Almada, Carlos de Lemos / Barros, Guilherme Sauerbronn de / Coelho de Souza, Rodolfo / Gerling, Cristina Capparelli / Nogueira, Ilza (2018): The Reception and Dissemination of European Music Theories in Brazil. Riemann, Schenker, and Schoenberg. ZGMTH 15/2, 129–154. https://doi.org/10.31751/981
eingereicht / submitted: 18/04/2018
angenommen / accepted: 11/08/2018
veröffentlicht / first published: 18/12/2018
zuletzt geändert / last updated: 18/12/2018

The Reception and Dissemination of European Music Theories in Brazil

Riemann, Schenker, and Schoenberg

Carlos de Lemos Almada, Guilherme Sauerbronn de Barros, Rodolfo Coelho de Souza, Cristina Capparelli Gerling, Ilza Nogueira

The history of music theory in Brazil is still not adequately represented in Brazilian musicology. When the Brazilian Association for Music Theory and Analysis (Associação Brasileira de Teoria e Análise MusicalTeMA) was founded in 2014, it took upon itself the task of redressing this imbalance by creating a study group dedicated to the “Historiography of Brazilian Music Theory and Analysis” (“Produção teórica e analítica no Brasil: trajetórias e identidades”). This article represents the group’s first step toward developing a historiographical and critical literature related to theoretical and analytical music studies in Brazil. It aims at historicizing the absorption and development of European theories in the country and at showing how the idiosyncratic use of European theories in Brazil has been informed by pedagogical and research practice. Mostly dedicated to Brazilian musical contexts, theoretical-analytical studies developed in Brazil have creatively deployed imported theoretical models for pedagogical, analytical, or compositional purposes. European theories, such as those of Hugo Riemann, Heinrich Schenker, and Arnold Schoenberg, have been subject to distinctive interpretations in Brazilian academic research.

Die brasilianische Musikwissenschaft ist bislang der Geschichte der Musiktheorie in Brasilien nicht gerecht geworden. Als die Brasilianische Gesellschaft für Musiktheorie und Musikanalyse (Associação Brasileira de Teoria e Análise MusicalTeMA) im Jahr 2014 gegründet wurde, nahm sie sich vor, diesem Defizit entgegenzuwirken und gründete die Studiengruppe “Historiographie der brasilianischen Musiktheorie und Analyse“ (“Produção teórica e analítica no Brasil: trajetórias e identidades”). Dieser Aufsatz stellt den ersten Schritt der Gruppe zur Entwicklung einer historiographischen und kritischen Literatur zu den musiktheoretischen und -analytischen Studien in Brasilien dar. Er zielt darauf ab, die Rezeption und Entwicklung von europäischen Theorien in Brasilien nachzuzeichnen und zeigt dabei, wie Pädagogik und Forschung einen eigenständigen Gebrauch dieser Theorien bestimmt haben. Die in Brasilien erarbeiteten theoretischen und analytischen Studien, die hauptsächlich brasilianischen musikalischen Kontexten gewidmet sind, haben in kreativer Weise eingeführte theoretische Modelle für pädagogische, analytische oder kompositorische Zwecke weiterentwickelt. Unter den Theorien europäischer Herkunft haben diejenigen von Hugo Riemann, Heinrich Schenker und Arnold Schönberg in der brasilianischen Forschung eine spezifische Prägung erhalten.

Schlagworte/Keywords: brasilianische Literatur über europäische Musiktheorie; Brazilian literature on European music theory; dissemination of European music theories in Brazil; music theory in Brazil; Musiktheorie in Brasilien; Verbreitung von europäischen Musiktheorien in Brasilien

German-Austrian music theories have played a significant role throughout the history of music-theoretical research in Brazil. They were first introduced in the early twentieth century, when composer Alberto Nepomuceno (1864–1920) was appointed director of the Instituto Nacional de Música in Rio de Janeiro for the second time (1906). As a young student in the Northeastern town of Recife, Nepomuceno was influenced by Tobias Barreto (1839–1889), a well-known scholar of German philosophy and law and a prominent figure in the so-called “Escola do Recife,” an intellectual movement of the late nineteenth century.[1] In 1916, Nepomuceno was involved in translating Arnold Schoenberg’s Harmonielehre and planned to adopt it as a textbook at the Instituto. In the first two decades of the twentieth century, however, the French-Italian tendency of Brazilian musical culture inhibited the acceptance of German and Austrian music theories. Indeed, the academic music scene in Brazil during the first half of the twentieth century was not yet open to a rational absorption of music-theoretical arguments. At that time, music education was predominantly limited to musical performance and consequently treated the theoretical disciplines of harmony, counterpoint, and fugue as codifications of specific rules to be applied in practical exercises clearly separated from composition and music analysis.

German immigrants that arrived in the late 1930s and early 1940s first intended to promote German and Austrian theories to Brazilian music institutions (mainly Hugo Riemann’s theory of functional harmony and Schoenberg’s twelve-tone theory). In those years, however, nationalistic aesthetics emerged that openly rejected European influences including music theories.[2] Drawing on rural folkloristic sources, Brazilian musical nationalism favored theoretical models that explained modal and rhythmic systems of ethnic origin. Thus, the period in which German theories arrived in Brazil was not conducive to its immediate and unproblematic absorption. This especially applies to the reception of the Schoenbergian dodecaphonic method, introduced to Brazil by Hans-Joachim Koellreutter (1915–2005).[3]

Unlike Riemannian and Schoenbergian theories, which entered Brazilian music schools through Koellreutter’s pedagogical work, Heinrich Schenker’s theory was introduced by Brazilian musicians who had encountered it during their graduate studies at North American universities. During the 1980s, the implementation of graduate music courses at Brazilian universities demanded faculty members with doctoral degrees. Many Brazilian teachers received grants to study in the United States from the Fulbright Commission and from LASPAU (Latin American Scholarship Program of American Universities) under the joint sponsorship of the Brazilian CAPES Foundation (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior).[4] As part of the requirements for master’s and doctoral degrees, most American East Coast universities offered a plethora of theoretical courses many of which focused on Schenkerian theory. In 1985, the first Brazilian PhD/DMA music graduates returned from their studies at North American Universities with Schenker’s analytical theories as well as Milton Babbitt’s and Allen Forte’s set theory. As a result, structuralist analytical approaches flourished in the country during the 1990s, notwithstanding a developmental shift toward newer interdisciplinary approaches brought about by the emergence of the New Musicology in North America. Schenkerian theory is still a highly influential part of the academic discourse in Brazil and is viewed favorably by the majority of scholars. This continues a trend that has been evident from the very first introduction of Schenkerian theory to the country and throughout its subsequent 30 years of dissemination.[5] The extensive literature written during this period speaks for itself.

This article focuses on key aspects of the reception and propagation (early advocates, institutional homes, receptive journals, and conference presentations) of Riemannian, Schenkerian, and Schoenbergian theories in Brazil both historically and critically and surveys the current state of their development in Brazilian musical scholarship.

1. RIEMANN’S THEORY OF FUNCTIONAL HARMONY

The propagation of Riemann’s theory of functional harmony in Brazil is intrinsically linked to the activities of Hans-Joachim Koellreutter, a teacher, conductor, flutist, and composer born in Freiburg, Germany. His charisma and leadership, as part of the Brazilian modern music scene, form the basis of the Brazilian reception of Hugo Riemann’s functional harmony and Arnold Schoenberg’s method of twelve-tone composition during the late 1930s and early 1940s (theories unknown among Brazilian musicians at that time).

There is little available information about Koellreutter’s studies at the Akademische Hochschule für Musik in Berlin, where he met Kurt Thomas (1904–1973) who was a former student of Hermann Grabner (1886–1969). After founding the Arbeitskreis für Neue Musik in response to Nazi cultural policy, he was expelled from the Berlin Hochschule and continued his studies in Geneva. There, he had a short but fruitful relationship with Hermann Scherchen (1891–1966) who reinforced his interest in contemporary music. In the following year, 1937, Koellreutter travelled to Rio de Janeiro, Brazil, taking part in an orchestral tour as a flutist. He decided to stay there and began a career as a teacher of music theory and mentor to young composers.

Brazilian universities only started to offer undergraduate courses in music during the second half of the twentieth century. Up until then, music was exclusively taught at conservatories where harmony courses adopted Italian or French models based on figured bass practice and later models of Stufen theory. Among some young composers who studied privately with Koellreutter, functional harmony was considered a more modern and advanced theory. Knowledge of functional harmony spread when university programs started to hire Koellreutter’s former students to teach music theory during the 1970s. Since the 1980s, functional harmony has become the standard theory for about half of the Brazilian musical community, competing with Stufen theory for prominence.

Although Koellreutter taught tonal harmony to many composers, paradoxically he did not believe it was useful for them. He considered his pedagogical system

a concise and practical method of teaching harmony […], sufficient for the musician of the present time when musical composition requires new principles of organization in face of new and possibly inexhaustible sound materials that do not require anymore the use of the principle of tonality.[6]

For Koellreutter, the study of tonal harmony was only useful for performers and analysts of common practice repertoire. For the composer, he considered it an anachronism.

