A Triumph of Musical Order? Multiple Sources of Inspiration in “ Prelude and Canon, ” Forty-Four Duos no. 37

It has been a hot topic in Bartók literature whether he followed some particular order, or relied on creative intuition when he composed. His own statem ents appear to be ambiguous, that is, he occasionally stressed that he consciously worked out his musical language, but on other occasions he emphasised the role of intuition. A contrapuntal short piece from the Forty-Four Duos , namely no. 37 “ Prelude and Canon ” , can be considered an appropriate material in order to examine how these different viewpoints are applied in an analysis (and to evaluate how appropriate the application of these viewpoints is). From a technical point of view, the Canon part of this piece deserves special attention, as it contains three different types of canon one after another. While the dux always remains in E, each comes is on different degrees (G, A, then B) and different temporal distances (one, two, and three crotchets). This can be regarded as a kind of compositional virtuosity; especially because it is not easy to write such canons on an original theme, much less on an original folk tune. Thus, this piece might be considered an example of how Bartók rationally and consciously worked out his compositions. Such a view can be re ﬁ ned, or possibly superseded by the examination of the original folk tune. The genre of the original folk tune, “ párosító ” [matchmaking song], as well as the way of its actual performance on the original recording gives us an insight into how an apparently systematic application of the compositional technique is nevertheless related to what we would call a secret programme. Thus, it was probably not only a particular folk song but also the people ’ s life surrounding the folk song which fascinated the composer, and he tried to vividly encode a typical village scene into a piece of art music. – Where is all my wisdom, then? I behaved stubbornly, pursuing a semblance of order, when I should have known well that there is no order in the universe. – But in imagining an erroneous order you still found something ... – What you say is very ﬁ ne ... The order that our mind imagines is like a net, or like a ladder, built to attain something. But afterward you must throw the ladder away, because you discover that, even if it was useful, it was meaningless ... The only truths that are useful are instruments to be thrown away. main types can be distinguished among [folk arrangements]. In the one case accompaniment, introductory and concluding phrases are of secondary importance, and they only serve as an ornamental setting for the precious stone: the peasant melody. It is the other way round in the second case: the melody only serves as a “ motto ” while that which is built round it is of real importance. All shades of transition possible between two extremes and sometimes it is even possible to decide which of the elements is predominant in any given case. But in every case it is of the greatest importance that the musical qualities of the setting should be derived from the musical qualities of the melody, such characteristics as are contained in it openly or covertly, so that melody and all additions create the impression of complete unity.


INTRODUCTION
The pursuit of order has always been a hot topic in the Bartók literature, and it continues to be so. Although Ernő Lendvai's analytic concepts, such as the Axis System, Fibonacci numbers, or the Golden Section, have been criticised in certain musicological circles, they still attract an audience. These concepts may offer inspiration for composers' search for newer compositional means or may fulfill non-musicians' curiosity about esoteric secrets of musical structure.
The question of whether Bartók himself tried to construct strict order cannot be answered unambiguously. Bartók's own statements in this regard can be considered somewhat ambiguous. In the paper titled "The Folk Songs of Hungary" (1928) Bartók explained an (at that time) unusual minor-seventh final chord in his composition as a vertical projection of the horizontal, melodic form, which was "obtained by a logical process" and not "through sheer whimsicality" (as, according to him, many of his critics believed). In addition, various kinds of folk music, especially Romanian and Slovak folk songs offered freer harmonic treatment of the twelve tones thus Bartók emphasises the background and the logic of his musical language and defends his style against critics. 1 On the other hand, in a 1937 interview with Denijs Dille, Bartók explained: Let me make it clear: although I carried out my harmonic research in a rational and reasonable way, the role of intuition is greater than one would think. I must state that all my music and this question of harmony we are talking about is a matter of instinct and sensibility: so no one should ask me why 1 I wrote this or that, or did something in this rather than that way. I have but one explanation: that is how I feel it, and that is how I wrote it down. 2 He acknowledges the rational approach but rather emphasises the role of intuition. In the Harvard Lectures (1943), he further elaborated this idea. 3 The apparent shift of emphasis from rational research to an intuitive approach, however, might have reflected the actual shift of his compositional style less than the change of circumstances, against which he intended to defend his music. A further good example is a short letter from Edwin von der Nüll (the author of the first systematic study on Bartók's music), quoted by Mária Pataky: It is apparent to me that his [Bartók's] razor-sharp logical thinking completely disappears when he has to talk about his own works. In such occasions he talks with naiveté but without intricacy, thus it can immediately be realised: how far Bartók the composer is from any theoretic speculation, because of which he has often been accused of. 4 Thus, both Bartók's apparent "sheer whimsicality" and his theoretic approach were criticised. This implies that it is difficult to categorize Bartók as either rational or intuitive composer.
