UNIVERSITY OF CINCINNATI Date:___________________

I, _________________________________________________________, hereby submit this work as part of the requirements for the degree of:

in:

It is entitled:

This work and its defense approved by:

Chair: _______________________________ _______________________________ _______________________________ _______________________________ _______________________________

Alberto Ginastera’s String Quartets Nos. 1 and 2:

Consistencies in Structure and Process

A Thesis Submitted to the

Division of Graduate Studies and Research

of the University of Cincinnati

in partial fulfillment of the

requirements for the degree of

Master of Music

in the Division of Composition, Musicology, and Theory

of the College-Conservatory of Music

2007

by

Jessica R. Barnett

B.M. Drake University, 2004

Committee Chair: Dr. C. Catherine Losada

iii

ABSTRACT

Ginastera’s first and second string quartets are characterized by strong stylistic

contrasts: the first is non-serial and the second represents the composer’s first attempt at

serialism. Despite differences in stylistic orientation, these works exhibit striking similarities

with respect to pitch organization and other structural processes. The primary objective of this

study is to identify and explicate the consistencies in Ginastera’s musical language. The

discussion places particular emphasis on the motivic pitch structure of both works and the way it

interacts with the formal design of each movement.

Foreground compositional processes in this music involve Ginastera’s emphasis on

completing the chromatic aggregate and his penchant for symmetrical constructs. This study also

explores the deeper-level compositional process of composing-out, which involves the projection

of motivic or intervallic events over larger spans of music. The concept of the associational

pathway is introduced to illuminate the musical narratives that unfold in Ginastera’s slow

movements.

iv

v

ACKNOWLEDGEMENTS

This project would not have been possible without the continual support of my family

and close friends. I especially thank my parents, who encouraged me to keep doing by best no

matter how many obstacles deterred me. My primary advisor, Dr. Catherine Losada was a

constant source of support and motivation. Her careful reading of every draft and insightful

comments in our weekly meetings helped strengthen this project in countless ways. Above all,

her confidence in me over the past two years enabled me to accomplish goals that at times

seemed impossible. Dr. David Carson Berry also read drafts of my work at every stage and

helped polish my prose. Most importantly, he brought a sense of humor to our conversations,

which encouraged me to face every challenge knowing that somehow it would all work out in the

end. Dr. Miguel Roig-Francolí offered suggestions to several of my examples, which helped to

further solidify my arguments. I am most grateful for his efforts to help me finish this project.

Finally, I thank Brian for staying up with me on those very late nights and getting up extra early

to make me coffee.

vi

TABLE OF CONTENTS

Chapter 1: Introduction……………………………………………………………………………1

Chapter 2: Large-Scale Form and Source Collections…………………………………………...12

Chapter 3: Motivic Pitch Structure and Compositional Processes……………………………....47

Chapter 4: Composing-Out Techniques………………………………………………………….73

Conclusion……………………………………………………………………………………….91

Bibliography……………………………………………………………………………………..94

1

CHAPTER 1:

INTRODUCTION

The compositional style of Argentine composer Alberto Ginastera (1916–1983) has

typically been divided into three stylistic periods. In the 1960s, Ginastera himself identified these

as follows: “objective nationalism” (1937–1947), “subjective nationalism” (1947–1957), and

“neoexpressionism” (1958–1983).1 Completed exactly a decade apart, the first and second string

quartets represent respectively the beginning of Ginastera’s second and third stylistic periods.

Thus, a study of these two works yields insight into general features of his musical language as

well as elements that are representative of different stylistic periods.

The String Quartet No. 1, Op. 20, represents the early part of Ginastera’s “subjective

nationalism” period. The quartet was completed in 1948 and premiered the same year in Buenos

Aires.2 In describing the musical style of “subjective nationalism,” Ginastera states that “the

Argentine character begins to acquire a new physiognomy and the musical language begins its

evolution towards dodecaphony.”3 The musical language of this quartet is characterized by a

1 Several studies still refer to these three periods; however, due to Ginastera’s early periodization of his

works (some twenty years before his death), recent scholars have pointed out the inaccuracy of the arbitrary dates

defining these periods. Debates among these scholars can be found in Michelle Tabor, “Alberto Ginastera’s Late

Instrumental Music,” Latin American Music Review 15 (1994): 1–5, 28; Malena Kuss, introduction in Alberto

Ginastera: A Complete Catalogue, rev. ed. (New York: Boosey and Hawkes, 1986), 8; and Deborah Schwartz-

Kates, “Alberto Ginastera, Argentine Cultural Construction, and the Gauchesco Tradition,” The Musical Quarterly

86, no. 2 (2002): 267–274.

In a 1983 interview conducted shortly before his death, Ginastera recanted his periodization from the

1960s, citing two broader periods: he describes the first as being “tonal and polytonal” and the second as using

“atonality.” In reference to his most recent (and ultimately his last) works, Ginastera characterized his style as

“taking the form of a kind of reversion, a going back to the primitive America of the Mayas, the Aztecs and the

Incas.” See Lillian Tan, “An Interview with Alberto Ginastera,” American Music Teacher 33 (1984), 7.

2 David Edward Wallace, “Alberto Ginastera: An Analysis of His Style and Techniques of Composition”

(Ph.D. diss., Northwestern University, 1964), 144.

3 “El carácter argentino comienza a adquirir una nueva fisonomía y el lenguaje musical inicia su evolución

hacia la dodecafonía.” Alberto Ginastera, quoted in Pola Suárez-Urtubey, Alberto Ginastera (Buenos Aires:

Ediciones Culturales Argentinas, 1967), 68; translated in Erik Carballo, “De la Pampa al Cielo: The Development of

Tonality in the Compositional Language of Alberto Ginastera” (Ph.D. diss., Indiana University, 2006), 2.

2

subtle combination of the rhythmic and melodic elements of Argentine folk music, which

influenced many of Ginastera’s early works, and the more avant-garde techniques (including

composition with twelve-tones) developed extensively in his later works.4

The String Quartet No. 2, Op. 26, was completed ten years after the first (in 1958) and

literally marks the beginning of Ginastera’s self-professed “neoexpressionism” period.5

Considered the work that earned Ginastera an international reputation, the second quartet was

commissioned by the Elizabeth Sprague Coolidge Foundation and premiered by the Julliard

String Quartet at the first Inter-American Music Festival in Washington D.C.6 Ginastera

describes “neoexpressionism” as a period in which “the material [becomes] more transcendent

while the musical language acquires greater power of synthesis due to switching openly to

serialism.”7 This subtle shift in Ginastera’s style marks a movement in his compositional

approach toward more experimental techniques (e.g., serialism, the use of microtones, and

indeterminacy), several of which he continued to develop over the next two decades. Harold

Taubman, who wrote a review of the premiere of the second quartet, described his experience as

follows: “When one arrived at the Ginastera work one felt one had reached a composer who has

made an original and exciting synthesis of contemporary trends. For this is a quartet that employs

4 Gilbert Chase was the first scholar to explore the influence of Argentine folkloric music and the

gauchesco tradition on Ginastera’s music; indeed, Chase refers to the compositional style of the first quartet as

exhibiting “a subjective sublimation” of national elements. See Chase, “Alberto Ginastera: Argentine Composer,”

The Musical Quarterly 43, no. 4 (1957): 439–458.

5 Tabor, “Alberto Ginastera’s Late Instrumental Music,” 2.

6 Howard Taubman, “Three New Works Heard in Capital,” New York Times 20 April 1958, 79.

7 “El material se hace aquí más trascendente mientras el lenguaje musical adquiere mayor poder de síntesis

al volcarse abiertamente al serialismo.” Alberto Ginastera quoted in Suárez-Urtubey, Alberto Ginastera, 69;

translated in Carballo, “De la Pampa al Cielo,” 2.

3

polytonality, serial technique and a variety of novel timbres with compelling naturalness. The

means serve the expressive intent.”8

The second string quartet is particularly significant in that it represents Ginastera’s first

attempt at serial composition. In the earlier Piano Sonata No. 1 (1952), from the “subjective

nationalism” period, Ginastera introduces a linear presentation of the twelve-tone aggregate in

both the second and third movements, but never develops it in a strict serial manner. Similarly,

there are several passages within the first quartet where Ginastera more assertively places

emphasis on the completion of the total chromatic, without ever utilizing a twelve-tone row per

se. In the “neoexpressionistic” second quartet, however, twelve-tone rows within each movement

act as the primary source of virtually all subsequent pitch material. Although not every

movement of the second quartet is serial in the strictest sense (i.e., not all movements are based

upon P, I, R, and RI permutations of the row), each movement does (at least at some point) make

explicit reference to an ordered twelve-tone collection. As such, the twelve-tone collections

utilized in the second quartet often function as abstract constructs from which much of the

music’s motivic and intervallic relations are derived.

Significantly, the pitch structure of the second quartet is not radically different from that

of the first quartet, despite the fact that the two works differ in stylistic orientation. Indeed, these

stylistically different works share a common resonance, through which Ginastera’s characteristic

sound is at all times present in the music. Both quartets emphasize motivic constructs and

structural processes that remain consistent, even though Ginastera shifts his focus toward

composition with twelve-tones in the second quartet. Thus, the string quartets provide

compelling evidence as to how Ginastera was able to maintain his characteristic sound while

experimenting with a new stylistic approach.

8 Taubman, “Three New Works Heard in Capital,” 79.

4

The primary objective of the present study is to identify and explicate the compositional

consistency in the musical language of Ginastera’s first and second quartets. The discussion will

place particular emphasis on the pitch structure of both works and the way it interacts with the

formal design of each movement. Furthermore, this analysis will discuss the large-scale

processes that result from deeper-level associations, and the projection of motives over spans that

coincide with important structural moments in the music.

Relatively few scholars have analyzed Ginastera’s music, and an even smaller number

have discussed his string quartets. David Wallace was the first to write extensively about

Ginastera’s compositional approach. In his 1964 dissertation, Wallace discusses the first quartet

in a chapter titled “Old and New Techniques (1947–1954)” and the second quartet in a different

chapter titled “Recent Tendencies (1958–1963).”9 As his chapter titles suggest, Wallace’s

analyses generally focus on the broader characteristics of Ginastera’s style and compositional

method. In particular, he examines the use of nationalistic elements in Ginastera’s music, and

how the gradual dissolution of these elements gave Ginastera the freedom to experiment with

twelve-tone composition. Wallace’s discussion of the string quartets is relatively short and the

level of detail does not extend much beyond the surface of the music. Nonetheless, he was the

first to take a closer look at elements of pitch, rhythm, and form in several of Ginastera’s

compositions.

Although Wallace is the only scholar to have discussed Ginastera’s use of serialism in the

second quartet, other scholars have discussed Ginastera’s idiosyncratic approach to twelve-tone

composition in the context of his opera Don Rodrigo (1964). Malena Kuss was the first scholar

9 See Wallace, “Alberto Ginastera: An Analysis of His Style and Techniques of Composition,” chapters 4

and 5.

5

to discuss the structure of the row forms used in the opera.10

In her 1980 article, Kuss discusses

the derivation of the opera’s multiple rows, and how each relates to the dramatic narrative of the

opera’s plot. James Richards’s 1986 analysis of the same work thoroughly explores Ginastera’s

segmentation and musical projection of multiple row forms; he further comments on how these

aspects relate to and interact with other non-serial materials in the opera.11

The most recent—and by far the most comprehensive—study of Ginastera’s music

appears in Erick Carballo’s 2006 dissertation, “De la Pampa al Cielo: The Development of

Tonality in the Compositional Language of Alberto Ginastera.” Carballo’s research not only

explores the development of tonality in Ginastera’s compositional output, but also

“contextualizes certain features—already recognized as intrinsic stylistic characteristics in

Ginastera’s earlier music—by extending them through later works.”12

In order to account for the

music’s large-scale organization as well as its more local “tonal” processes, Carballo adopts a

Schenkerian-Salzerian analytical approach.

The present study differs from previous scholarship in two important ways. First, it offers

an analysis of two works that have not received a great deal of attention in Ginastera scholarship.

In order to maintain a focus on tracing the “unfolding of Ginastera’s tonal language,” Carballo’s

research excludes the composer’s twelve-tone compositions (and thus the second quartet) from

consideration.13

The focus of the present study, however, invites a comparison between the serial

10

See Malena Kuss, “Type, Derivation, and the Use of Folk Idioms in Ginastera’s Don Rodrigo,” Latin

American Music Review 1, no. 2 (1980): 176–195.

11

See James Edward Richards, Jr., “Pitch Structure in the Opera Don Rodrigo of Alberto Ginastera” (Ph.D.

diss., University of Rochester, 1986).

12

Carballo, “De la Pampa al Cielo,” ix.

13

Carballo, “De la Pampa al Cielo,” 12.

6

language of the second quartet and the non-serial language of the first quartet in order to show

their striking similarities.

Second, the present study differs from previous scholarship in that it does not presume a

tonal hierarchy to be the primary means of pitch organization operative in this music. The vast

majority of analytical examples herein illustrate relationships among elements of the music’s

thematic material and motivic structure. This study is not concerned with the tonal structure of

the music, and considers harmonic events as they originate from motives on the surface of the

music.14

Thus, the discussion of deeper-level connections between non-adjacent pitch events in

this music is based on motivic associations; the reader should make note that these associational

relations in no way signify (or represent) prolongational relations. This is in keeping with Joseph

Straus’s definition of association as “the grouping of together of notes [which may be separated

by considerable spans of time] according to similarities in register, metrical placement, duration,

dynamics, instrumentation, and so forth.”15

Chapter 2 is divided into two parts. The first will introduce issues of large-scale form as

they pertain to each individual movement of the quartets. In general, the formal design of each

movement is unambiguous. Addressing the importance of form in music, Ginastera remarked:

I always think about the form. I have always told my students that music is architecture in

movement, and the form must always be born with the music. It is not a different thing. It is the

same thing. And a work without form is a work deformed . . . Also, in aesthetics—in nature—

there exists the law of contrasts: day and night, sun and moon, black and white, Allegro and

Adagio. We must return to contrasts within music.16

14

To be sure, there most certainly are interesting tonal references in this music; however, a consideration of

these references, in addition to melodic-motivic relations, would require an investigation beyond the scope of this

study.

15

Joseph N. Straus, “The Problem of Prolongation in Post-Tonal Music,” Journal of Music Theory 31, no.

1 (1987), 21, note 13.

16

Alberto Ginastera in an interview with Barbara Nissman, “Alberto Ginastera: Composer of Latin

America,” Keynote 6, no. 6 (1983), 10.

7

The “law of contrasts,” as Ginastera explains it, is represented in the string quartets by marked

changes in texture, dynamics, articulation, and/or tempo coinciding with important formal

junctures. Such changes are often used to herald the introduction of new material (e.g., a

secondary theme or a development section) and result in a certain amount of clarity of formal

design in this music. Because Ginastera felt that musical form ought to be “born with the music”

this study interprets the formal design of each movement in terms of the organization and

repetition of thematic and motivic materials.

The second part of Chapter 2 will identify and explain the presence of source

collections in both quartets. A source collection is a collection of pitch classes (e.g., a twelve-

tone row) that represents the nexus of important pitch material used within an entire work (as in

the first quartet) or within individual movements or sections of movements (as in the second

quartet). The source collection is essentially the parent collection from which smaller motivic

cells are derived and to which they can be traced back; thus, the identification of source

collections and their structural content is crucial to our understanding of motivic associations.

To a certain extent, these source collections function as Grundgestalten, in the sense

described by Arnold Schoenberg. In an entry from 1934 contained within his Gedanke

manuscripts, Schoenberg defined Grundgestalten as “such gestalten as (possibly) occur

repeatedly within a whole piece and to which derived gestalten can be traced back.”17

In a

similar sense, the source collections discussed in this study are often stated in Ginastera’s

quartets as prominent motives in and of themselves, while they also produce smaller motivic

events (or “derived gestalten”) that can be found both on the melodic surface of the music and on

deeper levels.

17

Arnold Schoenberg, The Music Idea and the Logic, Technique, and Art of Its Presentation, edited and

translated by Patricia Carpenter and Severine Neff (Bloomington: Indiana University Press, 2006), 129.

8

Chapter 3 will discuss in more detail the motivic pitch structure of both quartets and

highlight the correspondences between Ginastera’s serial and non-serial compositional

languages. This chapter will continue to emphasize the relationship between the motivic

materials of each piece and their source collections. The discussion of Ginastera’s approach to

twelve-tone composition, particularly his construction and manipulation of row forms, will help

elucidate why the first and second quartets share a common resonance despite their differences in

stylistic orientation. Ginastera often drew parallels between his twelve-tone approach and that

practiced by the Second Viennese School. Considering his own tendencies to be more in line

with compositional styles of Schoenberg and Berg rather than Webern, Ginastera observed that

his serial technique in the second quartet “adapted to the expressive necessities of the music.”18

Thus, Ginastera often abandoned the confines of the row in order to emphasize individual pitch

classeses or specific motives that prove to be of particular importance within a work.

Throughout the discussion in chapter 3, the reader may notice several similarities (if only

superficial ones) between Ginastera’s music and that of composers such as Bartók, Copland, and

Stravinsky.19

Richard Crichton described Ginastera’s first two quartets as “Bartókian, with

driving, sometimes convulsive rhythms, grinding seconds, piled-up fourths and fifths. There is

18

Alberto Ginastera, untitled review of Inter-American Music Festival, Boletin Interamericano de Música

(November 1959), 3–4, quoted in David Edward Wallace, “Alberto Ginastera: An Analysis of His Style and

Techniques of Composition,” 220. See also Ginastera’s comments regarding Berg in Lillian Tan, “An Interview

with Alberto Ginastera,” 7.

19

Ginastera especially admired Copland as both a composer and a personal friend. Having participated in

Copland’s Tanglewood composition course in 1941, Ginastera would eventually go on to dedicate the ninth prelude

of his Twelve American Preludes (1944) to the composer; see Schwartz-Kates, “Ginastera, Alberto,” in The New

Grove Dictionary of Music and Musicians, 2d ed., edited by Stanley Sadie and John Tyrrell (New York: Macmillan,

2001), 9: 875. Stravinsky, whose early nationalistic style and late serial style also influenced Ginastera, visited

Buenos Aires in the 1930s, when Ginastera was still a very young composer; see, Schwartz-Kates, “Alberto

Ginastera, Argentine Cultural Construction, and the Gauchesco Tradition,” 264. Nonetheless, Ginastera has

admitted the profound influence Stravinsky’s music had on his own. See Barbara Nissman, “Alberto Ginastera:

Composer of Latin America,” Keynote 6, no. 6 (1983), 11, 13; and also Tan, “An Interview with Alberto Ginastera,”

7.

