Bartok at Harvard: An introduction to chromatic polymodality and tonal centricity
TABLE OF CONTENTS
ACKNOWLEDGMENTS ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ iii ABSTRACT ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ v
CHAPTER 1. INTRODUCTION TO POLYMODALITY ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 1
CHAPTER 2. KEY SIGNATURES IN BARTÓK’S POLYMODAL MUSIC ∙∙∙∙∙∙∙∙∙ 22 2.1 Key Signatures in Hungarian Folk Music ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 29 2.2 Key Signatures in Bartók’s Mikrokosmos ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 50 2.3 Conclusion ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 96
CHAPTER 3. CADENCES IN BARTÓK’S POLYMODAL MUSIC∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 98 3.1 General Characteristics of Bartók’s Cadences ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 99 3.2 Bartók’s Melodic Cadences ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 120 3.3 Bartók’s Harmonic Cadences ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 137 3.4 Conclusion ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 158
CHAPTER 4. PLAGAL MODULATION IN BARTÓK’S POLYMODAL MUSIC ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙160 4.1 Real Plagal Modulation ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 165 4.2 Modal Plagal Modulation ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 188 4.3 Conclusion ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 210
CHAPTER 5. CONCLUSION ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 212
SELECTED BIBLIOGRAPHY ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ 218
ABSTRACT This dissertation investigates Bartok’s polymodal language from the perspective his new concept of tonality, referred as “polymodal chromaticism,” which superposes or juxtaposes two or more modes with the same fundamental tone. Bartok’s polymodal music is based on the pentatonic and various folk modal scales. In particular, the pentatonic system in the Hungarian folk songs provides him with a rich resource as well as unique musical system. In addition, Bartok’s compositional principle of polymodality is further developed by his free use of various scales, which ultimately lead to a new way of constructing phrases. Thus, his polymodal music comprises several prominent and unique features. First, in his creative concept of the key signature, he invents an unorthodox notational function for the key signature. Secondly, his cadential forms are represented in both melodic and harmonic configurations and are characterized by their distinctive modal features and bass-lines. Bartok also effectively articulates sections of his forms by using new kinds of cadences in different metrical positions. Finally, the unique formal structure, the Hungarian plagal form, figures prominently in his polymodal music. The two different plagal modulations, real plagal modulation and modal plagal modulation, are developed in terms of this form. In these modulations, we notice certain recurring patterns and the tonal motion of a descending fifth. This unique polymodal phraseology is generated from Bartok’s great insight into the spirit of Hungarian folk songs. Bartok seemed to intimately understand the properties of these songs, which he eventually exploited in his chromatic musical language through his unique notation, harmonizations and formal structures.
INTRODUCTION: BARTÓK’S POLYMODALITY
At the turn of the twentieth century, many composers began to challenge the traditional tonal system in the exploration and development of unique compositional languages, for what is commonly described as post-tonal music.
Among these experimental composers, in particular, the pitch organization of Bartók’s music has been diversely disputed in terms of its tonality. 1 Indeed, many theorists have pointed out that there is a certain undeniable centric tone in much of it. Thus, we must ask the following questions:
Why do we feel a sense of centricity in his music? What musical factors create this tonal centricity? 2
1 For the comparison of different theoretical approaches to pitch organization in Bartók’s music, in general, see the critical articles by: Mark D. Nelson “Folk Music and the ‘Free and Equal Treatment of the Twelve Tones’: Aspects of Béla Bartók’s Synthetic Methods” College Music Symposium 27 (1987): 59-116; Malcolm Gillies, “Bartók Analysis and Authenticity,” Studia Musicologica (1995): 319-27; Laszlo Somfai, “Perspectives of Bartók Studies in 1995,” Studia Musicologica (1995): 241-47; Ivan Waldbauer “Theorist’s Views on Bartók from Edwin von der Null to Paul Wilson,” Studia Musicologica (1996): 93-121; Elliott Antokoletz, “Theories of Pitch Organization in Bartók’s Music: A Critical Evaluation,” International Journal of Musicology 7 (1998): 259-300.
