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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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