Formal Considerations in Bela Bartok's
Fourth String Quartet

by Michael Ladd
Analytical Techniques
Musth 621
April 30, 1999



Bartok, Fourth String Quartet, Movement 1, 1st theme
Introduction

The works of Bela Bartok are generally approached from either of two theoretical premises. The first being an extension of traditional western art music that has preceded him (particularly the expanded harmonic resources which emerged during the 'Romantic' musical period), the other being from Bartok's own research into the folk music of Europe. It has been said that through this research, Bartok was able to free himself from the "tyrannical rule of the major and minor keys, leading eventually to a new conception of the chromatic scale, every tone of which came to be considered of equal value and could be used freely and independently."1 Bartok was not noted for his use of 12-tone concepts per se, but his search for harmonic freedom did parallel the concepts of the 12-tone composers of his time.


There have been theorists who have attempted to present Bartok's compositional products as the result of serial processes.2 There are select moments that reveal these types of procedures, but overall his music rarely displays the consistent vocabulary that would prove a set-theory approach to be worthwhile.3 There are certain pitch collections that do appear consistently in his work. Collections such as the whole-tone scale (02468t), the pentatonic scale (02479), and the heptatonia seconda (013468t) seem to stem more obviously from his studies of ethnic music rather than the application of serial processes.


Although Bartok was not the first composer to look for musical inspiration in the music of folksong or use ethnic melodies, he was one of the first to delve so deeply into this area of music. "Bartok achieved something that no one had before his time, the symbolic handshake between East and West: synthesis, a seamless blending of two sources into a single style."4 Bartok was a knowledgeable ethnomusicologist who wrote and lectured on his areas of research into the cultural music of Europe in general, and of Hungary in particular.


Due to Bartok's intense level of musical research, and craftsmanship as a composer, his works offer a variety of approaches to the analyst. Bartok wrote little in regards to the theoretical developments that appeared in his work, leaving theorists with only his lectures and compositions themselves. There have evolved a variety of approaches to attempt to describe the compositional practices that have evolved in his works. Erno Lendvai was one of the first theorists to write on the appearance of the Golden Section and Fibonacci Series and how these are implemented in Bartok's music.5


Lendvai also makes note of the use of the Pitch Axis, which may be viewed as a method of assigning functional harmonic significance to pitch classes. One of the pitches must be noted as the 'tonic', following this, the interval from tonic determines the functional role that each note performs. The remaining functions include the dominant and the subdominant. Each of these acts as a category, containing four notes that are functionally equivalent within the musical context.


Another principle of pitch organization that appears in the works of Bartok is the use of symmetrical structures. Symmetrical structures are pitch organizations created by the equal division of the octave into varieties of complex interval cycles. This occurrence has been noted by theorists such as George Perle and Elliott Antokoletz.6 Symmetrical structures will not be addressed; rather this paper will focus on the structural formations that Bartok incorporated as well as the harmonic and melodic considerations that are necessary to contribute to the overall form in a successful manner.


The nature of form will be examined in Bartok's Fourth String Quartet. Bartok's quartets have been noted for being some of the most important visions of this medium since the works of Beethoven. " There have not been many 'series' of quartets since Beethoven at all . . .It is quite rare to find, as we do in Bartok, a composer who has turned to the string quartet at every stage of his creative career and put into his quartets the very best of himself."7


The fourth quartet itself presents an overview of the concepts that Bartok was beginning to evolve. Experiments in form, timbre, and harmony are all presented within this work, giving a look into the upcoming period of Bartok wherein these ideas and concepts were solidified in his later works. The composition of the fourth quartet occurred when Bartok was awaiting word regarding the submission of his third to the Philadelphia Musical Fund Society competition. Assuming that the winning of this award would draw some attention away from his recently completed fourth quartet, Bartok felt it might be better to wait on the publishing of this work.8


One of the most instantly notable factors of this work is the unusual nature of the overall form. This work, along with the fifth quartet is presented in five movements. This allows Bartok to incorporate some of his concepts in regards to symmetry. The work is set up with corollaries between diametrically opposing movements incorporating similar features. Concepts that are initially presented in the first movement return again in the fifth movement. Similarly, the second and fourth movements have features that are similar in terms of tempo, motivic content, and alterations of timbre. The third movement stands alone in nearly all factors. While the other movements focused on the use of counterpoint, this movement is almost completely homophonic, with single lines being played over a static harmonic background. This presents the entire work in an arch form with movements I and V being related, II and IV being related, and movement III offering total contrast to the rest of the piece.