Koellreutter had a strong propensity for exploring aesthetical issues, but not for the intricacies of abstract theoretical reasoning. Dualism, for instance, a key premise for Riemann’s functional harmony, is not ever mentioned in Koellreutter’s 1978 Harmonia Funcional: Introdução à teoria das Funções Harmônicas, published three decades after the initial circulation of his handwritten notes in Brazil. In the preface of this textbook, Koellreutter declares that his approach follows Max Reger and Hermann Grabner.[7] He also states that these authors “developed and perfected Riemann’s theory as an improvement of Stufen theory.”[8] Alexander Rehding points out that this has been a common feature of the propagation of Riemann’s theories: “[T]he version of Riemann’s theory that is taught under the name of Riemann is in fact based on the textbooks by [Wilhelm] Maler and Grabner – whose theories are entirely devoid of harmonic dualism.”[9]

On the contrary, one of the consequences of dualism is the concept of subsidiary harmonies (Nebenklänge), namely parallel (Parallelklang i.e., relative harmony) and leading-tone exchange (Leittonwechselklang, labelled Gegenparallelklang [anti-parallel harmony] by Grabner) transformations of tonic, dominant, or subdominant harmonies. The functional designations introduced by Koellreutter follow the standard proposed by Grabner (for instance, in major: Tp, Tg, Sp, Sg, Dp, Dg). However, he translates the suffixes “p” and “g” to the equivalent initials “r” and “a” of the words in Portuguese (“relativa” and “antirrelativa”).

The structure of Koellreutter’s book closely resembles Riemann’s 1893 and Grabner’s 1944 publications. It proposes five “tonal laws”:[10]

  1. Main Functions (T, S, D) (Riemann, chapter 1: Der Satz mit den reinen Hauptharmonien (Tonika und Dominanten); Grabner, chapter 2: Die Hauptfunktionen);

  2. Secondary Functions (Tp, Tg, Sp, Sg, Dp, Dg, etc.) (Riemann, chapter 2: Charakteristische Dissonanzen. Parallelklänge. Leittonwechselklänge; Grabner, chapter 4: Nebenfunktionen in Dur, chapter 5: Nebenfunktionen in Moll);

  3. Secondary Dominants (Riemann, chapter 3: Dissonanzlehre. Sequenzen. Zwischenkadenzen; Grabner, chapter 12: Erweiterte Tonalität, § 51 Zwischendominanten);

  4. Expanded Tonality (Grabner, chapter 12: Erweiterte Tonalität);

  5. Modulation (Riemann, chapter 4: Der Wechsel der tonalen Funktionen (Modulation); Grabner, chapters 9–11, 13, 14).

Despite these minor differences in the organization of chapters, we may observe that Koellreutter reproduces Grabner’s table of secondary dominants (Zwischendominanten) (Fig. 1). This comparison does not leave any doubt that Grabner’s book was the main source for Koellreutter’s Riemannian teachings in Brazil.

Abbildung

Abbildung

Figure 1: Table of Secondary Dominants (Koellreutter 1978, 30; top); Tafel der Zwischendominanten [Table of Secondary Dominants] (Grabner 1944/2005, 171; bottom)

The fourth chapter is the most peculiar in Koellreutter’s book, inasmuch as it opens with the following statement, in capital letters: “ANY CHORD MAY FOLLOW ANY OTHER CHORD. CHORDS OF DISTANT TONES NEED PREPARATION WITH INTERMEDIARY HARMONIES.”[11]

Daniel Harrison attributes this phrase to Max Reger, adding in a footnote that this quote is rendered in a 1920 book by Grabner on Reger’s teachings.[12] Considering that Koellreutter also mentions Reger as a source of his knowledge of functional harmony, it is likely that he appropriated Reger’s phrase from the same source.

Particularly amazing is how Koellreutter’s short textbook on functional theory jumps, after only thirty pages, into matters of advanced chromatic harmony, without preparing the topic with a careful examination of standard chromatic chords such as the augmented sixth. Moreover, he does not offer the reader any clue of how to make sense of an excerpt quoted from Richard Strauss’s Elektra (Ex. 1), which he uses to illustrate the idea of tonal expansion and the principle that “any chord may follow any other chord.” While this may look odd, it is consistent with Koellreutter’s usual pedagogic method of pushing his students towards harmonic experiments without progressive methodological guidance (Video Ex. 1).

Abbildung

Example 1: Richard Strauss, Elektra, four measures after rehearsal number 67 (Koellreutter 1978, 31) (the B3 in the third measure of the example is missing in Koellreutter’s book)

Video Example 1: Excerpt from the TV program Harmonia “H. J. Koellreutter. O Maestro dos Maestros” [H. J. Koellreutter. The Master of the Masters], 27:20–28:12,
21 December 2005, Rede Minas, director Gerusa Coelho; https://www.youtube.com/watch?v=PWtuox4vlvg (24 October 2018); translation:
“People always ask me, ‘what should I do to penetrate this world of [post-tonal] music?’ I always answer that there is only one way: to listen, to listen, and to listen. There is no other way. You have to live the time phenomenon, which is not a palpable element. Time is not a river that passes from the past to the future. It does not exist… physically speaking it does not exist. Time is an existential process that occurs in every aspect of our lives.”

Koellreutter and his followers often ignored the ambiguities of the functional system when they taught functional harmony in Brazil. For example, they offered no explanation for simple problems such as when to analyze an E minor triad in C major as a Dp or a Tg. Issues such as this impeded the acceptance of the theory among Brazilian scholars. Meanwhile, Koellreutter had developed an abacus to simplify the application of the functional theory.[13] The student was supposed to use it in order to speed up analytical decisions (Fig. 2).

Abbildung

Figure 2: Rotatory Abacus of Harmonic Functions (Koellreutter 1978, appended material; the blue color is not original; it was added to the figure by the authors to illustrate that one circle rotates over the other)

Brazilian scholars considered other issues in functional theory, as taught by Koellreutter, controversial. Among them was the generalized acceptance of altered chord tones and pitches added to chords. This procedure is often left out of current formulations of functional theory, but Riemann pursued this concept in his Katechismus der Harmonie- und Modulationslehre.[14] The problems caused by this line of reasoning became obvious when Koellreutter explicitly allowed the addition of sixths to any chord function. The theoretical description of a subdominant with an added sixth has its origin in Jean-Philippe Rameau’s Traité de l’harmonie (1722). For reasons that Rehding has already thoroughly addressed,[15] Riemann followed Rameau in this respect. Koellreutter cautioned that added sixths were different from the sixths in first inversion chords.[16] However, he did not provide an explanation of how to differentiate these two types of sixths, causing confusion among Brazilian analysts, inducing some of them to almost deny the existence of chord inversion, something that goes against the core of Rameau’s (and consequently Riemann’s) theory.

What made Koellreutter move in that direction? One can guess that it was because many of his students were popular musicians interested in jazz. In line with common jazz practice, they understood chord extension or pitch alteration as simple procedures that enrich harmonic sonorities. Thus, functional harmony played an unpredictable role in the development of bossa nova, one of the most internationally successful styles of Brazilian popular music. Tom Jobim (1927–1994), leading composer of that style, was a private student of Koellreutter from 1941. Koellreutter’s influence on Jobim’s particular brand of functional harmony (especially concerning the principle of adding pitches to chords or making whatever alteration the composer felt interesting) cannot be overlooked.

We may highlight other controversial proposals in Koellreutter’s book. One such case is his novel solution for analyzing the diminished chordal sonority built on the second scale degree in minor. Koellreutter explains this harmony as a dominant with added ninth and seventh, omitting the root and third of the chord. He notates its function as dominant with a dominant symbol crossed by two lines. In other words, he claims that the function of the second degree in minor is similar to the seventh degree in major (Ex. 2). We could not find a source for this odd analytical solution in any version of the Riemannian theory.

Abbildung

Example 2: The second degree in minor (after Koellreutter 1978, 23)

As mentioned above, Koellreutter’s approach added an aura of jazz to functional theory, making it applicable for musicians of that practice. His efforts went as far as to include a chapter in his book dealing with a progression supposedly idiomatic to jazz. However, even a superficial evaluation reveals that this progression is just a cycle of fifths that may be found as frequently in jazz standards (for instance, in George Shearing’s Lullaby of Birdland) as in any other style of tonal music. To demonstrate this, Examples 3 and 4 compare the chord progression labelled “Jazz Cadence” by Koellreutter with a well-known composition of the tonal repertoire – an excerpt from Gabriel Fauré’s Après un rêve – which presents a similar progression, as do many other pieces. Notice the addition of sixths to tonic chords in Example 3. As mentioned above, this is supposed to represent jazz stylization.

Abbildung

Example 3: Koellreutter’s “Jazz Cadence” (Koellreutter 1978, 36)

Abbildung

Example 4: Excerpt of Gabriel Fauré’s song Après un rêve op. 7/1, mm. 1–6 (reduction)

The first generation of Koellreutter’s followers in Brazil, with few exceptions, continued his method of teaching without alteration. Zula de Oliveira introduced the notation of minor chords with lowercase letters in 1978.[17] Cyro Brisolla revised and critiqued functional theory in 1979 and Mário Ficarelli reviewed and expanded Brisolla’s book in a second edition (2006) by adding more topics (basic categories of cadences; phrases and elements of classical form; non-chord tones; more examples of harmonic analysis, including late Romantic compositions) and more complex examples.[18] In the 1980s, some professors searched for new theoretical sources due to the perceived lack of quality in Koellretter’s method. Since these new sources were usually written in German, language often acted as an obstacle for readers, particularly students. The general theoretical standard improved in the mid-1980s when some teachers started to use Wilhelm Maler’s textbook.[19]

At that point, the competition between function theory and Stufen theory reached fever pitch and as a compromise some publications – such as Maria Lúcia Pascoal’s and Alexandre Pascoal’s Estrutura Tonal: Harmonia (2000) – adopted both systems simultaneously.[20] Other treatises started to be adopted, particularly Diether de la Motte’s Harmonielehre as it was available in English, Italian, and Spanish.[21] More recently, Thomas Krämer’s Lehrbuch der harmonischen Analyse[22] has been used to supplement analytical materials. However, Koellreutter’s materials continue to be used in spite of the gaps in his teaching method.