2 According to Bartók’s statements, “tonality” simply refers to a tonal centricity not the narrower traditional concept. In his interview with Malcolm Gillies in 1929, Bartók states that “in the works I refer to tonality (in the broad sense of the word, of course) is not lacking, but at times is more or less veiled either by idiosyncrasies of the harmonic texture or by temporary deviation in the melodic curves.” See Malcolm Gillies, “A Conversation with Bartók: 1929,” The Musical Times 128 (1987): 556-57.
My dissertation began with these questions, thus, according to Bartók’s own statements, I will explore his highly innovative concept of tonality, which he himself referred to as a system of “polymodal chromaticism.” I will also investigate the various phraseological aspects found in his polymodal music.
Therefore, in the analysis of Bartók’s compositions, the question of tonality is one of the more intriguing issues, which for years has been debated by theorists. 3
Some often have argued for opposing theoretical interpretations concerning the tonal centricity of his music. 4
3 Edwin von der Nüll, Béla Bartók: Ein Beitrag zur Morphologie der neuen Musik (Halle: Mitteldeutsche Verlags-Actien-Gesellschaft, 1930); George Perle, “Symmetrical Formations in the String Quartets of Béla Bartók,” Music Review 16 (1955): 300-12; Allen Forte, “Bartók’s ‘Serial’ Composition,” The Musical Quarterly 46/2 (1960): 233-45; Roy Travis, “Tonal Coherence in the First Movement of Bartók’s Fourth String Quartet,” The Music Forum 2 (1970): 298-371; Peter Petersen, Die Tonalität im Instrumental-Schaffen von Béla Bartók (Hamburg: Karl Dieter Wagner, 1971); János Kárpáti, “Tonal Divergences of Melody and Harmony: A Characteristic Device in Bartók’s Musical Language,” Studia Musicologica (1982): 373-80; Ivan F. Waldbauer, “Intellectual Construct and Tonal Direction in Bartók’s ‘Divided Arpeggios,’” Studia Musicological 24 (1982): 527-36; Elliott Antokoletz, The Music of Béla Bartók: A Study of Tonality and Progression in Twentieth-Century Music (Berkeley and Los Angeles: University of California Press, 1984); Richard Cohn, “Inversional Symmetry and Transpositional Combination in Bartók,” Music Theory Spectrum 10 (1988): 19-42; Malcolm Gillies, Notation and Tonal Structure in Bartók’s Later Works (New York and London: Garland Publishing, Inc., 1989); Charles D. Morrison, “Prolongation in the Final Movement of Bartók’s String Quartet No. 4,” Music Theory Spectrum 13/2 (1991): 179-96; Paul Wilson, The Music of Béla Bartók (New Haven: Yale University Press, 1992); István Németh G., “Bitonale und bimodale Phänomene in den Klavierwerken Bartóks (1908-1926),” Studia Musicologica (2005): 257-94.
4 Representative theoretical research concerning tonal aspects includes: approaches to a tonal centered structure (Edwin von der Nüll, Malcolm Gillies, Roy Travis, Charles Morrison), discussions of a bi- or multiple-centered structures (János Kárpáti, József Ujfalussy, Ivan Waldbauer), applications of atonal theory or axes of symmetry (Paul Wilson, Allen Forte, Richard Cohn, George Perle, Elliott Antokoletz).
These contradictory musical perspectives invite us to return to Bartók’s own statements about his compositional concepts. Beginning in February 1943, two years before he died, Bartók gave four lectures at Harvard University. In these lectures, Bartók discusses the differences between the new Hungarian art music and Western music. He goes on to provide an important insight into atonality, polytonality, and polymodality in terms of Hungarian peasant music. First, he briefly examines three kinds of terms related to his music. In no uncertain terms, he clarifies the fact that his work, influenced by Hungarian peasant music, is built on a tonal basis, but one that differs from the traditional concept of major-minor tonality.