9

also something of Copland’s lean-bony, open-air quality.”20

The influence Bartók’s music had on

Ginastera is especially apparent, and is perhaps captured best in Ginastera’s own words:

The rhythmic strength [and] the construction of the melody from cells and repetition of parts of

those cells . . . these aspects captivated me. Later on, when I was able to analyze Bartók’s work, I

found in it the answer to another concern I had felt since my youth: the problem of form and style.

Bartók always finds the musical structure which originates and develops from the basis of the

work itself.21

Two ideas expressed by Ginastera in the statement above are also evident in his

compositional approach: (1) his proclivity to construct melodies from motivic cells, and (2) his

careful consideration of the relationship between the music’s pitch structure and formal design.

Even the specific motives that predominate in Ginastera’s music also predominate in Bartók’s.

The reader may notice similarities between some Bartók scholarship and the discussion of

compositional processes that concludes chapter 3. Specifically, approaches to Bartók’s music

have largely centered on discussions of his use of motivic cells (e.g., the “x,” “y,” and “z cells”)

and symmetrical relations.22

As in Bartók’s music, Ginastera’s music also features compositional

processes that result in densely chromatic pitch material and symmetrical constructs. Both of

these processes, and the was they form correspondences between the first and second quartets,

are discussed in Chapter 3.

Chapter 4 will conclude this study with an exploration of composing-out techniques,

which are found in both quartets. Composing-out is a deeper-level compositional process that

involves the projection of motivic or intervallic events over larger spans of music. Although the

20

Ronald Crichton, “Ginastera’s Quartets,” Tempo 111 (1974), 33–34.

21

Alberto Ginastera, “Homage to Béla Bartók,” Tempo 136 (1981), 4.

22

There is a great deal of scholarship on the music of the Bartók, and much of it stems from the work of

George Perle. Studies that particularly focus on motivic cells and symmetry in Bartók’s music include (among

others) Perle, “Symmetrical Formations in the String Quartets of Béla Bartók,” Music Review 16 (1955): 300–312;

Leo Treitler, “Harmonic Procedures in the Forth Quartet of Béla Bartók,” Journal of Music Theory 3, no. 2 (1959):

292–298; and Elliot Antokoletz, The Music of Béla Bartók: A Study of Tonality and Progression in Twentieth-

Century Music (Berkeley: University of California Press, 1984).

10

term “composing-out” originates in the writings of Heinrich Schenker,23

this study does not

invoke the concept of prolongation, which is an integral component of the composing-out

process in tonal music; instead, this study will interpret composing-out techniques in Ginastera’s

music as giving rise to associational relations among pitch events. Joseph Straus has explained

the crucial differences between prolongational and associational approaches in twentieth-century

music; according to Straus, the associational approach considers how “musical tones separated in

time may be associated by any contextual means, including register, timbre, metrical placement,

dynamics, and articulation.”24

The present study will consider three composing-out procedures

proposed by Straus: (1) “melodic frame,” (2) “register,” and (3) “transpositional projection.”

The final portion of chapter 4 will focus on the slow movements of both quartets.

According to Wallace, “Ginastera, in earlier works, reserved his most intellectual music for slow

movements.”25

The same can be said of the slow movements of the string quartets. The third

movement of the first quartet and the second movement of the second quartet both unfold in a

musical narrative, which develops from a seemingly unimportant gesture presented at the

beginning of the movement. The path traversed within this narrative will be called the

associational pathway.

Another one of Schoenberg’s compositional concepts will be helpful to our

understanding of the associational pathway. Schoenberg’s musical idea (which is intimately

23

“Composing-out” is the common English translation of Schenker’s “Auskomponierung”; for a formal

discussion of Schenker’s use of the term, see Oswald Jonas’s introduction to Schenker’s Harmony, edited and

annotated by Oswald Jonas, trans. Elisabeth Mann Borgese (Chicago: The University of Chicago Press, 1954), v–

xxiv.

24

Joseph N. Straus, “Voice Leading in Atonal Music,” in Music Theory in Concept and Practice, edited by

James Baker, David Beach, and Jonathan Bernard (Rochester, NY: University of Rochester Press, 1997), 241. See

also Straus, “The Problem of Prolongation in Post-Tonal Music,” Journal of Music Theory 31, no. 1 (1987): 1–22.

25

Wallace, “Alberto Ginastera: An Analysis of His Style and Techniques of Composition,” 228.

11

related to his concept of the Grundgestalt described above) is like the associational pathway in

that it involves a seminal musical gesture that acts as an impetus for subsequent events.

Schoenberg describes the musical idea and its relation to the Grundgestalt in the Gedanke

manuscripts:

The furtherance of the musical idea . . . may ensue only if the unrest—problem—present in the

grundgestalt or in the motive . . . is shown in all its consequences. These consequences are

presented through the destinies of the motive or the grundgestalt. Just how the grundgestalt is

altered under the influence of the forces struggling within it, how this motion to which the unrest

leads, how the forces again attain a state of rest—this is the realization of the idea, this is its

presentation. [Emphasis Schoenberg’s]26

Like the presentation of the musical idea, the associational pathway also involves the dynamic

trajectory of musical events as they are set in motion by an initial sense of unrest—that is, the

sense that something is not as it should be. The associational pathway traces a single motivic or

pitch event (which is a contributing factor to this underlying sense of unrest) as it is subsequently

developed and transformed through a series of consequential and logical musical relationships.

The events forming this pathway often stem from the primary motive of the movement, and thus

relate back to this motive in significant ways, affecting how we interpret the work as a collective

whole. The analyses of Ginastera’s “intellectual” slow movements will seek to illuminate the

concept of the associational pathway and reflect upon the motivational force behind it.

26

Schoenberg, The Musical Idea, 161.

12

CHAPTER 2:

LARGE-SCALE FORM AND SOURCE COLLECTIONS

Large-Scale Form

Ginastera remains true to traditional models of formal structure in many of his

compositions, and the individual movements of the first and second string quartets are no

exception.27

In many respects, the forms of each movement conform to the established norms of

the classical quartet.28

For example, both quartets begin with a sonata-form movement, in which

at least two themes are prominently contrasted with one another and a central section of the

music—a development—is devoted to the fragmentation and manipulation of these themes. By

drawing upon the various thematic traditions associated with sonata form, Ginastera is able to

evoke a considerable amount of large-scale formal associations without emulating also the

harmonic constraints. This affords him the opportunity to be innovative in his approach to pitch

structure and still present a relatively unambiguous sense of the underlying form.29

In accordance with tradition, both quartets also feature a rondo-form finale, in which two

thematic ideas compete for attention until they reach a dramatic conclusion. The slow

movements of the quartets follow a ternary plan that features a return of material from the first

large section within the closing section. The remaining traditional form-types Ginastera uses as

models are the scherzo and trio, and the theme and variations. Interestingly, the scherzo (third

27

The term “traditional” in this context refers to Ginastera’s predilection for normative large-scale forms,

which were commonly used by composers in the eighteenth and nineteenth centuries (e.g., sonata, rondo, sonata

rondo, etc.).

28

Charles Rosen provides a succinct overview of the Classical traditions associated with the string quartet

and its formal organization in his book, The Classical Style: Haydn, Mozart, and Beethoven (New York: W.W.

Norton & Company, Inc., 1997, expanded edition), 111–142, 264–287.

29

Joseph Straus has noted that several twentieth-century composers have interpreted the traditions of sonata

form in order to achieve their own compositional goals: see Straus, Remaking the Past: Musical Modernism and the

Influence of the Tonal Tradition (Cambridge: Harvard University Press, 1990), 96–132.

13

movement) of the second quartet features two trios, which results in an overall rondo-like formal

structure—thus, making four of the nine movements a type of rondo form (see chart below).

String Quartet No. 1, Op. 20 (1948)

I. Allegro violento ed agitato (Sonata)

II. Vivacissimo (Sonata Rondo)

III. Calmo e poetico (Ternary)

IV. Allegramente rustico (Rondo)

String Quartet No. 2, Op. 26 (1958, rev. 1968)

I. Allegro rustico (Sonata)

II. Adagio angoscioso (Ternary)

III. Presto magico (Scherzo and Two Trios - Rondo)

IV. Libero e rapsodico (Theme and Variations)

V. Furioso (Sonata-Rondo)

The importance of formal design within this music should not be undervalued. Indeed,

the recurrence of thematic materials provides the basis for large-scale associations in this music.

Ginastera’s careful organization of contrasting materials within each movement helps to

illuminate some particularly interesting connections that occur over larger spans of music.

Prominent thematic material will be the primary focus of this study’s inquiry into motivic

associations. Thus, the analysis will explain how important thematic materials actually

strengthen the relevance of these associations. An overview of primary and secondary themes

and their respective roles in the unfolding of each movement’s formal structure is essential and

will be discussed in some detail below.30

Often, Ginastera clearly delineates important thematic material with sharp contrasts

resulting from changes in texture, rhythm, tempo, dynamics, range, or articulation, or a

combination of several of these. The conclusions drawn in the discussion of form below are

30

This approach to form, based on the formal function and organization of motivic and thematic devices,

was most notably promulgated by Arnold Schoenberg and his student Erwin Ratz. More recently, William Caplin

has adapted this method to the instrumental music of Haydn, Mozart, and Beethoven; see Caplin, Classical Form: A

Theory of Formal Functions for the Instrumental Music of Haydn, Mozart, and Beethoven (New York: Oxford

University Press, 1998).

14

largely based upon careful consideration of each of these musical elements and how they

highlight significant motivic material in this music.31

Sonata Form

As mentioned above, the first movement of both of the quartets follows a typical

sonata-form thematic design. Example 2.1 is a formal diagram of the opening movement of the

first quartet. As the diagram shows, three theme groups are featured prominently within the

exposition, and only the first theme returns in the recapitulation. As is typical of sonata form, the

middle development section is characterized by fragmentary pitch material based on motives

derived from all three thematic ideas presented within the exposition.

Example 2.1 Sonata Form, String Quartet No. 1/I, Allegro violento ed agitato

The introduction and coda sections frame the three larger components of the sonata form.

More specifically, the introduction contains what this analysis will refer to as the basic motive:

an ordered collection of pitches, stated in the opening measures of the movement that contains

the primary pitch classes of the entire movement. In their recent book, Elements of Sonata

Theory, James Hepokoski and Warren Darcy have identified this particular formal design as the

“introduction-coda frame,” whose use in tonal sonata forms represents a “striking deformation of

31

Christopher Hasty has written extensively on issues of form and segmentation in twentieth century

music: Hasty, “On the Problem of Succession and Continuity in Twentieth-Century Music,” Music Theory Spectrum

8 (1986), 58–74; and idem, “Segmentation and Process in Post-Tonal Music,” Music Theory Spectrum 3 (1981), 54–

73.

15

normative practice . . . in which the material from the introduction returns as all or part of the

coda.”32

They have generalized that in sonata forms that exhibit the introduction-coda frame,

“the interior sonata seems subordinated to the outward container. The introduction and coda

represent the higher reality, under whose more immediate mode of existence—or under whose

embracing auspices—the sonata form proper is laid out as contingent process, a demonstration of

an artifice that unfolds only under the authority of the prior existence of the frame.”33

This

description is highly appropriate to the discussion of the first movement of Ginastera’s first

quartet: the prominent thematic materials of the central three sections (i.e., the exposition,

development, and recapitulation) exist because they are derivatives of the introductory basic

motive, which returns at the end of the sonata to reassert its importance. Thus, the similarity

between the material of the introduction and coda sections achieves a sense of balance across the

movement as a whole and contributes to its highly unified structure.

In addition to the framing introduction and coda sections, Ginastera also inserts passages

of transition material before and after the contrasting theme groups. Example 2.1 illustrates these

passages in parentheses. The fundamental purpose of transition sections in Ginastera’s music is

to maintain a certain amount of energy and fluidity across major formal divisions.34

Several of

the other movements that will be discussed in this study also contain recurring transition

passages, and in all scenarios, the transitions provide a vital rhythmic sustenance that helps to

connect larger sections of the underlying form.

32

James Hepokoski and Warren Darcy, Elements of Sonata Theory (Oxford: Oxford University Press,

2006), 304.

33

Hepokoski and Darcy, Elements of Sonata Theory, 305.

34

Hepokoski and Darcy refer to the transition sections found within tonal sonata forms as “TR-zones”.

These TR-zones do not necessarily serve modulatory functions (and they most certainly do not in Ginastera’s

music); rather, their undisputed function in Allegro compositions is to provide “energy-gain” and “rhythmic verve.”

See Hepokoski and Darcy, Elements of Sonata Theory, 93–94.

16

Perhaps the most striking element of design Ginastera brings (or, in this case, does not

bring) to the form of this movement has to do with the restatement of only one of the

movement’s three themes in the recapitulation. This truncation of the recapitulation gives rise to

formal proportions akin to the Type 2 sonata form set forth by Hepokoski and Darcy.35

According to the authors, this seeming deformation of traditional (or “textbook,” to borrow their

term) sonata form is actually quite common in the instrumental repertoire of composers such as

Haydn, Mozart, Beethoven, and their contemporaries. However, Hepokoski and Darcy’s

description of the Type 2 sonata, or “binary variant” of a traditional sonata form (Type 3), is

based on the vast number of examples that give precedence to the secondary theme group, as a

opposed to the primary theme—which is the case in Example 2.1. The reason that the authors

consider this particular deformation to be more normative is because the function of the

secondary theme group is essential for achieving tonal closure. 36

The achievement of tonal closure is not a necessary component in Ginastera’s

organization of sonata form, but the achievement of motivic association is. By singling-out this

primary theme, Ginastera is able to focus the listener’s attention on the most important motivic

material of the movement. As will be discussed in greater detail in chapter 3, the primary theme

is indeed based entirely upon the pitch-class content of the basic motive stated in the

introduction. Thus, by placing the return of the primary theme in closer proximity to the coda,

Ginastera emphasizes the relationships among the common pitch material of these sections—

35

The Type 2 sonata is characterized by a shortened development that often elides seamlessly with the

return of primary material; see Hepokoski and Darcy, Elements of Sonata Theory, 353–355.

36

Hepokoski and Darcy do actually discuss truncated recapitulations in which the secondary theme has

been suppressed. In the tonal realm, they consider these forms to be “extreme deformations, registering some

catastrophe or act of violence that has befallen the structure as a whole.” Because tonality is of no consequence in

the formal organization of Ginastera’s music, an adaptation of the Type 2 sonata form design seems more

appropriate. For a discussion of the truncated recapitulation, see Hepokoski and Darcy, Elements of Sonata Theory,

247.

17

thereby drawing a strong connection between the introduction and primary theme in the

exposition, and the primary theme and coda in the recapitulation.

The first movement of the second string quartet also represents a sonata form, and

Example 2.2 diagrams the components of its design. The complete restatement of the materials

from the exposition within the recapitulation characterizes this movement as a Type 3 (or

“textbook”) sonata form according to Hepokoski and Darcy’s criteria.37

Like the opening

movement of the first quartet, this sonata-form design is framed by an introduction and coda, and

again these sections represent respectively the locus and summation of the primary pitch

materials used throughout the movement. More specifically, the material of the introduction

contains the first complete and ordered statement of the twelve-tone row from which the pitch

material of the movement is derived.

As the exposition proceeds, Ginastera introduces two theme groups that are delineated in

the music by a stark contrast in texture and tempo, yet neither theme features any canonical

transformations of the row.38

However unrelated the two themes may appear upon the beginning

of the secondary theme, the motivic pitch material that comprises both is drawn extensively from

the introductory material. This common origin of the two themes thus relates them in a more

abstract sense. As in the first quartet, it is Ginastera’s use of an introductory basic motive (here, a

twelve-tone row), upon which all pitch material in the movement can be derived, that creates a

sense of uniformity in design and unity in structure.

37

Hepokoski and Darcy, Elements of Sonata Theory, 16.

38

Canonical transformations refer to the four basic row forms: P (prime), I (inversion), R (retrograde), and

RI (retrograde-inversion).

18

Example 2.2 Sonata Form, String Quartet No. 2/I, Allegro rustico

Rondo Forms

Of the nine movements that make up both quartets, four exhibit a type of rondo form.

The basic component that unites these four movements is the frequent recurrence of a primary

thematic or motivic idea. This primary idea appears within each refrain, or A section, and is

presented in alternation with at least one other contrasting idea (i.e., B and C sections), giving

rise to the rondo form. The formal designs of the second movement of the first quartet and the

fifth movement of second quartet are similar and can be thought of as sonata-rondo hybrids: both

movements feature a central developmental section in addition to alternating sections of primary

and secondary material (A and B sections). Hepokoski and Darcy refer to the ABACAB A

formal design, with a developmental C section, as a standard Type 4 sonata form.39

Example 2.3 illustrates the sonata-rondo formal structure of the second movement of

the first quartet, and Example 2.4 illustrates the comparable design of the final movement of the

second quartet. Notice that both movements contain four appearances of the refrain (labeled A)

In addition to its alternation with contrasting B-section materials, both movements also contain a

lengthy, central C section, which develops material from previous sections. In the first quartet,

39

Technically speaking, the Type 4 sonata form is a mixture of a Type 3 sonata (AB//CAB) and a rondo

form (ABACA): the central C section gives rise to the Type 3 element of Type 4, while the second and final refrain

sections (A2 and A

4) give rise to the rondo element. Hepokoski and Darcy again base a large portion of their

definition of Type 4 sonata form upon clearly articulated tonal areas and definitive cadential closure; however, any

consideration of tonal criteria in the non-tonal language of Ginastera must necessarily be reinterpreted within the

realms of pitch-centricity and motivic association. For a description of Type 4 sonata form, see Hepokoski and

Darcy, Elements of Sonata Theory, 405–407.