Graduate level research has only very recently started to improve the state of functional theory research as theses and dissertations have begun to treat the original texts of Riemann and his predecessors.[23] The recent interest in Riemann has also been stimulated by the trend for neo-Riemannian studies that has reached Brazil through an increasing interaction between Brazilian and North American scholars (even though many neo-Riemannian studies are only indirectly related to functional theory). Both theories, Riemannian and neo-Riemannian, have proved fruitful for the analysis of nineteenth and twentieth century Brazilian music that employs chromatic harmony, such as that of Leopoldo Miguez, Henrique Oswald, Alberto Nepomuceno, and Heitor Villa-Lobos, among others.

2. HEINRICH SCHENKER’S METHOD OF ANALYSIS

2.1. Felix Salzer’s Structural Hearing: The First Introduction of Schenker’s Theory to the Brazilian Academic Community

During the mid-1960s, Georg Wasserman was part of the music theory faculty at the Pro Arte Seminars (a Summer music festival hosted in Teresópolis, then a resort town not far from Rio de Janeiro) and possibly taught Schenker-influenced analytical methods there.[24] Toward the end of the 1960s, the noted music theory pedagogue Esther Scliar (1926–1978), also on the faculty of the Pro Arte Seminars, referred to the significance of melodic stepwise contours in her teaching. She would point out the significance of stepwise contours as a fundamental characteristic of the tonal repertoire and enthusiastically described Urlinie prototypes in her teaching.[25] Scliar was aware of Felix Salzer’s Structural Hearing (probably the 1962 edition),[26] a work known by less than a handful of Brazilian musicians at that time.[27] It seems that Schenker’s concepts of structure and coherence in tonal music were transmitted to Brazil via Salzer’s book.

As Maria Lúcia Pascoal, one of the founding professors of the Music Department of the State University of Campinas UNICAMP, stated, the Brazilian composer Almeida Prado was enthusiastic about Salzer’s book since it included analyses of music by twentieth-century composers such as Béla Bartók, Sergej Prokof’ev, Igor Stravinsky, and Aaron Copland. In the early 1980s, Prado introduced Salzer’s book to Pascoal, who started to use it in her theory teaching and her analytical research of Brazilian twentieth-century music.[28] Salzer’s book has remained a strong presence in Pascoal’s eclectic analytical methodology particularly in her use of concepts like “basic harmonic structure” and “voice-leading graphs as expression of prolongation.”[29] Pascoal combines Salzer’s reductive voice-leading graphs with principles from Forte’s set theory.[30] Applying this mixture of theoretical concepts and analytical approaches, she has produced relevant studies of works from mid and late twentieth-century Brazilian composers such as Villa-Lobos, Claudio Santoro, and Almeida Prado.

2.2. Free Composition: Schenker’s Theory at Brazilian Universities

The full complexity of Schenker’s theories (Der freie Satz in Ernst Oster’s 1979 English translation) was only introduced to Brazilian academia in the late 1980s, as Brazilian musicians returned from doctoral studies in North America, among them Cristina Gerling (DMA from Boston University, 1985), Ilza Nogueira (PhD from the State University of New York at Buffalo, 1985), and Jamary Oliveira (University of Texas at Austin, 1986). This process took place alongside the establishment and consolidation of graduate music programs at Brazilian Universities and the foundation of the Associação Nacional de Pesquisa e Pós-Graduação em Música ANPPOM (April 1988), Brazil’s first society of musical scholarship.

During her doctoral studies at Boston University (1980–85), Gerling wrote a dissertation (Performance Analysis for Pianists: A Critical Discussion of Selected Procedures) that reflects her previous studies with Ernst Oster at the New England Conservatory (1973–76). Since 1987, she has promoted Schenkerian theory at the Universidade Federal do Rio Grande do Sul in the city of Porto Alegre and, since 1990, has occasionally taught as visiting professor at the Universidade Federal do Paraná in the city of Curitiba.

The activities of the ANPPOM, along with the increased number of academic music journals, promoted the production of scholarly texts. The First Conference of the ANPPOM (Salvador-Bahia, 21–25 November 1988), featured a round-table discussion on “Schenker’s Contribution to Interpretation” between Jonathan Dunsby (then at Reading University, UK), Nogueira (Universidade Federal da Paraíba), Gerling (Universidade Federal do Rio Grande do Sul), and Oliveira (Universidade Federal da Bahia).[31] This event was the “formal” introduction of Schenker’s theories to Brazilian academia. In the following year, Em Pauta (Journal of the Graduate Program of the Universidade Federal do Rio Grande do Sul) published an article by Gerling entitled “A Teoria de Heinrich Schenker: Uma Breve Introdução”[32] that explained the basic concepts, terms, and reductive processes of Schenkerian theory. This was the first publication on Schenkerian theory in Brazil and opened the doors for Schenkerian ideas in Brazilian music journals. In the same year, the ANPPOM Journal Opus published Gerling’s paper presented at the 1988 conference “A Contribuição de Heinrich Schenker para a Interpretação Musical”[33] that contains an analysis of Chopin’s Prélude op. 28/4. At that time, Brazilian musicologist Carlos Kater founded Brazil’s first journal exclusively dedicated to music analysis, Cadernos de Estudo: Análise Musical, the second issue of which (April 1990) included Gerling’s “Considerações Sobre a Análise Schenkeriana.”[34] A few months later (August 1990), ArT: Revista da Escola de Música da Universidade Federal da Bahia published Nogueira’s article “A Estruturação Tonal da Canção Mein Herz, das ist ein tiefer Schacht: Uma Aproximação Através da Teoria Schenkeriana” that includes a thorough Schenkerian graph of Schoenberg’s early song and appends a list of Schenker’s published and unpublished theoretical writings.[35] Gerling’s twin articles published in 1995 “Schenker e Seus Discípulos na América”[36] focus on North American theoretical literature. At this early stage, Brazilian texts on Schenkerian theory encompassed articles explaining the method and the technical terms of the theory. These early Brazilian theoretical publications reveal an orthodox attitude towards the theory: they focus on European classical music and closely reflect Oster’s teachings. Subsequent articles assimilated Salzer’s and Forte’s approaches, and still later articles covered pre-tonal music, twentieth-century repertoire, and popular music.

Around the turn of the century, we may observe the transition from a phase of introduction and absorption of Schenkerian Theory to a phase characterized by broader utilization of the method and critical reflection on its assumptions. Marcos Branda Lacerda’s “Breve Resenha das Contribuições de Schenker e Schoenberg para a Análise Musical” (1997) and Joel Luis Barbosa’s “Estudo para Clarineta de Gaetano Donizetti” (1998) show the same limitations found in the earlier essays of Gerling and Nogueira (that is, they predominantly focus on presenting Schenker’s concepts and terminology).[37] In contrast, Barbosa’s article from the following year “Gershwin and the Expansion of the Tonal System’s Relationships Through the Blue Note”[38] not only applies Schenker’s theory to a repertoire beyond the common-practice period but assumes that the definitions of underlying concepts are understood by his readers. We may also observe that, at the beginning of the twenty-first century, doctoral dissertations and master’s theses started to focus on Schenkerian theory.[39]

2.3. The Development of a Brazilian Literature on Schenkerian Theory

In the twenty-first century, notable scholars, such as Carole Gubernikoff, Carlos Almada, Norton Dudeque, Guilherme Sauerbronn de Barros, and Orlando Cézar Fraga, have expanded the research community dedicated to developing Schenker’s theory in Brazil.

Carole Gubernikoff is an active professor of music theory and analysis at the Universidade Federal do Estado do Rio de Janeiro UNIRIO. Her work as a graduate student supervisor has resulted in Schenkerian-based research into the analysis of Brazilian popular music,[40] expanding Schenkerian theory into the post-tonal repertoire and including critiques of the organicist metaphor in music.[41] Carlos de Lemos Almada teaches harmony and music analysis at the Universidade Federal do Rio de Janeiro UFRJ. Despite his strong emphasis on Arnold Schoenberg’s theories, he has occasionally produced Schenkerian analyses of Brazilian popular music as part of his prolific theoretical output.[42] Norton Eloy Dudeque (PhD in music theory from the University of Reading) is professor of music theory at the Universidade Federal do Paraná. He sometimes supervises studies in Schenkerian theory,[43] though mostly focuses on Schoenberg’s theories.

Pianist Guilherme Sauerbronn de Barros first came into contact with Schenkerian theory through Carole Gubernikoff during his PhD at the Federal University of the State of Rio de Janeiro UNIRIO (2000–05). His doctoral dissertation studies the music of Ernst Mahle[44] and required extensive readings on German authors of the eighteenth and nineteenth centuries. He recognized the potential affinities of Schenkerian theory and German philosophy of the period, and so decided to carry out research on Schenkerian analysis and entered Cristina Gerling’s research group GPPI – Grupo de Pesquisa em Práticas Interpretativas (Research Group on Interpretative Practices). This group explored the philosophical aspects of Schenkerian theory such as the impact of German Romanticist art criticism on Schenker.[45] As a piano teacher at the Universidade do Estado de Santa Catarina UDESC, Barros uses Schenkerian analysis extensively as an educational and interpretative tool at undergraduate and graduate levels.[46] His music analysis teaching is reflected in graduate student papers[47] and master’s theses at the university.[48]

Orlando Cézar Fraga (DMA, Eastman School of Music, 2001) holds a teaching position at the Escola de Música e Belas Artes do Paraná, where he teaches guitar and music analysis. He is the author of the first Brazilian book on Schenkerian theory Progressão Linear – Uma breve introdução à Teoria de Schenker.[49] Fraga’s book closely follows the principles and contents of two highly regarded textbooks, Introduction to Schenkerian Analysis by Allen Forte and Steven Gilbert[50] and Analysis of Tonal Music by Allen Cadwallader and David Gagné.[51] Fraga presents the main tenets of Schenkerian theory in a very coherent and concise manner and includes excerpts from the guitar repertoire.