Movement One

Bartok, Fourth String Quartet, Movement 1, 1st theme

Most often the first movement of the fourth quartet is described as being in sonata form. There have also been explanations that note that the entire work may be viewed as an extension of the sonata form, "stretched to the limits of the intelligible."9 The first movement does indeed demonstrate the use of two subjects, which do appear as if in recapitulation following a digression. One argument that may be made is the need for the alteration of the key center for the sonata form to hold true. While this work is not necessarily 'tonal', it should be noted that both of the subjects who appear in the first movement are indeed in the tonal area of 'C'.


There are other factors that may identify the movement as being in the sonata form. The first 13 bars present the principal theme. The motive is introduced in the first two bars and is answered by a second gesture of similar length. This motive has been termed the 'germ-motif' (D Eb E D Db) since it will later be seen to form many of the thematic ideas that return throughout the piece. One notable factor in regards to how these gestures differ is that the first presentation concludes with the parts closing together and the second presentation ends with the parts opening up. Bartok has described bars 14-29 as being a transition. There is an argument to be made about this truly being a transition. This 'transition' motive becomes so important, particularly in the last movement, that it may be termed the second principal theme.10 Following this motive is the occurrence of the germ-motif in mirror canon. This leaves the 'transition' with little in the way of transitional character since there is no movement to new material. Beginning at bar 30, the secondary theme is presented with its most characteristic elements being derived from the germ-motif. This is combined with the appearance of whole-tone elements.


The development (bar 49) begins with first subject; the cello (bar 60) takes up the second subject, under a vibrating, trill-like figure played by the violins. The motif that appeared in bars 14-24 is a form of canonic inversion, a turning backwards motion is now presented as an arching melodic form but transposed down a minor second. The motif begins to expand and is accompanied by full chords rather than the cluster-like elements that occurred in the opening of the movement. There is additional variation through a motion that expands the range of the melody. At bar 75, the motif is broken down into basic elements presented in glissandi and trills. The development then begins to restructure the theme and the germ-motive begins to assert itself (from 83) and leads back to recapitulation (bar 93) by contrasting the trills in the background and the germ-motif appearing in the foreground. The development section ends with the motif appearing in unison. The recapitulation ends in an expected manner, with the only noticeable difference being the length. The recapitulation is only 42 bars long rather than the 48 bar length of the exposition. The codetta (bar 126) of movement one begins with the germ-motif, moving into rushing scales in contrary motion. The codetta ends with triplet figures (bars 145-159), reflecting the 'normal' classical way of accenting a note. While this movement may not completely fall under the category of sonata form, it is more likely that Bartok used the sonata form as a mode of departure for his own concepts.

Movement Two
Bartok, Fourth String Quartet, Movement 2, near beginning

The second movement presents more of a virtuoso work, performed at a faster tempo (dotted half = 88-98) than the first movement. Mutes are used to alter the timbre of the instruments. This theme again features the arch type of figure that rises and then falls back within a perfect fifth. This figure is based on the chromatic scale initially announced in the lower instruments, which is then answered by the two violins performing the melody a fifth higher than the initial presentation, and low strings playing accented chords. It is also worth noting the rhythm is definitely influenced by ethnic music. There is also the use of 'guitar-like' strumming of all four strings. The form may be viewed as a scherzo and trio with the scherzo clearly being in binary form. The first 75 bars divide clearly into two sections with the second occurring in a different tonal area than the first section.


The middle section (bar 32) presents a theme (bar 36) that returns in close imitation in bar 54 in four-part canon at the octave but in diminution. At bar 62, there is a 16 bar transitional figure that prepares for the trio. The second section (bar 78) also contains an incomplete reference to the opening theme with a canon at the second. Further development of the section at bar 102 modulates into a series of glissandi. It becomes rather difficult to analyze the form at this point (bar 136). This section is built on the use of light glissandi and scale figures played sul ponticello. The emphasis at this point falls more so on the timbres generated rather than the counterpoint activity of the first movement, which is followed by a reprise of the scherzo. The middle of the scherzo recapitulation presents a combination of theme, and a complementary transitional motif that appears as new thematic material. This animated movement is ended with an ever more animated coda. Glissandi motives have again returned to the foreground with a background of fast scales, trills, pizzicato and sul ponticello.

