Example 4.5: Mm. 69-74 of Movement I.


15

&

&

&?

?

83

83

83

83

83

42

42

42

42

42

85

85

85

85

85

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

œb fœ œb œb

œn fœb œb œb

œ# œ ! œ œ ! œ œœ œ ! œ œ ! œ œ

"

œb œ œ œn

œ œ œ œ

œ# œ œ œ œ œ3 3


"

œ œb œ# œb

œb œb œn œ#



"

œƒœb œ# œ œ. œ.

œbƒœb œb œ œ. œ.

"

"

"

œ œb œ# œ œ. œ.œb œb œb œ œ. œ.

"

"

"

"œbpœb œb œ œ œ. œb . œb .

"œpœb œb œ œ œ. œ. œb .

"

&

&

&?

?

85

85

85

85

85

42

42

42

42

42

85

85

85

85

85

42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

Œ . ‰ JœfŒ . œfŒ jœf œ‰ œ

fœ œ

.œf

œ

˙

‰ Jœ œ

Œ œŒ ‰ Jœ

"

˙

˙

˙˙

˙

Œ . ‰ Jœ#fŒ . œfŒ jœf œ‰ œ

fœ œ

.œf

œ

.œ# œ

‰ œb œ œ

Œ jœ œŒ ‰ œ

Œ ‰ ‰ Jœ

Œ ‰ ‰ Jœ

Œ ‰ œŒ jœ œ‰ œ œ œ

.œ# œ

&&

&??

42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

œ œ ! œ œ ! œ œ


œ œ ! œ œ ! œ œ‰ Rœ ! ! Rœ ‰‰ Rœ# ! ! Rœ ‰H0(5)

‰ Rœ ! ! Rœ ‰‰ rœ ! ! rœ ‰

‰ rœ ! ! rœ ‰œ œ ! œ œ ! œ œ

œ# œ ! œ œ ! œ œ



œ œ ! œ œ ! œ œ‰ Rœ ! ! Rœ ‰‰ Rœ# ! ! Rœ ‰



œ œ ! œ œ ! œ œœ œ ! œ œ ! œ œ

œ# œ ! œ œ ! œ œ


œ œ ! œ œ ! œ œflœ œ ! œ œ ! œ œflœ œ ! œ œ ! œ œ

œ# œ ! œ œ ! œ œ

I 9

Example 4.6: Coda of Movement I, mm. 174-178.


16

Analysis of Movement II

In contrast to the first movement, “Strides Forward” uses predominantly the H0

sonority. The limited use of the more unstable sonorities affects the music in two primary

ways. First, the instances of sonorities other than H0 are more striking because of their

rarity, and second, if tension is to be created within passages that have only H0 sonorities,

it must be created by other means.

One method of creating tension is introduced in the first phrase. The beginning of

measure 1 is marked one dynamic—mezzo-piano in the horn and piano in the trombone

and tuba—and crescendoes through the rest of the measure arriving at an immediate

return to the original dynamic, illustrated in Example 4.7. The music drives toward a

dynamic goal which it does not typically attain. This unsatisfied dynamic motion creates

a more general motion forward through the movement.

In the opening four measures, a clear motivic development is discernible. The

three notes in the first measure are repeated exactly in the second and varied rhythmically

in the third. Finally in the fourth measure, the motive is inverted. The development

&&&?

?

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

Expressively and in time q = 100!!

P œ œ˙p

œ

˙p

œ

!!

P œ œ˙p

œ

˙p

œ

!!

œ-F œ- œ-œP

œ ŒœP

œ Œ

!!

œ œ œ œœ œ œ œœ œ œ œ

&

&

&??

43

43

43

43

43

45

45

45

45

45

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43

43

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42

42

42

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

5 !

!

P œ œ˙pœ

˙pœ

!

!

Pœ œb˙pœ

˙pœ

!

!

Pœ œN˙pœ

˙pœ

!

œ-Fœ- œ- ˙

.p ˙

.˙p

˙

.˙p

˙

Ó œp

˙ œpœb

Ó œpÓ œp!

œœœœ

˙ œœb

œŒ œœŒ œ

!

œœœœ œPœb

œ œœb œbPœ Œ œbœ Œ œb

!

Ó œpœbF

œ œb ˙bF

P Ó˙P

!

!

!

˙P œ œ˙pœ

˙pœ

!

!

œPœœœœPœœœœPœœœ

œb -fœ-

œb -fœ-

!

!!

!

!

œf œ œœœfœ œœœfœ œœ

&

&

&??

43

43

43

43

43

44

44

44

44

44

42

42

42

42

42

44

44

44

44

44

42

42

42

42

42

83

83

83

83

83

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

fp

fp

17 œb -

fp

œ-fŒ

œb - œ-fŒ

!

!!

!

!

P œ œ˙p

œ

˙p

œ

Œ ˙F

F œ œ

P œ œb˙p

œ

˙p

œ

œœ œ œ œ

œ œœœ œ

P œ œN˙p

œ

˙p

œ

œ œ œ œ œ œ œ


PÓ

˙p

Ó˙p

œ#"jœ ‰

œb"jœb ‰

œb"jœ ‰

œb" Jœ ‰œb" Jœ ‰

œb Jœbp‰

œN jœbp‰

œb jœbp‰

œb Jœp‰

œb jœp‰

!

!

!

!!

œ#pœ œb .œ JœbF

œbpœb œn .œ jœb

Fœbp œ œb .œ jœbFœbpœ œb .œ JœF

œbpœ œb .œ jœ

F

!

!

!

!!

10II

Strides Forward

Example 4.7: Beginning of Movement II, mm. 1-4.


17

apparent in this opening passage earmarks the step-down, skip-up motion as the principal

motive in the movement.

The opening statement of the theme in mm. 1-8, as illustrated in Example 4.8, is

followed by a brief development of the principal motive. After the second trumpet states

the motive in m. 8, the two trumpets play in imitation with one another while the horn

and trombone play longer notes to complete the harmonies. The passage is followed, in

m. 13-17 by a fragmentation of the first phrase in the lower three voices, interrupted by

the trumpets playing major seconds, repeating the last notes that they played in m. 12.

The major seconds can be analyzed as an inversion of the H0 sonority without the central

pitch. In mm. 18-21 the trumpets once again play an imitative development of the

principal motive while the other instruments play material from the final measure of the

theme. The motive played in the first trumpet during beats 1 and 2 of m. 21, the notes

within the square in Example 3.9, will later be developed during the B section of this

movement. The figure in both trumpets during beats 3 and 4 in m. 21, the circled notes in

Example 4.9, will become a structural motive in the third movement.

The first instance of a sonority other than H0 is in measure 23. The first sonority

is an H2(5) which is followed by an H7. This passage is illustrated in the last two

measures of Example 4.9. The two preceding sonorities are both H0’s. This H0-H0-H2-

& c ! ! !


General:!H0

wwwwwbbH1(5)

H1

www##H4(3)

H4

wwww#H7(4)

H7

wwwwwbbH5(5)

H5

& 42 !

& 43œ œ " œ œ " œ œRhythmic!Motive!1


& 43 42 43 45˙ œ œ ˙ œ œ œ- œ- œ- œœœ œ ˙ œ œ ˙ œ œb ˙ œ œN .˙ ˙

& ! ! ! ! !

& ! ! ! ! ! ! ! ! !

& ! ! ! ! ! !

[Title][Composer]


[Arranger]

Example 4.8: Theme of Movement II as stated in mm. 1-8.


18

H7 motion is accomplished by the trumpets planing perfect fourths ascending by

semitone and the other instruments planing H0(3) sonorities descending by semitone.

This H0-H0-H2-H7 motion is repeated twice with varying rhythms and then the music

returns to exclusively H0 sonorities until measure 39.

After a brief transition in m. 29, the theme returns in a more full instrumentation,

with the two trumpets playing the melody in perfect fourths and the trombone and tuba

playing the accompanimental figures, now in staccato quarter notes rather than the

original long-short rhythm. Following this statement of the theme, the two trumpets

return to imitative material in mm. 37 and 38, further developing the principal motive by

expanding the interval between the second and third notes.

Beginning in measure 39, the music becomes transitional. The passage is

illustrated in Example 4.10. The transition starts with a perfect fourth between the two

trumpets, which is held for three beats before the other instruments enter from top to

bottom, creating an H2(5) sonority. In m. 40, the trumpets both move down a semitone,

while the three lower voices plane up one semitone, creating an H0. All voices return in

&&&?

?

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba


P œ œ˙p

œ

˙p

œ

!!

P œ œ˙p

œ

˙p

œ

!!

œ-F œ- œ-œP

œ ŒœP

œ Œ

!!


&

&

&??