From the original pool of teachers that introduced Schenker’s theories to Brazilian institutions, Gerling remains the only one who continues to apply the theory as an analytical and interpretative tool. In her article “F. Chopin’s Barcarolle op. 60: Learning Strategies” she suggests Schenkerian analysis as an approach to “deliberate memorization” in performance practice.[52] She states that “Schenkerian analysis leverages the organization of long-term musical discourse in its linear path,” facilitating memorization strategies “based on a hierarchical scheme of organized recovery anchored on consciously implemented cues.”[53] This method, which involves the development of a mental map for “structurally opaque” pieces, was also presented at the 2013 International Symposium on Performance Science in Vienna and published in the symposium’s proceedings.[54]

Besides the historiographic project that stimulated the present article, the Brazilian Society for Music Theory and Analysis (TeMA) is carrying out a research project that aims to produce a Reverse Multilingual Dictionary of Theoretical Terms, including an extended glossary of Schenkerian terminology in the Portuguese language.[55]

Following North American eclectic tendencies, Brazilian adaptions of Schenkerian theory have gained wide acceptance as a tool for the analysis of a variety of genres and traditions including Brazilian concert and popular music. Advancing towards international recognition, the growing Schenkerian literature in Brazil seeks to solidify analytical approaches while continuing to critically appraise Schenker’s writings and the arguments found in the texts and pedagogical works of his followers.

3. SCHOENBERG’S THEORIES

The composer Alberto Nepomuceno (1864–1920) initiated the dissemination of Schoenberg’s theories in Brazil (see the beginning of this article). Nepomuceno was partly educated in Germany during the 1890s, where he studied composition with Heinrich von Herzogenberg (1843–1900). In 1902, he was appointed director of the Instituto Nacional de Música INM (National Institute of Music) in Rio de Janeiro, currently the School of Music of the Federal University of Rio de Janeiro. As Norton Dudeque and Rodolfo Coelho de Souza point out,[56] Nepomuceno’s German period profoundly impacted his music, including his conception of form, thematic treatment, and harmony. This impact was also reflected in his career as director of the INM: in the 1910s, Nepomuceno intended to adopt Schoenberg’s Harmonielehre as a textbook to be used in theory classes. Therefore, he started a Portuguese translation of Schoenberg’s book, which unfortunately was not completed. (Several decades later, Marden Maluf produced a new translation of the text which was published in 2001.[57])

Subsequently, Schoenberg’s music and theories remained largely forgotten (or unknown) in Brazil until the 1940s, when Hans-Joachim Koellreutter and some of his students established the Musica Viva movement in Rio de Janeiro and São Paulo.[58] These students later became important composers, notably Cláudio Santoro (1919–1989), César Guerra-Peixe (1914–1993), Edino Krieger (b. 1928), Geni Marcondes (1916–2011), and Eunice Katunda (1915–1990). Koellreutter introduced the principles for Schoenberg’s dodecaphonic method to his students who soon started to compose their own twelve-tone pieces. Apart from Koellreutter’s introduction of basic dodecaphonic postulates, however, Schoenberg’s influence on Musica Viva was limited. Schoenberg’s far-reaching theoretical principles (such as the two dualities monotonality/tonal regions and Grundgestalt/developing variation) – as well as his copious writings on harmony, counterpoint, form, composition, and orchestration – were largely ignored by Musica Viva’s members. Some Brazilian nationalist composers developed strong opposition to the new movement’s aesthetic, which prematurely ended the group’s activities only a few years after its foundation. However, Koellreutter continued to teach dodecaphonic composition (alongside other musical disciplines) and became an influential figure in the Brazilian musical scene (see part one of this article).[59]

With the creation of the first Brazilian graduate programs in music during the 1980s, Schoenberg’s theories eventually became the object of profound systematic studies. Norton Dudeque is perhaps the pioneer among Brazilian Schoenberg scholars. His master’s thesis[60] examines the vast theoretical corpus of Schoenberg’s writings on harmony, especially investigating the concepts of monotonality, tonal regions, suspended/floating tonality, and vagrant chords, and presents a reference guide for subsequent studies. In 2005, Dudeque published an important book that originated from his doctorate research in England under the supervision of Jonathan Dunsby.[61] In this book, Dudeque extends the scope of his previous study to encompass all major aspects of Schoenberg’s theories and analytical methodologies.[62] The concepts most thoroughly treated in Dudeque’s book are the principles of Grundgestalt and developing variation. Both certainly represent the essence of Schoenberg’s contribution to the theory of musical composition and emerge from a conception of organic musical creation. Dudeque also published articles based on these principles in which the thematic structure of pieces by Mozart, Nepomuceno, and Schoenberg are analyzed according to Schoenbergian principles.[63]

It is also noteworthy that Schoenbergian theories have been employed as reference points in studies focusing on Brazilian music such as analysis of serial procedures in a song collection[64] and the last string quartets of Claudio Santoro[65] as well as in studies on issues of popular music.[66] In general, Schoenberg’s music and theory have provoked considerable interest among Brazilian scholars, which may be demonstrated by a survey of dissertations and thesis in the sub-areas of composition and theory.[67]

In 2007, Carlos Almada finished his master’s thesis that comprises a detailed formal analysis of Schoenberg’s First Chamber Symphony op. 9 and applies a theoretical framework built exclusively on Schoenbergian concepts. Almada continued with this approach in his PhD thesis,[68] in which he examines the tonal-harmonic structure of the Chamber Symphony in great detail. From this thesis, a number of new concepts and analytical tools emerged (such as “zones of tonal instability,” “harmonic clouds,” “cadential curtains,” “formal-harmonic layered analysis,” and “special developing variation charts”)[69] that were applied and improved in later studies. In part, these new formulations are intimately related to the concepts of Grundgestalt and developing variation. Almada instigated a research project in 2011 which aims at developing a model for systematic analysis of organically-constructed music, named Model of Derivative Analysis (MDA). The current version of MDA traces Schoenberg’s principles to their original premises and covers such eclectic fields of study as mathematics, computation, theory of formal systems, and evolutionary biology. Several theoretical[70] and analytical publications have emerged from the project, such as analyses of works by Beethoven,[71] Schoenberg,[72] Alban Berg,[73] the Brazilian Romantic composer Leopoldo Miguéz,[74] and two popular music composers, Antônio Carlos Jobim and George Harrison.[75] In 2012, MDA’s concepts and structure became the basis of a new theoretical approach dedicated to algorithmic composition, motivating the creation of the so-called “Gr-System”[76] and related computational tools.[77]

Schoenberg’s theoretical legacy in Brazil has stimulated the production of a considerable corpus of studies and streams of research (resulting in countless ramifications), which confirms not only the remarkable germinative power of his thought, but also an extraordinary (and fast) evolution of Brazilian academia in the areas of theory and analysis.

4. FINAL CONSIDERATIONS

The theories of Hugo Riemann, Heinrich Schenker, and Arnold Schoenberg found fertile ground in the Brazilian academic world of the twentieth century. However, each of these theories had a distinctive developmental process in the country that involved different places, scholars, and institutions. This is reflected in the three-part organization of this article.

Riemannian functional theory and Schoenbergian dodecaphonic compositional theory were both introduced to Brazil by a German immigrant at the height of nationalist aesthetics fostered by the “Estado Novo” political regime of the 1940s. The prevailing cultural context – as well as their differences (i.e., tonal versus atonal) – caused each one to undergo a very distinct process of assimilation and development. Riemannian theory was gradually absorbed through Koellreutter’s pedagogical activities in Rio de Janeiro and São Paulo and quickly disseminated during Koellreutter’s annual Teresópolis International Summer Courses (1950–60) and the International Music Seminars (1954–59) in Salvador. On the contrary, by the time Koellreutter had begun to introduce Schoenberg’s dodecaphonic theory to Brazilian musicians in the 1940s and 50s, it had become an anachronism. Composition with twelve tones was mostly constrained to the Music Viva circle and lost its influence when, during the early 1950s, composers eagerly opted for a nationalist modernist idiom.

Koellreutter did not directly explore Schoenberg’s mature serial practice. During the 1940s, he taught the basic premises of the dodecaphonic grammar to his students while it took about thirty years more until the structural complexity of postwar serial syntax, as reflected in the seminal works of Milton Babbitt, George Perle, and Allen Forte, became part of the analytical discourse in Brazil. Only in the late 1980s, when Brazilian musicians returned from graduate studies in the United States, were notions such as “aggregate,” “hexachordal combinatoriality,” “invariants,” and “partitions” introduced to the Brazilian music community. This process took place at the same time as the arrival and dissemination of Schenkerian theory in Brazil.

