Symmetry in Béla Bartók's Cantata profana

© 2001

Kedves édes apánk
Te csak eredj haza
A mi édes jó anyánkhoz!
De mi nem megyünk!
     - Cantata profana, II


It is well known that Béla Bartók made heavy use of the Eastern European folk-modes that he collected on his pre-war trips to the countryside. He also made use of more abstract, cyclical pitch collections, such as octatonic and whole tone sets, in the vast majority of his work. The intersection of these two musical avenues was the Cantata profana of 1930. The work was to be the first part of a projected set of three cantata-oratorios that would celebrate and symbolize the brotherhood of the Eastern European peoples of Hungary, Romania, and Slovakia (despite the fact that the Hungarians have no genetic relationship to any of their neighbors). After Bartók's death, a draft was found of an unfinished text in Hungarian that was apparently meant for the second installment. That, however, is another story.

The harmonic language of the Cantata profana illustrates the intersection of the folk-modes and abstract patterns that Bartók was working with at the time, and in it, he achieved the most integrated presentation of this material. The folk-mode that allows this intersection is the so-called "harmonic" or "overtone" scale (so called because it approximates as closely as possible with an equally-tempered scale the eighth through fourteenth partials of the overtone series, C-D-E-F#-G-A-Bb), transposed to begin on D in the Cantata (thus D-E-F#-G#-A-B-C). This is the scale pattern that closes the work. Bartók uses the literal inversion (D-E-F-G-Ab-Bb-C) to open the work, thus setting up a pseudo-"minor"/"major" dichotomy (referring only to the quality of the third degree of each scale).

Out of these two modes (which are really one in the same, since in addition to being inversionally symmetric, they are rotationally symmetric) Bartók pulls not only the abstract octatonic and whole-tone pitch-collections, but also several interval cycles, especially the perfect fourth cycle and some partial minor third cycles. Over the course of the work, Bartók spins the abstract pitch-collections out of the folk-modes, then returns to the modal character, "reabsorbing" the abstractions.[1] These expansions and contractions occur at structurally important places in the work.

These points of structural and dramatic importance are dictated by two parallel factors. The first is the text itself. Bartók's text comes from a composite of two variations of a single colinda (labeled as 4a and 4b in the final published version of the collection) with melody that the composer collected on a trip to Transylvania in April of 1914 (the story of these texts is discussed below. The colinda (or kolinda) is a Christmas carol of Polish, Rumanian, or Bohemian origin which, unlike a typical western European Christmas song, deals with pagan ritual or mythology. The winter solstice, which represents the rebirth into spring, is also a common theme.[2] Bartók gave these two Rumanian texts to poet Jószef Erdélyi to translate into Hungarian.[3] The composer was unsatisfied with the poet's results, and appers to have gradually built up his own translation, making use of only sporadic borrowings from Erdélyi's version.[4]

Many translations of the text exist, almost all of which are found in a volume currently housed in the Budapest Bartók Archive. The contents of this volume:[5]

Rumanian texts:
  1. the "urlibretto" - contains only Parts I and II of the final text
  2. a later copy, sent to Brailoiu on July 2, 1930
  3. a fair copy sent to Universal Edition for final publication

Hungarian texts:
  1. two copies of Jószef Erdélyi's translation, one in the poet's hand, the other from the periodical Nyugat - contains only Parts I and II
  2. a Hungarian draft with many variant readings, especially in Parts I and II
  3. an independent draft - Part III is added in different ink
  4. a fair copy for Universal Edition
  5. glosses on the Brailoiu copy (Rumanian text #3) - a literal, word-for-word translation into Hungarian, presumably in preparation for Bartók's own German translation

German texts:
  1. draft of Bartók's literal translation
  2. a second copy of the same, written partially in Bartók's mother's hand, partially typewritten
  3. a typewritten copy of Bence Szabolcsi's German translation
  4. a fair copy of the same for Universal Edition (this is the German text used in all Universal and Boosey & Hawkes full scores and study scores)

English texts:
  1. a draft with corrections
  2. a second draft with further corrections
The second structural factor is Bartókšs use of the Golden Section. This is a mathematical ratio which has been put to use by artists of all media as a formula for constructing aesthetically satisfying works of art. It can be calculated in either of two closely related ways. The first is to take the ratio of the lengths of two line segments whose relationship is:

x : z :: y : x

The ratio is calculated by dividing the length of section [x] by the length of section [y]. The other is to take the ratio of any two consecutive numbers of the Fibonacci sequence.[6] Naturally, the further along the sequence the two chosen numbers are, the more precise the calculated ratio. Either way, the ratio comes out to approximately 0.618, or its inverse, 1.618. Bartók uses this ratio to situate moments of import in the story or in the harmonic and developmental structure of the work.