43

43

43

43

43

45

45

45

45

45

43

43

43

43

43

44

44

44

44

44

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

5 !

!

Pœ œ˙pœ

˙pœ

!

!

Pœ œb˙pœ

˙pœ

!

!

Pœ œN˙pœ

˙pœ

!

œ-Fœ- œ- ˙

.p ˙

.˙p

˙

.˙p

˙

Ó œp

˙ œpœb

Ó œpÓ œp!

œœœœ

˙ œœb

œŒ œœŒ œ

!

œœœœ œPœb

œ œœb œbPœ Œ œbœ Œ œb

!

Ó œpœbF

œ œb ˙bF

P Ó˙P

!

!

!

˙Pœœ˙pœ

˙pœ

!

!

œPœœœœPœœœœPœœœ

œb -fœ-

œb -fœ-

!

!!

!

!

œfœœœœfœœœœfœœœ

fp

fp

œb -

fp

œ-fŒ

œb - œ-fŒ

!

!!

&

&

&??

44

44

44

44

44

42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

!

!

P œ œ˙p

œ

˙p

œ

Œ ˙F

F œ œ

P œ œb˙p

œ

˙p

œ

œ œ œ œ œ

œ œ œ œ œ

P œ œN˙p

œ

˙p

œ



PÓ

˙p

Ó˙p

œ#"jœ ‰

œb"jœb ‰

œb"jœ ‰

œb" Jœ ‰œb" Jœ ‰

œb Jœbp‰

œN jœbp

‰

œb jœbp‰

œb Jœp‰

œb jœp

‰

10II

Strides Forward

Example 4.9: Mm. 18-23 of Movement II.


19

m. 41 to the same H2 as in m. 39. Measure 41 contains one fewer beat than the two

preceding 6/4 measures; the perfect fourth in the trumpets in this measure is sounded

alone for only two beats before being joined by the other instruments. Finally all the

voices continue planing in order to make an H3 in measure 42. Again one beat is taken

away in measure 42 and this time the perfect fourth in the trumpets is sounded alone only

for one beat. This entire passage is directly related to the material in mm. 22-28; the

harmonic motion in both passages is accomplished in the same way and the harmonies

themselves are the same. The transition ends in mm. 43-44 with an H2(5).

The B section starts in m. 45 with the horn playing figures derived from the

accompanimental material from the A section. Meanwhile the trombone arpeggiates an

H0(4) that, when combined with the horn note, creates an H1(5). On the third beat the

three lower instruments combine to sound an H0(3). This measure is repeated in m. 46

with the single alteration that the last trombone note is lowered a semitone, resulting in an

H4. For the next three measures the trombone and tuba plane perfect fourths so that, with

the horn notes, H0’s are sounded on beats 1 and 2 of m. 47 and on beats 1 and 3 of m. 48.

&

&

&?

?

44

44

44

44

44

42

42

42

42

42

83

83

83

83

83

41

41

41

41

41

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

45

45

45

45

45

42

42

42

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42

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46

46

46

46

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

24 !

!

!

!

!




œbpœ œb .œ jœ

F

!

!

!

!

!

œ#pjœ

œbpjœb

œbpjœ

œbpJœ

œbpJœ

œb Jœb

œN jœb

œb jœbœb Jœ

œb jœ

œpœb œœ#

œpœœœ#!

!

!

˙fœœ

f œœ

!œ.Fœ. œ.

œ.Fœ. œ.

˙fœœ

f œœ

!œ. œ. œ.

œ. œ. œ.

œ-fœ- œ-

œ-f œ- œ-

!œ. œ. Œ

œ. œ. Œ

œœb œœœœœœ!œœœœœœœœ

f œœb

f œœ!

œ. œ. œ.œ. œ. œ.

f œ œb

f œ œb!

œ. œ. œ.œ. œ. œ.

˙ œ œN

˙ œ œ!

œ. œ. œ.œ. œ. œ.

.˙ œœœ

œœœ˙ œœ!

.˙ ˙

.˙ ˙

œœœp

œ œœ

!

p

p

&

&

&?

?

46

46

46

46

46

45

45

45

45

45

44

44

44

44

44

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

.˙ .˙

.˙p

.˙

Ó Œ .˙#pÓ Œ Œ ˙#pÓ Œ Ó œ#p

.˙F

.˙

.˙F

.˙

Ó Œ .FÓ Œ Œ ˙

FÓ Œ Ó œF

˙p

.˙

˙p

.˙

Ó .˙#pÓ Œ ˙#

pÓ Ó œ#p

wb

wb

Œ .˙NÓ ˙NÓ Œ œN

.˙bf.˙b f.fœ.f

œ. œ.

œ.f œ. œ.

˙ Œ

˙ Œ

˙ Œ

œ. œ. œ.p

œ. œ. œ.p

&&&?

?

42

42

42

42

42

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

!!

P œ

" œbpœb œb œb œ

PÓ œ

P

!!

P œ

" œbpœb œb œb œb

PÓ œ

P

!!

œp œœ

œ#

œ œb œ œb

œ#

œ œ œ œb

!!

œœœœœ˙ œ œ# œ œ#

˙ œ œb œb œ

!!

œ œ œbœ# œ œ œ# œn

œb œ œb œ œ

!!.˙b fœb .F

œ. œ.

œb .F œ. œ.

!!

˙ Œ

œb . œ. œ.

œb . œ. œ.

11II



20

However, on beats 1 and 2 of m. 49 H4(3)’s are sounded. The planed fourths on four

sixteenth notess is based on measure 29. Meanwhile, the horn plays the inversion of the

material played by the first trumpet in m. 21, illustrated by the notes within the square in

Example 4.11. In m. 50 the music returns to the material from mm. 43-44, now on an H0

(3). This passage is illustrated in Example 4.11. Mm. 52-57 is simply a re-scoring of mm.

45-49.

A transition follows from mm. 57-62 in which the quarter-note staccato figure

from mm. 43-44 is developed. The harmony created by the first trumpet, trombone, and

tuba oscillates between H3 and H4 until the other two instruments enter in m. 59,

ultimately creating an H6(5). Finally in m. 62 the transition ends on an H5(5).

At this point the pulse, which has remained constant since the beginning of the

movement, doubles in length. The first harmony in m. 63 is an H6(5), which moves to an

H0(4) by contrary motion, this time the horn joins the two trumpets in moving against the

tuba and trombone. In the next measure, the voices slide from an H0(5) to an H0(4), the

horn now joining the lower two voices moving down a whole step. The homophonic

&

&

&?

?

44

44

44

44

44

42

42

42

42

42

83

83

83

83

83

41

41

41

41

41

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

24 !

!

!

!

!




œbpœ œb .œ jœ

F

!

!

!

!

!

œ#pjœ

œbpjœb

œbpjœ

œbpJœ

œbp Jœ

œb Jœb

œN jœb

œb jœbœb Jœ

œb jœ

œpœb œ œ#

œpœœ œ#!

!

!

˙fœœ

f œœ

!œ.Fœ. œ.

œ.Fœ. œ.

˙fœœ

f œ œ

!œ. œ. œ.

œ. œ. œ.

œ-fœ- œ-

œ-f œ- œ-

!œ. œ. Œ

œ. œ. Œ

œœb œœœœœœ!œœœœœœœœ

f œœb

f œœ!

œ. œ. œ.œ. œ. œ.

f œ œb

f œ œb!

œ. œ. œ.œ. œ. œ.

˙ œ œN

˙ œ œ!

œ. œ. œ.œ. œ. œ.

&

&

&?

?

45

45

45

45

45

42

42

42

42

42

46

46

46

46

46

45

45

45

45

45

44

44

44

44

44

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

37 .˙ œ œ œ

œ œ œ ˙ œ œ!

.˙ ˙

.˙ ˙

œœ œp

œ œ œ

!

p

p

.˙ .˙

.˙p

.˙

Ó Œ .˙#pÓ Œ Œ ˙#pÓ Œ Ó œ#p

.˙F

.˙

.˙F

.˙

Ó Œ .FÓ Œ Œ ˙

FÓ Œ Ó œF

˙p

.˙

˙p

.˙

Ó .˙#pÓ Œ ˙#

pÓ Ó œ#p

wb

wb

Œ .˙NÓ ˙NÓ Œ œN

.˙b f

.˙b f

.fœ.fœ. œ.

œ.f œ. œ.

˙ Œ

˙ Œ

˙ Œ

œ. œ. œ.p

œ. œ. œ.p

&&&?

?

42

42

42

42

42

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

!!

P œ


PÓ œ

P

!!

P œ


PÓ œ

P

!!

œp œœ

œ#

œ œb œ œb

œ#

œ œ œ œb

!!