Due to his heterogeneous career, Koellreutter’s teaching activities in Brazil were interspersed with other professional duties in Germany (1962–64), India (1965–69), and Japan (1970–74). During that period, the South American reception of European and North American avant-garde music led to waves of experimental research, new instrumental techniques, and sound-mass composition in Brazilian contemporary music. These circumstances explain Koellreutter’s belated educational publications systematizing the pedagogy of functional harmony, published toward the end of the 1970s.[78]

From the 1980s on, the implementation of graduate music courses induced a surge in academic activity in Brazil. New laboratory equipment was acquired; music journals were founded; research grants became available; and many congresses, conferences, and symposia were organized under the sponsorship of Brazilian governmental institutions such as the Conselho Nacional de Desenvolvimento Científico e Tecnológico CNPq (National Council for Scientific and Technological Development). Research subsidies, opportunities to publish, and new teaching at higher levels have all contributed to the stimulation of theoretical thought. This has led to the dissemination of analytical ideas using newly arrived music theories, namely Schenkerian theory and set theory (including its implications on Schoenbergian twelve-tone syntax). Therefore, it is fair to conclude that the development of Brazilian literature on music theory and analysis did not truly begin before the last two decades of the twentieth century.

In the last forty years, a relatively short period, three distinct phases may be distinguished. Up to the year 2000, most publications were essentially informative:[79] for nearly two decades, analytical studies published in Brazil characteristically presented technical terms, concepts, and methods, and academic theses demonstrated proficiency with these theoretical tools. The second phase extends until 2012 and reveals a degree of maturity as documented by the transition toward more critical approaches. This trend includes a significant development towards the compositional “systemic modelling” of theoretical subjects such as musical contour, partitions, and developing variation.[80] During the ongoing third phase, the growth of interdisciplinary research groups has brought about original compositional and analytical theories that advance from theoretical presuppositions toward the analysis of aesthetic effects. The following groups should be mentioned in this regard: NICS (Núcleo Interdisciplinar de Comunicação Sonora; State University of Campinas), Mus3 (Mus3 – Musicologia, Sonologia e Computação; Federal University of Paraíba), Composição e Cultura (Federal University of Bahia), and MusMat (Federal University of Rio de Janeiro).[81]

Since a detailed account of the historical development of analytical and compositional theories in Brazil would have far exceeded the scope of this account, the brief overview presented here attempted to place the three investigated theories in the context of a broad evolution of almost eighty years. Considering that this article was written only four years after the foundation of the Brazilian Society for Music Theory and Analysis (TeMA) in 2014,[82] we hope that it might provide a starting point for new research.

Notes

1

A determined advocate of German culture as opposed to what he considered the inferior French culture, Tobias Barreto founded a Brazilian journal entirely written in German (Deutscher Kämpfer, 1875) in the small hinterland town of Escada, which had little repercussion and a short life.

2

As a movement of the centralistic and anticommunist “Estado Novo” regime (1937–46), musical nationalism in Brazil developed with the substantial support of Getúlio Vargas’s government. In this political context, Heitor Villa-Lobos (1887–1959) played an important role in implementing choral singing as a powerful tool for awakening the feeling of national identity. Later, the movement resonated with young composers such as José Siqueira (1907–1985) and Claudio Santoro (1919–1989), who diverged from Vargas’s political project and joined the Brazilian Communist Party (PCB), defending socialist realism and employing ethnic sources as a means of courting the masses. In addition to those internal and external political causes defending and stimulating Brazilian nationalism, the musicologists and music critics Mário de Andrade (1893–1945) and Mozart de Araújo (1904–1988) contributed to an enthusiastic invigoration of a genuine Brazilian cultural identity, while fighting against the importation of cultural ideas.

3

With regard to Koellreutter’s active role in the implementation of twelve-tone compositional techniques during the late 1940s, special mention should be made of the “Open Letter to Musicians and Music Critics of Brazil,” written by nationalist composer Camargo Guarnieri (1907–1993) and published in the newspaper O Estado de São Paulo on 17 December 1950. In Guarnieri’s words, the dodecaphonic aesthetic is condemned as “refuge of mediocre composers, of stateless human beings.”

4

The CAPES Foundation is linked to the Brazilian Ministry of Education and has performed a vital role in the expansion and consolidation of graduate programs in all Brazilian states.

5

The first publications on Schenkerian analysis in Brazil date from 1989 (Gerling 1989a; Gerling 1989b).

6

Koellreutter 1978, 4. Translated by the authors. Translations from Brasilian sources in this article are by the authors except where otherwise indicated.

7

Ibid., 1; see Reger 1903; Grabner 1944/2005.

8

Koellreutter 1978, 5. Here Koellreutter also mentions that Riemann’s theory “was recreated [sic] at the end of the nineteenth century (1893)” (ibid.) without indicating which publication he is referring to. It is likely that this reference is Riemann’s Vereinfachte Harmonielehre of 1893, one of his most widely read treatises (Riemann 1893). Nevertheless, in Koellreutter’s text, we do not find any of Riemann’s idiosyncratic propositions, besides what had been incorporated by Grabner in his 1944 textbook Handbuch der Harmonielehre (praktische Anleitung zum funktionellen Tonsatz) (see below).

9

Rehding 2003, 7.

10

Koellreutter 1978, 14–44.

11

Ibid., 31.

12

Harrison 1994, 1. See Grabner 1920, 7.

13

In the third edition of Koellreutter’s book there is an explanation on the abacus, written by Brasil Rocha Brito (Koellreutter 1978/86, 67–73): “The abacus is composed by two concentric discs, allowing the rotation of the internal (smaller) disk upon the external (greater) disk. The external disk contains the symbols for tonalities. The internal disk contains the names of functions which are related to pitches, chords and tonalities.”

14

Riemann 1906.

15

Rehding 2003, 115.

16

Koellreutter 1978, 19.

17

See Oliveira/Oliveira 1978.

18

See Brisolla 1979; Brisolla 2006.

19

Maler 1931/75.

20

Pascoal/Pascoal 2000.

21

La Motte 1976. Translations of la Motte’s textbook appeared in English (1990, Deutscher Taschenbuch Verlag), Spanish (1998, Idea Books) and Italian (2007, Casa Editrice Astrolabio), among others.

22

Krämer 1997.

23

See Taddei 2015; Salles 2016; Albuquerque/Salles 2016.

24

Georg Wasserman(n) was the son of writer Jacob Wassermann and emigrated to Brazil in 1941 with a group of 48 emigrants led by Hermann M. Görgen (Eckl 2015, 233–234). Not much else is currently known about Georg Wasserman’s Brazilian period, except from anecdotal evidence. One of his students, Marly Bernardes Chaves (Federal University of Uberlândia), reports that Wasserman had a “fascinating” approach to harmony integrated with counterpoint (personal communication). This could support the idea that Wasserman was a Schenkerian.

25

Information on Esther Scliar’s pedagogy derive from personal communication with her former students Cristina Capparelli Gerling and Fredi Vieira Gerling, who attended the Teresópolis summer courses in the period from 1969 to 1972, while also privately studying with Scliar.

26

Salzer 1952/62.

27

Dedicated to the memory of Heinrich Schenker, Salzer’s book represents a modified, expanded, and completed version of Schenker’s work, as argued by Leopold Mannes in his foreword. Considering that many points of Schenker’s theory required clarification and many terms needed concise definitions to be presented at a more elementary level, Salzer’s purpose was to mold Schenker’s concepts into “a workable, systematic approach for use by […] anyone interested in the problems of musical continuity, coherence and structure” (ibid., xv).

28

Maria Lúcia Pascoal obtained her doctoral degree from Universidade Estadual de Campinas UNICAMP in 1990, advised by Almeida Prado.

29

See Pascoal 2005; Pascoal/Moreira 2005.

30

Moreira 2002a; Moreira 2002b; Pascoal 2005; Pascoal/Moreira 2005.

31

Presented papers included Ilza Nogueira, “Schenker, o Editor: As Edições Críticas de Quatro das Últimas Sonatas Para Piano de L. van Beethoven”; Cristina Gerling, “Os Gráficos Schenkerianos como Fator de Direcionamento da Interpretação Musical: Exemplificação Através do Prelúdio op. 28 n.º 4 de F. Chopin”; Jamary Oliveira, “Interpretação e Música Contemporânea Brasileira: Heitor Villa-Lobos, O Gatinho de Papelão (A Prole do Bebê n.º 2)”; Jonathan Dunsby, “Vantagens e Desvantagens do Método Analítico Schenkeriano”.

32

Gerling 1989a.

33

Gerling 1989b.

34

Gerling 1990.

35

Nogueira 1990.

36

Gerling 1995a; Gerling 1995b.

37

See Lacerda 1997; Barbosa 1998.

38

Barbosa 1999. Barbosa’s article analyzes Gershwin’s songs The Man I Love, Looking for a Boy, A Foggy Day, and Somebody Loves Me.

39

Franco 2002; Moreira 2002b (advisor: Maria Lúcia Pascoal).

40

Carneiro 2015.

41

Fortes 2017a; Fortes 2017b.

42

Almada 2010c; Almada 2011c.

43

Silva 2012; Vasconcelos 2012; Wildt/Dudeque 2017.

44

Barros 2005. Ernst Mahle (b. 1929), a Brazilian citizen since 1962, studied composition with Johann Nepomuk David in Germany and Hans-Joachim Koellreuter in Brazil. 

45

Barros/Gerling 2007a; Barros/Gerling 2007b; Barros/Gerling 2007c; Gerling/Barros 2009; Gerling/Barros 2017.

46

Barros 2018.

47

Silva/Barros 2009.

48

Thompson 2010.

49

Fraga 2011.

50

Forte/Gilbert 1982.

51

Cadwallader/Gagné 1998.

52

Gerling 2014.

53

Ibid., 62.

54

Chaffin/Gerling/Demos/Melms 2013.

55

See Gerling/Barros 2017.

56

Dudeque 2005b; Coelho de Souza 2006.