19

the addition of second B section before the C section represents the only divergence from the

Classical sonata-rondo form; however, this extra B section actually enhances the underlying

sonata-form structure by creating the effect of a repeated exposition section (ABAB).40

Example 2.3 Sonata-Rondo Form, String Quartet No. 1/II, Vivacissimo

Example 2.4 Sonata-Rondo Form, String Quartet No. 2/V, Furioso

The basic motive indicated before the final refrain in Example 2.3 requires further

explanation. For a brief eight measures of music, Ginastera interrupts the established rondo

pattern and inserts a direct reference to the basic motive of the first movement. This ethereal

moment emerges through the texture with staggered tremolo entries of each instrument playing

pianissimo and sul ponticello. An interruption of this sort further reinforces the importance of the

basic motive, which Ginastera established so convincingly within the first movement. The

unifying power of the basic motive, along with its abstract intervallic properties, will be

discussed in greater detail in the second half of this chapter and in chapter 3.

40

According to Hepokoski and Darcy, the retransition sections of true rondos are “crucial markers” of the

form, and as such, their absence from Examples 2.3 and 2.4 is somewhat suspicious. Indeed, without retransition

sections between each episode and refrain, the form of both movements looks more like a symmetrical seven-part

rondo (AB-AC-AB -A) than a Type 4 sonata. But what is “crucial” for Hepokoski and Darcy is not the mere

existence of retransitions, but rather the dominant preparation they provide for the return to tonic. Because the

function of the retransition sections is eminently tonal in nature, their absence in Ginastera’s rondo forms is

unproblematic. See Hepokoski Darcy, Elements of Sonata Theory, 398–399.

20

In accordance with tradition, the final movement of the first quartet also adheres to a

rondo-form design, shown in Example 2.5. Unlike the sonata-rondo movements described above,

this rondo does not contain a central developmental section; instead, the movement features a

strict alternation of only the refrain and one episode (i.e., the B section).41

Clear instances of

transition (and retransition) material are readily identifiable in this movement because of the

consistency of pitch material Ginastera uses among such passages. As the movement comes to a

close, the coda section is announced in the music by the abrupt introduction of a new rhythmic

figure; this figure is coupled with a shift in texture from the homophonic texture of the final

transition section to the imitative entries that begin the coda.

Example 2.5 Rondo Form, String Quartet No. 1/IV, Allegramente rustico

The final type of rondo form requires some qualification. Example 2.6 illustrates the

formal design of the scherzo and two trios that makes up the third movement of the second

quartet.42

Ginastera’s use of two trio sections, interposed with a reprise of the scherzo, creates an

overall ABACA form that is, in the abstract, akin to the traditional five-part rondo form.43

It

should be noted, however, that while the first and final A sections are rather similar, the central

41

Hepokoski and Darcy describe the revisitation of episode 1 in place of episode 2 as a variant of the

traditional five-part rondo; see Hepokoski and Darcy, Elements of Sonata Theory, 400–401.

42

Ginastera revised the second quartet ten years after its first publication in 1958. The revision primarily

affected this movement and the fourth movement (Example 2.9). In both movements, Ginastera omitted relatively

small sections of music that contained references to Argentine folk melodies; however, these omissions are not

significantly large enough to alter the form of the movement. The third variation of the fourth movement, in

particular, contains a direct quotation of the melody, “Triste” from Ginastera’s Cinco Canciones Populares

Argentinas (1943). The measures numbers included in Examples 2.6 and 2.9 are based upon the 1958 (unrevised)

edition.

43

See Hepokoski and Darcy, Elements of Sonata Theory, 399–400.

21

A section is different from the other A sections with respect to texture and pitch material.

Specifically, Ginastera utilizes the same row forms in the outer sections, while he employs

different transformations of the row within the central reprise of the scherzo.44

The two trio sections share no commonalities in either texture or pitch material. The first

trio (section B) features a secondary twelve-tone row that is unrelated to the primary row that

governs the scherzo A sections. The second trio (section C) contains yet another configuration of

the twelve-tones, and it bears no relation to the rows used in either the scherzo or first trio.

Ginastera never presents the aggregate within the second trio as an ordered linear event; instead,

he immediately abandons it in favor of more freely atonal pitch material.45

Later in this chapter, I

will illustrate exactly how the aggregate is formed in the second trio and point out a significant

parallelism with regard to the basic motive of the first quartet.

Example 2.6 Rondo Hybrid, String Quartet No. 2/III, Presto magico

The examples above have illustrated the importance of a primary thematic or motivic

idea in Ginastera’s approach to rondo and sonata forms. The repetition of a primary idea, which

rondo form affords, most likely made this formal design attractive to Ginastera, who was highly

concerned with the articulation and clarity of form in his music. Furthermore, the repetitive (or

rounded) nature of both rondo and sonata forms helps to reinforce the motivic connections this

44

Because the same basic series governs the pitch material of scherzo and the two reprises, I have chosen

to use the same label (A) to denote each section.

45

“Freely atonal” does not imply that pitch events in second trio are not structurally organized—they most

certainly are. The label simply designates that this section is both aurally and analytically distinguishable from the

serially organized sections that surround it.

22

analysis will seek to illuminate. The composing-out of larger events over longer spans of music,

which will be discussed in chapter 4, emerges as a prominent feature of this music because the

formal designs of each movement are made so clearly evident. Ginastera was undoubtedly aware

of the associative power his pitch material could attain if presented in such a decidedly structured

manner.

Slow-Movement Forms

The remaining three movements to be discussed are related to one another in the most

general sense in that they are all slow movements. These three movements represent two formal

designs that are typical of slow movements: two are ternary and one is a theme and variations.

Speaking in terms of chronology, the first of these is the third movement of the first quartet. This

movement is illustrated in Example 2.7. The ternary form is made clear by the delineation of the

music into three independently complete formal units; these formal units are articulated in the

music by the fermatas placed between each section.

The two A sections present the primary thematic material. In the first A section, it is

passed along as a solo from the first violin to the cello. A written-out rallentando, ending with a

fermata, demarcates the end of the first A section and the B section. The B section features a

dramatic contrapuntal texture between instrumental pairs, which is cast against incessant ostinati

accompaniment. As the movement comes to a close, the truncated return of the A section recalls

the opening chordal gesture, and Ginastera indicates perdendo (dying away) so that the final

movement may enter with exhilarating contrast.

23

Example 2.7 Ternary Form, String Quartet No. 1/III, Calmo e poetico

Example 2.8 Ternary Form, String Quartet No. 2/II, Adagio angoscioso

Example 2.8 illustrates the ternary form of the second movement of the second quartet.

Again, the fermatas indicate that each formal section is independently closed. The pitch material

of the framing A sections of this movement is based on a single twelve-tone row and represents

Ginastera’s first attempt at strict serial composition. The B section, although it contains

fragments of the row used in the A sections, is for the most part composed in a freely atonal style

and features a much fuller ensemble of instruments, playing louder than forte for the entire

section. Thus, the primary determinates of musical form in this movement, as in all other

movements, are based upon Ginastera’s use of varying pitch materials and stark contrasts in

texture.

The primary theme of this movement, which is showcased in each A section and

appears once within the B section, does not consist of the entire twelve-tone row; rather, it is

made up of an order-number segmentation of the row, whose pitch classes reveal an interesting

relationship to the row forms used throughout the movement. (This feature will be discussed in

24

more detail in chapter 3.) In addition to the motivic fragment of the row used in the A sections,

these sections also contain a cello solo and a short canonic section. The cello solo is made up of a

strict presentation of the twelve-tone row that retains a characteristic rhythmic identity

throughout the movement. The canonic sections feature imitative entries of different forms of the

row, and periodically each instrument breaks away from the ordering of the row so as to allow

another instrument to carry the theme.

The fourth movement of the second quartet might be considered the “extra” movement

of the traditional quartet. After all, without the fourth movement the quartet already comprises a

sonata-allegro first movement, a slow second movement, a scherzo third movement, and a rondo

finale. But the theme and variations form of this “extra” movement provides a welcome contrast

to the other, similarly organized movements. As Example 2.9 shows, the theme and three

variations are represented as four cadenzas, each featuring a different member of the ensemble.46

While each instrument plays its cadenza, the other instruments provide a harmonic background at

a few specific points in the solo.

I have made a subtle distinction between “solo” and “cadenza” in Example 2.9 with

regard to the second variation. In this variation, the cello performs a solo that alternates almost

every measure with motivic material presented by the other three instruments. Given that this is

the only instance in the movement when the accompanying instruments play a more integral role

46

The use of cadenzas in conjunction with theme-and-variation form can be found in Ginastera’s Piano

Concerto No. 1 (1961), in which the piano begins with a cadenza containing the theme upon which the following

movements are based. A detailed discussion of this piece can be found in Pablo Eduardo Furman, “An Analysis of

Alberto Ginastera’s Piano concerto No. 1 (1961)” (Ph.D. diss., University of California, Los Angeles, 1987).

Extensive solo cadenzas also make up a large portion of Gianstera’s Piano Quintet, op. 29 (1963): movements two,

four, and six, of this seven-movement work feature cadenzas for the viola and cello, the second violin, and the

piano, respectively. For further discussion of Ginastera’s Piano Quintet, see Michelle Tabor, “Alberto Ginastera’s

Late Instrumental Style,” Latin American Music Review 15, no. 1 (1994): 1–31.

25

in the texture of the music, the term solo seems slightly more appropriate in conveying the

contrast of this variation with the more improvisatory other sections.

Example 2.9 Theme and Variations, String Quartet No. 2/IV, Libero e rapsodico47

Source Collections

Now that the formal structure of each movement has been discussed, an introduction to

the pitch material Ginastera uses within each movement is in order. The consistent use of

specific trichords and tetrachords, as harmonic and motivic entities, creates correspondences

between Ginastera’s serial and non-serial works.48

When considered together, these two string

quartets demonstrate the compositional processes by which Ginastera is able to retain his

characteristic sound, while expanding his pitch resources to the total chromatic. Furthermore, in

both quartets, the consistency of motivic collections can be traced back to a single parent

collection, or source collection, which sometimes (but not always) is given structural prominence

when presented as a primary thematic event in the piece.

47

Measures 50–53 of the viola’s cadenza contain a direct quotation of the melody, “Triste” from

Ginastera’s Cinco Canciones Populares Argentinas (1943), and Ginastera actually provided the lyrics in the score

above the viola part. These four measures were later omitted in the 1968 revised edition: the viola’s quotation was

removed entirely and the accompanimental sonorities in mm. 51 and 53 appear earlier in mm. 48 and 49,

respectively. The revision does not, however, affect the measure numbers provided in this analysis, which is based

on the 1958 (unrevised) edition.

48

Deborah Schwartz-Kates was one of the first scholars to point out that Ginastera’s second quartet does in

fact embody many of the nationalistic traits (or criollo traditions) found in his earlier works; see Schwartz-Kates,

“Alberto Ginastera, Argentine Cultural Construction, and the Gauchesco Tradition,” 248–281. The analytical

approach of the present study, which is based on pitch-class set theory, is a more precise way of illuminating exactly

what connections exist between Ginastera’s serial and non-serial compositional styles.

26

For example, the source collections of the first, second, and third movements of the

second quartet are simply the twelve-tone rows upon which each movement is based. The

twelve-tone row of the first movement is featured prominently in the five-measure introduction

of the movement, but is not used as a basis for any subsequent serial transformations. Instead,

Ginastera bases the rest of the movement’s thematic material upon trichordal subsets of the

initial row, which are not limited to any specific order-number combinations. In contrast, the

twelve-tone row of the second movement does appear several times as a primary theme of the A

section and is, furthermore, subjected to multiple transformations using the four canonical

operations (P, I, R, and RI). This is not to say, however, that the row is not segmented into

smaller motives: it most certainly is, and one motive in particular plays a crucial role in

determining the succession of row forms.

Although the first quartet is not based upon any twelve-tone row, the first movement

prominently presents a source collection at its opening that is analogous to the presentation of the

row at the beginning of the second quartet. Just as Ginastera begins the second quartet with an

assertive introductory statement of the total chromatic, he begins the first quartet with an equally

assertive introduction of the work’s source collection. However, unlike the twelve-tone source

collections of the second quartet, the source collection of the first quartet governs all four

movements.

The following analysis will investigate the source collections of both quartets, and

comment on the general consistencies of their subset configurations. In regard to the first quartet,

this analysis invokes the term basic motive to refer to the ordered collection that begins the work

and contains fewer than twelve pitch classes. In regard to the second quartet, the term basic

series will be used to refer to the ordered twelve-tone collection that governs a particular

27

movement; the term secondary series refers to a twelve-tone collection of secondary importance

within a movement, and specifically one that is used in conjunction with a basic series.

Quartet No. 1, First Movement

As the first quartet begins, the musical energy is focused on a dramatic six-measure

introduction that features the source collection as prominent motive. In fact, within the first

twelve measures of the first movement, Ginastera emphasizes a number of motivic cells derived

from this introductory motive that will be of importance in the coming movements. Example

2.10 reproduces the introduction of the movement. The assertive quality of this passage is due in

part to the unison presentation of the basic motive in measures 1 and 4 (the first presentation is

circled in Example 2.10); and the clear demarcation of its constituent parts through the use of

fermatas in measures 2 and 5, and complete silence in measures 3 and 6.

Example 2.10 String Quartet No. 1/I, introduction mm. 1–6

28

Example 2.11 abstracts the ordered collection that makes up the basic motive. The

pattern of directed intervals, <+4, -1, +4, -1, +4>, introduced by the first violin in mm. 1–2 and

4–5 results in the chain of overlapping and inversionally related (014) trichords.49

As the top of

Example 2.11 shows, the inversion operation, which relates adjacent trichords, maps the first

pitch of the first trichord onto the last pitch of the second trichord. The bottom of the example

illustrates that the first and third (014) trichords are related by transposition up a minor third, or

T3. This transpositional relationship is emphasized in the music by the metric articulation of the

pitch-classes D and F, marking the level of the beat. The second violin and viola also echo the

interval of transposition (interval 3) by outlining the diminished triad, D–F–Ab, in measures 1

and 4 (see again Example 2.10).

Example 2.11 (014) trichordal chain of the basic motive

The first chordal sonority of the introduction, shown in Example 2.10, overlaps with the

ending of the basic motive in measure 2 and consists of the exact same pitch classes as the basic

motive, with D again emphasized as the lowest note. The distribution of the six pitches among

the four instruments results in two registrally superimposed (037) trichords: a D-major triad

sounds in the cello and viola and an F-minor triad sounds in the violins (see Example 2.12). This

configuration of the basic motive is transposed up by two semitones (T2) in measure 5; however,

the T2 transposition of the (037) trichords is formed crosswise between the instrumental pairs,

49

The set-class of the entire basic motive is 6-Z49; however, it is the constituent subsets of this larger

collection that will be of primary interest to the present analysis.

29

while an inversion transformation prevails between adjacent pairs. Significantly, both inversion

operations result in a single common tone among trichord mappings. The invariant pitch-classes

D and Ab (G#) are indicated by the inversion labels, and their significance is revealed as the

movement proceeds.

Example 2.12 (037) mappings between the chordal sonorities in mm. 2 and 5

In addition to the trichords (014) and (037) described above, three more motivic cells are

delineated by the basic motive and its immediate transformations within the introduction.

Example 2.13 extracts the notes that are prominent because of the rhythmic accentuation and

registral boundary pitches of the chordal sonorities in measures 2 and 5. The rhythmically

accentuated pitches D, F, and C in the first violin compose-out a (025) trichord; the intervallic

unfolding of this motive is illustrated by the transformations shown below the example.

The registrally accentuated pitches of the chordal sonorities create a (027) trichord,

represented by the pitches D, G, and C. The T5 transformation that connects D to G is

particularly pronounced in the music because it appears between the lowest notes of the two

sonorities; this transformation is perhaps even more striking than the T2 transformation that

relates the complete chordal sonorities (see Example 2.12). The (025) and (027) trichords are

closely related in that they share two of their three interval classes: ic2 and ic5. This might

30

account for the fact that Ginastera uses the two set classes almost interchangeably. Moreover, it

is the combination of these two trichords that results in the most characteristic sonority found in

virtually all of Ginastera’s early works: the (0257) tetrachord, here formed by the pitch-classes

[CDFG].

Within the first string quartet, the (0257) tetrachord typically appears harmonically as

two perfect fifths separated by a whole-step (e.g., F–C and G–D). But whether it appears as the

juxtaposition of two perfect fifths (interval 7) or two perfect fourths (interval 5), this tetrachord

(which is also common in the music of Copland and Stravinsky, for example) contributes to

Ginastera’s distinctive sound.

Example 2.13 Formation of (025), (027), and (0257) from the basic motive

As Examples 2.11–2.13 have illustrated, the motivic cells (014), (025), (027), (0257), and

(037) can all be derived from a single source collection and are given prominence in the way this

collection is represented in the basic motive. By nature of their association with the basic motive,

these motivic cells (along with the transformations by which they unfold and relate to one

another) are potentially important features of this quartet’s pitch organization. The motivic cells

are given priority in this analysis, not only because they are an integral part of the musical

surface, but because they are traceable back to a single source collection. Chapter 3 will deal

with this issue in more detail, but for now it will beneficial to discuss the transition passage that

31

immediately follows the introduction, because it sheds more light on the identity and importance

of the basic motive.

Example 2.14 reproduces this transition passage; its relationship to the introduction that

precedes it is striking. The basic motive appears in the first violin and viola in measure 7, and is

simultaneously presented in inversion by the second violin and cello. The following two

measures then repeat the basic motive (along with its inversional presentation) so that it appears

transposed by T10 in measure 8, and again by T10 in measure 9. The climax of this pattern

occurs on the downbeat of measure 10, when the first violin and viola begin a retrograde descent

of the pitches presented in mm. 7–9, and the second violin and cello initiate a new pattern. The

circled pitch in measure 11 indicates that the perfect symmetry is momentarily broken when C#

replaces what was originally Ab in measure 7.

Example 2.14 String Quartet No. 1/I, transition mm. 7–12

The axis of symmetry, which is indicated by the dotted line in Example 2.14, helps to

accentuate another important motivic interval in this music: the ic6 or tritone formed by D–G#.

The tritone is often overtly emphasized in several of Ginastera’s compositions, and it also plays a

major role in the structure of the motives (and their transformations) within the first and second

quartets. The ic6 relation in this transition passage is strongly pronounced due to its registral and

metric disposition. Significantly, the relation is specifically formed by the pitch-classes D and

32

G#: these are the same pitch classes that were held invariant under the transformations relating

the two chordal sonorities in measures 2 and 5 (see Example 2.12).