One point, in particular, I must again stress: Our peasant music, naturally, is invariably tonal, although not always in sense that the inflexible major and minor system is tonal. (An “atonal” folk-music, in my opinion, is unthinkable.) Since we depend upon a tonal basis of this kind in our creative work, it is quite self-evident that our works are quite pronouncedly tonal in type. I must admit, however, that there was a time when I thought I was approaching a species of twelve-tone music. Yet even in works of that period the absolute tonal foundation is unmistakable. 5 In addition, in his essay of “Harvard Lectures,” Bartók emphasizes that atonal music does not exist in our physical environment.
6 He explains that harmonics usually accompany the sound of a single tone according to pre-determined acoustical phenomena. Moreover, when we hear tones that follow an initial tone, we intuitively seek their pitch relation with the initial or fundamental tone. Thus, he declares that perfectly atonal music is actually not possible. On the other hand, Bartók defines polytonality as the simultaneous use of different diatonic keys in two (bi-tonal) or more parts (polytonal). 7 Here, polytonality exists only for the eye when one looks at such music. But our mental hearing again will select one key as a fundamental, and will project the tones of the other keys in relation to the one selected. The parts in different That is, in these keys, each part is supposed to develop an independent tonal progression under its own tonal system. However, Bartók insists that polytonality exists only in the score, thus strongly rejecting the possibility of any aural recognition of polytonal music. He also doubted the effect of the simultaneous use of two different keys.
5 Béla Bartók, Béla Bartók Essays, ed. Benjamin Suchoff (New York: St. Martin’s Press, 1976; reprint, Lincoln and London: University of Nebraska Press, 1992), 338-39.
6 Ibid., 365. Bartók states that the only exception is found in the Austrian atonal composer Josef Hauer (1883-1959), in Suite no.7, op. 48 (1926), which demonstrates the sound of real atonal music. Bartók also underlines the fact that Schoenberg’s music is not really atonal in these lectures.
keys will be interpreted as consisting of altered tones of the chosen key.… And, similarly, our hearing cannot perceive two or more different keys with two or more different fundamental tones, as such; it will simplify matters by reducing the maze of keys to one principal key. 8 Ironically, his statements have been occasionally misapprehended by theorists, who take a bi-tonal approach to his music. Indeed, they have been used as evidence for his belief in bitonality and the perceptual relationship between two keys with different scale degrees.
9 However, this insistence by bi-tonal theorists is constructed on the incorrect supposition that Bartók acknowledged his music as bitonal or polytonal. Nowhere in the above quotation, does Bartók imply the existence of bitonality in his music; rather he objects to the labels of bitonal or polytonal by pointing out their unrealistic demands on the listener. In addition, the concept of bi-tonality consisting of a primary and a secondary key is often confused with bimodality; that is, theorists who adapt a bitonal approach often use concepts and features taken from Bartók’s explanation of bimodality. 10
8 Ibid., 365-66.
9 In order to justify the bitonal elements found in Bartók’s Sonata, Ivan Waldbauer, in his article, “Theorists’ Views on Bartók from Edvwin von der Null to Paul Wilson” Studia Musicologica (1996), 113, states that “The term bitonal element seems appropriate here, because the key of these elements…is recognizably subordinated to the prevailing primary key, quite in keeping with Bartók’s conception of bitonality (See Essays, p. 366).” However, in the reference provided by Waldbauer, Bartók consistently explains the problems of advocating for atonality and polytonality.
10 János Kárpáti explains the phenomenon of a brief bitonal passage in Bartók’s String Quartet no. 3 based on Bartók’s statements concerning polymodality. See János Kárpáti, “Tonal Divergences of Melody and Harmony: A Characteristic Device in Bartók’s Musical Language,” Studia Musicologica (1982): 378-79.