Still, considering the current common belief that, until now, no one has succeeded in establishing any comprehensive theory that can sufficiently explain the underlying logic of Bartók's mature works, it is reasonable to suppose that Bartók did not systematically work out his own compositional theory.
Even though many of his compositions are indeed based on their own rational framework, such as inversional symmetry (as I have discussed elsewhere), Bartók more often than not modified or partially abandoned the framework during the composition and revision, for the sake of musical quality. 5 Such a phenomenon might rather be regarded as the interaction of (both highly) rational and intuitive compositional approaches than exclusive exploitation of either of them. 2 Interview made in German but originally published in French, in La Sirène (Brussels, March 1937). English translation is quoted from László VIKÁRIUS, "Denijs Dille: Interview with Béla Bartók (1937)," Hungarian Heritage 7 (2006), 14. 3 See Béla BARTÓK,"Harvard Lectures",in Essays,376. 4 "Feltűnik nekemírja -, hogy a borotvaéles logikájú gondolkodásmód teljesen eltűnik nála, ha saját műveiről kell beszélni. Ilyen alkalmakkor olyan naivitással és komplikáltságok nélkül beszélt, hogy azonnal kitűnik: az alkotóművész-Bartóktól mennyire távol áll minden agyspekuláció, mellyel pedig gyakran vádolták." Mária PATAKY, "Emlékeim Bartókról" [My memories of Bartók], Új Zenei Szemle 7/4 (April 1956), 13. (In this article, all non-English text is translated by the author, unless otherwise mentioned.) Note that von der Nüll was the person who quite rationally examined Bartók's music, so it could be possible that Bartók tried to mitigate von der Nüll's obsession. See the discussion below, where von der Nüll's interpretation is contrasted with Bartók's. 5 Two of my conference papers presented in 2017 dealt with this question (although at those occasions I rather concentrated on the intuitive side of compositional process) examining nos. 67, 133, 141, 142, and 147  It is true that the existence of such rational structures can occasionally be considered the subject of purely analytic approaches. 6 The beauty of musical or logical coherence is indeed one of the attractions that one discovers in the classical masterpieces, as József Ujfalussy, a Hungarian musicologist, stated: "the autotelic formative spirit, that is, the joy of the artist who found autonomous beauty of the construction. It would be a pity to deny the role played by that kind of aesthetical-logical joy within the process of composition." 7 Ujfalussy, however, continues: "Those who are interested in the content are willing to know what kind of content required the composer to form the composition in this or that way." 8 Here the word "content" could be understood as "the spirit of the work," borrowing Bartók's own words.
From this point of view, a piece from the Forty-Four Duos for two violins (BB 104, 1931(BB 104, -1932 no. 37 "Prelude and Canon" may serve as a good example. This short folk song arrangement possesses great coherence, solely constructed by exploiting every element of a single folk tune. Furthermore, the second part of the piece, the "Canon," has an extraordinary structureit consists of three short successive canons each at a different interval and a different rhythmic distance. Was such a piece of outstanding counterpoint written purely from a musical point of view, or rather considerably affected by what Bartók called "the spirit of the work"? While Ujfalussy approached this kind of question from an aesthetical point of view, the present paper tries to examine comprehensively both the published version and the compositional sources, the draft, and even the original folk song recording.

ABOUT THE FORTY-FOUR DUOS
The Forty-Four Duos, a collection of pedagogical pieces, was commissioned by the German pedagogue, Erich Doflein, who planned to compile a new violin school consisting of pieces by contemporary composers (among others, Paul Hindemith also participated in this project). 9 While Doflein originally intended to ask permission for transcribing some of the For Children 6 To name a few studies which deal with symmetry: Elliott ANTOKOLETZ, The Music of Béla Bartók: A Study of Tonality and Progression in Twentieth-Century Music (Berkeley: University of California Press, 1984); Jonathan W. BERNARD, "Space and Symmetry in Bartók," Journal of Music Theory 30/2 (1986), 185-201; Christopher MARK, "Symmetry and Dynamism in Bartók," Tempo, New Series, no. 183 (1992) (BB 53) pieces, Bartók instead offered to write new pieces. There could have been several reasons behind his generous proposal.