In several other passages belonging to both quartets, Ginastera uses ic6 as a motivic

interval, which typically results in an emphasis on the collections (016), or (0167). However, ic6

is also found projected to a different musical space, where it functions as a transpositional

operation (T6).50

The T6 transposition will often times replace the more tonally associated T7 or

T5 transposition (i.e., transposition to the dominant or subdominant). This is especially the case

when the tonal tradition associated with a particular formal design (e.g., sonata form) would

likely call for the transposition of a theme to the level of the dominant, in which case Ginastera

replaces the T7 transposition with T6.

There are three compositional elements of particular interest in this transition passage that

need further explanation. These elements identify important features of Ginastera’s

compositional style that relate his two quartets, and as such, they will form the basis of a larger

discussion of pitch structure and compositional processes in chapter 3.

The first compositional element involves Ginastera’s use of symmetry, which appears in

two different spatial levels: (1) as an inversional wedge formed between each instance of the

basic motive (stated by the first violin and viola) and its simultaneous mirror-image presentation

(stated by the second violin and cello), and (2) as a linear unfolding of the melody in which the

G# axis marks the retrograde descent of the same pitches. Symmetry plays a significant role in

much of Ginastera’s music, and it is, without a doubt, a prominent feature of his compositional

technique.

50

The relating of intervals to transposition operations is the principal contribution of David Lewin’s

transformational approach. See, for example, Lewin’s Generalized Musical Intervals and Transformations (New

Haven: Yale University Press, 1987); and “Transformational Techniques in Atonal and Other Music Theories,”

Perspectives of New Music 21 (1982): 312–371.

33

The second element of interest concerns the completion of the total chromatic.

Considering only the top line in Example 2.14, Ginastera completes the chromatic aggregate

within the first three measures of the melody’s ascent, except for the pitch-class B; interestingly,

this is precisely the pitch that appears below the G# when the second violin and cello begin the

new pattern. Had it not been for the systematic transposition of the basic motive by T10,

occurring in measures 8 and 9, this completion of the chromatic aggregate would not have been

achieved, and Ginastera might have simply transposed the motive by an octave in each case. It

seems that completing the total chromatic is the goal of this passage given that each transposition

of the basic motive also appears alongside its inversional presentation (forming the wedge).

When we consider the passage in terms of its inversional wedge motion, the missing

pitch-class B does in fact appear in the second violin and viola in measure 7. Thus, Ginastera

achieves a general sense of chromatic saturation along the two symmetrical spatial levels

mentioned above (i.e., along the melody line and along the inversional wedge). Ginastera’s

fascination with completing the total chromatic appears throughout the first quartet and

essentially culminates in his movement toward serialism in the second quartet. Chapter 3 will

deal with this compositional feature and its development within both quartets in more detail.

The third element of interest that the transition passage introduces is the new trichords

(013) and (015), which first appear in the second violin and cello in mm. 10–12. These two

trichords function as variations on the prominent (014) trichord: all three trichords have ic1 in

common, and in the music, this interval nearly always appears as a semitone. The differences

between the trichords are reflected in Ginastera’s combined use of the semitone with one of the

following intervals: the major third in (014), the minor third in (013), or the perfect fourth in

(015). Example 2.14 shows that in the formation of every (014), (013) and (015) trichord the

34

semitone interval is presented together with, respectively, a major third, a minor third, and a

perfect fourth; therefore, it seems plausible, based on the way (013) and (015) are formed in the

music, that these two new trichords are variations on the familiar (014) trichord.51

The basic motive, as a source collection, provides the first quartet with nearly all of its

important motivic material, much like a twelve-tone row provides the material for a serial work

(as will be discussed in the examples below). Its importance to the quartet is further emphasized

when it appears again, with very little alteration, in the other movements. Example 2.15

reproduces the return of the basic motive within the second movement; this moment was first

described in conjunction with Example 2.3 above.

Example 2.15 String Quartet, No. 1/II, return of the basic motive (mm. 201–208)

51

One could interpret (013) and (015) as linear transformations of (014), or more specifically

transformations involving chromatic contraction and chromatic expansion, respectively. These and other extensions

of pitch-class sets are posited by Miguel Roig-Francolí in, “A Theory of Pitch-Class-Set Extension in Atonal

Music,” College Music Symposium 41 (2001): 57–90.

35

In stark contrast to the surrounding texture, the exact pitch classes of the original basic

motive unfold in overlapping major thirds across all four instruments. The pianissimo tremolos,

played sul ponticello, contribute to the ethereal quality of this moment. However, an alteration to

the basic motive occurs upon the final entrance of the first violin. The original interval pattern of

the motive, <+4, -1, +4, -1, +4>, is extended by yet another <-1, +4> interval segment, with the

pitches B–D#. This extension of the basic motive results in the formation of a complete octatonic

scale: C, D, D#, F, F#, Ab, A, B. The dynamic feature of this passage, however, has less to do

with the completion of the octatonic collection, and more to do with multiple transformations of

motivic material by T3 and T6 shown in Example 2.15. The staggered entrance of each

instrument highlights the consecutive T3 relations, and the registral pairings of instruments (i.e.,

cello and viola; first and second violins) accentuate the T6 transformation between the two

tetrachords of the extended basic motive.

Example 2.16 presents another statement of the basic motive as it appears in the fourth

movement. This moment occurs right before the return of the final refrain (section A3 in

Example 2.5). Above the melody, which appears in the cello and viola in Example 2.16, the

basic motive is stated in the first violin. The second violin accompanies the motive, forming a

series of parallel interval 3s. Again, the collection of pitches represents an extension of the basic

motive to include B and D#, and the accompaniment of the motive below represents a rotation of

the basic motive that begins with B–D#.

36

Example 2.16 String Quartet, No. 1/IV, basic motive in parallel thirds (mm. 173–174)

Quartet No. 2, First Movement

The source collections of the second string quartet involve the twelve-tone rows upon

which three of the five movements are based. The ordered twelve-tone row, or basic series, used

within the first movement is shown in Example 2.17 and the discrete trichords are labeled below

the row. The familiar (014) trichord from the basic motive of the first quartet begins the row. As

mentioned earlier, ic6 is given a great deal of prominence in Ginastera’s music, and when it is

combined with two of the composer’s other favored interval classes, ic1 and ic5, the resultant

trichord is (016). The third and fourth trichords of the basic series are new to the collection of

commonly used trichords, but Ginastera’s subtle manipulation of the basic series in the

introduction of the movement reveals an emphasis on motivic cells that are different from those

formed by the discrete trichords of the ordered row.

Example 2.17 String Quartet No. 2/I, basic series

173

37

Example 2.18 reproduces the five-measure introduction of the movement. The basic

series begins to unfold as shown in Example 2.17, until the fourth eighth note in measure 3

sounds; this high Bb disrupts the presentation of the row by repeating the second pitch-class of

the series. The row continues where it left off, until the second eighth note in measure 4 disrupts

the order again by repeating the third pitch-class of the series. The second pitch-class, Bb, returns

once more in measure 4 before the final pitch-class sounds in measure 5.

Example 2.18 String Quartet No. 2/I, introduction mm. 1–5

Several interesting motivic features result from Ginastera’s repetition of Bb and C#

within the unfolding of the basic series. First of all, the musical surface is easily parsed into

motivic trichords based on the 6/8 meter; these trichords are identified within the example.

Notice that the repetition of Bb and C# results in an emphasis on ic1 (found in the (012) and

(016) trichords, and between the second and third, and fourth and fifth trichords, respectively)

and ic5 (found in (016) and (027)). Thus, by not limiting himself to strict ordering of the basic

series, Ginastera is able to continue articulate his favored trichords, (014), (016) and (027).52

The remainder of the first movement is not composed in a strict serial manner; Ginastera

abandons the row immediately after this introduction and uses it again only to recall the music of

the introduction. Like the basic motive that begins the first quartet, the basic series that begins

52

Other authors have discussed Ginastera’s propensity to repeat (and often reorder) the pitches of his

twelve-tone rows. See Michelle Tabor, “Alberto Ginastera’s Late Instrumental Style,” 8–12, 18–20; and also

Richards, “Pitch Structure in the Opera Don Rodrigo of Alberto Ginastera,” see especially chapter 2.

38

the second quartet functions primarily as a source collection from which motivic cells are drawn;

as such, the basic series does not fully achieve status as a primary thematic or motivic event.

Quartet No. 2, Second Movement

The basic series of the second movement is treated much differently than that of the

first movement. Whereas the basic series of the first movement does not recur as a primary

motivic or thematic event throughout the movement, the basic series of the second movement

does appear as a succinct theme within both A sections of the ternary form (see the “cello solo”

in Example 2.8). Example 2.19 reproduces mm. 3–10 of the second movement, and the basic

series appears as a solo theme presented by the cello in mm. 9–10. The rhythmic grouping of this

theme emphasizes the trichords of the row, and a glissando at the end of the phrase between A–

G# highlights the ic1 between order numbers 12 and 1.

Example 2.20 illustrates the set-class memberships of the discrete trichords of the basic

series, which include only two types, (037) and (016). Ginastera’s use of these two trichord

collections needs very little explanation, as they appear prominently throughout both quartets.

The most interesting aspect of the basic series, however, is not how it appears thematically

within the cello part in Example 2.19 (to be sure, this theme occurs only twice in the entire

movement), but rather it is how Ginastera segments specific pitch classes of the basic series for

motivic emphasis. The primary motive of the movement, which appears multiple times within

each section of the piece, and often at structurally significant moments, is always formed

between the order-number segment, <1,6,7,12> of the basic series.53

These pitches form the

53

The work of Milton Babbitt in the 1950s and early 1960s paved the way for theory and analysis of

twelve-tone music; among others, see his “Twelve-Tone Invariants as Compositional Determinants,” in The

Collected Essays of Milton Babbitt (Princeton: Princeton University Press, 2003). Since Babbitt’s seminal work,

several authors have discussed the motivic associational possibilities of order number parsing in twelve-tone music.

See, for example, David Lewin, “A Theory of Segmental Association in Twelve-Tone Music,” Perspectives of New

39

boundary pitch classes of the row’s hexachordal segments, and together they make up the

chromatic set class (0123).

Example 2.19 String Quartet No. 2/II, primary motive of section A1 (mm. 3–10)

Example 2.20 String Quartet No. 2/II, basic Series

The first appearance of the chromatic motive is indicated in Example 2.19 by the box

around the viola melody in mm. 4–7. Here, Ginastera seamlessly extends the motive by two

additional semitones by juxtaposing P3 and P7 forms of the basic series. In measure 3, the viola

begins the theme that is later presented by the cello (mm. 9–10); however, this theme is abruptly

abandoned after the first six pitches, and the pitch classes from order positions 8 through 11 are

Music 1, no. 1 (1962): 89–116; and also Andrew Mead, “Large-Scale Strategy in Arnold Schoenberg’s Twelve-Tone

Music,” Perspectives of New Music 24, no. 1 (1985): 120–157.

40

relegated to the chordal accompaniment. The chromatic motive thus begins with order numbers 7

and 12 from P3, and extends directly into the order-number segment <1,6,7,12> of P7 to form set

class (012345), [EFF#GG#A]. As with the presentation of P3, the remaining pitch classes of P7

are stated by the violins’ accompaniment. Notice that the ic1 glissando formed by A–G# appears

for the first time in measure 9, where the second violin echoes the last interval stated by the

viola.

Besides the repetition of order number 1 at the conclusion of P9 in measure 10, the only

other pitch-class to occur out-of-order is the G# in measure 5. Here, the G# embellishes the

chromatic motive to help fill in the ic3 gap that exists between order numbers 6 and 7, F# and A.

Just as in the first movement, Ginastera subtly organizes the pitches of this basic series so that he

may give more emphasis to motivic ideas that are highly characteristic of his compositional

style. Furthermore, the consistent voicing of the sonorities in mm. 4–7—such that the order

numbers ascend in order, beginning with the lowest note of the second violin—allows for the

characteristic (014) trichord (common to both the basic motive of the first quartet and the basic

series of the first movement of the second quartet) to be formed by the highest pitches of the

accompaniment texture, C#–D–F.

The notes in Example 2.19 that remain unaccounted for are the cello pizzicato pitches,

A and Eb, in measures 4 and 8. These pitch classes do not easily fit into the unfolding of either

the P3 or P7 row forms: as part of P3, they form the order-number pair <10,1>, and as part of P7,

they form the order-number pair <7,3>—both are unusual combinations in this context. These

pitches really do not “belong” to either row form at all; rather, they represent a motivic entity

separate from the row itself, but not devoid of association with the row. In fact, this motive forms

two different associations that exist on two different levels of abstraction: one on the surface

41

level and one on a more global level. On the surface level, A and Eb emphasize the important

interval ic6. The function of ic6 in this context is to defy any tonal allusion that might result from

the (037) trichords of the melody, particularly those that appear in the viola in measure 3 and in

the cello in mm. 9–10. Throughout the movement Ginastera explicitly avoids motion by fifth in

the bass and instead replaces it with ic6.

On a more abstract level, pitch-classes A and Eb form an associational pathway between

the row form that begins the movement, P3, and the row form that appears as the cello theme,

P9.54

Pitch-class 9, or A, appears several times before the cello theme, stating P9, enters in

measure 9; in a sense, the pizzicato A foreshadows the sequence of events that is about to unfold.

The viola begins the presentation of P3 but shortly thereafter abandons the theme in order to

introduce the primary motive. The primary motive then chromatically elides P3 with P7, and the

second-to-last note of the motive, A, receives the highest registral placement and the longest

duration of all the pitches of the motive. A is also repeated by the second violin’s glissando in

measure 8. Meanwhile, the cello reiterates the A–Eb pizzicato motive in the lowest register.

Without delay, the cello introduces the complete theme on P9, and the journey to arrive at A is

complete.

The remainder of the movement contains similar associational pathways, in which the

pitch classes of the primary motive (the chromatic tetrachord) foreshadow subsequent

transformations of the basic series. Consequently, the associational power of this primary motive

enables Ginastera to draw connections across formal boundaries, so that even the non-serial B

section plays an integral role in the unfolding of a large-scale associational pathway. This and

other associational pathways will be discussed in more detail in chapter 4.

54

As will be thoroughly explained in chapter 4, the associational pathway of the type described here can be

thought of as an abstract kind of composing-out technique in which the literal pitch classes of a motive become part

of a larger compositional scheme.

42

Quartet No. 2, Third Movement

The scherzo (third movement) of the second quartet is the only other movement that

contains a distinct basic series; the fourth and fifth movements, while containing prominent

statements of the chromatic aggregate, are explicitly non-serial. As Example 2.6 illustrated, the

third movement contains two trio sections, which are framed by the scherzo and its two reprises.

To complement the formal design of the movement, Ginastera uses a single basic series for the

scherzo section and its reprises and two secondary series for the two trio sections.

Example 2.21 reproduces the basic series of the scherzo sections. Because Ginastera

treats the row differently in the scherzo and the two reprise sections, the following discussion

will only deal with inherent features of the row that are emphasized consistently throughout the

movement. The row is neatly divided into two hexachords: the first consists of two (016)

trichords and the second consists of two (013) trichords. The intervals of the first hexachord are

symmetrically arranged around the central ic3, B–D, and Ginastera consistently emphasizes the

intrinsic symmetry of the row in pitch space.

Example 2.21 String Quartet No. 2/III, basic series (scherzo, reprises 1 and 2)

The intervals of the second hexachord are not symmetrically arranged, but they are

inversionally arranged around their own central ic3, G–E. The most characteristic feature of this

hexachord that receives emphasis in the music involves its contour. Notice that the order of the

interval classes remains the same between the two trichords, and yet the contour of the second

43

trichord is inverted. The interplay of these (013) trichords throughout the scherzo mimics a

dialog between a motive and its answer at the dominant. This tonal allusion results from the

transposition of the first pitch of the motive, A, by T7 (or T-5) to begin on E, where the rest of

the motive is then presented in inversion.

In addition to the (016) and (013) discrete trichords of the basic series, Ginastera also

emphasizes on the surface of the music a motive that stresses the (014) trichord formed by the

order-number segment <9,10,11>. The (014) trichord is, without a doubt, one of Ginastera’s

favorite trichords, and its appearance within the scherzo illustrates another example of how

Ginastera is able to manipulate the source collection in order to highlight motivic pitch events

that are emblematic of his style.

Example 2.22 reproduces the secondary series that governs the pitch material of the

first trio. All four discrete trichords are typical of Ginastera’s music, although (015) appears less

frequently than its close relative (016). To avoid this minor inconsistency altogether, Ginastera

manipulates the grouping of pitch events so that the third discrete trichord is blurred by a pattern

of repeated pitches that give rise to overlapping (016) and (025) trichords, as indicated above the

series in Example 2.22.

Example 2.22 String Quartet No. 2/III, secondary series 1 (first trio)

44

Example 2.23 reproduces the cello solo that dominates the texture of the entire first trio.

The trichords most typical of Ginastera’s style, (016) and (014), are emphasized through

repetition at the beginning and ending of the solo. The pattern of singularly repeated pitches

begins with the (012) trichord in measure 69. As the pattern continues, a subtle shift in the

rhythmic grouping of trichords occurs, and (016) and (025) emerge from the repetition of order

numbers 6 and 8 in measure 70. In this context, the original (015) trichord of the basic series is

not given the degree of rhythmic articulation that the more common (016) and (014) trichords

receive; moreover, Ginastera replaces (015) with two trichords that are highly representative of

his characteristic sound, (016) and (025).

Example 2.23 String Quartet No. 2/III, second trio cello solo (mm. 64–73)

As mentioned above, the second trio section also features its own twelve-tone row,

which is identified as secondary series 2 in Example 2.24. The row consists of four discrete

(037) trichords, which actually never appear in a strict linear order within the trio section. In fact,

Ginastera does not limit himself to this collection alone; he also uses several other motivic

trichords that are unrelated to the secondary series. The order of the trichords shown in Example

2.24 is thus the order that illustrates most effectively the transpositional relations. The first and

last trichords are related by T2 transposition, as are the second and third trichords.