However, in his Harvard lectures, Bartók clearly differentiates these terms. While bitonality has two different keys arranged in separate parts, bimodality consists of two different modes sharing the same fundamental tone.
Here, we can question why a bitonal or polytonal approach has occurred in the study of Bartók’s music and what musical aspects have driven this theoretical approach. In his essays “Harvard Lectures,” Bartók also indicates that in his piece, Bluebeard’s Castle and in Stravinsky’s Sacre, “The Dance of the Adolescents,” it is possible to misinterpret bitonality or polytonality for bimodality or polymodality due to their misleading notation. As illustrated in Example 1.1, although the music in both cases seems to be either bitonal or polytonal, he emphasizes the fact that their pitch organizations are certainly not either.
Incidentally, much of Stravinsky’s music, and also of my music, looks as if it is bitonal or polytonal. Therefore, the pioneers of polytonality used to regard Stravinsky as one of their fellow polytonalists. Stravinsky, however, deliberately denies this circumstance, even in such exterior features as orthography. 11
Example 1.1 Bartók’s Example 2 from his Bluebeard’s Castle Especially Bartók’s seemingly bitonal passage (Example 1.1), provided in his essay, is enlightening. The melody in the upper part and the chord in the lower appear to be in different keys due to the exclusive use of accidentals. However, both parts prolong an F-major eleventh chord, F–A–C–E –G –B, combining two voices, rather than differentiating each voice in a polytonal texture. Indeed, this phenomenon is
11 Béla Bartók, Béla Bartók Essays, 366-67.
frequently found in his music and has often been regarded by theorists as an example of bitonal or polytonal music. In addition, another misleading notation often occurs. In several of his works, Bartók notates a bi-key signature, where each part has a different key signature, rather than accidentals, as illustrated below in Example 1.2. 12
Example 1.2 Mikrokosmos, No. 70, “Melody against Double Notes” However, Bartók proclaims that all the work in question is actually based on one fundamental tone. 13 To point out the essential difference between atonality, polytonality, and polymodality, in a final word on this subject, we may say that atonal music offers no fundamental tone at all, polytonality offers–or is supposed to offer– several of them, and polymodality offers a single one. Therefore our music, I mean the new Hungarian art music, is always based on a single fundamental tone, in its sections as well as in its whole…. Polymodality is to be found especially in my works…
In the comparison of the three terms (atonality, polytonality, and polymodality), he instead combines two different modes based on the same fundamental tone. Thus, in the Harvard lectures, he introduces the new term “polymodality,” in contrast to polytonality, in which several fundamental tones exist at the same time.
12 These seemingly polytonal presentations actually show the unique application of a polymodal compositional language.
We will investigate the details of this phenomenon in Chapter 2, which are classified into two types of key signatures according to their characteristics, the bi-key signature and the absence of a key signature.
13 Béla Bartók, Béla Bartók Essays, 365-71.
14 Ibid., 370-71.
In order to define his term “chromatic polymodality,” Bartók provides two significant examples in his “Harvard Lectures.” Bartók first begins discussing the concept of bimodality with two familiar minor scales in a minor mode, a natural minor and a melodic minor. 15 As shown in Figure 1.1a (Example 3 in his essay),
when two minor scales of C-natural and C-melodic are superposed, there exists a kind of bimodality, which produces the dissonant sounds of A and A, and B and B. 16 (a) Combination of C-melodic/natural minor scales
Likewise, the Phrygian and Lydian modes with the common fundamental tone, C, can be used simultaneously in superposition. Figure 1.1b (Example 4 in his essay) apparently illustrates a C-Phrygian mode, C-D -E -F-G-A -B -C, in the upper voice without a key signature and a C-Lydian, C-D-E-F#-G-A-B-C, in the lower voice.