œœœœœ˙ œ œ# œ œ#

˙ œ œb œb œ

!!

œ œ œbœ# œ œ œ# œn

œb œ œb œ œ

!!.˙b fœb .F

œ. œ.

œb .F œ. œ.

!!

˙ Œ

œb . œ. œ.

œb . œ. œ.

11II



21

texture is broken in m. 65 when all the voices but the horn begin playing off-beats during

beat one while voicing an H2(4). This continues from mm. 65-66 followed by a pause

and then two minor seconds alone, recalling m. 15. The material from m. 65 returns twice

more, punctuated by a shorter pause and more major seconds, echoing those stated in

mm. 15 and 17.

The return to the A section begins in m. 74, this time with the theme in the tuba.

Because the melody is in the lowest voice, the pitches that create the H0 sonorities have a

different intervallic relationship to the melody, resulting in a slightly different harmonic

color. The theme is followed by the transitional material from m. 29, bringing the music

back to the theme with the melody now back in the highest voice, the second trumpet.

However, in m. 84 the music quickly diverges from a strict restatement where the four

eighth-note gesture is extended by the addition of three eighth notes. This measure,

together with m. 83, is sequenced down, finally transitioning in m. 87 and arriving, in m.

88, at a return of the material from m. 23. This material is extended until m. 99

The most full statement of the theme, in terms of instrumentation, begins in m.

100 with all the voices playing the theme, creating exclusively H0(5)’s on every attack.

The theme itself remains unchanged until the very last measure of the statement, m. 107,

where it is extended by two beats. The last five beats are then repeated, followed by a

transition to the coda.

The principal motive is stated three times in quarter notes by the solo horn and

then one last time by the second trumpet. The rhythms in this last statement are

augmented and accompanied by H0’s in the lower three voices.


22

Analysis of Movement III

“Ostinato” begins with a tuba cadenza and introduces all the motivic material that

will be employed in the third movement. While the cadenza begins in a very free and

improvisatory style, the tempo becomes more strict near the end of the passage and the

music begins to transition from the soloistic material into the ostinato pattern, which is

the principal material of the A section, shown, with the transition, in Example 4.12.

The harmonies outlined in the ostinato pattern are all H0’s. The first four eighth

notes of the pattern outline an H0(5) built on A, omitting the D. The next four eighth

notes arpeggiate an H0(4) rooted on F. Finally the last two eighth notes fill in the D

missing from the first H0(5). In the next measure the pattern repeats up a major third for

the first eight eighth notes. The second ascending arpeggio in this measure returns the

lower four notes of the first H0(5) on A from the first measure. The last two eighth notes

are taken from the H0(4) on F. In this first ostinato pattern, there are three different H0

sonorities represented, if it is assumed that the first four eighth notes in the second

measure constitute an H0(5) on C-sharp that is missing the F-sharp. The enclosures in

Example 3.12 indicate the different H0’s.

& c ! ! !


General:!H0

wwwwwbbH1(5)

H1

www##H4(3)

H4

wwww#H7(4)

H7

wwwwwbbH5(5)

H5

& 42 !

& 43œ œ " œ œ " œ œRhythmic!Motive!1


& 43 42 43 45˙ œ œ ˙ œ œ œ- œ- œ- œœœ œ ˙ œ œ ˙ œ œb ˙ œ œN .˙ ˙ ?

? 45In time q = 80Œœn -p œn - œn - œ œ œ œn . Œ œn œn œn œn . Œ œn œn ‰ œn œn œnaccel.

œ œ œ œn . œ œ œ œ.

? 45q = 126

œf œ œ œ. œ œb œb œb . œ. œ. œ œ# œ œ. œ œ œ œ. œb . œ.? !& ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

[Title][Composer]


[Arranger]

Example 4.12: Transition from cadenza into two-measure ostinato figure, mm. 1-2, in Movement III. Matching enclosures indicated notes from the same sonorities


23

In m. 5 the horn enters, doubling the ostinato pattern at the octave. Almost

immediately the trombone relieves the tuba, doubling the last note of the first ascending

arpeggio in the pattern. This two-voice, octave-doubled texture continues through m. 8,

with the trombone alternating between the two octaves.

The second trumpet enters in m. 9, playing a melody made up of notes taken from

the two H0’s in the ostinato in that measure. The trombone then responds with a similar

figure. Finally the first trumpet ends the phrase with its own figure that remains

unanswered through m. 12. The music then shifts out of the ostinato pattern, and out of

the 5/4 meter in which it has been since the end of the tuba cadenza. The top three

instruments plane H0(3)’s for two measures of 7/8 and then, in m. 15, the first trumpet,

trombone, and tuba plane H3(3)’s on the same pattern. This passage is illustrated in

Example 4.13. After this brief interlude, the ostinato pattern is played in fourths by the

trombone and tuba. In m. 18, after four measures of the ostinato pattern, the trumpets

play similar melodic material to that in mm. 9-12, however this time the material is

sounded only by the two trumpets and the phrase is three measures long rather than four.

&

&

&?

?

87

87

87

87

87

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

11

œF œ œ œ œb œb œb œb œ

Œ ‰ jœ.P œ œb œb œb . œ. œ.œP œ œ œ. Ó Œ

.˙ ˙

œP

œ œ œ. œ œb œb œb . œ. œ.

.˙ ˙

œ œ# œ œ. œ œ œ œ. jœb .‰

! œb . œ.Ó œF

œ œ œ. œb . œ.œ œ# œ œ. jœ ‰ Ó

&&

&??

87

87

87

87

87

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

œf

œ œ œ œ œb œbœf

œ œ œ œ œ œb

œf

œ œ œ œ œ œ

!!

œ œ œ œ œ œ œbœ œ œ œ œ œ œ

œ œ œ œ œ œ œ!!

œp

œ œ œ œ œb œb!

!

œbp

œb œ œ œ œb œnœbp

œb œ œ œ œ œ#

&&&?

?

45

45

45

45

45

89

89

89

89

89

87

87

87

87

87

85

85

85

85

85

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

16 !!!

œPœœœb . œb œb œb œb

.œ.œ.

œPœœœ. œœb œb œb

.œ.œ.

!!!

œœ# œœ.œœœœ.œb . œb .

œœ# œœ.œœœœ.œb . œ.

!

œfœœœb . œœb œb œb œœ

Œ ‰ jœ.Fœœb œb œb .œ.œ.

œFœœœb . œb œb œb œb

.œ.œ.

œFœœœ. Ó Œ

œfœœœœœœœ. œb œ˙ ˙ Œ

œœ# œœ.œœœœ. jœb .‰

œœ# œœ.œœœœ.œb . œb .

! œb .Fœ.

˙ ˙ Œœfœœb œb œœb œb œœœÓ œbF

œb œb œb .œ.œ.œœœœb . jœb ‰ Ó

œœœœ. œœb œb œb.œ.œ.

œbƒœ.œœ.œœ.œœb œb

œƒœb .œœ.œœ.œœb œb!

!jœ.ƒ‰ jœ# .‰Œ jœ. Œ

Jœb . ‰Œ Œ .

Jœb . ‰Œ Œ .

œbƒœb œœ.œb œb œbœbƒœb œœ.œœœb

jœ. ‰ jœ# .‰jœ. Œ

Jœ.F‰ jœb .Œjœb .F‰Jœ.Œjœb ..F‰jœ.Œ

Jœb .F‰Jœ.Œ

œbfœb œb œœ

œPœœb œb œœœœœœ!

! œ.Pœ.

Ó œPœœœ.Œ

œPœb œb œb .Ó Œ

˙# Ó Œ

œbPœœb œb œb œœb œœœ

œ# œb œb œb .Ó Œ

! œb .Pœ.Ó œ

Pœœœ# .Œ

16 III

Example 4.13: Mm. 13-15 in Movement III.


24

The interlude material is developed starting in m. 21. The trumpets play the motive from

m. 22 of Movement II, indicated by the oval in Example 4.9, producing an aggregate

H0(3) which, along with the notes played by the tuba, creates an H0-H4-H0 harmonic

motion. In the next measure, the motive is played by the horn and trombone. Together

with the tuba, the harmonic motion in m. 22 is H0-H2-H0. Interestingly, the tuba plays

the exact same pitches in m. 22 that it did in m. 21, however, its role in the sonorities has

changed from the root pitch to the top pitch, significantly altering the harmonic motion.

Finally, in m. 23, the tuba plays the melodic material while the other instruments play

pitches that complete H0(5) and H1(5) sonorities. The meter in this passage begins with a

2+2+2+3 division in m. 21, followed by 2+2+3—as in mm. 13-15—in m. 22, and ending

with 2+3 in m. 23. This reduction in measure length is reminiscent of the transition in

mm. 39-42 in Movement II, illustrated in Example 4.10. Measures 21-23 can be seen in

Example 4.14, with instances of the motive from Movement II, m. 22, enclosed in ovals.