Textual symmetries

The text itself has a rough symmetrical structure, if viewed by number of lines. The text is in five paragraphs, which have eleven, eight, forty-six, thirteen, and twenty-three lines, respectively. Paragraph three, being the longest, is a textual axis. Paragraphs one and two form a rough golden section, as do paragraphs four and five. The five paragraphs also form a symmetry of length: medium, short, long, short, medium. The overall textual symmetry is as follows:[7]

Paragraph:12345
Length:mediumshortlongshortmedium
# lines:118461323
\/\/
GSGS

Generally, the setting of the text is in five broad sections. The opening section introduces the father and his nine sons. The boys, described as "szép" (beautiful), were not taught to farm or raise livestock, only to hunt in the mountains. The second section is the so-called "hunting fugue", which draws a picture of the nine boys as humans, spending all their time hunting and wandering through the mountains and forests. When the boys are magically transformed into stags after following magic deer tracks into the woods, their father begins his quest. Just as he is raising his rifle to shoot one of these magical stags, unaware that they are his own children, his eldest and most beloved son cries out to him, "Kedves édes apánk, ránk te sose célozz!" ("Sweet, beloved father, do not raise your rifle!"). This utterance begins the passage of conflict, in which the father attempts to persuade his sons to return home to humanity, while the eldest son insists that a return to human life is impossible. The story is summarized by a final chorus, which recapitulates text from all preceding sections. This summary constitutes the entire third movement of the Cantata. A chart of the tempi taken in each of the five sections shows a basic symmetry:[8]

The Golden Section: Dramatic structure

As was previously mentioned, Bartók places important dramatic moments in or near measures which correspond to the golden section of various levels. For the purposes of this discussion, the golden section will always be calculated by measure number, not by playing time (which can vary from conductor to conductor) or number of beats (which changes depending on the metrical structure). Some of the relevant dramatic moments do not coincide exactly with their associated golden section, but the difference is never of more than a dozen or so measures.[9]

This is the case with the highest level golden section, that of the entire work. This occurs at measure 115 of the second movement,[10] and it coincides roughly with the entrance of the father (his actual first note is in m. 103). Here the father begins his impassioned plea that his children return home to him and their mother (the text is "Jöjjetek ti vélem a jó anayátokhoz..." - "Come with me, come back to your mother..."). Further implications of this moment will be discussed below.

Ignoring the first movement for the moment, and taking the golden section of only movements two and three, the dramatic turning point of the work is placed at m. 190. In mm. 188-208, the father and son sing together for the first and only time, both acknowledging that the nine stags can never return to the human life. They are supported by the chorus, which reiterates that "de ók nem mennek, nem, jaj, nem" ("they will never return, no, oh, no"). The eldest son is listing the many reasons why they cannont return, while the father has lost his composure; he is powerless to do anything but repeat "ó mért, ó mért nem?" ("why not, why not?"). Yet another moment of dramatic import occurs in m. 42 of the second movement, the golden section of the entire work up until the duet at m. 190 (i.e., the golden section of the first 388 measures of the work). Here the eldest son reveals himself to his father for the first time, imploring him not to shoot at his children.

One last moment deserves a brief mention. The second-level golden section of the third movement occurs in m. 35.[11] The chorus, which had been summarizing their text from the first movement, turns to the words sung by the tenor soloist when asked why the nine stags cannot return to civilization. From this moment until the end of the work, the choir repeats the eldest stag's words, until they are finally joined by the stag himself, in one last, brief, ecstatic melisma on the words "csak tiszta forrásból" ("but only from clear mountain springs").

The first movement does not appear to have interesting mathematical properties which concern the text setting or the dramatics (some harmonic events occur in select mathematically derived measures, however). No important moments in the second movement yield a convincing mathematical focus in the first movement, and none of the dramatic turning points of the first movement can be extrapolated into important junctures further into the work.

The Golden Section: Musical and harmonic structure

It would be somewhat disappointing, and not at all like Bartók, if the great dramatic high point at the golden section of the work (in m. 115) were not accompanied by an equally momentous harmonic event. Luckily, this is not the case. In m. 110, the winds and low strings play a sustained F7 chord, minus a third. This chord is approached by the skeleton of a perfect authentic cadence in F (the mode is unclear at the cadence, but it soon becomes clearly minor). The sense of F as tonal-center is quickly obscured, and is only alluded to until a more concrete sense of tonality is re-established in m. 187. Despite this unsettled nature, this moment of "F-ness" is, in fact, the central axis of the harmonic structure of the entire work. From this central point, Bartók extends a tree of intervallically symmetrical tone-center relationships, as illustrated in the following table.[12]

Other important harmonic events occur at various previously discussed golden sections. The opening modal pitch material (the D "minor" folk-mode) returns at long last in m. 190, the golden section of the second and third movements alone. The second-level golden section of the entire work occurs in m. 192 of the first movement. It is at this moment that two complete octatonic collections are presented in the winds. Interestingly enough, the closely related golden section of the arrival on F in m. 110 of the second movement coincides with the presentation of both complete whole-tone collections in alternating groups of four descending notes.