Figure 1.1 Bartók’s examples of bimodal scales
(b) Bimodality of C-Lydian/Phrygian modes
15 Ibid., 364.
16 Ibid., 367.
Remarkably, this combination of Phrygian and Lydian based on the same fundamental tone always contains twelve different notes. As Bartók emphasized in his Harvard lectures, this polymodal construction provides a valid basis for each seemingly chromatic note of twelve unlike the temporarily altered chromatic notes in traditional tonal music. Thus, these chromatic notes in bimodality or polymodality do not need to move or resolve other diatonic notes according to the rules of conventional voice-leading; thus, they can be used freely and independently. As a result, he notes that it is possible to make melodic chromaticism in polymodal music, in contrast to the harmonic chromaticism found in nineteenth-century music. 17 Before I go into details, I must recapitulate in regard to what results the superposing of the various modes led us to. First, a kind of restricted bi- modality or polymodality. Second, bi-modality led toward the use of diatonic scales or scale portions filled out with chromaticized degrees which have a totally new function. Consequently, Bartók creates chromatic polymodal music consisting of variously combined modes or scales based on a common fundamental tone. In combining various diatonic or chromatic modes, I found that there are three categories of polymodality in his music. Among theme, Bartók mentions are two categories of polymodality, as follows: 18 Bartók’s above classification is very vague, and he does not provide any examples. But we can derive the important fact that there are two possible polymodal presentations superposing two or more modes. Specifically, while one method
17 Ibid., 376.
develops an inhibited bimodal or polymodal combination, the other creates a more flexible chromatic polymodality. Firstly, an example of the first case can be easily defined as stated above because, generally, each mode in polymodal music is distinctively stated. Actually, Figure 1.1b, provided by Bartók, abstractly demonstrates his restricted bi-modality, a C-Phrygian mode in the upper voice and a C-Lydian in the lower. Likewise, Mikrokosmos No. 59 in Example 1.3, as seen below, clearly shows the restricted bimodality of superposing two different modes based on the same fundamental tone, F. That is, while the melody in the upper voice is in an F-Dorian or F-Aeolian, F–G–A –B –C, the countermelody in the lower voice is in an F-Lydian, F–G–A –B –C. The modes are developed separately in each voice, but retain the same fundamental tone.
Example 1.3 Mikrokosmos No. 59, “Major and Minor”
In most of the restricted polymodality, two elemental modes are saliently presented arranging each mode in a different voice. Thus, we are able to recognize their modal identities. In addition, each mode in bimodality or polymodality need not continue in the same part. For instance, No. 59 consists of three parts. A polymodal arrangement at the beginning of No. 59, an F-Lydian in the lower and an F-minor in the upper, is inverted in the second part, creating an F-minor in the lower and an F- Lydian in the upper. Such an interexchange of modal arrangements is a frequently
used method in Bartók’s polymodal music. In the Harvard Lectures, Bartók directly describes this characteristic principle of bimodal or polymodal music in more detail, as follows:
We may say that music based on such principles can be labeled with a third ‘slogan’: bimodality, or polymodality….In our works, as well as in other contemporary works, various methods and principles cross each other. For instance, you cannot expect to find among our works one in which the upper part continuously uses a certain mode and the lower part continuously uses another mode. So if we say our art music is polymodal, this only means that polymodality or bimodality appears in longer or shorter portions of our work, sometimes only in single bars. So changes may succeed from bar to bar, or even from beat to beat in a bar. 19 On the other hand, Bartók’s description of the second category of bimodality or polymodality is more abstract and complex. In fact, it can be subcategorized into two; “toward the use of a diatonic scale” and “use of scale portions filled-out with chromaticized degrees.” Here we will first explore how polymodal music is developed chromatically in a portion of a diatonic scale. In fact, this method is already represented in Figure 1.1a by Bartók. As illustrated in Figure 1.1a, the G-tetrachord of a C-minor scale is filled by chromatic notes when the G-tetrachord of a melodic minor, G–A –B –C is subsequently followed by that of a natural minor, G–A–B–C.