45

Example 2.24 String Quartet No. 2/III, secondary series 2 (second trio)

Example 2.25 reproduces the first two measures of the second trio. The T2

transpositional relations between (037) trichords is clearly articulated between the instrument

pairs: viola/first violin, and cello/second violin. In measure 195, the Ab-major trichord of the

viola actually appears before the Gb-major trichord of the first violin, and therefore the

transpositional operation is labeled T-2, in place of T10. The overall T2 relation between the first

and second hexachords of the secondary series is made more explicit in measure 196, when the

Gb-major trichord actually appears before the Ab-major trichord (as shown in Example 2.24).

Example 2.25 String Quartet No. 2/III, second trio (mm. 195–196)

Ginastera’s use of (037) trichords that are T2-related to one another recalls his treatment

of the basic motive within the introduction of the first quartet. As Example 2.12 illustrated, the

basic motive, after its presentation as a chain of (014) trichords in measure 1, recurs as a vertical

46

sonority in measures 2 and 5. Both vertical sonorities articulate the (037) trichords, and the T2

operation is emphasized across instrumental pairs, as shown in Example 2.25. The

correspondences between these two excerpts underline the consistency with which Ginastera

manipulates pitch material in both the first and second quartets.

*****

In sum, this chapter has presented some of the more general features of Ginastera’s

compositional style and has provided an analytical framework for the discussion of more specific

motivic processes that will follow in chapter 3. Ginastera’s approach to form is based on

traditional models such as sonata, rondo, and ternary forms; and the formal structure of each

movement is clearly articulated by Ginastera’s organization of contrasting thematic areas. The

pitch material of the most prominent thematic areas is based upon source collections, which are

typically stated at the beginning of a movement or section. Ginastera’s treatment of these source

collections results in a general consistency of motivic materials between the non-serial first

quartet and the serial second quartet. Chapter 3 will discuss the motivic pitch structure of both

quartets as it relates to the source collections described above. Compositional processes—

including Ginastera’s penchant for a specific transpositional relations, his use of the total

chromatic, and his use of symmetry—will also be considered.

47

CHAPTER 3:

MOTIVIC PITCH STRUCTURE AND COMPOSITIONAL PROCESSES

There are several similarities between the motivic pitch structures of Ginastera’s first and

second quartets. Even when Ginastera turns to composition based upon a twelve-tone row, as he

does in the second string quartet, he still focuses the structure of his pitch material—specifically,

that of his primary motives—on a limited number of pitch-class sets. It is, therefore, significant

that Ginastera chooses to favor the same motivic trichords and tetrachords in both his serial

second quartet and his non-serial first quartet. Indeed, specific motivic set-classes represent the

hallmark of his style. As chapter 2 revealed, the consistency of pitch material used in both works

is largely due to the composer’s manipulation of source collections (i.e., the basic motive and the

basic series). This chapter will discuss how motivic subsets derived from each source collection

are used as the basis for prominent thematic material within individual movements. The

examples that accompany the discussion will expose the general consistency of motivic pitch

structure found within these two stylistically different works.

Following the discussion of motivic pitch structure, the remainder of the chapter will

explore two compositional processes that are common to both quartets. The first process involves

Ginastera’s technique of completing the total chromatic via permeating the musical surface with

the motivic pitch-class sets (012) and (0123). Through this process I understand Ginastera’s

movement toward serialism as a logical outgrowth of the stylistic techniques he was already

using in the first quartet. The second compositional process involves Ginastera’s use of

symmetry, which he sometimes uses in conjunction with the projection of chromatic motivic

material.55

Significantly, this technique commonly occurs either within transitional passages or at

55

From here on, “chromatic motivic material” will refer to the following pitch-class sets and their

extensions: (012), (0123), (01234), etc.

48

important cadential moments, and the symmetrical design is often manifested in both the melodic

and harmonic dimensions.

Motivic Pitch Structure

Ginastera’s manipulation of source collections, as described in chapter 2, illustrates his

predilection for specific motivic trichords, especially (014), (025), and (016). These three

collections, in particular, are derived from the basic motive of the first quartet, and their

importance within the first movement is confirmed by the pitch structure of the primary,

secondary, and closing themes. Example 3.1a reproduces the primary theme of the first

movement, which is presented by the first violin. This theme consists of only six different pitch

classes, whose ordered appearance, D–F–F#–A–G#–C, replicates the original presentation of the

basic motive in the introduction (reproduced here as Example 3.1b). The original motivic chain

of overlapping (014) trichords is made more explicit within the primary theme by Ginastera’s

elaboration of the melody. Between measures 18 and 19, the shared (014) pitches, F–F# (which

originally overlapped in the basic motive), are repeated to form consecutive (014) trichords; and

in measure 21, the melody returns to F between statements of G#–A in measures 20, forming the

third (014) trichord. The final (014) trichord derived from the basic motive is emphasized in mm.

24–26 and again in mm. 27–29.

The (025) trichord, which was originally formed from the rhythmic accentuation of the

pitch-classes D–F–C of the basic motive, now appears within the primary theme as a cadential

motive in measures 31 and 34. These pitch-classes also receive rhythmic and durational

accentuation over the span of the entire melody: D is accentuated as the first pitch of the melody,

while F (mm. 16–18) and C (mm. 24–26) are held (or repeated) longer than any other pitch.

49

Example 3.1 String Quartet No. 1/I, primary theme mm. 16–34

a)

b)

The cadential (025) trichord returns in the secondary theme, reproduced in Example 3.2.

However, in this theme (016) replaces (014) as the most prominent motive. In this example, the

trichords are realized as vertical sonorities formed between the first violin, viola, and cello—with

the lower two instruments moving in contrary motion to the first violin. The (016) trichord

receives dynamic and durational emphasis in measure 60 and again in mm. 64–65, before it

passes through the (015) sonority to cadence on (025) in measures 61 and 66. Notice that the

repeated gesture also passes through (027) in measure 65; this minor alteration allows Ginastera

to emphasize the (014) trichord as a linear motivic event in all three instruments (see, for

example, the cello part in Example 3.2).

50

Example 3.2 String Quartet No. 1/I, secondary theme mm. 60–66

The closing theme of the first movement (reproduced in Example 3.3) is reminiscent of

the modal melodies that abound in Ginastera’s early works. The viola and cello, moving in

contrary motion to one another, present the melody thereby creating a gesture similar to that of

the secondary theme. The pronounced rhythmic identity of this melody permits segmentation

into motivic trichords, which either occupy entire measures or are accented at the level of the

beat.56

The (025) trichord permeates the melody of this closing theme, so that its once-local

cadential function is now transferred to a deeper structural level, in which it functions as the

cadential gesture of the entire exposition.

It is also interesting that this closing theme is centered on the perfect fifth A–E, which is

sustained as a pedal point in the first and second violins in mm. 85–89 and picked up by the viola

and cello in measure 90. The perfect fifth A–E is T7-related to the fifth D–A that serves as the

pitch center of both the primary and secondary themes; thus, the new pitch center represents a

56

The oscillation between 3/4 and 6/8 metric patterns in this passage is reminiscent of the Argentine gato, a

folk dance that Ginastera incorportated into much of his music. For a more formal explanation of the gato and its

musical characteristics, see Deborah Schwartz-Kates, “Alberto Ginastera, Argentine Cultural Construction, and the

Gauchesco Tradition,” 249. Recently, Erick Carballo has extensively discussed Ginastera’s interpretation and

amalgamation of Argentine dances such as the gato and the malambo. Specifically, he introduces the idea of the

“Ginasterian Malambo,” suggesting that Ginastera uniquely combined characteristics of the gato, malambo, and

other native devices to achieve his own artistic goals. See Carballo, “De la Pampa al Cielo,” chapter 3.

51

kind of tonal allusion to the modulation to the dominant that typically occurs in tonal sonata-

form expositions.57

Example 3.3 String Quartet No. 1/I, closing theme mm. 85–90

The motivic pitch structure of the second quartet shares many commonalities with that

of the first quartet. Notably, the (014) trichord, which is essential to the basic motive and primary

theme of the first quartet, takes on an equally prominent role in the second quartet. Example 3.4a

reproduces the primary theme presented by the first violin in the first movement of the second

quartet. The instrumentation alone—solo first violin—recalls the opening of the first quartet (see

Example 3.1). The contour of both primary themes is also similar in that both themes gradually

ascend to a central goal-point, which is incessantly repeated before the melody begins a gradual

descent. In Example 3.4a, the melody begins its ascent but is momentarily cut off by an

accompanimental gesture in mm. 32–45. It is then picked up again in measure 46, where it

repeats the gesture initiated in mm. 28–29 (see the motive indicated by the box). The central

goal-point of the melody is Bb (order number 2 of the basic series) and it is emphatically

57

Ginastera creates a similar tonal allusion in the exposition of his Piano Sonata No. 1, Op. 22 (1952),

where the transition following the primary theme group establishes a pedal on a pseudo V/V before the secondary

theme arrives in a pseudo dominant relation to the exposition’s opening.

(P)

(P)

52

repeated beginning in measure 48. Following the arrival of this goal, Bb is elaborated by its

semitone upper and lower neighbor, forming a (012) trichord. This motivic gesture eventually

gives way to a presentation of the basic series in mm. 54–56 (note that this is the same gesture

that begins the movement, see Example 3.4b).

Example 3.4 String Quartet No. 2/I, primary theme mm. 24–43

a)

b)

The (014) trichord first appears in measure 27 of Example 3.4a, where it forms a

descending gesture in preparation for the melody to begin again in the following measure. When

the melody repeats its opening gesture the intervallic structure is slightly altered so that each

interval ascends in the pattern <+3, +1, +3>. The result of this slight change creates two

overlapping and inversionally related (014) trichords: [DFF#] and [FF#A]. The same pitches are

repeated in mm. 46–47. As Example 3.4b illustrates, the basic series originally began with a

(014) trichord, formed by the pitch-classes D–Bb–C#. Now within the primary theme, the pitches

of the overlapping (014) trichords in mm. 28–29 and 46–47 (i.e., D–F–F#–A) strongly recall the

53

primary theme of the first quartet. These pitches do not conform to the original pitches of the

(014) head motive of the basic series; rather, they are part of a lengthy elaboration (mm. 24–53)

of the head motive. Not until the rest of the pitch classes of the basic series appear in mm. 54–56

does it become evident that the D–F–F#–A motive is standing in for the original (014) head

motive.58

The (014) trichord takes on a far more obvious motivic role within the secondary theme,

the beginning of which is reproduced in Example 3.5. This theme appears after a lengthy

transition section based on the G pedal initiated at the end of the primary theme, and it is marked

by Ginastera’s indication, Abbastanza meno mosso e piacevole Tempo II. The theme begins with

the cello’s entrance on D in measure 98; this pitch is of course a fifth higher than the G pedal and

perhaps represents another example of Ginastera’s mimicking of a tonal modulation to the

dominant. Regardless, this pitch initiates the imitative entries of four transpositionally related

(014) trichords, the first of which comprises the same pitch classes as the (014) trichord of the

primary theme, D–F#–F.59

The final (014) entrance, which is presented by the first violin,

overlaps with another statement of (014) and is followed by the omnipresent (025) trichord. The

juxtaposition of (014) and (025) then returns in retrograde in the cello in measure 104.

58

One might also read this passage as a large-scale delay of the D–Bb–C# head motive: D is firmly

established at the beginning of each subphrase (mm. 24, 28, and 46); Bb is continually reiterated in mm. 48–53); and

C# overlaps with the descent of the basic series in mm. 54–56.

59

Ginastera was clearly very fond of the (014) trichord and used it frequently as a primary motive in

several of his compositions. More specifically, in a number of his twelve-tone compositions, Ginastera abandons the

serial organization of the row in order to highlight the (014) motive. See for example the third movement of

Ginastera’s Piano Quintet (1963); an analysis of this piece appears in Michelle Tabor’s article, “Alberto Ginastera’s

Late Instrumental Style,” 5–17.

54

Example 3.5 String Quartet No. 2/I, secondary theme mm. 98–104

In measure 101, the melody gives way to a new motivic gesture, {EBBbF}, which is a

member of set-class (0167).60

The motive is then restated at a different transpositional level in

the viola in mm. 103–104. The (0167) motive is derived from the vertical sonority on the

downbeat of measure 100, in which the last pitch of each (014) trichord aligns to form the

tetrachord [FF#BC]. To accompany the linear presentation of the motive, Ginastera completes

the twelve-tone aggregate by assigning chromatic motivic gestures to each of the other

instruments: the second violin presents the pitches [FF#GAbA], the viola presents the pitches

[CC#DD#E], and the cello chromatically links the F in measure 100 to the A in measure 104

60

The (0167) tetrachord has often been referred to as the “Z-cell,” a term that originated in Bartók

scholarship; see Perle, “Symmetrical Formations in the String Quartets of Béla Bartók,” Music Review 16 (1955):

300–312, and also Treitler, “Harmonic Procedures in the Forth Quartet of Béla Bartók,” Journal of Music Theory 3,

no. 2 (1959): 292–298. The “Z-cell” motive is also pervasive in Ginastera’s music. Malena Kuss has investigated its

role in Ginastera’s twelve-tone opera, Don Rodrigo, and essentially concludes that the tetrachord can be thought of

as an alteration of the familiar trichord, (027): for example, E–A–B–E (027) becomes E–A–Bb–Eb (0167). Kuss

posits a connection between the “folk” (027) trichord derived from the guitar’s open strings and its structural

counterpart (0167) used in dramatic narrative of Don Rodrigo. See Kuss, “Type, Derivation, and Use of Folk Idioms

in Ginastera’s Don Rodrigo,” 176–195; and idem, “The Structural Role of Folk Elements in 20th

-Century Art

Music,” in Transmission and Reception of Musical Culture: Proceedings of the XIVth Congress, International

Musicological Society, edited by Lorenzo Biaconi, F. Alberto Gallo, Angelo Pompilio, and Donatella Restani, 3

(1990): 99–120.

55

with the pitches [GbGAb]. The remaining two pitch classes of the aggregate, B and Bb, are

stated within the first violin’s (0167) motive.61

Furthermore, the boundary pitch classes of the motive, E and F, each correspond to a

boundary pitch of the chromatic pentachords presented by the second violin and viola: the F

forms the lower boundary pitch in the second violin part, and the E forms the upper boundary

pitch in the viola part. These correspondences between pitch events of the motive and its

accompaniment align rhythmically and essentially unfold a voice exchange, which is indicated

by the dotted lines in Example 3.5. This moment coincides with the dramatic climax of the

phrase and further highlights the importance of ic1.

In both the primary and secondary themes of this movement, Ginastera avoids a strict

adherence to the pitch-class ordering of the basic series. Instead, he draws attention to motivic

trichords and tetrachords that are emblematic of his style, and completes the aggregate along the

way, either by transposing these motives to different pitch levels, or by saturating the musical

surface with ic1. These processes, which will be discussed in more detail below, add a certain

amount of expectation and expressivity to this music due to the consistency with which they are

employed and the important structural moments with which they coincide.

The next two examples focus on a movement that is, for the most part, composed

entirely of canonical transformations associated with serial music. Chapter 2 explained that the

scherzo and two reprise sections (A1, A

2, and A

3) of the third movement of the second quartet are

based upon the same basic series (reproduced here as Example 3.6a). The discrete trichords of

this series, (016)(016)(013)(013), are each given a substantial amount of motivic emphasis on the

musical surface; however, another motive receives special attention within the movement’s

61

Interestingly, the next time the (0167) motive recurs, in mm. 107–108, it is transposed so that, with the

two statements of (0167) that appear in Example 3.5, it completes the chromatic aggregate: {EBBbF}, {GbDbCG},

{AbEbDA}.

56

opening. This motive is formed from the (014) trichord that occurs between the order-number

segment <9,10,11> of the basic series.

Example 3.6b reproduces the first statement of the motive, which appears just before the

transition to the first trio (B section) and coincides with a contrast in texture, timbre, and

dynamic marking. Ginastera uses this motive at a conjunctive point between the end of a P0 form

of the row and the corresponding fragment of I0. Following both presentations of the (014)

motive, {GED#} and {FAbA}, the pitch F# fulfills order number 12 in both row forms.

Significantly, F# forms the inversional axis about which the (014) trichords are disposed.

Example 3.6c illustrates how the pitches of the (014) motives form a symmetrical chromatic

wedge, emanating from F#. This symmetry is slightly obscured in the context of Example 3.6b

because the pitches of I0 actually appear an octave lower than illustrated in Example 3.6c.

Example 3.6 String Quartet No. 2/III, scherzo (A1) mm. 32–35

a)

b) c)

57

Example 3.7 reproduces a new motivic gesture that appears within the first reprise (A2) of

the same movement. Here the gesture presents an I11 form of the basic series. Instead of having

each instrument present a discrete trichord of the row, Ginastera actually switches

instrumentation between order numbers 3/4 and 9/10 so that the viola’s trichord overlaps with

the cello’s, and the first violin’s trichord overlaps with the second violin’s. Ginastera’s

manipulation of the basic series within this gesture thus results in explicit emphasis on the

familiar trichords: (025), (016), and (014).

Example 3.7 String Quartet No. 2/III, first reprise (A2) mm. 129–132

The following three examples show further evidence that Ginastera especially favored

(014), (016), and (025) as motives within his principle melodic themes. Example 3.8 reproduces

the first ten measures of the third movement of the first quartet. The movement begins with a

collection of pitch-classes commonly associated with the six open strings of the guitar: E–A–D–

G–B.62

Above this sonority, the first violin presents the primary theme, which spans two octaves

62

This sonority appears in many of Ginastera’s composition, including (to name only a few): Danzas

Argentinas (1937), Malambo (1940), Suite de danzas criollas (1946), Piano Sonata No. 1 (1952), and the

Variaciones concertantes (1957). Gilbert Chase was the first scholar to suggest the Argentine symbolism embodied

by this musical reference; see Chase, “Alberto Ginastera: Argentine Composer,” 449–454. Deborah Schwartz-

Kates’s scholarship delves even deeper into the issue of musical codes in Ginastera’s music and how they relate to

58

from the initial E–F gesture (measure 5) to the final F–E gesture two octaves lower (mm. 8–9).

Despite the 3/4 meter, the contour of the melody suggests two large beats per measure; such a

reading parses each measure into two motivic trichords. As in many of the examples discussed

above, a (014) trichord forms the opening motivic gesture of the theme. The following five

consecutive (016) trichords form the melody’s descent, which closes with a (027) trichord.