Following the second interlude, the ostinato pattern is developed. The harmonies

exchange places in the pattern and the contours are altered so that the pattern arcs through

&

&

&?

?

87

87

87

87

87

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

11


Œ ‰ jœ.P œ œb œb œb . œ. œ.œP œ œ œ. Ó Œ

.˙ ˙

œP

œ œ œ. œ œb œb œb . œ. œ.

.˙ ˙


! œb . œ.Ó œF


&&

&??

87

87

87

87

87

45

45

45

45

45

89

89

89

89

89

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

œfœœœœœb œbœfœœœœœœb

œfœœœœœœ

!!

œœœœœœœbœœœœœœœ

œœœœœœœ!!

œpœœœœ œb œb!

!

œbpœb œœœ œb œn

œbpœb œœœ œ œ#

!!

!

œPœœ œb . œb œb œb œb . œ.œ.

œPœœ œ. œ œb œb œb . œ.œ.

!!

!

œ œ# œœ. œœœœ.œb . œb .

œ œ# œœ. œœœœ.œb . œ.

!

œfœœ œb . œ œb œb œb œœ

Œ ‰ jœ.Fœ œb œb œb . œ.œ.œFœœ œb . œb œb œb œb . œ.œ.

œFœœ œ. Ó Œ

œfœœœœœœœ. œb œ

˙ ˙ Œ

œ œ# œœ. œœœœ. jœb .‰

œ œ# œœ. œœœœ.œb . œb .

! œb .Fœ.

˙ ˙ Œœfœœb œb œ œb œb œœœ

Ó œbFœb œb œb . œ.œ.

œœœ œb . jœb ‰ Ó

œœœ œ. œ œb œb œb . œ.œ.

&&&?

?

89

89

89

89

89

87

87

87

87

87

85

85

85

85

85

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

œbƒ œ. œ œ. œ œ. œ œb œb

œƒ

œb . œ œ. œ œ. œ œb œb!

!jœ.ƒ‰ jœ# . ‰ Œ jœ. Œ

Jœb . ‰ Œ Œ .

Jœb . ‰ Œ Œ .

œbƒ œb œ œ. œb œb œbœbƒ

œb œ œ. œ œ œb

jœ. ‰ jœ# . ‰ jœ. Œ

Jœ.F‰ jœb . Œ

jœb .F‰ Jœ. Œ

jœb ..F ‰ jœ. Œ

Jœb .F‰ Jœ. Œ

œbf

œb œb œ œ

16 III

Example 4.14: Mm. 21-23 in Movement III. Ovals indicate the motive from Movement II, m. 22.


25

the lower three instruments (see Example 4.15). Meanwhile, the trumpets play more short

melodic gestures, the final gesture, in mm. 26-27, doubled at the fourth below by the

trombone. From mm. 29-32 material from the ostinato pattern is exchanged between all

the instruments with no more than three playing simultaneously. Then, in m. 33, the two

trumpets play a rearranged version of the ostinato pattern.

After a brief transition, the closing material for the A section is played starting in

m. 37. The material is taken from the ostinato pattern, with the trumpets playing the

pattern and the trombone and tuba playing staccato notes to make the harmonies more

&

&

&?

?

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

œP œ œb œb œ œ œ œ œ œ!

! œ.Pœ.

Ó œPœ œ œ. Œ

œPœb œb œb . Ó Œ

˙# Ó Œ

œbP œ œb œb œb œ œb œ œ œ


! œb .P œ.Ó œ

Pœ œ œ# . Œ

œF œ œb œb œ œ œ œ œ œ

˙ Ó Œ

œFœ œ œb œ œ œ œ œ œ

Ó œFœb œb œb . œ. œ.

œF œ œ œ. Ó Œ

˙# Ó œb ." œn .!

˙# œFœ œ œn . Œ

œ œ# œ œ. Ó Œ

! œb ." œ.

&

&

&?

?

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

Œ œ. œb . ‰ jœ. œ. œ. œn .

œ." œ. ‰ Jœb . œ. œ. ‰ jœ. œb .

œ"œb œb œb . Ó œn . œn .

Ó œ" œ œ œ. Œ

! œ."œ.

œ# œb œb œb . Ó Œ

Ó œ œ œ œ# . Œ

Œ œ. œ.‰ jœ. œ. œ. œb .

œ.

pizz.

œ. ‰ Jœ. œ. œ. ‰ Jœ. œb .

! œb ." œ.

!

! œ.P œ.œPœ œ œb .

Ó œ. œ.œP œ œ œ. œb œb œb œb . Œ

Ó œPœb œb œb . Œ

Ó œPœ œ œ. Œ

Ó œ œ œ œ. Œ

! œb .Pœb .œP

œ# œ œ. Ó œb . œ.œ œ# œ œ. Ó Œ

&

&

&?

?

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

32 !

! œ.œ.Ó œFœ

œœb . œ.œ.œb œb œb œb

.œFœœœ. Œ

œœb œb œb.Ó Œ

œfœbœb œb . œn œn œœ.œb .œb .

œ#fœbœb œb . œn œn œœ.œb .œn .!

!

!

œœœœb .œb œb œb œb.œ.œ.

œœœœ.œœb œb œb .œ.œ.!

!

!

œFœ# œœ.Ó Œ

œFœ#œœ.œœœœ.Œ

Ó œFœœœ.Œ

! œb .Fœb .

! œb .Fœ.

!

!

!œ"œœb œ.œb œn œœn .œ. œ# .

œ"œœb œ.œb œœ# œn .œ. œb .

œfœœb œb .œb œb œb œb .œ.œn .

œfœœœb .œb œb œb œb

.œ.œ.!

Jœf‰ Œ Jœ‰ Œ

œ.œ.

jœflf‰ Œ jœfl

‰ Œ œ.œ.

œ# œ# œ# œ. œœœœn . œ# . œ# .

œ# œb œ# œ# . œ# œn œœ. œ# . œ# .!

Jœb˘‰ Œ Jœb˘‰ Œ œb . œ.

jœbfl‰ Œ jœbfl

‰ Œ œ. œ.

‰ jœœœ.‰ jœœœ.Œ

!

‰ jœ#f œœ.‰ jœœœ.Œ

jœfl‰Œ jœfl‰Œ Œ

jœ#fl‰Œ jœfl‰Œ œflpœfl

‰ jœpœœ.‰ jœœœ.Œ

!

‰ jœ#p œœ.‰ jœœœ.Œ

jœflp‰Œ jœfl‰Œ Œ

jœ#fl‰Œ jœfl‰Œ œflœfl

jœflƒ‰Œ jœfl

‰Ójœ#flƒ‰Œ jœfl‰Ó

‰ jœ#ƒ œœ.‰ jœœœ.Œ

‰ jœƒœœ.‰ jœœœ.Œ

! œflƒœfl

17III



26

full. This material is sequenced down twice by major third, creating a bass line that

descends by major second (see the tuba line in Example 3.16). In the last measure, m. 39,

of the sequence, the second trumpet’s part is taken over by the horn and the texture is

thinner because a maximum of two instruments play simultaneously. Measure 39 is

repeated note for note at a quieter dynamic. Finally, in m. 41, m. 39 is re-scored, with the

staccato fourths played above the ascending arpeggios. See Example 4.16 for the entire

passage, mm. 37-41.

The B section starts immediately in m. 42. The second trumpet, horn, and

trombone play staccato eighth notes, together sounding an H4(3) rooted on E. The first

trumpet begins the first real theme of the movement in the last two beats of m. 42. The

main motive of this theme is the first arpeggiation from the ostinato pattern in sixteenth

notes. The harmony played by the middle three instruments changes in m. 45 to an H4(3)

rooted on B and returns to the original H4 in the following measure. See Example 3.17

for the entire first statement of the theme. Following the first statement of the theme, it is

taken up by the tuba. The tuba’s statement has some subtle differences, most notably the

&

&

&?

?

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

24

œPœ œb œb œœœœœœ!

! œ.Pœ.

Ó œPœœœ.Œ


˙# Ó Œ

œbPœ œb œb œb œœb œœœ


! œb .Pœ.Ó œ

Pœœ œ# .Œ

œFœœb œb œ œ œ œœœ

˙ Ó Œ

œFœœœb œ œ œ œœœÓ œF

œb œb œb .œ.œ.œFœœœ. Ó Œ

˙# Ó œb ."œn .!

˙# œFœœ œn .Œ

œ œ# œœ. Ó Œ

! œb ."œ.