Movement Three
Bartok, Fourth String Quartet, Movement 3, near beginning

The third movement offers a complete departure from the previous two movements. The concept of the third movement is of a background of static blocks of harmony, with melodies unfolding within the harmonic environment. Throughout the first two movements, counterpoint has dominated; the third movement is based almost entirely on homophony. The movement begins with the cello playing a chromatic, recitative-like melody accompanied by sustained chords. These chords alternate between 'vibrato' and 'non vibrato' offering a change in timbre. The first violin then takes over (bar 35), playing a more free, improvisatory melody. Bartok's introduction of the melody appears to be influenced by Beethoven in his use of tiny fragments before the melody is completely revealed. The second violin begins with an 'agitated' melody (bar 42) and a return to the first melodic idea with imitation occurring between the cello and first violin (bar 55). Following a pause, there is a coda that again makes use of brief, melodic fragments. This melody is notable for its avoidance of notes contained within the accompanying chord.


A noticeable factor in the harmony is the chordal content versus how it is structured. Both the opening and closing sections feature the same harmonic content, but they are structured differently in the end section. In the opening chord, the interval of a major second dominates while the closing structure is laid out in fifths. The chord itself consists of five interrelated fifths. The point of rest occurs at bar 41 where the perfect fifth structure is altered to the perfect fourth. The harmonic and melodic action contributes to the unfolding of the Hungarian style melody. The closing 8-bar theme is divided into two equal parts where the first is more improvisational in character, moving around a central note. The second section of this theme contributes more of a melodic arch idea, being more diatonic in nature than the first part of the theme.


The central section of this movement evolves differently. When the melody reaches its climax, it breaks down into tiny, birdlike fragments. At the Agitato climax, the melodic character returns to reciting on a single note followed by a variation on the second part of the theme. The mood becomes tranquil with a diatonic melody played in the cello with a mirror canon type of accompaniment in the violin.

Movement Four
Bartok, Fourth String Quartet, Movement 4, near beginning

As stated previously, the fourth movement is related to the second movement to maintain the arch construction of the overall shape. Like the second movement, the tempo is faster than the preceding movement and the rhythmic structure again demonstrates the Hungarian influences. The timbre is also altered due to the entire movement being played pizzicato (single notes, double stops, and Bartok pizzicato). The theme is reminiscent of the theme of movement two, but the previously chromatic gesture becomes diatonic in this section. It is also worth noting that in movement two the theme occurs in the narrow range of a fifth, while in movement four it is extended over an octave.


The second part of this movement (bar 45) is related to the 'trio' area of movement two. This movement also introduces some interesting rhythmic relationships between the melody and the accompaniment. The symmetrical 8-bar melody is accompanied by chordal structures that are asymmetrically divided. There is also a reference to the 'guitar-like' ideas in the second movement, only this time they are more similar to a folk-like line (bar 88-90). This movement also introduces the use of the 'Bartok' pizzicato which is a strong pizzicato making the string rebound off the fingerboard. The scherzo theme undergoes a free recapitulation (bar 88) with the fugato structure being replaced by a two-part octave canon in diminution between the cello and violin one. The thematic material is broken up, similar to a development, by means of rhythmic imitations and inversions. These 'chunks' have a tendency to mirror one another. The coda presents material that is derived from the last part of the scherzo theme, but tends to have more of an independent nature.

Movement Five
Bartok, Fourth String Quartet, Movement 5, near beginning

To complete the arch-like shape to the form, the fifth movement incorporates thematic material extracted from the first movement. The theme is announced to accompaniment of asymmetrically accentuated quarter notes reminiscent of Stravinsky. What was initially the secondary theme in the first movement is now the principal theme in the fifth movement. This short, Hungarian-flavored theme is altered by use of inversion, register changes, and expansion. The theme is presented and then heard two octaves higher (bar 23) but presented as a mirror inversion. Several other variations follow (bar 31, 37), wherein the interval structure is expanded outward. The theme is altered in this movement to make notable use of the augmented second, an interval prominently found in ethnic eastern-European music. This interval is highlighted in several ways, through reiteration and combining it with pizzicato scales.