Although the primary theme contains several repeated pitches, interestingly Ginastera

supplies every pitch-class of the total chromatic except for one, B. In the discussion of chromatic

completion and composing-out techniques that will follow, a possible reason for the absence of

B will be posited. For now, it is interesting to note that this is the same pitch class that is missing

in the transition section of the first movement (see Example 2.14). Passages such as these

demonstrate how Ginastera’s compositional style was soon to turn toward twelve-tone

composition and the processes of systematic completion of the aggregate.

Example 3.8 String Quartet No. 1/III, primary theme (violin I) mm. 1–10

Argentine nationalism; see Schwartz-Kates, “Alberto Ginastera, Argentine Cultural Construction, and the

Gauchesco Tradition,” 267–275. More recently, Erick Carballo has investigated the structural role the guitar chord

serves in the harmonic dimension of Ginastera’s music; see Carballo, “De la Pampa al Cielo,” chapter 9.

59

Examples 3.9 and 3.10 are taken from the B-section themes of both rondo finales. Both

themes are modally oriented and feature persistent repeated-note figurations. In Example 3.9, the

theme is stated in parallel motion between the first and second violin. Alternating with the

repeated-note gestures are motivic trichords derived from the basic motive: (014), (037), (025),

and (027). The motivic gestures of Example 3.10, however, are far more limited; here, (025)

trichords permeate the melody. More specifically, the theme may be divided into two parallel

parts, consisting of two motives: (025) occupies the beginning of both parts (mm. 36–39 and

mm. 41–42) and (0257) closes both parts (mm. 40 and 43). The restatement of the (025) motive

consists of the same pitch classes as the initial (025), while the (0257) motive is transposed by

T7. This interval of transposition is significant in that it is an integral interval of the motive itself.

Notice, however, that Ginastera disposes the pitches of both motives in a manner that

highlights their near-inversional relationship. The order of pitch events, along with the directed

intervals that relate them, is indicated below both motives. The second motive begins as an exact

intervallic inversion of the first motive, but then diverges in its approach to the final pitch of the

motive. Interestingly, Ginastera also alters the rhythmic pattern of the second motive, so that

measure 43 is a rhythmic retrograde of measure 40.

Example 3.9 String Quartet No. 1/IV, B section theme mm. 47–57

60

Example 3.10 String Quartet No. 2/V, B section theme mm. 36–44

Chromatic Completion / Chromatic Motives

In chapter 2 it was proposed that chromatic completion and the use of chromatic

motives (i.e., (012) and its expansions) are general characteristics of Ginastera’s compositional

style, and that they afforded him a natural transition into twelve-tone composition. As we saw in

Example 2.14, the basic motive of the first quartet is immediately subjected to a series of

transpositions within the first transition section, allowing Ginastera to present every pitch-class

member of the total chromatic in a systematic manner. In a different situation within the second

movement of the second quartet (Example 2.19), we saw how Ginastera abandoned the strict

confines of the basic series in order to emphasize the chromatic motive (0123), which pervades

the melodic material over much of the movement. These two situations—completion of the

aggregate and proliferation of chromatic motives on the musical surface—are often used in

combination, and together they represent a compositional process present in several movements

of Ginastera’s first and second string quartets.

Example 3.11 illustrates a particularly overt manifestation of chromatic completion

within the middle B section of the third movement of the first quartet. In this section the viola

presents the theme, which consists of a chromatic octave descent between the B that begins the

61

phrase and the same pitch-class on which it cadences in measure 59.63

All twelve pitch classes

are present and unfold mostly as a string of descending semitones.

More importantly, the theme in Example 3.11 makes compositionally explicit an idea that

was only suggested in the theme of the previous A section. Recall that in Example 3.8, the first

violin presented the theme of the A section, which consisted primarily of (016) trichordal

motives connecting the initial E with its recurrence two octaves lower. The continual

transposition of this motive resulted in a completion of the total chromatic except for one pitch

class: B. Not only is the theme of the B section explicitly chromatic, but the total chromatic that

it serves to complete is initiated by the one pitch class missing from the theme of the A section.

Example 3.11 String Quartet No. 1/III, B section theme mm. 52–59

Chromatic completion and chromatic proliferation are fundamental compositional

processes operative throughout the entire second movement of the first quartet. Literally every

section of this sonata rondo, including the transition sections, features these processes in some

fashion. The theme of the A section is reproduced in Example 3.12; it begins with a

characteristic pedal on D, which is interjected several times by the familiar (0257) motivic

tetrachord in mm. 2–5. In the following two measures, a (025) motive is passed across all four

instruments so that each subsequent statement of the motive is T6 higher than the previous

statement. Then in mm. 7–8 the (025) motive is replaced by pizzicato (027) trichords and each

63

Significantly, the theme is framed by the motion B–Bb at the beginning and the retrograde motion A#–B

at the end. This motivic correspondence is analogous to the one found in the theme of the A section, where the first

violin’s solo begins E–F and ends two octaves lower with F–E (see Example 3.8).

62

instrument contributes to the unfolding of a complete circle of fifths (an ic5 cycle). The complete

series of ic5s introduces every member of the total chromatic before returning to the pedal D in

measure 9.

Example 3.12 String Quartet No. 1/II, A section theme mm. 1–9

The theme of the B section that follows also features a systematic completion of the

aggregate, as shown in Example 3.13. This theme is presented by the first violin and is slightly

varied by the second violin’s simultaneous elaboration of the same theme. The theme is made up

of two gestures: a chromatic ascent in mm. 27–30 and a cadential descent in mm. 31–32. The

cadential gesture is consistent with other cadences in the first quartet in that it is comprised of

(025) and (027) motivic trichords. This gesture may be divided into two parts that are related by

T6: the first half begins with A and the second half begins with Eb.

The first four measures of the theme exemplify the compositional process of chromatic

completion: the chromatic hexachord spanning A to D in the first two measures is repeated at T6

(D#–Ab) in the following two measures. The lower boundary pitch classes of both hexachords

correspond to the initiating pitches of the cadential gesture and its repetition in measures 31 and

63

32. Emphasis on the tritone, here created by the T6 relations within both gestures, is thus an

integral part of both the A and B sections of this movement.

Example 3.13 String Quartet No. 1/II, B section theme mm. 27–32

The following two examples illustrate one of the most important functions of chromatic

motives in both quartets: to transition between larger contrasting sections within a movement.

Specifically, Ginastera uses chromatic motives (e.g., (012) and (0123)) as the basis of material

within short transition sections; the result of this technique forms transition sections that are

melodically static in comparison to the material of surrounding larger sections. Despite the

restricted number of materials Ginastera uses within these transitions, significant dynamic

processes and motivic associations are still operative on larger levels of the music’s structure.

Example 3.14 represents the transition section that links the first A and B sections of the

sonata rondo. The viola and the cello continue to repeat the characteristic D pedal of the A

section, while the first and second violin introduce a transitional motive based on the chromatic

tetrachord (0123). This motive results from the violins’ presentation of whole-tone dyads that are

related by semitone. As the instruments alternate with one another, moving by whole step, the

harmonic tetrachords move by T1. The motive ascends by a large-scale T2, only to descend by

T-2 back to the initial tetrachord. The general effect of this passage is a sense that the semitone

(or ic1) and the whole-tone (or ic2) are in conflict with one another. The tension caused by this

64

conflict is reflected on a deeper level between the respective themes of the A and B sections: the

thematic material of the A section (shown in Example 3.12) exclusively features (0257) and its

subsets (025) and (027), all of which prominently feature ic2; contrastingly the thematic material

of the B section (shown in Example 3.13) primarily features the chromatic hexachord (012345).

Thus, the transition section in Example 3.14 introduces, on a local level, the larger-scale

dramatic tension that unfolds between the surrounding sections.

Example 3.14 String Quartet No. 1/II, transition material mm. 11–14

Chromatic motives functioning within transition sections can also be found in the

second quartet. Example 3.15 reproduces the first transition section that follows the basic series

in the first movement. In this passage, two motives are repeated above a G pedal sustained in all

four instruments. The first motive, (012) emphasizes the semitone upper and lower neighbor of

the pedal: Ab and F#. The second motive, (016) emphasizes ic6 along with ic1; ic6 (sometimes

manifested as T6) is an interval commonly associated with chromatic processes in Ginastera’s

music (see Examples 3.12 and 3.13, and the discussion of Example 3.16 below). These two

motives also form a strong motivic association with the basic series: in Example 2.18

65

(reproduced as Example 3.4b) we saw how Ginastera subtly manipulates the basic series to place

emphasis on both (012) and (016). The transition section shown here follows the basic series and

consequently reemphasizes the same motivic ideas.

Example 3.15 String Quartet No. 2/I, transition material mm. 5–16

Example 3.16 provides an instance of proliferation of chromatic motives and the

completion of the chromatic aggregate working as complementary forces within the same section

of music. The A-section theme of the second quartet’s final movement consists of a neighboring

chromatic motion around an F# pedal, as in the previous example.64

In mm. 7–8 the neighboring

motion centers on A#. This motion results in multiple recurrences of the harmonic motive (012).

Both (012) trichords also appear as melodic diminutions echoed by each of the instruments; the

boxes in measures 5 and 9 indicate examples of such motives.

64

The cello in this passage plays only one note: F# in measure 3. When the theme returns in measure 15,

however, the cello begins a new motivic idea which conveys a sense of a “battle” between (0167) and (0257), or the

perfect fifth and tritone. Intriguingly, the perfect fifth triumphs over the tritone within the local melodic and

harmonic realms, yet the tritone continues to reappear in the form of T6 transformations relating events on a larger

scale.

66

Chromatic completion is achieved by the systematic transposition of new motives

beginning in measure 11. Here the viola continues the neighbor motive, this time limiting the

motion to an upper semitonal neighbor only; simultaneously the first and second violins repeat

their own tetrachordal motives. The continual transposition of all three motives by T1 in mm.

11–12 resembles the process discussed in Example 3.14 above; notice in particular that the

motive of the first violin consists of descending whole-steps, which significantly contrasts with

the semitone motive of the viola and the T1 interval of transposition. The total chromatic slowly

unfolds as each beat presents a chromatically saturated tritone (or ic6) interval formed by the

boundary pitches of each motive in the first violin. For example, the first beat of measure 11

consists of the pitches E–F–F#–G–G#–A–A#(Bb); the second and third beats chromatically fill

in the ic6 intervals, F–B(Cb) and Gb(F#)–C respectively. The pattern continues until the third

beat of measure 12, when all twelve pitches have been stated.

Example 3.16 String Quartet No. 2/V, A section theme mm. 1–13

67

The Process and Function of Symmetry

Symmetry plays an important role in several of Ginastera’s compositions and has been

discussed by multiple authors.65

However, symmetry is often a natural byproduct of the motivic

collections Ginastera favors, particularly (0257) and (0167). The focus of this discussion is,

therefore, not to present every instance of symmetrical construction in these two quartets—to be

sure, the sheer number of examples would be quite astounding—but rather to illuminate (1) some

of the most common compositional processes that result in symmetry and (2) the most common

formal junctures where symmetry occurs.

Compositional processes that result in symmetry in Ginastera’s music have already

been mentioned to some extent in earlier examples. The most common processes include

inversional wedge motion and chromatic saturation. The formal junctures involved are almost

exclusively transition sections and prominent cadences. Examples of wedge motion were first

discussed in Example 2.14 and Example 3.6. In the first example, the basic motive was repeated

simultaneously with its inversional presentation; this wedge motion climaxed with the first

violin’s G#, resulting in a completion of the chromatic aggregate. A new dimension of symmetry

was then formed by the first violin’s descent from the G# axis. In Example 3.6, the chromatic

wedge motion resulted from the convergence of two inversionally related (014) motives. The

following examples explore other particularly striking uses of symmetry in both quartets.

Example 3.17 illustrates symmetry within the third movement of the first quartet; a

chromatic wedge is formed between the first violin and cello in mm. 82–86 and marks the

transition back to the return of the large A section (see the return of the theme in measure 88).

65

Erick Carballo has recently revisited the topic of symmetry in Ginastera’s music, using as his point of

departure the symmetrical properties of the twelve-tone row appearing in the second movement of the Piano Sonata

No. 1 (1952); see his “De la Pampa al Cielo,” chapter 9. Grace Campbell also focuses on symmetry as a central

topic in her dissertation, “Evolution, Symmetrization, and Synthesis: The Piano Sonatas of Alberto Ginastera,”

(D.M.A. diss., University of North Texas, 1991); see especially the discussion on pp. 16–34.

68

Throughout this transitional passage, the second violin, viola, and highest pitch of the cello

sustain a cadence on the (016) trichord—a significant motive of the primary theme (see Example

3.8). Notice that the wedge motion appears at a slightly louder dynamic level above this sonority.

The symmetrical motion is brief yet strategically placed at a moment that highlights the juncture

of contrasting formal sections.

Example 3.17 String Quartet No. 1/III, transition to the return of the A section (mm. 82–90)

Example 3.18 resembles Example 3.6, also from the same movement, in that both

feature a tremolo chromatic wedge motion around a central sustained pitch. The symmetrical

wedge in Example 3.18, however, is not technically a part of the scherzo section as it is in

Example 3.6, but rather represents the retransition to final reprise of the scherzo. Notice that the

same pitch class, F# marks the first symmetrical axis (see Example 3.18b). In the retransition, the

chromatic wedge motion is then repeated around Bb in mm. 213–215. This repetition, followed

by the arrival of a pedal on D in measure 16, actually completes the chromatic aggregate and

marks the end the second trio, which characteristically rejected a strict ordering of the basic

series from its beginning.

69

Example 3.18 String Quartet No. 2/III, retransition to the second reprise (A3) mm. 212–216

a)

b)

The following two examples reproduce the final cadences of the first and third

movements of the first quartet.66

Neither example involves symmetrical wedge motion; instead,

both cadences begin with a harmonic sonority that is symmetrically disposed in pitch space.

Moreover, both cadences have two important characteristics in common. The first commonality

involves the resolution of the symmetrical sonority: in both movements, the “dissonant”

symmetrical chord is resolved to a sonority that is contextually “consonant” within the

movement—here, (027) and the so-called “guitar chord.” The second commonality between

these two cadences involves their shared axis of symmetry.

66

A “near-symmetrical” cadence ends the second movement of second quartet (mm. 64–66) as well. Here

the symmetrical chord consists of the chromatic heptachord, [ABbBCDbDEb], and the intervals are disposed around

a central interval 6. From the bottom to top of the chord, the following intervals are projected in pitch space: <11, 8,

3, 6, 3, 11>. Only the “extra” interval 8 upsets the symmetrical construction of the chord.

70

Example 3.19a reproduces that final cadence of the first movement and Example 3.19b

condenses the symmetrical chord to a single staff in order to illustrate more clearly the disposal

of intervals in pitch space.67

The axis of symmetry, while not literally present in the music,

centers on the pitches C#/D. Interestingly, the same pitch classes function as the central dyad-

axis about which the pitches of the third movement’s final cadence are disposed (see Example

3.20a). Example 3.20b reproduces this cadence in order to show how the collection of interval-

11 gestures result in the chromatic pentachord E–D#–D–C#–C–B. Notice in Example 3.20a that

the boundary pitches, E2 in the cello and B6 in the first violin, are sustained while the

symmetrical sonority resolves to the “consonant” guitar collection that began the movement.

Example 3.19 String Quartet No. 1/I, final cadence mm. 224–229

a) b)

67

It is especially interesting that the pitch G# is given such registral prominence in the first violin (mm.

224–226): this pitch has been associated with symmetrical design since the very beginning of the movement (refer

back to the discussion of Example 2.12 and 2.14). Notice also that the cello’s resolution of G to D harks back to the

introduction of the basic motive (mm. 1-5), when the cello emphasized the reverse motion, D–G.

71

Example 3.20 String Quartet No. 1/III, final cadence mm. 107–113

a) b)

Examples 3.21 and 3.22 illustrate a particularly interesting correspondence between the

symmetrical construction of the opening chord in the first movement of second quartet and the

beginning of the secondary theme within the same movement. Example 3.21a reproduces the

introduction of the movement, which features the unison presentation of the basic series. A

conspicuous, dynamically accented chord appears doubled in the viola and cello in measure 3,

and its pitch-space symmetrical construction is shown in Example 3.21b. Example 3.21c has

omitted the doubled pitches to show how the chord essentially consists of a central tritone

interval (G#–D) flanked by two perfect fifths (C#–G# and D–A).68

The interval content of the opening chord may be thought of as a collection of

transformations (i.e., transpositional operations); thus, Example 3.21c illustrates the symmetrical

structure of the chord as T7–T6–T7. An analogous symmetrical design also shapes the opening

gesture of the secondary theme, shown in Example 3.22. This theme, which begins with imitative

entrances of the prominent (014) motive, culminates in the symmetrical chord appearing on the

68

This tetrachord is a member of set-class (0156).

72

downbeat of measure 100.69

The transpositional operations that relate each motive, and

subsequently each member of chord, are the same as those shown in Example 3.21c. Notice,

however, the T7 and T6 operations are exactly opposite in Example 3.22, so that the secondary

theme is symmetrical around a central T7 (the perfect fifth B–F#).

Example 3.21 String Quartet No. 2/I, introduction mm. 1–5

a) b)

c)

Example 3.22 String Quartet No. 2/I, secondary theme mm. 98–100

69

This tetrachord is a member of set-class (0167). As was shown in Example 3.5, the continuation of the

secondary theme introduces (0167) as a prominent melodic motive, which is subjected to a deeper-level voice

exchange.

73

CHAPTER 4:

COMPOSING-OUT TECHNIQUES

The examples presented in this chapter will focus exclusively on a deeper-level

compositional process known as composing-out or enlargement. This process refers to the

projection of motivic or intervallic events over larger spans of music. Various techniques of

composing-out, which will be discussed in detail below, can be found in Ginastera’s string

quartets, where they to produce motivic associations over considerable spans of music.

Consequently, non-adjacent pitch events are found to relate to one another in coherent and

compelling ways, forming associations that are operative on deeper structural levels.