His statements inform us that he uses a bimodal or polymodal passage flexibly, regardless of its length; thus it is possible that two polymodal scales can be employed either briefly or at length. In fact, the change of the polymodal phenomena occurs in section by section, as well as in the configuration of a modal mixture in a single bar. These methods will be more thoroughly investigated in the following dissertation.
19 Ibid., 370.
Example 1.4 Improvisations on Hungarian Peasant Songs, No. IV, mm. 1–4
Likewise, Improvisations on Hungarian Peasant Songs, No. IV exemplifies the second type of polymodality. No. IV is based on a folk song in a G-tonality, which is represented in the lower voice. Example 1.4 illustrates the beginning of the piece, mm. 1–4. In the first measure, a G-tetrachord is formed by two individual segments, and is filled in with chromatic notes. These segments are actually from portions of two different diatonic modes; one is G–A–B–C# of from a G-Lydian mode, and the other is G– A –B –C from a G-Phrygian mode. Interestingly, in both examples of Figure 1.1a and Example 1.4, each segment of each scale is separately arranged according to the melodic motion (an ascending or a descending motion). In other words, in Example 1.4, the G-Lydian tetrachord is recurrently presented in an ascending melodic motion, while the G-Phrygian tetrachord is in a descending one. In many examples of Bartók’s polymodal music, he frequently provides an independent characteristic to each elemental mode of polymodality depending on melodic motion. Moreover, in the second subcategory in this type of polymodality, two complete diatonic scales are superposed on one common fundamental tone, for instance, the C-Phrygian/Lydian mode in Figure 1.1b. The superposition of the two scales provides twelve different chromatic notes in polymodal music. We will further discuss this feature below.
Example 1.5 Mikrokosmos, No. 41, “Melody with Accompaniment”
Bartók’s third type of bi-modality or polymodality demonstrates another unique polymodal method that provides a new polymodal scale. Although Bartók does not mention it specifically, I will separately classify this category as a third type of polymodality not only because Bartók uses it frequently, but also because it differs from the two other types. While restricted polymodality is mainly comprised of diatonic modes (such as the five ecclesiastical modes, the major/minor scale, and the pentatonic scale), the scales found in this third type are new and unconventional. For example, in Mikrokosmos, No. 41, Bartók uses a unique kind of diatonic or non- diatonic scale in a G-tonality. He expresses the principal scale of No. 41 as a “G major with an augmented fourth and a minor seventh.” 20
20 Benjamin Suchoff, Bartók’s Mikrokosmos: Genesis, Pedagogy, and Style (Lanham: The Scarecrow Press, 2002), 49.
Actually, these altered notes, C# and F, originate in a G-Lydian and a G-Mixolydian mode, respectively. In fact, these are the distinct characteristic notes of each mode and comprise a new modal scale, G- A-B-C#-D-E-F -G. Indeed, as shown in Example 1.5, the melodic theme in No. 41 does not include the other chromatic notes C and F# at all, and exclusively uses the notes C# and F in the melodic line. Thus, we conclude that the notes C# and F are not altered notes of a traditional G major, but are independent scalar elements in the
new scale. 21 Therefore, I call this kind of modal scale a “composite polymode,” following Suchoff’s terminology. 22 Unfortunately, Bartók does not clearly identify the modes used in his polymodal music. Thus, many Bartókian scholars have tried to prescribe either specific modes in terms of a composite polymode or explore all of his modal scales. In this dissertation, however, I propose the existence of a more creative and flexible conception of modal scales. In other words, Bartók’s modal scales are created based on the simplest characteristic mode found in old Hungarian rural music– the pentatonic. It is expanded to heptatonic diatonic modes and, ultimately, creates twelve different notes in his polymodal system. Such a concept can be deduced from Bartók’s own statements. In his Harvard Lectures, Bartók criticizes the musical phenomena of opposites, the oversimplication and overcomplication found in the music of contemporary composers, such as Alois Haba and I. Wesshous.