This motive and inversion provide for most of the material until bar 102 where the passage ends with a statement in quartel harmony and then a general pause. This is followed by an apparent recapitulation of the first part of the movement, but not so; the music is continually disturbed by the falling third, always in octaves (this figure is similar to last movement theme). The recapitulation begins (bar 238), and the work ends with strong enunciation of 'germ-motive'. The theme is presented in fragments, between reiterations of the falling third giving signal of the emergence of a new section. At bar 272 a melody is heard played by the full ensemble in octaves, the only moment in the work where this occurs. A folk tune emerges, tying together all the thematic elements of this movement; the dance rhythm, the falling third, and the three-note germ-motif. The coda (bar 344) recalls the schezando passage, and the germ motive completes the work.

Overview

There are some rather distinguishing traits that must be noted in the fourth quartet. One is the lack of traditional 'themes'; the work exists based almost entirely on the use of motives and their development. This is most obvious in movements I and V which share the same motivic pattern. Movements II and IV also share similar ideas, but these only utilize two motives which can be viewed as variations rather than the transformation process which occurs in the other movements. It is only movement III that contains information exclusive to itself. This movement is also in ternary form, so that the outer parts may be viewed to parallel the outer movements of the quartet. Other similarities between II and IV include the chromatic line of the viola and cello at the beginning of movement II, ascending from E to B and returning to E. This may be viewed as an expansion of the basic motive of movements I and V, which follows the same direction, but with far fewer notes. The third movement also gives some indication of the Halsey Steven's concept of 'night music' with the focus being on the texture particularly in the use of chord textures and subdued dynamics.


The basic motive of the entire work is the simple 'germ-motif' that consists of a succession of semitones moving from B to Db and back to B in a simple rhythmic succession. One of the other nuances that ties the work together is the underlying tonal structure of the entire work. Movements I and V end with a feeling of 'C', not necessarily major or minor, but somewhere in that harmonic area. Movements II and IV conclude with a harmonic feeling of a major third above in movement three, and a major third below in movement four. This demonstrates the outlining of an augmented triad at the largest level of the quartet. There is also a layer of symmetry in the lengths of the individual movements. Movements I, III and V are approximately six minutes long and movements II an IV are nearly three minutes long.11


This work is also notable for the use of canons " . . a thorough analysis of the polyphonic methods in the work would be a Herculean task; but almost every note could be accounted for."12 There are innumerable canons at work in this piece, although Bartok approaches the use of canons in an unusual manner. He is apparently more concerned with the independent progress of individual lines rather than the subtleties of harmonic flavor. This is noted via his use of free canons, as well as free imitation with no restrictions placed on the movement of individual parts. Frequent use is also made of the mirror canon that can be viewed as a canon in contrary motion without a time distance between voices (mvmt I bar 54). The inner voices contain simultaneous mirror cannon beginning a minor ninth apart while the outer voices display a free canon. A free canon is also apparent at bar 14 of the first movement where a subsidiary theme is presented in the form of a free, perpetual canon.13 Wallace Berry also makes note of a multivoiced canon that appears in bar 106. The second violin imitates the cello line at the fifth and in bar 107 the first violin imitates the cello at the tritone.14


The last discussion will focus on the use of the golden section and its appearance in the Fourth String Quartet. The Golden Section (G.S.) is a reference to an 'ideal' ratio that has been implemented in a variety of activities from architecture, graphic arts, and music. It may be derived from the Fibonacci series that is a numerical series that occurs often in nature. The Fibonacci series is built on the sums of previous values. For example, beginning with 1, the sum of 1 and what precedes it, 0, equals 1. Then 1 + 1 = 2, 2+1=3, and so on, presenting a series such as: 1,1,2,3,5,8,13, . . . . The values of the G.S. may be derived from dividing values from the Fibonacci series by its following component. For example the value of 55 divided by 89 results in the value of 0.8=618. Taking the value of any whole (1) by 0.618 gives the indication of the golden ratio. So a rectangle built of the longest sides being 8 ft. would need the shorter sides to be 4.9 ft represent a G.S. Bartok was interested in proportions and how they occurred in nature. For example the Fibonacci series occurs in the symmetries of pinecones and sunflowers. Derek Locke demonstrated how some of these ratios appear in several of Bartok's string quartets.15 The total number of beats the result from all five movements is 2584 which is the 18th Fibonacci number in the series.