Two other golden moments deserve mention. The first occurs in m. 101 of the first movement, which is the golden section of the first 164 measures of the work (m. 164 is the beginning of the transformation of nine boys into nine stags). Here is a brief return to a D tonality, this time inflected towards the major. This is also the conclusion of the cycle of fourths that unfolded over the course of the "hunting fugue" (mm. 60-105). The last is m. 57 of the third movement, which is the golden section of that movement alone. The last statement of the whole-tone collection begins here, in stretto entrances of four ascending notes each. This statement also signals the end of the formal thematic and dramatic recapitulation. The text here, "csak tiszta forrásból" ("but only from clear mountain springs"), is the culmination of the story. What follows is a brief coda, which contains the tenor's last ecstatic outburst, and the final return to the opening non-diatonic mode (albeit the inversion/rotation of the original mode).

Local symmetries

These large-scale symmetries are mirrored on the local level by symmetrical harmonies and melodic phrases, as well as some intra-movement symmetries. Many examples of symmetrical harmonies can be found, and a complete list would likely take up several pages. A select few which are present at important moments in the first movement are worth noting. The last of these chords is an interesting case, since it displays symmetry on two levels. This harmonic event is not a "chord", per se, rather it is the abstract distillation of a cross-relation between harmony and melody. Here the strings and winds are holding a first-inversion D major triad, while four voices (a soloist from each section) sing a brief stretto in D dorian.

Each of the three movements has an internal symmetry of choral texture. Alterations of polyphony and homophony form patterns of symmetry, which are especially complex in the first movement. The second and third movements have simple odd-numbered alternations of polyphony and homophony. In the second movement, a solo (monophonic) voice is considered to fall into the homophony category.[13]

Conclusions

Bartók himself did not write much about his compositional method. If he spoke about it with others, they did not write it down for posterity. Thus, determining how much of Bartók's symmetry was intentional and how much was chance is sometimes difficult.[14] In cases like the Fourth String Quartet (1928), concerning which Dr. Antokoletz has written volumes, the meticulous construction of symmetrical structures and modulations leave no doubt that Bartók put a great deal of thought into his harmonic language. Making this determination when looking at temporal structure can be problematic if an overwhelming body of evidence is not present.

In the case of the Cantata profana, there is too much symmetry for there to be any doubt. It would simply be too coincidental for the symmetrical correspondences to be accidental, given that such symmetries exist on multiple levels, and always indicate a moment of harmonic or dramatic import. Support can also be taken from the remainder of Bartók's oeuvre, which displays symmetry of all shapes and sizes in every period of his career.[15]

Notes:

[1] Elliott Antokoletz, Victoria Fisher and Benjamin Suchoff, eds., Bartok Perspectives (New York: Oxford University, 2000), 62.

[2] Gail Geary, "Béla Bartók's Cantata profana: An Analytical Study" (PhD diss., Baylor University, 1985), 30.

[3] László Vikárius, "Béla Bartók's Cantata profana (1930): A Reading of the Sources," Studia musicologica Academiae Scientiarum Hungaricae 35/1-3 (1993-94): 252-53.

[4] Ibid., 263.

[5] Ibid., 265-6.

[6] The Fibonacci sequence is formed by adding the two last numbers in the series to get the next one. So: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597...

[7] Geary, 37.

[8] Ibid., 36.

[9] The analysis contained in the following two sections is taken directly from the score, although the jumping-off point was Gail Geary's dissertation.

[10] The exact location is just shy of three-fourths of the way through m. 114. The entire work is 506 measures long - multiply by 0.618 to get 312.708 measures. Subtract the 198 measures of the first movement to get 114.708 measures. The golden section will always be rounded to the nearest whole number, and will be assumed to occur at the beginning of that measure.

[11] That is, the golden section of the golden section. The third movement lasts 93 measures. The golden section of this movement alone occurs at m. 57. The golden section of this segment is in m. 35, hence the term "second-level golden section". As far as I know, I made up this term myself.

[12] Geary, 70-71.

[13] Ibid., 77.

[14] Remembering that the golden section should also be considered a form of symmetry when dealing with Bartók.

[15] Elliott Antokoletz, Twentieth-Century Music (Englewood Cliffs, NJ: Prentice-Hall, 1992), chapter 5.


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