57

Schoenberg 1911/2001.

58

According to Carlos Kater (2001), the Musica Viva movement was established in 1938 and went through three phases until its decline during the early 1950s. These phases, or “moments” in Kater’s words, are marked by two manifestos dated 1 May 1944 and 1 November 1946. The final paragraph of the second document, entitled Declaration of Principles, describes the movement as an avant-garde group: “Musica Viva accompanies the present in its path of discoveries and conquests, struggling for new ideas for a new world, believing in the creative force of the human spirit and in the art of the future” (ibid.). This manifesto is signed by Cláudio Santoro, Egydio de Castro e Silva, Eunice Katunda, Geni Marcondes, César Guerra Peixe, Heitor Alimonda, Hans-Joachim Koellreutter, and Santino Parpinelli.

59

For more information about Koellreutter’s life and work, see Kater 2001 and Béhage 2003.

60

Dudeque 1997.

61

Dudeque 2005a.

62

See also part three of John Covach’s article in the present issue (https://doi.org/10.31751/991).

63

Dudeque 2003; Dudeque 2005b; Dudeque 2007.

64

Almada 2008a.

65

Coelho de Souza 2011.

66

Araújo/Borém (2013a, 2013b) adapted concepts from Schoenberg’s theory of harmony and form (developing variation) in the recreation of Hermeto Pascoal’s lead sheets (“Calendário do Som”).

67

Biato 1995; Vidal Junior 1999; Hartmann Sobrinho 2001; Zaghi 2005; Oliveira 2010; Freitas 2012; Leong 2013; Vasconcelos 2013; Maia 2013.

68

Almada 2010a; Almada 2016a.

69

See, for example, Almada 2009a, Almada 2009b.

70

Mayr/Almada 2016; Mayr/Almada 2017; Mayr/Almada forthcoming.

71

Almada 2008b.

72

Almada 2011a; Almada 2016c.

73

Almada 2010b; Almada 2011b; Almada 2013b.

74

Mayr 2015a; Mayr 2015b; Mayr/Almada 2014.

75

Almada 2013c.

76

Almada created the “Gr System” (Gr for Grundgestalt) in 2013. It aims to explain the use of variations in composition. Considering the existence of isomorphic relations between structural elements (pitch, interval, and duration) and integers, the system allows for musical parameters to be isolated and manipulated by means of arithmetic operations.

77

Almada 2012, 2013a, 2015a, 2015b, 2016b, 2016d, 2017a, 2017b.

78

See Koellreutter 1978; Oliveira/Oliveira 1978; Brisolla 1979.

79

Of course, this generalized observation admits creative exceptions.

80

See Oliveira 2015.

81

See https://www.nics.unicamp.br; https://www.nics.unicamp.br/mus3; http://dgp.cnpq.br/dgp/espelhogrupo/1073777136298429; https://musmat.org (28 Sep 2018).

82

See http://tema.mus.br (28 Sep 2018).

References

Albuquerque, Joel / Paulo de Tarso Salles. 2016. “Rede de projeções por inversão, relações entre Tonnetze de diferentes tricordes.” Musica Theorica 2/1: 139–167.

Almada, Carlos de L. 2008a. “O Dodecafonismo Peculiar de Cláudio Santoro: Análise do Ciclo de Canções A Menina Boba.” Opus 14/1: 7–24. https://www.anppom.com.br/revista/index.php/opus/article/view/233 (17 Oct 2018)

Almada, Carlos de L. 2008b. “O Conceito de Variação em Desenvolvimento no Primeiro Movimento da Sonata para Piano op. 2/1, de Beethoven.” Música Hodie 8/2: 83–94. https://www.revistas.ufg.br/musica/article/view/6015/12357 (17 Oct 2018)

Almada, Carlos de L. 2009a. “A Funcionalidade Tonal Expandida Através de Nuvens Harmônicas.” Ictus 10/1: 56–68.

Almada, Carlos de L. 2009b. “Texturas Harmônicas Presentes na Primeira Sinfonia de Câmara Op. 9, de Arnold Schoenberg.” Cadernos do Colóquio 10/1: 50–65. http://www.seer.unirio.br/index.php/coloquio/article/view/470 (17 Oct 2018)

Almada, Carlos de L. 2010a. “Nas Fronteiras da Tonalidade: Tradição e Inovação na Harmonia da Primeira Sinfonia de Câmara Op. 9, de Arnold Schoenberg.” Doctoral dissertation, Universidade Federal do Estado do Rio de Janeiro.

Almada, Carlos de L. 2010b. “Variação em desenvolvimento na construção do tema principal da Sonata para Piano Op. 1, de Alban Berg.” Opus 16/1: 99–112. https://www.anppom.com.br/revista/index.php/opus/article/view/227 (17 Oct 2018)

Almada, Carlos de L. 2010c. “Chovendo na Roseira de Tom Jobim: Uma Abordagem Schenkeriana.” Per Musi 22: 99–106. http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1517-75992010000200009 (17 Oct 2018)

Almada, Carlos de L. 2011a. “A Variação Progressiva Aplicada na Geração de Ideias Temáticas.” In Teoria, Crítica e Música na Atualidade: Anais do II Simpósio Internacional de Musicologia da UFRJ, edited by Maria Alice Volpe. Rio de Janeiro: UFRJ, 79–90.

Almada, Carlos de L. 2011b. “Derivação Temática a Partir da Grundgestalt da Sonata para Piano op. 1, de Alban Berg.” Anais do II Encontro Internacional de Teoria e Análise Musical. São Paulo: UNESP-USP-UNICAMP. CD-ROM.

Almada, Carlos de L. 2011c. “A Ursatz Jobiniana: Considerações sobre Aplicações da Análise Schenkeriana em Estudos de Música Popular.” In 3er Congreso Latinoamericano de Formación Académica en la Música Popular – Apertura e Integración en la Música Popular, edited by Hernán Conen. Córdoba: Universidad Nacional de Villa Maria, 1–10.

Almada, Carlos de L. 2012. “Aplicações Composicionais de um Modelo Analítico para Variação Progressiva e Grundgestalt.” Opus 18/1: 127–152. https://www.anppom.com.br/revista/index.php/opus/article/view/179 (17 Oct 2018)

Almada, Carlos de L. 2013a. “GENEMUS: Ferramenta Computacional para Composição com Grundgestalt e Variação Progressiva.” In XXIII Congresso Anual da ANPPOM – Caderno de Resumo e Anais, edited by Adriana Lopes Moreira. Natal: ANPPOM. http://www.anppom.com.br/congressos/index.php/23anppom/Natal2013/paper/view/2006/301 (17 Oct 2018)

Almada, Carlos de L. 2013b. “Simbologia e Hereditariedade na Formação de uma Grundgestalt: a primeira das Quatro Canções Op. 2 de Berg.” Per Musi 27: 75–88. http://www.scielo.br/scielo.php?pid=S1517-75992013000100008&script=sci_abstract&tlng=pt (17 Oct 2018)

Almada, Carlos de L. 2013c. “Considerações Sobre a Análise de Grundgestalt Aplicada à Música Popular.” Per Musi 29: 117–124. http://www.scielo.br/scielo.php?pid=S1517-75992014000100013&script=sci_abstract&tlng=pt (17 Oct 2018)

Almada, Carlos de L. 2015a. “Genetic Algorithms Based on the Principles of Grundgestalt and Developing Variation.” In Proceedings of the 3rd Biennial Conference on Mathematics and Computation in Music, edited by Anja Volk and David Meredith. London: Queen Mary University.

Almada, Carlos de L. 2015b. “Evolution in Musical Contexts: The Software DARWIN.” In XXV Congresso da ANPPOM Caderno de Resumo e Anais. Vitória: ANPPOM. https://www.anppom.com.br/congressos/index.php/25anppom/Vitoria2015/paper/view/3396 (17 Oct 2018)

Almada, Carlos de L. 2016a. Nas Fronteiras da tonalidade: Tradição e inovação na Primeira Sinfonia de Câmara, op. 9, de Arnold Schoenberg. Curitiba: Prisma Editora.

Almada, Carlos de L. 2016b. “Improvements of a Computational Tool intended to Systematical Production of Abstract Melodic Variations.” In Anais do XXVI Congresso da Associação Nacional de Pesquisa e Pós-Graduação em Música, edited by Marcos Holler. Belo Horizonte: ANPPOM. https://www.anppom.com.br/congressos/index.php/26anppom/bh2016/paper/view/3965 (17 Oct 2018)

Almada, Carlos de L. 2016c. “Derivative Analysis and Serial Music: The Theme of Schoenberg’s Orchestral Variations Op. 31.” Per Musi 33: 1–24. http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1517-75992016000300002 (17 Oct 2018)

Almada, Carlos de L. 2016d. “Artificial Selection Strategies Implementation in a Model for Musical Variation.” Musica Theorica 1/1: 1–15. https://tema.mus.br/revistas/index.php/musica-theorica/article/view/5/11 (17 Oct 2018)

Almada, Carlos de L. 2017a. “Gödel-Vector and Gödel-Address as Tools for Genealogical Determination of Genetically-Produced Musical Variants.” In The Musical-Mathematical Mind: Patterns and Transformations, edited by Gabriel Pareyon. New York: Springer, 9–16.

Almada, Carlos de L. 2017b. “Evolutionary Variation Applied to the Composition of CTG, for Woodwind Trio.” MusMat: Brazilian Journal of Music and Mathematics 1/1: 1–14.

Araújo, Fabiano / Fausto Borém. 2013a. “A Harmonia Tonal de Schoenberg: Uma Proposta para a Análise e Composição de Lead Sheets.” Per Musi 28: 35–69.