Œ œ. œb . ‰ jœ. œ.œ. œn .

œ."œ.‰ Jœb . œ

.œ. ‰ jœ. œb .

œ"œb œb œb . Ó œn . œn .Ó œ"œ

œœ. Œ

! œ."œ.

œ# œb œb œb . Ó Œ

Ó œœ œ œ# . Œ

Œ œ.œ.‰ jœ. œ. œ. œb .

œ.

pizz.

œ. ‰Jœ. œ. œ. ‰ Jœ. œb .

! œb ."œ.

!

! œ.Pœ.œPœœœb .

Ó œ.œ.œPœœœ. œb œb œb œb . Œ


&

&

&?

?

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

31 Ó œPœœœ. Œ

Ó œœœœ. Œ

! œb .Pœb .œPœ# œ œ. Ó œb . œ.

œ œ# œ œ. Ó Œ

!

! œ. œ.Ó œFœ

œœb . œ. œ.œb œb œb œb .

œFœœœ. Œ

œ œb œb œb . Ó Œ

œf œb

œb œb . œn œn œœ. œb . œb .

œ#f œb

œb œb . œn œn œœ. œb . œn .!

!

!

œœœœb . œb œb œb œb . œ. œ.œœœœ. œ œb œb œb . œ. œ.

!

!

!

œFœ# œœ. Ó Œ

œF œ# œœ. œœœœ. Œ

Ó œFœœœ. Œ

! œb .Fœb .

! œb .Fœ.

!

!

!œ"œ œb œ. œb œn œ œn . œ. œ# .

œ"œ œb œ. œb œ œ# œn . œ. œb .

&

&

&?

?

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

œf œœb œb . œb œb œb œb . œ. œn .

œfœ œ œb . œb œb œb œb . œ. œ.

!

Jœf‰ Œ Jœ ‰ Œ œ. œ.

jœflf‰ Œ jœfl

‰ Œ œ. œ.

œ# œ# œ# œ. œ œ œ œn . œ# . œ# .

œ# œb œ# œ# . œ# œn œ œ. œ# . œ# .!

Jœb˘ ‰ Œ Jœb˘ ‰ Œ œb . œ.

jœbfl‰ Œ jœbfl

‰ Œ œ. œ.

‰ jœ œœ. ‰ jœ œœ. Œ

!

‰ jœ#f œœ. ‰ jœ œœ.Œ

jœfl ‰ Œ jœfl ‰ Œ Œ

jœ#fl‰ Œ j

œfl‰ Œ œflp œfl

‰ jœp œœ. ‰ jœ œœ. Œ

!

‰ jœ#p œœ. ‰ jœ œœ.Œ

jœflp‰ Œ jœfl ‰ Œ Œ

jœ#fl‰ Œ j

œfl‰ Œ œfl œfl

jœflƒ‰ Œ jœfl

‰ Ójœ#flƒ‰ Œ jœfl ‰ Ó

‰ jœ#ƒ œœ. ‰ jœ œœ.Œ

‰ jœƒœœ. ‰ jœ œœ. Œ

! œflƒ œfl

17III



27

eighth notes in the first full measure of the theme where, instead of sevenths, the tuba

plays four E’s, each preceded by a grace note F. The rest of the differences are in the

contour, rather than the pitch-classes, of some of the sixteenth-note gestures.

The trombone begins a development of the theme in m. 51, extending the first

sixteenth-note gesture up a tritone and then back down a perfect fourth. This descending

perfect fourth is echoed twice by the first trumpet and horn, doubling at the octave. This

first measure is extended and the echo returns in m. 53, followed in m. 54 by two

inversions of the first ascending gesture to end the phrase. This entire phrase is re-scored

in mm. 55-58, with the tuba, first trumpet, and horn trading off the melody.

A three-measure sequence descending by minor seconds follows, with the middle

three instruments planing H4(3)’s that, together with the notes in the tuba, produce

H3(4)’s. After a brief pause the theme is stated one more time in the tuba, which is

&??

45

45

45 1

Tuba

!!!

!!!

!!!

&??

Bb Tpt. 1

Bb Tpt. 2,Hn.,Tbn.

Tuba

! œP œ œb œb

‰ Jœœœbb .p

œœœ. œœœ. œœœ. œœœ. œœœ. œœœ. œœœ. œœœ.

˙ .˙

˙N œ. œ. œ. œ. œ œ œb œb

‰ Jœœœbb .p

œœœ. œœœ. œœœ. œœœ. œœœ. œœœ. œœœ. œœœ.

!

&?

?

Bb Tpt. 1

Bb Tpt. 2,Hn.,Tbn.

Tuba

œN ˙ œ œb œ. œ. œ œb œ. œ.‰ J

œœœbb .pœœœ. œœœ. œœœ. œœœ. œœœ. œœœ. œœœ. œœœ.

!

˙b œb œb œ œb œ œ‰ Jœœœb .pœœœ. œœœ. œœœ. œœœ. œœœ. œœœ. œœœ. œœœ.

!

˙ ˙ Œ

‰ Jœœœbb .pœœœ. œœœ. œœœ. œœœ. œœœ. œœœ. œœœ. œœœ.

! œPœ œb œb

&??

Bb Tpt. 1

Bb Tpt. 2,Hn.,Tbn.

Tuba

!!

˙N rœ œ. rœ œ. rœ œ. rœ œ. œPœœb œb

!!!

!!!

!!!

!!!

[Title][Composer]


[Arranger]

Example 3.17: Mm. 42-46 in Movement III, the B section theme.


28

followed by a second three-measure sequence, this time ascending by major second. At

the end of the sequence, the solo tuba plays the accompanimental staccato eighth notes,

which morph into a transition made up of ascending major seconds, leading eventually

back to the original ostinato pattern. See Example 4.18 for the transition following the

second sequence.

The recapitulation includes almost exclusively material already stated in the A

section, however, the fragments of the section are re-ordered. The interlude that came

second in the A section, becomes the first interlude in the recapitulation at m. 84 (see

Example 4.19) and is extended by the addition of a single measure of three eighth notes,

thereby completing the subtraction of all the divisions of two in the meter, thus:

2+2+2+3, 2+2+3, 2+3, 3.

&

&

&?

?

42

42

42

42

42

83

83

83

83

83

42

42

42

42

42

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

!

!

!

!

‰ jœ.

pizz.

p œ. œ. œ. œ. œ. œ. œ. œ.

!

!

!

!

œ"œŒ

!

!

!

!

œ œ Œ

!

!

!

!

Œ œ œ

!

!

!

œ"œ Œ

!

!

!

!

œpœ Œ

œp œŒ

!

!

!

œ œ ‰

œ œ ‰

!

!

!

œ œ ‰

œ œ ‰

Œ œ"œ

Œ œ"œ!

œ"œ Œ

œ"œŒ

!

!

!


œf œœ œ. œ œb œb œb . œ. œ.

&&

&??

89

89

89

89

89

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

80 !!

!

œ œ# œ œ. œ œ œ œ.œb . œb .

œ œ# œ œ. œ œ œ œ.œb . œ.

!

œf œœ œb . œ œb œb œb œ œ

Œ ‰ jœ.F œ œb œb œb . œ. œ.œFœ œ œb . œb œb œb œb . œ. œ.

œF œ œ œ. Ó Œ

œfœ œ œ œ œ œ œ. œb œ

˙ ˙ Œ



! œb .F œ.

˙ ˙ Œœf œ œb œb œ œb œb œ œ œ

Ó œbFœb œb œb . œ. œ.

œ œ œ œb . jœb ‰ Ó

œ œ œ œ. œ œb œb œb . œ. œ.

&

&

&?

?

89

89

89

89

89

87

87

87

87

87

85

85

85

85

85

83

83

83

83

83

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

84 œbƒ œ. œ œ. œ œ. œ œb œb

œƒœb . œ œ. œ œ. œ œb œb

!


Jœb . ‰ Œ Œ .

Jœb . ‰ Œ Œ .

œbƒ œb œ œ. œb œb œœbƒ


jœ. ‰ jœ# . ‰ jœ. Œ

Jœ.F‰ jœb . Œ

jœb .F‰ Jœ. Œ

jœb ..F‰ jœ. Œ

Jœb .F‰ Jœ. Œ

œbfœb œb œ œ

!œƒœ œ

œƒ œ œ!

œƒ œ œ

!

œPœ œ œ œb œb œb œb œ

œp œ œœ. œ œb œb œb . œ. œ.

Ó œ œb œb œb . Œ

œpœ œ œ. Ó œ. œ.

20 III

Example 4.18: Mm. 70-79 in Movement III, the transition from the B section back to the ostinato pattern. Note accompanimental eighth notes in the m. 70 becoming transitional ascending major seconds in m. 71 and finally the return of the ostinato in m. 79.