On the one hand, Bartók had long been interested in pedagogy, and, although he had not completed any pedagogical work since the Piano Method (BB 66, 1913) co-authored by Sándor Reschofsky, 10 he had probably been planning a new collection of pedagogical pieces. 11 Doflein's concept of ideal pedagogical pieces -"The series of the pieces, from the very beginning, constitutes a way which leads to the basic technique of violin playing, the music, as well as the musical understanding simultaneously" 12might have coincided with what Bartók had tried (but in his own judgement failed) to achieve in the previous pedagogical works. 13 On the other hand, Doflein's requirements, which included "the independent and strict voice leading of the individual parts as possible," 14 quite certainly corresponded with Bartók's creative interest at the time. Probably stimulated by Stravinsky's Neo-Classical compositions, which galvanised Bartók into composing in 1926 after a long break of creative activity, his music 10 Three sets of Romanian folk music arrangements (Romanian Christmas Songs, BB 67, Romanian Folk Dances, BB 68, and Sonatina, BB 69, all composed in 1915) were originally drafted together, possibly as a Romanian continuation to the series For Children (consisting of Hungarian and Slovak folk song arrangements); however, due to lack of publication prospects Bartók had to put aside the work, and they finally became three short cycles instead of a series of independent pieces. See László SOMFAI, "Komponálás a kiadás esélye nélküli években" [Composition without pro- The comprehensive education of music must also have been the purpose of the Piano Method with Bartók's short pieces intended to introduce new musical elements one after the other. (The better-known pedagogical work For Children was primarily intended as a collection of pedagogical pieces for performance rather than as a self-sufficient textbook.) Bartók himself reported and acknowledged some criticism towards the Piano Method, especially by Margit Varró, and these critical observations eventually bore fruit when the Mikrokosmos was completed about a decade later. Still, it is quite likely that the cooperation with Erich Doflein also affected the designation of the Mikrokosmos to a certain extent. became increasingly contrapuntal, as can be observed in the first part of the Nine Little Piano Pieces (BB 90, 1926), "Four Dialogues." 15 Bartók later mentioned these pieces as forerunners to another collection of pedagogical pieces, Mikrokosmos (BB 105, 1932(BB 105, -1939 but the equal treatment of two individual parts is also related to the Forty-Four Duos. One may even discover similarity between the two works, for instance, musical character (between the Nine Little Piano Pieces no. 4 and the Forty-Four Duos no. 38 "Serbian Dance") or experimentation with the combination of different canons (the Nine Little Piano Pieces no. 1). The fact that Bartók composed the Forty-Four Duos in the spring and early summer of 1931 (contrary to his habit, not during the summer vacation) suggests how interested he was in this project. He intensively composed the pieces one after the other, and sent them to Doflein in four separate units. Bartók occasionally consulted Doflein concerning the desired technical difficulty. For instance, about the timing when the use of double stop or the change of position or change of strings should be introduced, and occasionally revised the piece in order to better match Doflein's expectations.
How satisfied Doflein was with Bartók's pieces can be known from a letter of May 1931: First of all, allow me to say how much I like the pieces. At first, I was surprised by them but after a more thorough study I was filled with an increasing satisfaction on the recognition of how the changes that your way of writing has undergone since you wrote your earlier easy piano pieces also make their effect on these new easy folk song arrangements. And what inner necessity justifies every harsh sound, every clash of melody. The pieces naturally demand a very fine ear. 16 The pieces in question were nos. 2, 7, 17-22, 30-31, 37-41, 44; thus, the first parcel contained quite a wide range of pieces. The "harsh sound" and "clash of melody" justified by "inner necessity" can be found everywhere in Bartók's music and certainly in many of the Forty-Four Duos (the unprepared semitones and whole tones indeed appear in the very first pieces), but in this case they may primarily be related to no. 37, as Doflein wrote in the same letter that "We like this piece [no. 37] the best." 17 It is probable that Doflein favoured this piece because of the extraordinary canon, which fulfilled his requirement for pedagogical pieces, leading to a better understanding of a historical compositional technique embedded in a contemporary style.
Baroque music, tells nothing about the piece's particular musical character. 18 A good contrasting example is "Mosquito Dance," no. 22, which is actually a canon in perfect fifths. The title refers to the picturesque effect of the music rather than the technique of canon; the two independent voices essentially embody two dancing mosquitos. Thus, Bartók here signals an extra-musical idea instead of emphasizing the compositional technique used in the piece. In the case of no. 37, the lack of such unambiguous reference may suggest that the technical aspect of the music was his main concern.