Before we begin exploring techniques of composing-out in Ginastera’s string quartets, a

few comments concerning the general nature of composing-out will be helpful. Composing-out

and the related concept of enlargement are typically associated with Schenkerian analysis.70

As

such, they are concepts most frequently invoked in tonal analysis, where they function as

techniques of prolongation. Brian Alegant and Donald McLean have specified two qualities that

need to be assessed in order to justify analytically a case for enlargement; these qualities involve

what they call “match” and “fit.” “Match” concerns whether or not “an object and its

enlargement share a definable sameness,” while “fit” concerns how “the object and its

enlargement lie within—or cut across—prolongational strata and formal boundaries.”71

Alegant

and McLean have demonstrated that enlargement processes are also possible in post-tonal music;

70

Composing-out (Auskomponierung), enlargement (Vergrößerung), and the related concealed repetition

(verborgene Wiederholung), are all discussed in Heinrich Schenker’s later writings and especially his Free

Composition; see Schenker, Free Composition, edited and translated by Ernst Oster (New York: Longman, 1979).

Other related techniques referred to by Schenker include compression (Verkleinerung) and linkage technique

(Knüpftechnik). For a more formal discussion of these and other Schenkerian concepts, see also Charles Burkhart,

“Schenker’s ‘Motivic Parallelisms,’” Journal of Music Theory 22 (1978): 145–175.

71

Brian Alegant and Donald McLean, “On the Nature of Enlargement,” Journal of Music Theory 45, no. 1

(2001), 32–33.

74

however, they admit that “fit” no longer serves as a necessary requirement for enlargement,

given that prolongational strata no longer exist. In no sense does the present study assume

prolongation to be an operative force in Ginastera’s music; all deeper-level events acquire status

in this music based solely on shared motivic correspondences.72

Indeed the relationships

discussed here should be considered associational and not prolongational (as per the discussion

in chapter 1).73

Other authors have also discussed techniques of composing-out in post-tonal repertoires.

Among them, Joseph Straus has described eight procedures for composing-out motives in post-

tonal music; some of these procedures occur very near the surface of the music and some occur

on much deeper structural levels.74

This study will invoke three of Straus’s composing-out

procedures that are operative in Ginastera’s music. They will be presented from nearer to the

surface to further from the surface(i.e., from least abstract to most abstract). Using Straus’s

terminology, the three types will include: (1) “melodic frame,” (2) “register,” and (3)

“transpositional projection.” Some minor extensions to Straus’s definitions will be necessary to

account for a few of the examples, but generally speaking, the broad characteristics of each type

will remain unaltered. To conclude, this analysis will propose a different form of composing-out,

which will be called the associational pathway. The associational pathway is a type of

72

The reasons for such a stance are thoroughly explained in Joseph Straus’s “The Problem of Prolongation

in Post-Tonal Music,” Journal of Music Theory 31, no. 1 (1987): 1–22. However, it should be noted that the recent

scholarship of Erick Carballo has sought to find grounds for prolongation in Ginastera’s music; see Carballo, “De la

Pampa al Cielo,” chapters 6–8. The focus of the present study is less concerned with harmonic entities as it is with

motivic associations; as such the analytical approach differs a great deal from Carballo’s.

73

In chapter 8 of his dissertation, Carballo develops an analytical system that combines models of

prolongation and association in Ginastera’s music. Ultimately, the author concludes that “understanding a work’s

associational units as well as their correlation (or lack of correlation) to the prolongational structure illuminates that

work much better than either one of the methods could have done independently.” See Carballo, “De la Pampa al

Cielo,” 240.

74

Joseph N. Straus, “Atonal Composing-Out,” in Order and Disorder: Music-Theoretical Strategies in

20th

-Century Music (Leuven University Press, 2004), 31-51.

75

composing-out that does not so much project a motivic idea as it follows a unique characteristic

of a motive as it travels and is transformed across a significant portion of the music.

Melodic Frame

Straus’s discussion of the melodic frame states that “a succession of notes or intervals is

composed-out within a melodic frame [if it is] comprised of the first, last, highest, and lowest

notes [of the melody].”75

Example 4.1 reproduces the opening theme of the theme-and-variation

fourth movement of the second quartet. The succession of notes, which includes the first, last,

highest, and lowest pitches, collectively forms a (016) trichord. The first and last pitch in this

case is G, which is reiterated twice as the melody descends to the lowest pitch, D. Notice how

Ginastera juxtaposes the highest and lowest members of the melodic frame (D–C#) so as to

emphasize their relation to one another; this striking juxtaposition, coupled with the repetition of

G, contributes to the relative explicitness of this particular composing-out process.

Example 4.1 String Quartet No. 2/IV, theme mm. 1–4

Example 4.2 requires an extension to Straus’s original definition of the melodic frame.

Instead of considering the first, last, highest, and lowest pitches of the opening of the second

quartet, here we will consider the first, last, and longest pitches (a different yet equally viable

measure of prominence). Given that the lowest pitch is also the last pitch in this example, our

75

Straus, “Atonal Composing-Out,” 41.

76

reading does not entirely change the nature of the melodic frame, although it does change the

motive we interpret as being composed-out.

In Straus’s terms, the melodic frame composes out a G-minor triad, or (037); however,

there are two reasons for choosing instead (016) as the composed-out motive. In the first place,

(016) is a far more important motive in the movement than (037): (016) appears twice as a

surface-level motive in the movement’s introduction alone, due to Ginastera’s manipulation of

the basic series (see Examples 2.17 and 2.18). Furthermore, if (016) is interpreted as the deeper-

level motive, a striking relationship between the first and fourth movements is unveiled. Not only

do both Examples 4.1 and 4.2 compose-out a (016) motive, they literally compose-out the same

(016) motive: D–C#–G. The uniformity of pitch classes and the type of composing-out procedure

(i.e., the melodic frame) operative in both movements is surely more than coincidental;

nevertheless, this compositional process results in a compelling motivic association that adds a

new dimension to the idea of coherence in this music.

Example 4.2 String Quartet No. 2/I, Introduction mm. 1–5

Register

According to Straus’s types of composing-out procedures, register alone may play an

integral role in the projection of a temporally expanded motive. More specifically, he states that

“a succession of notes or intervals is composed-out within a single registral line, often the

77

bass.”76

This is precisely the composing-out process that unfolds across formal boundaries and

often traverses entire movements within Ginastera’s quartets. In most cases, the registral line that

carries the associative power is accentuated by a pedal point or an ostinato pattern.77

Example 4.3a illustrates the composing-out process that takes place in the second

movement of the first quartet. D is an emphatic pedal point throughout much of the movement,

appearing within all the refrain (or A) sections (see Examples 3.12 and 3.14) and also the third

statement of the B section; significantly, D is the lowest pitch in each of these sections as well

(not considering the fleeting grace-note C that precedes it in mm. 9 and 209). Without a doubt, D

functions as the centric pitch class of most of the movement.

The first two B sections present their own theme based on the chromatic hexachord

(012345) (see Example 3.13), but the D pedal is not present. Because the B theme features a

completion of the total chromatic by semitonal ascent, the temporary pitch-class center within

these sections is determined by the initiating (i.e., lowest) and terminal (i.e., highest) pitches of

the chromatic theme. The chromatic ascent A–A in the first B section, is transposed by T6 in the

second B section to form the chromatic ascent Eb–Eb.

As is shown in Example 4.3a, the ubiquitous (016) motive is composed-out through the

lowest registral line of the first half of the rondo form. The importance of ic1 and ic6 in this

movement was already discussed in chapter 3, and now we can see the magnitude of influence

surface-level events might have on the organization of deeper structural events via the process of

composing-out.

76

Straus, “Atonal Composing-Out,” 36.

77

The present analysis is particularly indebted to Straus’s discussion of registral lines in the music of

Stravinsky. Although the present study does not invoke Straus’s concept of “pattern-completion,” it does borrow

many of the author’s ideas concerning the organization of large-scale harmonic structure in pitch-centric music. See

Straus, “A Principle of Voice Leading in the Music of Stravinsky,” Music Theory Spectrum 4 (1982): 106–124.

78

The pedal point returns in the developmental C section, where it progresses from F# to

D#. There are several viable interpretations of how this affects the large-scale composing-out of

motivic events. If we consider the D# pedal to be an enharmonic reiteration of the B2 section’s

Eb, and take the F# to be the more prominent pitch-class center of the C section, then perhaps the

composing-out of the major third D–F# (in reference to D major) could be seen as the operative

enlargement process; this interpretation is supported by the A-centered B1 section. The D-major

triad is, after all, a prominent component of the original basic motive. The (014) trichord, here

created by the pitches D–F#–D#, is also a prominent subset of the basic motive and perhaps

would explain Ginastera’s reason for using two other pedal points in addition to D in this

movement. Furthermore, chapter 2 first explained how the basic motive is explicitly repeated and

extended in this movement to include D# as the highest pitch of the (014) trichordal chain,

thereby increasing the trichord’s prominent role in the movement (see Example 4.3b).

Example 4.3 String Quartet No. 1/II, (a) pedal points coinciding with large-scale form; (b)

return of the basic motive

a)

b)

201

79

The following example demonstrates how the composing-out of motivic events also

occurs in Ginastera’s serial language. Example 4.4a illustrates the organization of the registral

bass line over the entire third movement of the second quartet. The key to the formation of this

line is based on Ginastera’s use of twelve-tone regions, that is, collections of row forms sharing

the same index number, or boundary pitch class (e.g., P0, I0, R0, RI0) .78

The first and last

reprises (sections A1 and A

3) feature the same twelve-tone region, sharing the boundary pitch C

(or pitch-class 0), which is repeatedly emphasized as the lowest pitch in the cello part. The

second reprise (section A2), however, features an amalgamation of two twelve-tone regions:

“11” and “5.” All the row forms present in this section—I11, P11, R11, RI11, R5, RI5—share

the same two boundary pitch-classes: B (pc 11) and F (pc 5), which are emphasized as lengthy

pedal points in the cello part.

The registrally emphasized boundary pitches of these three twelve-tone regions

compose-out a large-scale (016) motive, which establishes a deeper connection between the three

reprise sections. The pitch classes forming this motive are also significant because they

correspond with the first three pitches of the original basic series, P0 (reproduced as Example

4.4b). Not only does (016) pervade the musical surface, but it also becomes part of the

movement’s background structure.

78

Alegant and McLean have identified the organization of twelve-tone regions in Schoenberg’s music as a

special type of enlargement; see their article, “On the Nature of Enlargement,” 47–49. See also Andrew Mead,

“Large-Scale Strategy in Arnold Schoenberg’s Twelve-Tone Music,” Perspectives of New Music 24, no. 1 (1985):

120–157; and Mead, “Twelve-Tone Organizational Strategies: An Analytical Sampler,” Intégral 3 (1989): 93–169.

80

Example 4.4 String Quartet No. 2/III, (a) twelve-tone regions and pedal points; (b) basic

series

a)

b)

Transpositional Projection

The last composing-out technique Straus discusses is based on a procedure he calls

“transpositional projection.” He describes this procedure as a “particularly rich compositional

resource [in which] a motive is composed-out by being projected along a transpositional path . . .

[formed by] the intervals it contains.”79

In Ginastera’s string quartets, the transpositional path

often projects a crucial interval belonging to a prominent motive, as in the opening of the first

quartet’s final movement, shown in Example 4.5. Here the transposition of the theme by T7 is a

reflection of the opening motive (027), which is formed by the oscillation of two perfect fifths

(interval 7) around the central pitch G in mm. 1–2 and 4–5. When the motive recurs in measure 7

the local projection of interval 7 is now formed around the central pitch D. The larger collection,

(0257) is formed when the C–G dyad returns in measure 8. The transpositional path thus

confirms that the perfect fifth formed by G–D is acting as an axis of symmetry about which A

and C are disposed.

79

Straus, “Atonal Composing Out,” 45–46.

81

Example 4.5 String Quartet No. 1/IV, A section theme mm. 1–10

The previous example is about as close to the surface as the technique of transpositional

projection will appear. Sometimes the composing-out process is far more abstract, forming a

connection between the recurrences of a single musical event throughout a work. The following

example will illustrate how an accompanimental motive in the first movement of the first quartet

traces the same transpositional (or transformational) path as an integral motive of the source

collection from which it is derived. The composing-out of these identical paths results in a

strongly isographic80

relationship between the intervallic structure of the local event and the

transpositional path of the derived event; this relationship is confirmed by the one-to-one

mapping of transformations between the respective graphs (i.e., the node/arrow systems) of both

events.

Example 4.6a reproduces the derivation of (025) and (0257) from the basic motive as it

appears in the introduction of the first quartet. The following are issues to recall from the

discussion in chapter 2: (025) is formed by the rhythmically accentuated pitches D–F–C, and

(0257) is formed from the combination of (025) and (027)—that latter is formed by the boundary

80

Isography is a concept borrowed from mathematical group theory, which in recent years has been

eloquently and beneficially adapted to musical analysis by David Lewin and his proponents. A formal definition of

isography and an explanation as to how it relates to Lewin’s “transformation network” is offered in Lewin’s book,

Generalized Musical Intervals and Transformations, 198–199.

82

pitches of the basic motive and its subsequent transposition. Both (025) and (0257) have proven

to be very significant motivic collections in the string quartets.

In the first movement of the first quartet, (0257) forms the characteristic

accompanimental motive of the primary theme. Example 4.6b reproduces the first appearance of

the theme in the exposition (measure 16), its return in the recapitulation (mm. 165–166), and the

final (025) cadence of the theme in the recapitulation (mm. 195–196). The (0257) motive

consistently appears as a pedal point in each excerpt, as the boxes in the example indicate. The

transpositional path of this motive, T3 followed by T7, is shown below the example and is

identical to the series of transformations that form (025) in Example 4.6a.

Example 4.6c shows the identical paths of (025) and (0257) in the form of two

transformational networks, which are strongly isographic with one another. The projection of

(0257) across the movement actually follows a transpositional path formed by the intervals

contained in (025), the integral subset of the basic motive. Composing-out in this context helps to

elucidate a connection—albeit in a more abstract sense—between the internal structure of a local

motivic event and the structure of a large-scale progression of motivic events.

83

Example 4.6 String Quartet No.1/I, strong isography between (025) and the path of (0257)

a)

b)

[ABDE] [CDFG] [GACD]

T3 T7

T10

c)

(025)

84

The Associational Pathway

Straus’s categories of composing-out processes provide useful analytical models that

explain deeper-level motivic associations, which might at first be overlooked in Ginastera’s

music. Even so, a number of other meaningful large-scale musical relations and associations,

which do not necessarily constitute motivic composings-out, abound in this music. The present

study invokes the associational pathway, which essentially traces a musical narrative as it

develops and transforms over the course of a section or entire movement. Musical events often

have logical consequences that are realized in the series of events that follow, collectively

forming an associational pathway. As mentioned in chapter 1, this concept is analogous to

Schoenberg’s musical idea (and even his notion of the Grundgestalt) in that the opening gestures

of a work typically instill within the music a vital and motivating sense of unrest, with which the

composer must grapple musically and overcome compositionally. To put it another way, the

music begins with an idea (or gestalt) that struggles to develop and realize all of its inherent

consequences as it seeks a state of rest.81

The following two analyses seek to illuminate the

concept of the associational pathway and reflect upon the motivational force behind it.

Chapters 2 and 3 discussed the large-scale form and motivic pitch structure of the first

quartet’s third movement. This lyrical slow movement exhibits a ternary form in which the outer

A sections contrast thematically with the central B section. The movement begins and ends with

the “guitar chord” represented by the pitches E–A–D–G–B–E. In the previous two movements of

this quartet, (0257) was the most prevalent harmonic sonority; in this movement the opening

gesture begins with (0257), E–A–D–G, but then B is added to the sonority, cutting off the

accumulation of perfect fourths. The arrival of B not only completes the “guitar chord,” but also

81

See Schoenberg’s explanation of this process in The Musical Idea, 161.

85

initiates the associational pathway, which traces this single pitch class as it recurs at important

moments throughout the movement.

Example 4.7a represents a reduction of the initial A and B sections. The guitar

collection opens the movement and in measure 5 the first violin begins the solo theme. Recall

that this theme consists of a series of transpositionally related (016) motives, which span two

octaves, E–E, and gradually complete the chromatic aggregate—except for B (see Example 3.8).

The end of the solo theme is accompanied by a T7 transposition of the guitar collection. The

interval of transposition is suggestive of the intervallic structure of the guitar collection itself;

furthermore, T7 is later reemphasized by a partial ic5 cycle (or circle of fifths) that begins in

measure 35. Notice that the first four pitches of the cycle imitate the pitch classes of the opening

guitar gesture, E–A–D–G; however, B is again omitted and this time is replaced by C.

The momentum of the ic5 cycle culminates in a sonority that begins in measure 37 and

is held through the end of the A section (notice the fermata in the example). Below this sonority,

the cello restates the beginning of the primary theme. More important to the associational

pathway is the cadential sonority, which is sustained for ten measures. This sonority is

symmetrically disposed in pitch space, with an axis centered on B. The journey of B does not

end here; the reader will recall that the viola’s theme in the following B section forms a

chromatic line spanning the octave B–B (see Example 3.11). The important pitch returns for the

last time at the close of the movement, reproduced here as Example 4.7b. The chromatic

pentachord, E–D#–D–C#–C–B, ultimately resolves to a restatement of the guitar collection,

while B is held continuously in the highest register.

The associational pathway presented here traces the journey of a single pitch-class as it

curiously disappears and conspicuously reappears throughout the movement. This is by no

86

means the only associational pathway that unfolds in this movement; there are undoubtedly

several. The present analysis seeks to find deeper meaning in Ginastera’s use of the guitar

collection as the opening gesture of the movement. Does the “extra” pitch B provide the impetus

for the unraveling of events that follow? Perhaps Ginastera is attempting to evoke a “tonic-

dominant” relation between E and B? Either interpretation senses an underlying tension present

between B and its surroundings; this tension forms a dynamic pathway, which in this case leads

us full circle to a return of the source—the guitar collection.