29

Instead of the full second interlude, the coda begins at m. 92 with the interlude

material. It diverges from a strict restatement of the interlude, first, by including all the

instruments planing H0(5)’s, and second, by extending the second measure by one eighth

note duration and the inclusion, in that measure in the trumpet and tuba, of the

transitional sixteenth-note motive from m. 29 of Movement II. Measures are repeated

once, with the eighth notes appearing this time in the middle three instruments. Following

this repetition, the material is fragmented and the sixteenth notes continue to be traded

between the instruments until the movement ultimately ends on an H0(5) rooted on B in

m. 101. The coda is illustrated in Example 3.20.

&

&

&?

?

42

42

42

42

42

83

83

83

83

83

42

42

42

42

42

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

!

!

!

!

‰ jœ.

pizz.

p œ. œ. œ. œ. œ. œ. œ. œ.

!

!

!

!

œ"œŒ

!

!

!

!

œ œ Œ

!

!

!

!

Œ œ œ

!

!

!

œ"œ Œ

!

!

!

!

œpœ Œ

œp œŒ

!

!

!

œ œ ‰

œ œ ‰

!

!

!

œ œ ‰

œ œ ‰

Œ œ"œ

Œ œ"œ!

œ"œ Œ

œ"œŒ

!

!

!



&&

&??

89

89

89

89

89

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

80 !!

!



!

œf œœ œb . œ œb œb œb œ œ

Œ ‰ jœ.F œ œb œb œb . œ. œ.œFœ œ œb . œb œb œb œb . œ. œ.

œF œ œ œ. Ó Œ

œfœ œ œ œ œ œ œ. œb œ

˙ ˙ Œ



! œb .F œ.

˙ ˙ Œœf œ œb œb œ œb œb œ œ œ

Ó œbFœb œb œb . œ. œ.



&

&

&?

?

89

89

89

89

89

87

87

87

87

87

85

85

85

85

85

83

83

83

83

83

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

œbƒ œ. œ œ. œ œ. œ œb œb

œƒ

œb . œ œ. œ œ. œ œb œb!


Jœb . ‰ Œ Œ .

Jœb . ‰ Œ Œ .

œbƒ œb œ œ. œb œb œœbƒ


jœ. ‰ jœ# . ‰ jœ. Œ

Jœ.F‰ jœb . Œ

jœb .F‰ Jœ. Œ

jœb ..F‰ jœ. Œ

Jœb .F‰ Jœ. Œ

œbf

œb œb œ œ

!œƒ

œ œ

œƒ œ œ!

œƒ œ œ

20 III

Example 4.19: Mm. 84-87 in Movement III, the first interlude in the recapitulation.


30

&&

&?

?

45

45

45

45

45

87

87

87

87

87

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

88 !œPœ œ œ œb œb œb œb œ

œp œ œœ. œ œb œb œb . œ. œ.



!.˙ ˙

œ œ# œ œ. œ œ œ œ. œb . œ.œP

œb œ œ œ œ œ œ œb



Œ ‰ jœ.P œ œb œb œb . œ. œ.œPœ œ œ. Ó Œ

.˙ ˙

œPœ œ œ. œ œb œb œb . œ. œ.

.˙ ˙


! œb . œ.Ó œ œ œ œ. œb . œ.œ œ# œ œ. jœ ‰ Ó

&&

&??

87

87

87

87

87

44

44

44

44

44

87

87

87

87

87

44

44

44

44

44

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

œfœ œ œ œ œb œb

œfœ œ œ œ œ œb

œf œ œ œ œ œ œœfœ œ œ œ œ œ

œf œ

œ œ œ œ œ

œ œ œ œ œ œ œ œ œ œ#

œ œ œ œ œ œ Œ

œ œ œ œ œ œ Œœ œ œ œ œ œ# Œ

œ# œ œ œ œ œ# œ œ# œ œ#

œP

œ œ œ œ œb œbœP

œ œ œ œ œ œb

œP œ œ œ œ œ œœP

œ œ œ œ œ œ

œP œ œ œ œ œ œ

œ œ œ œ œ œ Œœ œ œ œ œ œ œ œ œ œ#

œ œ œ œ œ œ œ œ# œ œ#œ œ œ œ œ œ# œ œ# œ œ#

œ# œ œ œ œ œ# Œ

&&

&

??

43

43

43

43

43

83

83

83

83

83

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

œƒ

œ œ œ œ œ œ œ#

œƒ

œ œ œ Œ

œƒ

œ œ œ Œœƒ

œ œ œ œ œ# œ œ#

œƒ

œ œ œ œ# œ# œ œ#

œpœ œ œ Œ

œpœ œ œ œ œ œ œ#

œpœ œ œ œ œ# œ œ#

œpœ œ œ Œ

œpœ œ œ Œ

œ"œ ‰

œ"œ ‰

œ"œ ‰

œ"œ ‰

œ"œ ‰

œƒœ ‰

œƒœ ‰

œƒœ ‰

œƒœ ‰

œƒœ ‰

œ#

œ œ œ œ œ# œ œ œn œ#ƒ

œ#

œ œ œ œ œ# œ œ œn œ#ƒ

œ#

œ œ œ# œ œ# œ œ œn œ#ƒœ

#œ œ œ# œ œ# œ œ œn œ#

ƒœ#

œ œ# œ# œ œ# œ œ œn œ#ƒ

Œ ˙Ï

Œ ˙Ï

Œ ˙Ï

Œ ˙Ï

Œ ˙Ï

21III


31

CHAPTER VCONCLUSION

Flux represents an initial answer to the compositional question posed by quartal

sonorities in general, and the quartal hierarchical system specifically. While it is true that

the system was developed simultaneously with and specifically for the composition of the

piece, the work still serves as a presentation of a comparatively complete and self-

contained theory of harmony. If the piece is interesting and functions well, the system

shows the potential to work in a variety of contexts. My intention is to continue

experimenting with it, while not narrowing my musical horizons to exclude the

possibilities of composing in other idioms and harmonic languages. But more than a

fleshing out of a theoretical idea, Flux was meant to tell a story. Not a story of specific

events, but of growth, transition, and arrival. For me, as I said in the introduction, it

mirrors my own journey through the harmonic landscape of the quartal hierarchical

system, even as the contained structures were still taking shape and acquiring function. It

is obvious that this interpretation is very personal and will not work for any other

individual; it is not for me to decide how my work is understood by anyone but myself.

My hope is that other listeners will be able to find within the piece other stories and other

meanings. Ultimately, the goal of the piece was to create interesting, structurally sound,

and enjoyable music. The tools may be interesting and their development may take time,

energy, and concentration, and may infuse the music with internal consistency, but it is

Flux the piece that remains its own measure of success.


32

WORKS CONSULTED

Adler, Samuel. The Study of Orchestration. 2nd ed. New York: W. W. Norton and Company, 1989.

Dallin, Leon. Techniques of Twentieth Century Composition. 2nd ed. Dubuque, IA: WM. C. Brown Company Publishers, 1964.

Debussy, Claude. Preludes (Book I.). London: United Music Publishers Limited, 1910.

Fischer, Peter. “Formal presentation on my compositional technique to student composers and faculty,” Presentation text for presentation given as part of the Visiting Composers Seminar at the University of Arizona, Tucson, AZ. 24 March 2005.

Kostka, Stefan. Materials and Techniques of Twentieth-Century Music. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 1999.

Schoenberg, Arnold. Theory of Harmony. Translated by Roy E. Carter. Berkeley: University of California Press, 1978.


33

APPENDIX ACOMPLETE SCORE OF FLUX: FOR BRASS QUINTET


34

APPENDIX ACOMPLETE SCORE OF FLUX: FOR BRASS QUINTET

Flux

Robert DeVet

for Brass Quintet


35

Flux explores a quartal harmonic system that controls dissonance by the expansion of one or two perfect fourths to tritones in quartal sonorities. This creates two scales of dissonance, one based on the number of tritones within a given sonority, and one that based on how the tritone or tritones relate to the lowest interval when sonority is inverted so that it ascends by fourth. This second scale is much subtler than the first and is most perceptible when moving between two sonorities that share the same number or included tritones, of when two such sonorities are accented in close temporal proximity.

"Waiting to Win" begins with the most stable sonority in this harmonic system. Throughout the rest of the movement, the music attempts to return to this chord. The furious A section starkly contrasts the plodding and highly dissonant B section, painting a picture of two different anticipatory mindsets, hurry up and wait.

The music in "Strides Forward" is about creating interest with consonance and tension and release within a gently sloping phrase. While more dissonant sonorities are present, most of the chords simply do not have any tritones. The atmosphere of the piece is one of calm resolve, always moving in one direction.