Araújo, Fabiano / Fausto Borém. 2013b. “Variação Progressiva de Schoenberg em Hermeto Pascoal: Análise e Realização de Duas Lead Sheets do Calendário do som.” Per Musi 28: 70–95. http://www.scielo.br/scielo.php?pid=S1517-75992013000200006&script=sci_abstract&tlng=pt (17 Oct 2018)

Barbosa, Joel L. 1998. “Estudo para Clarineta de Gaetano Donizetti.” http://www.manuka.com.br/artigos/barbosa/barbosa1.htm (17 Oct 2018)

Barbosa, Joel L. 1999. “Gershwin and the Expansion of the Tonal System’s Relationships Through the Blue Note.” Ictus 1/1: 109–123.

Barros, Guilherme A. Sauerbronn de. 2005. “Goethe e o Pensamento Estético-Musical de Ernst Mahle: Um Estudo do Conceito de Harmonia.” Doctoral dissertation, Universidade Federal do Estado do Rio de Janeiro.

Barros, Guilherme Sauerbronn. 2018. “A Humoreske Op. 20 de Schumann e a Urlinie de Schenker.” Revista Música 18/1: 9–24. https://www.revistas.usp.br/revistamusica/article/view/147206 (17 Oct 2018)

Barros, Guilherme A. Sauerbronn de / Cristina C. Gerling. 2007a. “O Intérprete Schenkeriano e o Conceito de Organicidade.” Anais do IV Simpósio de Pesquisa em Música, edited by Norton Dudeque. Curitiba: Editora do Departamento de Artes da UFPR, 202–208.

Barros, Guilherme A. Sauerbronn de / Cristina C. Gerling. 2007b. “O Conceito Schenkeriano de Organicidade e a Sonata K. 533 de Mozart.” DAPesquisa 1: 1–9.

Barros, Guilherme A. Sauerbronn de / Cristina C. Gerling. 2007c. “Análise Schenkeriana e Performance.” Opus 13/2: 1–20. https://www.anppom.com.br/revista/index.php/opus/article/view/307 (18 Oct 2018)

Béhague, Gerard. 2003. Koellreutter, Hans-Joachim. In MGG Online, edited by Laurenz Lütteken. Kassel: Bärenreiter. https://www.mgg-online.com/mgg/stable/47243 (18 Oct 2018)

Biato, Eduardo Bertolossi. 1995. “Arnold Schoenberg: Variations on a Recitative Op. 40: Análise Formal e Realização Tímbrica no Órgão da Escola de Música da UFRJ.” Master’s thesis, Universidade Federal do Rio de Janeiro.

Brisolla, Cyro. 1979. Princípios de Harmonia Funcional. São Paulo: Novas Metas.

Brisolla, Cyro. 2006. Princípios de Harmonia Funcional. Revisado e ampliado por Mario Ficarelli. São Paulo: Annablume.

Cadwallader, Allen Clayton / David Gagné.1998. Analysis of Tonal Music: A Schenkerian Approach. Oxford: Oxford University Press.

Carneiro, Josimar M. G. 2015. “O Design Musical em Canções de Antônio Carlos Jobim.” Doctoral dissertation, Universidade Federal do Estado do Rio de Janeiro.

Chaffin, Roger / Cristina C. Gerling / Alexander P. Demos / Andrea Melms. 2013. “Theory and Practice: A Case Study of How Schenkerian Analysis Shaped the Learning of Chopin’s Barcarolle.” In Proceedings of ISPS 2013, edited by Aaron Williamon and Werner Goebl. Brussels: AEC, 21–26. http://performancescience.org/wp-content/uploads/2018/08/isps2013_proceedings.pdf (18 Oct 2018)

Coelho de Souza, Rodolfo. 2006. “Aspectos de Modernidade na Música de Nepomuceno Relacionados ao Projeto de Tradução do Harmonielehre de Schoenberg.” Em Pauta 17/29: 63–81. https://seer.ufrgs.br/EmPauta/article/view/7472 (18 Oct 2018)

Coelho de Souza, Rodolfo. 2011. “A Recepção das Teorias do Dodecafonismo nos Últimos Quartetos de cordas de Cláudio Santoro.” Revista Brasileira de Música 24/2: 329–350. https://revistas.ufrj.br/index.php/rbm/issue/viewFile/374/130 (18 Oct 2018)

Dudeque, Norton. 1997. “Harmonia Tonal e o Conceito de Monotonalidade nos Escritos de Arnold Schoenberg (1874–1951).” Master’s thesis, Universidade de São Paulo.

Dudeque, Norton. 2003. “Variação Progressiva Como um Processo Gradual no Primeiro Movimento do Quarteto A Dissonância, K. 465, de Mozart.” Per Musi 8: 41–56.

Dudeque, Norton. 2005a. Music Theory and Analysis in the Writings of Arnold Schoenberg (1874–1951). Aldershot: Ashgate.

Dudeque, Norton. 2005b. “Aspectos do Academicismo Germânico no Primeiro Movimento do Quarteto n. 3 de Alberto Nepomuceno.” Ictus 6: 211–233.

Dudeque, Norton. 2007. “Schoenberg: Emancipação da Dissonância, Tonalidade Expandida e Variação Progressiva em Friede auf Erden, op. 13.” Debates 9: 7–33. http://www.seer.unirio.br/index.php/revistadebates/article/view/3987 (18 Oct 2018)

Eckl, Marlen. 2015. “‘Everywhere Paradise Is Lost’: The Brazilian National Myth in the Works of Refugees of Nazism.” In KulturConfusão – On German-Brazilian Interculturalities, edited by Anke Finger, Gabi Kathöfer and Christopher Larkosh. Berlin: de Gruyter, 219–246.

Forte, Allen / Steven E. Gilbert. 1982. Introduction to Schenkerian Analysis: Form and Content in Tonal Music. New York: Norton.

Fortes, Rafael Moreira. 2017a. “O Organicismo no pensamento musical: conceito e crítica.” In Anais do II Congresso da TeMA, edited by Carlos Almada. Salvador: TeMA, 62–71. https://drive.google.com/file/d/0B25FEDImmu_ud01pVm1WdGpXYjQ/view (18 Oct 2018)

Fortes, Rafael Moreira. 2017b. “A Expansão da análise schenkeriana para o repertório pós-tonal.” In XXIII Colóquio do PPGM/UNIRIO, edited by Caderno de Resumos, Daniel Lemos Cerqueira, Rafael Moreira Fortes and Joana Martins Saraiva. Rio de Janeiro: UNIRIO, 87–88. http://www.unirio.br/ppgm/coloquio/2017_arquivos/caderno-de-resumos-2017-pdf (18 Oct 2018)

Fraga, Orlando. 2011. Progressão Linear: Uma Breve Introdução à Teoria de Schenker. Londrina: Eduel.

Franco, César Henrique Rocha. 2002. “Um Estudo da Forma-Sonata. Análise de Brahms-Sinfonia n.º 3 (Allegro con brio), Segundo os Modelos de Felix Salzer e Heinrich Schenker.” Master’s thesis, Universidade Estadual de Campinas.

Freitas, Philippe. 2012. “Antinomia da Expressão: Adorno Ante o Sismógrafo de Erwartung Op. 17, de Schoenberg.” Master’s thesis, Universidade Estadual Paulista Júlio de Mesquita Filho.

Gerling, Cristina Capparelli. 1985. “Performance Analysis for Pianists: A Critical Discussion of Selected Procedures.” DMA dissertation, Boston University.

Gerling, Cristina Capparelli. 1989a. “A Teoria de Heinrich Schenker: Uma Breve Introdução.” Em Pauta 1/1: 22–34.

Gerling, Cristina Capparelli. 1989b. “A Contribuição de Heinrich Schenker para a Interpretação Musical.” Opus 1/1: 24–31. https://www.anppom.com.br/revista/index.php/opus/article/view/3/7 (18 Oct 2018)

Gerling, Cristina Capparelli. 1990. “Considerações Sobre a Análise Schenkeriana.” Cadernos de Estudo: Análise Musical 2: 1–8.

Gerling, Cristina Capparelli. 1995a. “Schenker e Seus Discípulos na América.” Em Pauta 6–7/9–10: 53–60.

Gerling, Cristina Capparelli. 1995b. “Schenker e Seus Discípulos na América: Os Ortodoxos.” ArT 23: 81–87.

Gerling, Cristina Capparelli. 2014. “F. Chopin’s Barcarolle op. 60: Learning Strategies” / “Barcarola op. 60 de F. Chopin: Etapas e estratégias de aprendizagem.” Art Research Journal 1/2, 59–75. https://periodicos.ufrn.br/artresearchjournal/article/view/5364 (25 Oct 2018)

Gerling, Cristina Capparelli / Guilherme A. Sauerbronn de Barros. 2009. “Análise Schenkeriana: Interpretação e Crítica.” In Pesquisa em Música no Brasil 1: Métodos, Domínios, Perspectivas, edited by Rogério Budaz. Goiânia: ANPPOM, 87–121.

Gerling, Cristina Capparelli / Guilherme A. Sauerbronn de Barros. 2017. “Considerações Acerca de um Glossário de Termos Schenkerianos.” In Teoria e Análise Musical em Perspectiva Didática, edited by Ilza Nogueira. Salvador: UFBA, 185–189.

Grabner, Hermann. 1920. Regers Harmonik, Munich: Halbreiter.

Grabner, Hermann. 1944/2005. Handbuch der Harmonielehre (praktische Anleitung zum funktionellen Tonsatz) [since the third edition 1955 published as Handbuch der funktionellen Harmonielehre], Berlin: Hesse. (13th edition. Kassel: Bärenreiter 2005.)