An analysis of the piece, together with an investigation of its compositional source, may reveal the profundity of the musical coherence, as well as the compositional effort invested in achieving this coherence. It can be observed in the very first measures that almost every element of this piece is closely related to the original folk tune "Két szál pünkösdrózsa" [Two peonies]. The song was recorded on phonograph cylinder by the pioneer of research into Hungarian musical folklore, Béla Vikár in Western Hungary, in 1906, and it was later transcribed by Bartók (see Facsimile 1). 19 It is unmistakable that the head motif of the folk tune, marked as a (B 2 -FY 2 -GY 2 ), is immediately used as imitation, at a perfect fifth lower and in different note values, marked as a' (E 2 -B 1 -CY 2 ) (see Example 1).
It can also be interesting that the sequential passage in the second violin, gradually descending in major secondsmarked as a 0 -a 0 2 -a 0 3 -a 0 4 (the lower index numbers indicate the intervallic relationship with the original motif)is not an entirely fanciful idea but possibly also related to a latent sequence in the folk tune itself. 20 Following the motif a (B 2 -FY 2 -GY 2 ) in measures 3-4, a major second lower transposition a 2 (A 2 -(FY 2 )-E 2 -FY 2 ) can also be detected. One may regard this as an artificial division of the musical unit (which may be considered a problematic characteristic of certain kinds of analysis); however, in this case, the underlying logic may nevertheless be understood as the superimposition of another metric structure ( ) on the ordinary measures, which Bartók frequently encountered in Romanian instrumental folk music. For instance, in Romanian Folk Dances no. 5 "Romanian Polka," Bartók applied unusual changing time, þ þ instead of a regular time to show what he called "shifted rhythm," although in a later transcription of the original folk melody, he eventually used regular time throughout. 21 In the case of the prelude, he might have 18 Since the combination "Prelude and Canon" did not exist in the Baroque era, it is very likely that Bartók coined this ad hoc title merely describing the musical form. (There are actually two earlier compositions with the same title, "Prelude and Canon," by the Russian composer Mikhail Mikhaylovich Ippolitov-Ivanov, and the American composer Henry Cowell, but it is unlikely that Bartók knew about these pieces.) 19 Various sources of the folksong (e.g., Bartók's transcription and the original recording) are also available online: "Két szál pünkösdrózsa" in Hungarian Folk Songs. Complete Collection by Béla Bartók, Second revised digital edition, http:// systems.zti.hu/br/en/browse/13/737 (accessed 11 September 2017). 20 It is Bartók's favoured compositional technique to differently harmonise the same musical material. It can frequently be observed in the folksong arrangements, for instance, no. 14 of the Fifteen Hungarian Peasant Songs (BB 79, 1914(BB 79, -1918.  Example 1. 44 Duos no. 37 "Prelude and Canon," mm. 1-9 of the canon section "discovered" a motif in a kind of "shifted rhythm" and then he accordingly elaborated the detail. 23 These analytic observations, however, may partially be modified by the information gained through the examination of the compositional draft. 24 The second violin originally contained only falling perfect fourths (Example 2); thus, the insertion of the passing notes into the sequential motif, which eventually made this contrapuntal second violin part similar to the head motif of the folk tune, was an afterthought. This fact, however, does not mean that the similarity is accidental; conversely, it suggests that Bartók gradually arrived at a more concise and logical musical solution. 25 The overall tonal relationship also deserves attention, as Bartók exploited formal schemes inherent in Hungarian folk music. For instance, the intervallic relationship between the two Example 2. 44 Duos no. 37 "Prelude and Canon," beginning of the prelude, transcribed from the draft 23 The combination of musical elements derived from different kinds of (folk) music can be regarded as one of Bartók's favourite compositional techniques. For instance, the theme of the third movement of the Sonata (BB 88, 1926) in Hungarian character is combined with Romanian colind a-rhythm, see János BREUER, "Kolinda Rhythm in the Music of Bartók," Studia Musicologica 17 (1975), 39-58; the last pieces of the Mikrokosmos nos. 148-53 "Six Dances in Bulgarian Rhythm" have, according to Bartók, Hungarian themes embedded in Bulgarian rhythms. In these nationally hybrid elements, one may discover covert manifestation of his credo, "the brotherhood of peoples," which he explained in a private letter to Octavian Beu on 10 January 1931; see Béla Bartók Letters, ed. It can also be interesting that an apparently irregular phrase in measures 13-14, namely D 2 -A 1 -C 2 instead of D 2 -A 1 -B 1 (as in the second violin of measures 4-5), can be traced back to the original layer of the draft (measures [14][15] in the transcription). Similarly to measures [2]ff., Bartók originally notated falling perfect fourths in downward sequence, E 2 -B 1 , D 2 -A 1 , C 2 -G 1 , BX 1 -F 1 , AX 1 -EX 1 (the last note is omitted from the transcription), but in slightly different rhythm. This can be an example of where Bartók originally drafted a regular structure, which he later abandoned, probably for the sake of musical quality.