The tuba solo that begins "Ostinato" introduces all the motivic material that the movement draws upon. Once the first ostinato pattern begins, the music become relentless, carried by its own momentum through to the piece's conclusion.

Overall, Flux is in a constant state of becoming. The arrivals throughout the piece, while often conveying a sense of finality, are brief. The inference is that the arivals are not quite stable enough to provide a lasting musical foothold. Most of all, this piece about motion, constant and unflagging. The rate of motion may change, but not the direction.


36

I “Waiting to Win”

&

&

&?

?

42

42

42

42

42

Trumpet in Bb 1

Trumpet in Bb 2

Horn in F

Trombone

Tuba

With nervous energy q = 132˙f‰ Jœf

œ

Œ œf

Œ ‰ Jœf

!

˙

˙

˙˙

˙#f

œ#pœ " œn œ " œ# œ

œpœ " œ œ " œ œ

œpœ " œ# œ " œ œ‰ Rœp

" " Rœ ‰

‰ rœ#p" " rœ ‰

˙F˙F˙FF˙F

œ#pœ " œn œ " œ# œ

œpœ " œœ " œ œ

œpœ " œ# œ " œ œ‰ Rœp

" " Rœ ‰

‰ rœ#p" " rœ ‰

˙f˙f˙fbf˙f

!

!

œPœ " œ# œ " œ œ

!

!

!

!

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!

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&

&

&?

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83

83

83

83

83

42

42

42

42

42

85

85

85

85

85

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

10 !

œb . œ œ œb

!

!

!

œbFœ " œ œ " œ œ

œbFœ " œ œ " œ œ!

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œpœb œb œ œ œ. œ. œb .

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&

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85

85

85

85

85

42

42

42

42

42

85

85

85

85

85

165

165

165

165

165

85

85

85

85

85

42

42

42

42

42

85

85

85

85

85

165

165

165

165

165

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

18 Œ . ‰ Jœ# fŒ . œfŒ jœf œ‰ œf œ

.œf œ

!

Œ ‰ jœpŒ œp‰ .œp˙bp

Œ . ‰ Jœ# fŒ . œfŒ jœf œ‰ œf œ

.œf œ

œ œ œb œb . œ# .!

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pŒ ‰ ‰ Jœp

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P!

.œF

œ‰ œF œŒ jœF œŒ ‰ œ

FŒ ‰ ‰ JœF

3I

Robert DeVet

Copyright © 2010 Robert DeVet, ASCAP

ScoreWaiting to Win


37

&

&

&?

?

165

165

165

165

165

42

42

42

42

42

166

166

166

166

166

42

42

42

42

42

167

167

167

167

167

42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

25 œ œ# œ# œ# . œ.

œ œ œ œ. œ# .

!

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42

42

42

42

42

166

166

166

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42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

30 œN œ " œb œ " œ œ

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166

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166

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42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

37 Œ ‰ JœbpŒ ‰ jœpœ œ# œ

Jœ ‰ Œjœ ‰ Œ

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38

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42

42

42

42

42

167

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167

167

167

42

42

42

42

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

46 œN œ ! œ œ ! œ œ"

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166

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42

42

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167

167

167

167

167

42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

54 œfœ ! œb œ ! œ œ

˙bfœ# f œ

! œ œ ! œ œœ#fœ ! œ œ ! œ œ

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œ œ ! œb œ ! œ œ˙

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

60 "

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œbPœ ! œ œ ! œ œœbPœ ! œ œ ! œ œ

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œN œ ! œ œ ! œ œ

œ# ! œ œ ! œ œ œ




I 5


39

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

67

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43

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42

42

42

42

42

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

81 "

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42

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42

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

92 .˙#

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40

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

102 œfœ# œ œN

˙

˙PœbP

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43

43

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43

43

42

42

42

42

42

43

43

43

43

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42

42

42

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42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

114 !

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œF ˙b.˙

P!

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42

42

42

42

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

125 !!

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I 7


41

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42

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42

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42

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43

43

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43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

134 !!œF

œb

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42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

144

˙ œ œ

˙# Œ

˙ Œ˙ Œ

˙b Œ

U "U "U "U "U "

More frantic q = 132˙no mute

f‰ Jœ

no mute

fœ

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

153 !!

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!

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I8


42

&

&

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83

83

83

83

83

42

42

42

42

42

85

85

85

85

85

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

162 œbf

œ œ œb

œ# fœ œb œb

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42

42

42

42

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85

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42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

168 Œ . ‰ Jœ#fŒ . œfŒ jœf œ‰ œ

fœ œ

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42

42

42

42

42

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

174 œ œ ! œ œ ! œ œ



‰ Rœ ! ! Rœ ‰‰ Rœ# ! ! Rœ ‰

‰ Rœ ! ! Rœ ‰‰ Rœ ! ! Rœ ‰

‰ Rœ ! ! Rœ ‰œ œ ! œ œ ! œ œ

œ# œ ! œ œ ! œ œ




‰ Rœ ! ! Rœ ‰‰ Rœ# ! ! Rœ ‰




œ# œ ! œ œ ! œ œ

œ œ ! œ œ ! œ œÏ

œ œ ! œ œ ! œ œÏ

œ œ ! œ œ ! œ œÏœ œ ! œ œ ! œ œÏ

œ# œ ! œ œ ! œ œÏ

I 9


43

II “Strides Forward”

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43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba


˙P

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45

45

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45

45

43

43

43

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44

44

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44

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43

42

42

42

42

42

43

43

43

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

8 !œ# -F

œ- œ- ˙

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&

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43

43

43

43

43

44

44

44

44

44

42

42

42

42

42

44

44

44

44

44

42

42

42

42

42

83

83

83

83

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

fp

fp

17 œb -

fp

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œpœb œn .œ jœb

Fœbpœ œb .œ jœnFœb

pœ œb .œ JœF

œbpœ œb .œ jœ

F

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10II

Strides Forward


44

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83

83

83

83

83

41

41

41

41

41

43

43

43

43

43

42

42

42

42

42

43

43

43

43

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45

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45

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45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

27 œ#p Jœ

œpjœb

œbp

jœœbpJœ

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f œ œ

f œ œ!

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f œ œ!

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45

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42

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46

46

46

46

46

45

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44

44

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

37 .˙ œ œ œ

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wb

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42

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42

42

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43

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42

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

43 .˙bf.f .˙fœ.fœ. œ.

œ.f œ. œ.

˙ Œ

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!!

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˙ œ œb œb œ

!!

œ œ œ

œ# œ œ œ# œn

œb œ œb œ œ

11II


45

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43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

42

42

42

42

42

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

50 !

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œ. œ.

œb .F œ. œ.

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œb . œ. œ.

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43

43

43

43

43

23

23

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23

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

57 .˙#Frœ#F" ‰ Œ Œrœ#F" ‰ Œ Œ

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23

23

23

23

23

42

42

42

42

42

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

63 ˙#f

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12 II


46

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23

23

23

23

23

43

43

43

43

43

23

23

23

23

23

43

43

43

43

43

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

69 œP

˙ ˙ œ

œP ˙ ˙ œ

P ˙ ˙œP

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42

42

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43

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43

43

43

87

87

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

76 !!

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!!

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!!

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!!

p œ˙p

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˙P

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!!

p œ œ œ œ#˙p

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42

44

44

44

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42

42

42

42

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83

83

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

85 !

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!

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13II


47

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83

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44

44

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41

41

41

41

41

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42

42

42

42

42

43

43

43

43

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

94 œF

jœb

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jœ

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42

42

42

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

104 œ. œ. œ œ

œ. œ. œ œ

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22

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

112 !!

˙

œ Œ

œp œ# œ

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14 II


48

III “Ostinato”

?Tuba

Leisurely, freely q ~ 80

Rests cancel all accidentals

œnPœn œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œn œn

ƒœn œ œ œ œ œ œ œ œ œ œ œ

PŒU œn

Fœn œ œ Œ œn

Pœn œ œ

?Tuba Œ œb œb œn œn Œ œb

Fœb œn œn ˙ Œ ˙bp

ŒU œbF œb œb œb Œ œb œb œb3 œb œb œb œb œn œ œ œnfŒU œb

Pœb œn œn Œ

? 45Tuba œb œ œbf

œb œn œn ˙ Œ ˙bPŒ

wnuƒ

In time q = 80Œœn -pœn - œn - œ œ œ œn . Œ œn œn œn œn . Œ œn œn ‰ œn œn œnaccel.

œ œ œ œn . œ œ œ œ.

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45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

q = 126

Accidentals behave normally

!

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Bb Tpt. 2

Hn.