21 Likewise, Mikrokosmos, No. 58 is a contrapuntal work based on the scale, G-A-B -C#-D-E-F-G, consisting of a minor third from a G-minor mode and an augmented fourth of a G-Lydian, in a G-minor tonality. These examples will be analyzed in Chapter 2 in my discussion of Bartók’s key signatures.
22 Benjamin Suchoff, Bartók’s Mikrokosmos: Genesis, Pedagogy, and Style, 49.
23 Ibid., 354-61. Bartók states that the oversimplifed compositional styles are not very interesting because of too much repetition without change. He also believes that the overcomplicated musical styles realistically give too much information for the ear. In the meantime, he observes that the other fine arts, such as literature and painting, show a similar trend toward simplification in a reaction to exaggeratedly complicated formulations developed in the late-nineteenth century. In such a contemporary cultural milieu, Bartók points out that these simplified trends can be seen in the paintings of Wassily Kandinsky (1866–1944) and Piet Mondrian (1872–1944), who draw abstract configurations using geometric lines, rather than realistically expressing the world. In
particular, through Mondrian’s pictures, Bartók discovers the fact that seemingly simple drawings may be the products of very complicated creative processes. Figure 1.2 illustrates Bartók’s representation of Mondrian’s picture. 24
Figure 1.2 Bartók’s representation of Mondrian’s picture In other words, Bartók realizes that simplified means can be an effective compositional tool, and may better convey artistic expression. Thus, he explores the great musical potential in the simple pentatonic system of rural music, rather than in Wagner’s highly chromatic style. In fact, Bartók discovers that pentatonic melodies can only imply one chord, G–B –D–F, but nonetheless provide the most innovative harmonies.
Pentatonic melodies are very well imaginable with a most simple harmonization, that is, with a single chord as a harmonic background. Such kinds of harmonization, reduced to the extreme limit of simplification, should be used only exceptionally, in well-chosen, appropriate portions of a work, or else its exaggerated use would lead us to a monotonous oversimplification.... Melodies in such an archaic style can very well be provided also with the most daring harmonies. It is an amazing phenomenon that just the archaic features will admit of a much wider range of possibilities in harmonizing and treating
24 Ibid., 357-58.
melodies or themes of the pentatonic kind, than would be the case with the common major or minor scale melodies. 25 Indeed, in the process of accompanying these pentatonic melodies, Bartók freely creates both simple pentatonic chords and various chromatic modal harmonies. Although Mondrian uses simplified means, he carefully arranges these geometric figures and colors in a pre-determined formal texture. Likewise, Bartók elaborately arranges his diverse harmonies based on simple melodies according to a formal plan. Consequently, according to his compositional philosophy, openness to flexibility and freedom in using modal scales and harmonies allows more space for a creative expression.
26 The anhemitone pentatonic scale, with its peculiar leaps because of the missing second and sixth degrees, is the very opposite of the chromaticized heptatonic scale used, for instance, in Wagner’s music. So we took it—quite subconsciously—as the most suitable antidote for the hyperchromaticism of Wagner and his followers. Thus, we had two different starting points for our creative work: the modes of our rural melodies and the pentatonic scale of our oldest music.”
Accordingly, in the Harvard lectures, Bartók defines two categories of modes as the basic elements in new Hungarian art music, as follows:
25 Ibid., 373-74.
26 The philosophical principle of openness or flexibility is also related to the Chinese aesthetic of openness in poetry, as follows: “In contemporary theory, openness means that a literary text is not an enclosure of words, the messages of which are finite and limited, but a hermeneutic space constructed with verbal signs capable of generating unlimited interpretations.” For more details, see Ming Dong Gu, “Aesthetic Suggestiveness in Chinese Thought: A Symphony of Metaphysics and Aesthetics,” Philosophy East &West 53/4 (2003): 490-513.