Hartman Sobrinho, Ernesto Frederico. 2001. “Aplicação da Análise Schoenberg-Schenkeriana à Sonata n.º 3 para Piano de Cláudio Santoro.” Master’s thesis, Universidade Federal do Rio de Janeiro.

Harrison, Daniel. 1994. Harmonic Function in Chromatic Music. Chicago: University of Chicago Press.

Kater, Carlos. 2001. Música Viva e H. J. Koellreutter: movimentos em direção à modernidade. São Paulo: Musa Editora.

Koellreutter, Hans-Joachim. 1978. Harmonia Funcional: Introdução à teoria das Funções Harmônicas. São Paulo: Ricordi. (Third edition. 1986.)

Krämer, Thomas. 1997. Lehrbuch der harmonischen Analyse. Wiesbaden: Breitkopf & Härtel.

La Motte, Dieter. 1976. Harmonielehre. Kassel: Bärenreiter.

Lacerda, Marcos Branda. 1997. “Uma Breve Resenha sobre a Contribuição de Schenker para a Análise Musical.” Revista Eletrônica de Musicologia 2/1. http://www.rem.ufpr.br/_REM/REMv2.1/vol2.1/BreveResenha/BreveResenha.html (18 Oct 2018)

Leong, Iris Maria da Silva. 2013. “A Literatura Simbolista em Obras de Arnold Schoenberg.” Master’s thesis, Universidade Estadual Paulista Júlio de Mesquita Filho.

Maia, Igor Leão. 2013. “Klangfarbenmelodie: Orquestração do Timbre.” Master’s thesis, Universidade Estadual de Campinas.

Maler, Wilhelm. 1931/75. Beitrag zur Durmolltonalen Harmonielehre [1931]. Eighth edition. Leipzig: Leuckart.

Mayr, Desirée. 2015a. “Os Processos Criativos de Leopoldo Miguéz no Primeiro Movimento da Sonata para Violino op. 14.” Master’s thesis, Universidade Federal do Rio de Janeiro – UFRJ.

Mayr, Desirée. 2015b. “Considerations on Developing Variation in Brazilian Romantic Music: The First Movement of Leopoldo Miguéz’s Violin Sonata Op. 14.” In Caderno de Resumos e Anais do XXV Congresso da ANPPOM. Vitória: ANPPOM. https://anppom.com.br/congressos/index.php/25anppom/Vitoria2015/paper/view/3398/1129 (18 Oct 2018)

Mayr, Desirée / Carlos de L. Almada. 2014. “Uma Aplicação da Análise Derivativa na Música Romântica Brasileira: O Primeiro Movimento da Sonata para Violino e Piano Op. 14, de Leopoldo Miguéz.” Anais dos Congressos da TeMA – I Congresso – “O Pensamento Musical Criativo: Teoria, Análise e os Desafios Interpretativos da Atualidade,“ edited by Marcos Sampaio. Salvador: TeMA, 19-26. https://drive.google.com/file/d/0B25FEDImmu_uSlNKNjNqeWhLbFU/view (18 Oct 2018)

Mayr, Desirée / Carlos de L. Almada. 2016. “Use of Linkage Technique in Johannes Brahms’ Op. 78 and Leopoldo Miguéz’s Op. 14 Violin Sonatas.” Opus 22/2: 429–449. https://www.doi.org/10.20504/opus2016b2216 (18 Oct 2018)

Mayr, Desirée / Carlos de L. Almada. 2017. “Geometrical and Vector Representation of Metrical Relations.” Anais dos Congressos da TeMA – II Congresso – “Teoria e Análise Musical em Perspectiva Didática,“ edited by Carlos Almada. Salvador: TeMA, 10–19. https://drive.google.com/file/d/0B25FEDImmu_ud01pVm1WdGpXYjQ/view (18 Oct 2018)

Mayr, Desirée / Carlos de L. Almada. forthcoming. “Correlations Between Developing Variation and Genetic Processes in the Analysis of Brahms’ Violin Sonata Op. 78.” In Ninth European Music Analysis Conference. Proceedings. Strasbourg.

Moreira, Adriana L. C. 2002a. “O Inter-relacionamento entre Performance e Análise Musical nos 16 Poesilúdios para Piano de Almeida Prado.” Música Hodie 2/1–2: 19–29. https://www.revistas.ufg.br/musica/article/view/19620/11326 (18 Oct 2018)

Moreira, Adriana L. C. 2002b. “A Poética nos 16 Poesilúdios para Piano de Almeida Prado: Análise Musical.” Master’s thesis, Universidade Estadual de Campinas UNICAMP.

Nogueira, Ilza. 1990. “A Estruturação Tonal da Canção Mein Herz, das ist ein tiefer Schacht: Uma Aproximação Através da Teoria Schenkeriana.” ArT 17: 39–62.

Oliveira, José Zula de / Marilena de Oliveira. 1978. Harmonia Funcional. São Paulo: Cultura Musical.

Oliveira, Reinaldo Marques de. 2010. “A Conclusão Cromática em Obras de Arnold Schoenberg e Cláudio Santoro.” Doctoral dissertation, Universidade Estadual Paulista Júlio de Mesquita Filho.

Oliveira, Liduíno José Pitombeira de. 2015. “A Produção de Teoria Composicional no Brasil”. In O Pensamento Musical Criativo, Série Congressos da TeMA 1, 61–89.

Pascoal, Maria Lúcia. 2005. “Villa-Lobos A Prole do Bebê n. 1 e 2: Estratégias da Textura como Recurso Composicional.” Per Musi 11: 95–105.

Pascoal, Maria Lúcia / Adriana L. C. Moreira. 2005. “Por uma Integração entre Percepção e a Análise Musical: Poesilúdio n. 16 de Almeida Prado.” In Anais do 1.o Simpósio Internacional de Cognição e Artes Musicais, edited by Norton Dudeque. Curitiba: De Artes/UFPR, 127–133.

Pascoal, Maria Lúcia / Alexandre Pascoal. 2000. Estrutura Tonal: Harmonia. São Paulo: Companhia Editora Paulista.

Reger, Max. 1903. Beiträge zur Modulationslehre. Leipzig: Kahnt.

Rehding, Alexander. 2003. Hugo Riemann and the Birth of Modern Musical Thought. Cambridge: Cambridge University Press.

Riemann, Hugo. 1893. Vereinfachte Harmonielehre oder die Lehre von den tonalen Funktionen der Akkorde. London: Augener.

Riemann, Hugo. 1906. Katechismus der Harmonie- und Modulationslehre. Leipzig: Hesse.

Salles, Paulo de Tarso. 2016. “Os Quartetos de Cordas de Villa-Lobos: o Discurso da Besta.” Habilitation thesis. Universidade de São Paulo.

Salzer, Felix. 1952/62. Structural Hearing: Tonal Coherence in Music. New York: Dover.

Schoenberg, Arnold. 1911/2001. Harmonia [1911]. Translated by Marden Maluf. São Paulo: Editora UNESP.

Silva, Rafael Palmeira da. 2012. “Estruturas Fundamentais no Blues: Adaptação de Conceitos Schenkerianos Considerando a Inflexão Melódica Afro-Americana e seu Desenvolvimento no Jazz.” Master’s thesis, Universidade Federal do Paraná.

Silva, Rodrigo Moreira / Guilherme A. Sauerbronn de Barros. 2009. “Dualidade Tonal no Prelúdio n.º 5 para Violão de Villa-Lobos.” Anais do XIX Congresso da ANPPOM. Curitiba: ANPPOM, 789–792. http://antigo.anppom.com.br/anais/anaiscongresso_anppom_2009/VIII_TeoriaeAnalise.pdf (18 Oct 2018)

Taddei, Rita de Cássia. 2015. “Alberto Nepomuceno, Artémis: Um Estudo de Análise Neorriemanniana.” Doctoral dissertation, Universidade de São Paulo.

Thompson, Claudio Laeber. 2010. “Alceu Camargo: Violinista Profissional, Compositor Diletante: Análise de sua Obra Completa para Piano.” Master’s thesis, Universidade do Estado de Santa Catarina.

Vasconcelos, Lúcia de Fátima Ramos. 2013. “‘Transcriação’: O Processo de Tradução da Obra Pierrot Lunaire de Arnold Schoenberg por Augusto de Campos: Uma Análise a Partir da Ótica Melopoética.” Doctoral dissertation, Universidade Estadual de Campinas.

Vasconcelos, Renato Luciano de. 2012. “A Análise Schenkeriana e a Ornamentação: Um Estudo Crítico.” Master’s thesis, Universidade Federal do Paraná.

Vidal Junior, Itamar. 1999. “A ‘Atonalidade’ de Arnold Schoenberg: As Composições e os Escritos Sobre Música, 1908–1912.” Master’s thesis, Universidade Estadual de Campinas.

Wildt, Francisco Koetz / Norton Eloy Dudeque. 2017. “Coesão Tonal e Progressão Linear nas Canções em Português de Alberto Nepomuceno: Ora Dize-me a Verdade op. 12 n. 1.” In Anais dos Congressos da TeMA – II Congresso, edited by Carlos Almada. Salvador: TeMA, 72–82. https://drive.google.com/file/d/0B25FEDImmu_ud01pVm1WdGpXYjQ/view (18 Oct 2018)

Zaghi, Rogério. 2005. “Perspectivas Analíticas e Interpretativas na Obra para Piano de Arnold Schoenberg.” Master’s thesis, Universidade de Campinas.

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