Tbn.

Tuba

6 !!

œ# œ# œ œ. œ œ œ œ.œn . œ.

œ œ# œ œ. œ œ œ œ. jœb . ‰

! œb .Pœ.

!!

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Œ ‰ Jœ.Pœ œb œb œb . œ. œ.


!!

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œP



15II I

Ostina to


49

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45

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

11 œF œ œ œ œ œ œb œb œ

Œ ‰ jœ.P œ œ œ œb . œ. œ.œPœ œ œ. Ó Œ

.˙ ˙

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45

45

45

45

45

89

89

89

89

89

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

16 !!

!

œPœœ œb . œb œb œb œb . œ. œ.

œPœœ œ. œ œb œb œb . œ. œ.

!!

!

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œ œ# œ œ. œœ œ œ.œb . œ.

!

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Œ ‰ jœ.F œ œ œb œb . œ. œ.œFœœ œb . œb œb œb œb . œ. œ.

œFœœ œ. Ó Œ

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œœœ œ. œ œb œb œb . œ. œ.

&&&?

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89

89

89

89

89

87

87

87

87

87

85

85

85

85

85

45

45

45

45

45

Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

21 œƒ œ. œ œ. œ œ. œ œb œb

œƒœ. œ œ. œ œ. œ œ œb

!


Jœ. ‰ Œ Œ .

Jœb . ‰ Œ Œ .

œbƒ œb œ œ. œb œb œbœbƒ


jœ. ‰ jœ# . ‰jœ. Œ

Jœ# .F‰ Jœb . Œjœb .F‰ Jœ. Œ

Jœb ..F‰ Jœ. Œ

Jœb .F‰ Jœ. Œ

œbfœb œb œ œ

œPœ œ œ œ œ œ œ œ œ

!! œ# .P

œ.Ó œPœ œ œ. Œ


˙# Ó Œ

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Pœ œ œ# . Œ

16 III


50

&

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

26

œFœœ œ œ œ œ œ œ œ

˙ Ó Œ

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pizz.

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

31 Ó œPœ œ œ. Œ

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œ#fœb œb œb . œn œn œ# œ. œn . œn .

œ#fœb œb œ. œ# œn œ# œ. œn . œn .

"

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Bb Tpt. 1

Bb Tpt. 2

Hn.

Tbn.

Tuba

36 "

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"œ!œ œb œ. œb œn œ œn . œ. œ# .

œ!œ œb œ. œb œ œ# œn . œ. œb .

œf œœœ. œ œb œb œb . œ. œn .

œfœœœ. œ œ œb œb . œ. œ.

"

Jœf‰ Œ Jœ ‰ Œ œ. œ.

jœflf‰ Œ jœfl

‰ Œ œ. œ.

œ# œ# œ# œ# . œ# œ# œ œn . œ# . œ# .

œ# œ œ# œ# . œ# œ# œ# œ. œ# . œ# ."

Jœb˘ ‰ Œ Jœb˘ ‰ Œ œb . œ.

jœbfl‰ Œ jœbfl

‰ Œ œ. œ.

‰ jœ# œœ. ‰ jœ œœ. Œ

"

‰ jœ# fœœ. ‰ jœ œœ. Œ

jœfl ‰ Œ jœfl ‰ Œ Œ

jœ#fl‰ Œ j

œfl‰ Œ œflp œfl

‰ jœ#p œœ. ‰ jœ œœ. Œ

"

‰ jœ#pœœ. ‰ jœ œœ. Œ

jœflp‰ Œ jœfl ‰ Œ Œ

jœ#fl‰ Œ j

œfl‰ Œ œfl œfl

17III


51

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41 jœ#flƒ‰ Œ jœfl

‰ Ójœ#flƒ‰ Œ jœ#fl ‰ Ó

‰ jœ#ƒœœ. ‰ jœ œœ. Œ

‰ jœƒœœ. ‰ jœ œœ. Œ

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! œPœœœ

‰ jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

‰ jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

‰ Jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

˙ .˙

˙# œ. œ. œ. œ. œ œ œ œn

‰ jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

‰ jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

‰ Jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

!

œ# ˙ œ œn œ. œ. œ œ œ. œ.‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.‰ Jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.

!

˙ œb œb œ œb œœ‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.!

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46

˙ ˙ Œ‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.‰ Jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.

! œPœœb œb

!‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.‰ Jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.

˙N rœ œ. rœ œ. rœ œ. rœ œ. œPœœb œb

!‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.‰ Jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.

œ ˙ œ œb œœœ œb œœ

!‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.˙b œb œb œœœœ

!‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.‰ Jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.

˙ ˙ Œ

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51 Ó Œ œF œ# . œ œ.

‰ jœ# .p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ# .p œ. œ. œ. œ. œF œ. œ œ.œPœ œb œb œ

FJœn . ‰ Ó

‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.

Ó Œ ˙#‰ jœ# .p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ# .p œ. œ. œ. œ. œ. œ. œ. œ.œPœ œb œb œ œ œ œ œ ˙NB ?

‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.

˙P

Œ œFœ. œ œ.

‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.Ó Œ œ

Fœ. œ œ.

‰ jœb .p œ. œ. œ. œ. œ. œ. œ. œ.

œ œ> œ .˙

‰ jœ# .p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ# .p œ. œ. œ. œ. œ. œ. œ. œ.œ œ> œ œ œ œ# œ œ œ œb ˙‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.

18 III


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55 Ó Œ œFœ. œ œ.

‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p œ. œ. œ. œ. œFœ. œ œ.‰ Jœb .p

œ. œ. œ. œ. œ. œ. œ. œ.

œbPœ œb œb œF Jœn . ‰ Ó

œPœ œb œb œ œ œ œ œ ˙‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ Jœb .p

œ. œ. œ. œ. œ. œ. œ. œ.

œbPœ œb œb œ œ œ œ œ˙

˙ Œ œFœ. œ œ.

‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.Ó Œ œ

Fœ. œ œ.‰ Jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

‰ Jœb .pœ. œ. œ. œ. œ. œ. œ. œ.

œ œ> œ .˙

‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.œ œ> œ œ œ œ œ œ œ œb ˙‰ Jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

‰ Jœb .pœ. œ. œ. œ. œ. œ. œ. œ.

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59 ‰ Jœb .pœ. œ. œ. œ. œ. œ. œ. œ.

‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ Jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.

P .˙

‰ Jœb .pœ. œ. œ. œ. œ. œ. œ. œ.

‰ jœb .p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœb .p œ. œ. œ. œ. œ. œ. œ. œ.‰ Jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.

˙b .˙

‰ Jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p œ. œ. œ. œ. œ. œ. œ. œ.‰ Jœ# .p

œ. œ. œ. œ. œ. œ. œ. œ.

˙ .˙

!!!!

˙ ˙Œ

!!!!

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!‰ jœb .p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœb .p œ. œ. œ. œ. œ. œ. œ. œ.‰ Jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.

˙N rœb œ. rœ œ. rœ œ. rœ œ. œb œ œb œb

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65 !

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‰ jœb .pœ. œ. œ. œ. œ. œ. œ. œ.

‰ Jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

œ ˙b œ œb œb œ œ œb œ œ

!

‰ jœb .p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœb .p œ. œ. œ. œ. œ. œ. œ. œ.‰ jœ.p

œ. œ. œ. œ. œ. œ. œ. œ.˙b œb œ œœ œ œb

!

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‰ jœb .pœ. œ. œ. œ. œ. œ. œ. œ.

‰ Jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

˙b ˙ Œ

!

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‰ jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

‰ Jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

˙ ˙ Œ

!

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‰ jœ.pœ. œ. œ. œ. œ. œ. œ. œ.

‰ Jœ# .pœ. œ. œ. œ. œ. œ. œ. œ.

˙ ˙ Œ

19III


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pizz.

p œ. œ. œ. œ. œ. œ. œ. œ.

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œf œœ œ. œ œb œ œb œ œ

Œ ‰ jœ.F œ œ œb œb . œ. œ.œFœœ œb . œb œb œb œb . œ. œ.

œFœœ œ. Ó Œ

œ#fœ# œ œ œ œ œ œ. œb œ

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œbƒ

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jœ. ‰ jœ# . ‰ jœ. Œ

Jœ# .F‰ Jœb . Œ

jœb .F‰ Jœ. Œ

Jœb ..F‰ Jœ. Œ

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œbfœb œb œ œ

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œp œ œœ. œ œ œb œb . œ. œ.



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œF œ œ œ œ œ œb œb œ

Œ ‰ jœ.P œ œ œ œb . œ. œ.œP œ œ œ. Ó Œ

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97 œp

œ œ œ Œœp

œ œ œ œ œ# œ œ#œp

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21III


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