Example 4.7 String Quartet No. 1/III, associational pathway of pitch-class B

a)

b)

87

The slow movement of the second quartet also suggests a particularly intriguing

associational pathway, which will be discussed below in conceptually different levels of

abstraction. Chapter 2 discussed the ternary form of this movement: the framing A sections are

based on a single basic series and the central B section breaks away from the constraints of the

row and introduces new (non-serial) material. The reader will recall that the primary motive of

this movement is based on the order-number segment <1,6,7,12> of the basic series, which

forms the chromatic tetrachord (0123). Example 4.8a reproduces the viola solo that opens the

movement; the chromatic motive first appears extended by two semitones in mm. 4–7, beginning

with order numbers <7,12> of P3 and continuing with <1,6,7,12> of P7, F–E–G–F#–A–G#. The

chromatic motive permeates the melodic material of both A sections and occurs at several

different transpositional levels, depending on the transposition of the basic series. (Note that

when the chromatic motive is presented, the other instruments simultaneously present the

remaining pitch classes of the row as a chordal backdrop.)

The associational pathway of this movement creates meaningful relationships among

the different forms of the basic series. Furthermore, the order in which row forms are presented

in this movement is, at specific points, foreshadowed by pitch events on the musical foreground.

The opening solo (shown in Example 4.8a) begins the associational pathway and is an impetus

for the events that follow. The solo begins with a presentation of P3, but pauses on order number

4, pitch-class G. As the G is the sustained, the accompaniment repeats a single chord four times;

however, the pitches of this chord do not correspond with the next order-number segment of P3.

A feeling of unrest is thus initiated by this incongruous chordal gesture at the beginning of the

movement, as its composite pitches actually prefigure the series form that follows.

88

After a momentary pause, the melody picks up again in measure 3 and this time continues

with the remaining pitches of P3. When the chromatic motive ascends to G in measure 5, the

basic series is transposed to P7. While this G is also sustained, the accompanying chord from

measure 2 returns. This time the chord is not “out of place”; in fact, the pitches provide order

numbers <2,3,4,5> of P7. Thus, the sense of unrest caused by the initial pause on pitch-class G

(i.e., pc7) and the appearance of the “wrong” accompanimental chord in measure 2, points

toward the arrival of P7 in measure 5.

Another break in the melody occupies all of measure 8. In the following measure the

melody is then transferred to the cello, where a complete statement of P9 is realized. Why is P9

the next row form? Like P7, P9 is also prefigured by an earlier event: pitch-class A (i.e., pc9) in

mm. 6–7 marks the climax of the chromatic motive and the entire melody (notice that it is

longest and the loudest pitch of the melody). In retrospect, we recognize that Ginastera provided

a number of clues that suggest the sequence of events to follow. Ultimately these clues create the

associational pathway and help us intuit the musical surface.

Example 4.8b illustrates a more abstract version of the associational pathway as it

appears across the entire movement. The ABA formal design is indicated above the example

(keep in mind that the B section contains non-serial material). T2 (or T-2) is by far the most

common transformation among row forms. The reader will recall from the discussion in chapter

2 (refer to Example 2.19) that the T6 transformation between rows P3 and P9 in the first A

section was also foreshadowed by an earlier motivic event: the cello’s pizzicato motive A–Eb.

As the T6 transformation is realized from P3 to P9, a more immediate T2 transformation is

realized between P7 and P9. In the imitative entrances of instrument pairs that follows in the A

section, the T2 transformation is utilized further, now as T-2. The first and second violin reverse

89

the previous transformation by presenting P9 P7; immediately thereafter, the viola and cello

present a second T-2 transformation between P0 P10.

Let us now observe the associational pathway as its different levels of abstraction, shown

in Examples 4.8a and 4.8b, interact. Although the B section consists of contrasting material, the

chromatic motive of the A section conspicuously returns in the middle of the B section, forming

the loudest, most dramatic moment of the entire movement. The motive (which is reproduced in

Example 4.8b) consists of the same pitch classes as the original chromatic motive in mm. 5–6,

G–F#–A–G#; however, it does not appear alongside any of the other members of P7 from which

it is derived. Additionally, the motive is extended to include pitch-class B. The sequence of

ascending pitches, G–A–B, will prove to be of great consequence to the events that later unfold

in the return of the A section.

The second A section features the same thematic material as the first A section, but does

not present the same row forms. Pitch-class B in measure 34 of the B section, which marks the

climax of the movement, is now reinterpreted as the initiating pitch of P11 in the A section’s

return. Toward the end of the movement the P7 P9 gesture is repeated, balancing the close of

this section with that of the first A section. Immediately before the return of P7, the chromatic

motive returns for the last time (see Example 4.8c) and marks the only instance in which the

motive appears in retrograde form. Interestingly, this permutation of the motive allows for a

retrograde descent of the same pitch classes appearing in the B section, B–A–G.

In sum, the associational pathway of this movement is formed by a series of subtle, yet

telling, pitch events. These events often stem from the primary motive of the movement (i.e., the

chromatic tetrachord) and relate to subsequent transformations of the basic series in significant

ways. Generally speaking, the associational pathway sheds light on events that may elude us in

90

our initial experience with a work. For example, ic1 pervades the motivic surface of second

quartet’s second movement, but ic2 (in the form of T2/T-2) determines the movement’s larger-

scale organization. A host of other relationships exist within this music; nevertheless, the

associational pathway is a valuable way of focusing our attention on musically compelling

relationships and discussing them in dynamic terms.

Example 4.8 String Quartet No. 2/II, associational pathway of the basic series

a)

b)

c)

91

CONCLUSION

The primary aim of this study has been to examine two important works by Ginastera

and to demonstrate that despite the stylistic differences between his first two quartets—the first

being non-serial and the second being serial—they exhibit a general consistency in pitch

structure and feature similar compositional processes. Chapter 2 discussed how the quartets’

consistency of pitch structure is primarily due to the similar manipulation of their respective

source collections, which underlie the prominent thematic material of each movement. Just as the

various forms of the basic series serve as the source collections of pitch material in the second

quartet, so the basic motive serves as the source collection of pitch material in the first quartet. In

emphasizing the same trichordal and tetrachordal motives (e.g., (014), (016), (0257) and (0167)),

which are derived from the source collections, Ginastera maintains his characteristic sound while

experimenting with new modes of composition, namely composition with twelve tones.

Chapter 3 further examined correspondences among the motivic subsets prominently

featured in the main thematic material of both quartets. The similarities exhibited by each

movement result in a single underlying resonance (or compositional sound) that emanates from

these stylistically opposed quartets. Ginastera’s manipulation of the basic series in the second

quartet, by subtly repeating, displacing, and overlapping order numbers within the series, results

in the projection of the same motivic subsets on the musical surface as those predominantly

featured in the first quartet.

Additionally, chapter 3 explored two compositional processes that further contribute to

the correspondences between the two quartets. The first compositional process involves

chromatic completion and the proliferation of chromatic motives (i.e., motives constructed by

semitonal motion: (012), (0123), etc.) on the musical surface. When we identify the instances of

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chromatic completion prominently articulated by motivic events in the first quartet, we can begin

to draw comparisons to Ginastera’s unique approach to serialism, which often abandons a strict

ordering of the row in order to present the systematic transformation of motives that gradually

fill in the total chromatic. Chromatic motives, while present in the thematic materials of both

quartets, are mostly found in the transitional passages that link together larger formal sections.

The complementary compositional process of symmetry, which concludes the discussion in

chapter 3, is also operative at particularly prominent formal junctions; moreover, symmetrical

constructs in the quartets often involve the projection of chromatic motives.

The final chapter of this study explored the deeper-level structural process of composing-

out in the quartets. In adding to the previous chapters’ discussions of formal structure and

motivic structure, the discussion of composing-out techniques underlines the significant role

other musical dimensions play in articulating the music’s cohesiveness. Each of the composing-

out techniques considered in our discussion resulted in the expansion of motivic or intervallic

events over larger spans of music. The analyses illustrated how non-adjacent pitch events relate

to one another in coherent and compelling ways, forming associations that are operative on

deeper structural levels.

In conclusion, the concept of the associational pathway was introduced in the discussion

of the slow movements of the quartets. The pathways illuminated in both quartets trace a single

motivic or pitch event as it travels and is transformed across the entire movement. Invoking

Schoenberg’s description of the presentation of the musical idea, the interpretation of the

trajectory of the associational pathway is primarily determined by an initial motivating sense of

unrest. In the third movement of the first quartet, it is the sense that pitch-class B of the “guitar

chord” was incongruous with the presentation of (0257), E–A–D–G. In the second movement of

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the second quartet, it is the sense that the work began with the wrong form of the basic series, P3

instead of P7. As the music progresses, a series of logical consequences result from the opening

gesture of each movement, thus forming the associational pathway. Ultimately, these

consequences, along with the associational pathway they form, affect how we interpret and intuit

multiple levels of structure in this music.

The objective of this study was to identify and explicate the compositional consistencies

between Ginastera’s first and second quartets. Even still, numerous other musical relationships of

great significance abound in this music, but simply could not be included in the present study. In

particular, an investigation of the interaction between the motivic structure and harmonic

structure would prove interesting. The rhythmic character of Ginastera’s music also deserves

considerable more attention.

Like the composers he greatly admired—Bartók, Stravinsky, and Copland—Ginastera

found a way to reinvent the voice of nationalism in his music and extend the materials with

which he composed to include the chromatic aggregate. In his admiration of the music of

Schoenberg and Berg, Ginastera’s approach to serialism always sought to exploit the expressive

potential of the row, even if that meant abandoning its confines so as to emphasize more

important musical relations. The string quartets represent two of Ginastera’s most brilliant

compositions, and it is my hope that this study contributes to an awareness of the mastery of

technique and expressiveness with which they were composed.

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BIBLIOGRAPHY

Alegant, Brian and Donald McLean. “On the Nature of Enlargement.” Journal of Music Theory

45, no. 1 (2001): 31–72.

Antokoletz, Elliott. The Music of Béla Bartók: A Study of Tonality and Progression in Twentieth-

Century Music. Berkeley: University of California Press, 1984.

Babbitt, Milton. The Collected Essays of Milton Babbitt. Edited by Stephen Peles, Stephen

Dembski, Andrew Mead , and Joseph N. Straus. Princeton: Princeton University Press, 2003.

Behague, Gerard. Music in Latin America: An Introduction. Englewoord Cliffs, N.J.: Prentice-

Hall, Inc., 1979.

Burkhart, Charles. “Schenker’s ‘Motivic Parallelisms.’” Journal of Music Theory 22 (1978):

145–175.

Campbell, Grace M. “Evolution, Symmetrization, and Synthesis: The Piano Sonatas of Alberto

Ginastera.” D.M.A. diss., University of North Texas, 1991.

Caplin, William. Classical Form: A Theory of Formal Functions for the Instrumental Music of

Haydn, Mozart, and Beethoven. New York: Oxford University Press, 1998.

Carballo, Erick. “De la Pampa al Cielo: The Development of Tonality in the Compositional

Language of Alberto Ginastera.” Ph.D. diss., Indiana University, 2006.

Chase, Gilbert. “Alberto Ginastera: Argentine Composer.” The Musical Quarterly 43, no. 4

(1957).

________. “Alberto Ginastera: Portrait of an Argentine Composer.” Tempo 44 (1957): 11–16.

________. “Remembering Alberto Ginastera.” Latin American Music Review 6 (1985): 80–84.

De los Cobos, Sergio. “Alberto Ginastera’s Three Piano Sonatas: A Reflection of the Composer

and His Country.” D.M.A. diss., Rice University, 1991.

Crichton, Ronald. “Ginastera’s Quartets.” Tempo 111 (1974): 33–34.

Epstein, David. Beyond Orpheus: Studies in Musical Structure. Cambridge: MIT Press, 1979.

Forte, Allen. “New Approaches to the Linear Analysis of Music.” Journal of the American

Musicological Society 41, no. 2 (1988): 315–348.

Furman, Pablo Eduardo. “An Analysis of Alberto Ginastera’s Piano Concerto No. 1 (1961).”

Ph.D. diss., University of California, Los Angeles, 1987.

95

Ginastera, Alberto. “Alberto Ginastera Speaks.” Musical America 82, no. 10 (October 1962):

10–11.

________. “Homage to Béla Bartók.” Tempo 136 (1981): 3–5.

________. “Personal Viewpoint.” Tempo 81 (1967): 26–29.

Gollin, Edward. “Transformational Techniques in Bartók’s Etude Opus 18, No. 2.” Theory and

Practice 20 (1995): 13–30.

Hanley, Mary Ann, Sister, C.S.J. “The Compositions for Solo Piano by Alberto Ginastera.”

D.M.A. diss., University of Cincinnati, 1969.

Hasty, Christopher. “On the Problem of Succession and Continuity in Twentieth-Century

Music.” Music Theory Spectrum 8 (1986): 58–74.

________. “Segmentation and Process in Post-Tonal Music.” Music Theory Spectrum 3 (1981):

54–73.

Hepokoski, James and Warren Darcy. Elements of Sonata Theory: Norms, Types, and

Deformations in the Late-Eighteenth-Century Sonata. Oxford: Oxford University Press, 2006.

Knafo, Claudia. “Tradition and Innovation: Balances within the Piano Sonatas of Alberto

Ginastera.” D.M.A. diss., Boston University, 1994.

Kuss, Malena. Introduction in Alberto Ginastera: A Complete Catalogue. Revised edition, New

York: Boosey and Hawkes, 1986.

________. “The Structural Role of Folk Elements in 20th

-Century Art Music.” In Transmission

and Reception of Musical Culture: Proceedings of the XIVth Congress, International

Musicological Society. Edited by Lorenzo Biaconi, F. Alberto Gallo, Angelo Pompilio, and

Donatella Restani, 3: 99–120. Torino, Italy: EDT/Musica, 1990.

________. “Type, Derivation, and Use of Folk Idioms in Ginastera’s Don Rodrigo.” Latin

American Music Review 1, no. 2 (1980): 176–195.

Lewin, David. Generalized Musical Intervals and Transformations. New Haven: Yale University

Press, 1987.

________. Musical Form and Transformation: 4 Analytical Essays. New Haven: Yale

University Press, 1993.

________. “Transformational Techniques in Atonal and Other Music Theories.” Perspectives of

New Music 21 (1982): 312–371.

96

Mead, Andrew. “Large-Scale Strategy in Arnold Schoenberg’s Twelve-Tone Music.”

Perspectives of New Music 24, no. 1 (1985): 120–157.

________. “Twelve-Tone Organizational Strategies: An Analytical Sampler.” Intégral 3 (1989):

93–169.

Morrison, Charles D. “Prolongation in the Final Movement of Bartók’s String Quartet No. 4.”

Music Theory Spectrum 13, no. 2 (1991); 179–196.

Nissman, Barbara. “Alberto Ginastera: Composer of Latin America.” Keynote 6, no. 6 (1983): 8–

13.

Perle, George. “Symmetrical Formations in the String Quartets of Béla Bartók.” Music Review

16 (1955): 300–312.

Richards, James Edward, Jr. “Pitch Structure in the Opera Don Rodrigo of Alberto Ginastera.”

Ph.D. diss., University of Rochester, 1986.

Roig-Francolí, Miguel. “A Theory of Pitch-Class-Set-Extension in Atonal Music.” College

Music Symposium 41 (2001): 57–90.

Rosen, Charles. The Classical Style: Haydn, Mozart, and Beethoven. New York: W.W. Norton &

Company, Inc., 1997.

Scarabino, Guillermo. “Pitch Materials in the Music of Alberto Ginastera: 1934–1954.” M.A.

thesis, University of Rochester, 1967.

Schenker, Heinrich. Free Composition. Translated and edited by Ernst Oster. New York:

Longman, 1979.

________. Harmony. Edited and annotated by Oswald Jonas, translated by Elisabeth Mann

Borgese. Chicago: The University of Chicago Press, 1954.

Schoenberg, Arnold. The Musical Idea and the Logic, Technique, and Art of Its Presentation.

Edited, translated, and with a commentary by Patricia Carpenter and Severine Neff. New

York: Columbia University Press, 1995. Bloomington: Indiana University Press, 2006.

Schwartz-Kates, Deborah. “Alberto Ginastera, Argentine Cultural Construction, and the

Gauchesco Tradition.” The Musical Quarterly 86, no. 2 (2002): 248–281.

________. “Ginastera, Alberto.” In The New Grove Dictionary of Music and Musicians, 2d ed.

Edited by Stanley Sadie and John Tyrrell, 9: 875–879. New York: Macmillan, 2001.

Simms, Bryan R. Music in the Twentieth Century: Style and Structure 2d ed. New York:

Schirmer Books, 1996.

97

Slonimsky, Nicolas. Music of Latin America. New York: Thomas Y. Crowell, 1945.

Straus, Joseph N. “Atonal Composing-Out.” In Order and Disorder: Music-Theoretical

Strategies in 20th

-Century Music, the fourth publication in the series Collected Writings of the

Orpheus Institute, edited by Peter Dejans. Leuven, Belgium: Leuven University Press, 2004.

________. Introduction to Post-Tonal Theory. 3d ed. Upper Saddle River, New Jersey: Prentice

Hall, 2005.

________. “A Principle of Voice Leading in the Music of Stravinsky.” Music Theory Spectrum 4

(1982): 106–124.

________. “The Problem of Prolongation in Post-Tonal Music.” Journal of Music Theory 31, no.

1 (1987): 1–22.

________. Remaking the Past: Musical Modernism and the Influence of the Tonal Tradition.

Cambridge: Harvard University Press, 1990.

––––––––. “Voice Leading in Atonal Music.” In Music Theory in Concept and Practice. Edited

by James Baker, David Beach, and Jonathan Bernard, 236–274. Rochester, NY: University

of Rochester Press, 1997.

Tabor, Michelle. “Alberto Ginastera’s Late Instrumental Style.” Latin American Music Review

15, no. 1 (Spring-Summer 1994): 1–31.

Tan, Lillian. “An Interview with Alberto Ginastera.” American Music Teacher 33, no. 3 (1984):

6–8.

Taubman, Howard. “Three New Works Heard in Capitol: Quartets by Ginastera, Salas and Villa-

Lobos Played at Inter-American Festival.” New York Times, 20 April 1958: 79.

Treitler, Leo. “Harmonic Procedures in the Fourth Quartet of Béla Bartók.” Journal of Music

Theory 3, no. 2 (1959): 292–298.

________. “Exit the Fifties: A Synthesis of Ideas Marked the Decade.” New York Times, 13

December 1959: 13.

Wallace, David Edward. “Alberto Ginastera: An Analysis of His Style and Techniques of

Composition.” Ph.D. diss., Northwestern University, 1964.