The paper does not serve as a complete theoretical examination of all the analytical possibilities inherent within this work. The possibilities for examining the symmetrical constructions, potentials for serial patterns, use of canons, and occurrences of the golden ratio would all serve as starting points for further in depth discussions. The goal of this paper was a study of the formal constructions, and a cursory look at the canonic and golden ratio facets of this work. This composition, like many of Bartok's compositions, offers a host of theoretical discussions that may be made to attempt to explain the unique compositional methodology that is entrenched within the musical output of Bela Bartok.


Bibliography

Abraham, Gerald, "The Bartok of the Quartets," Music and Letters, 4:26 (1945):
         185-194.
Antokoletz, Elliot, The Music of Bela Bartok: A Study of Tonality and Progression
         in Twentieth-Century Music,
Berkeley: University of California Press, 1984.
Babbitt, Milton, "The String Quartets of Bartok," The Musical Quarterly, 1949: 377-385.
Bartok, Bela, "The Six String Quartets," notes to CD recording, Phillips, 442 284-2, 1994.
Berry, Wallace, Form in Music, 2nd ed., New Jersey: Prentice Hall, Inc., 1986.
Forte, Allen, "Bartok's 'Serial' Composition," The Musical Quarterly, 46, 1960: 233-245.
Griffiths, Paul, Bartok, London: J.M. Dent, 1984.
Karpati, Janos, Bartok's String Quartets, Budapest: Franklin Printing House, 1975.
Lendvai, Erno, Bela Bartok: An Analysis of His Music, London: Kahn & Avrill, 1971.
Locke, Derek, "Numerical Aspects of Bartok's String Quartets," The Musical
         Times,
128:1732, 1987.
Monelle, Raymond, "Notes on Bartok's Fourth Quartet," The Musical Times,
         (1968): 123-129.
Perle, George, "Symmetrical Foundations in the String Quartets of Bela Bartok,"
         The Music Review, 16, 1955: 300-312.
Rands, Bernard, "The Use of Canon in Bartok Quartets," The Music Review, 1968:
         183-188.
Wilson, Paul, The Music of Bela Bartok, New Haven: Yale University Press, 1992.

Endnotes
  1. Paul Wilson, The Music of Bela Bartok (New Haven: Yale University Press, 1992).
  2. Allen Forte, "Bartok's 'Serial' Composition," The Musical Quarterly 46 (1960).
  3. Wilson, p. 20.
  4. ibid.
  5. Erno Lendvai, Bela Bartok: An Analysis of His Music (London: Kahn & Avrill, 1971).
  6. George Perle, "Symmetrical Foundations in the String Quartets of Bela Bartok," The Music Review (1955), and Elliot Antokoletz, The Music of Bela Bartok: A Study of Tonality and Progression in Twentieth-Century Music (Berkeley: University of California Press, 1984).
  7. Gerald Abraham, "The Bartok of the Quartets," Music and Letters 4:26 (1945): 185.
  8. Janos Karpati, Bartok's String Quartets (Budapest: Franklin Printing House,1975).
  9. Serge Seiber, "The String Quartets of Bela Bartok", appearing in Raymond Monelle, Notes on Bartok's Fourth Quartet (1968): 123.
  10. Karpati, p. 212.
  11. "The Six String Quartets," notes to CD recording, Phillips, 442 284-2, 1994.
  12. Halsey Stevens quoted in Bernard Rands.
  13. Bernard Rands, "The Use of Canon in Bartok Quartets," The Music Review, 1968.
  14. Wallace Berry, Form in Music, 2nd ed. (New Jersey: Prentice Hall, Inc., 1986), 389.
  15. Derek Locke, "Numerical Aspects of Bartok's String Quartets," The Musical Times 128:1732 (1987), 322.

NOTE by Kins Collins: The original of the article above is found at ? ? ? .
     Further analysis of the 4th Quartet can be found in:
          (1.) Halsey Stevens, Life and Music of Bela Bartok (1953).
          (2.) Leo Treitler, M.A. Thesis, Analysis of Bartok's Fourth String Quartet [approx. title], (ca. 1957), possibly obtainable from University of Chicago Microfilms.


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