violins, imitation a perfect fifth lower in the second violin, may be interpreted as originating in one of the most characteristic features of the old-style Hungarian folk song, "fifth-shifting." 26 This term marks the relationship between the first and the second halves of a folk song; the latter is a perfect fifth lower than the former. Despite the fact that the two halves of the folk tune do not strictly correspond to each other, the song can be considered as showing a "fifth-shifting" structure since both sections essentially move within a range of a perfect fourth a fifth apart (B 2 -FY 2 and E 2 -B, 1 respectively). 27 This perfect-fifth relationship can also be observed between the prelude (in B Dorian) and the canon (in E Dorian); thus, the formal logic of a single stanza of the folk tune is extended to the entire piece.
The overall tonal structure of the prelude itself also deserves attention. This prelude consists of five stanzas of the single folk tune and can be summarised by indicating the first note of each stanza as follows: B 2 -A 1 -G 1 -B 2 -B 1 (see Table 1). If we regard the last strophe, which considerably differs from the others, as a coda, this prelude can be described as consisting of four sectionssimilarly to the stanzas in the majority of Hungarian folk songsand can be labelled, in the manner of the analysis of stanza structure in Hungarian ethnomusicology, AA 9 A 10 A. Obviously there is no folk song stanza with inner lines in a lower register and with such an extraordinarily wide ambitus (more than two octaves!); however, the return to the initial range in the fourth section reminds us of the "architectonic" structure characteristic of the new-style Hungarian folk songs (which, however, generally have middle phrases a perfect fifth higher). 28 Thus, Bartók combined elements of the formal characteristics of new-style Hungarian folk songs with a Hungarian folk tune that he later grouped together with old-style songs.

COMPOSITIONAL PROCESS OF THE CANON
For further discussion, we should broadly reconstruct the compositional process of this canon, which will considerably affect our understanding of the music. There are three key facts. First, the draft of this piece can separately be found on the pages 6 and 7 of the manuscript. 29 While most of the piece was continuously written on page 6, the conclusion can be found on a separate sheet, in the middle of page 7, directly below another completed piece, no. 31. As Bartók generally drafted the pieces of the Forty-Four Duos one after the other, except for no. 37, such a separation is quite rare in this manuscript. 30 Further examination may reveal much about the details of the compositional process. It is very likely that the prelude and the canon were composed on two different occasions (and, furthermore, it is even possible that Bartók might not have planned this piece to consist of two sections, i.e. Prelude and Canon, as we know it). A difference of notational style in the two sections can clearly be observed in the manuscript: while the prelude is continuously written on the printed staves (although later considerably revised by deleting and inserting measures), for the rest of the piece Bartók extended all the staves in the right-hand margin during (or prior to) the first notation (see Example 3). Although he is known as a composer who used music paper in a surprisingly economical manner, he usually left some blank space on the paper for the sake 28 According to Bartók's own comment on the structure of the new-style tunes they "differ most obviously from the oldstyle tunes through their structure, which is rounded, architectural." And he mentions two of the oldest architectural forms as AA 5 BA and AA 5 A 5 Athe latter is close to the form of this piece, see BARTÓK, Hungarian Folk Music, 39. Bartók sometimes composed his own original themes in Hungarian character in this architectural form, such as the main theme of the Second Piano Concerto (BB 101), see László SOMFAI, "Statikai tervezés és formai dramaturgia a 2. zongoraversenyben" [Static planning and formal dramaturgy in the Second Piano Concerto], in Tizennyolc Bartóktanulmány [Eighteen Bartók studies] (Budapest: Zeneműkiadó, 1981), 201. Here an allusion to the new-style folk tune can also be interesting from another aspect: the genre of the original folk tune is "match-making song" (see also the discussion below), and "[a] small proportion of the 'match-making' songs are sung nowadays to tunes in the new style" (BARTÓK, Hungarian Folk Music, 13). Thus, the way of arrangement can also be related to Bartók's broad knowledge of Hungarian folk music. 29 For detailed information on the source, see footnote 24. Although these pages are continuously numbered, it is very likely that there had originally been another fragmentary sheet (three staves of this 16-stave music sheet were cut out, probably by Bartók) bearing page numbers 25-26. For a reconstruction of the draft, see ITO, Barutôku, 131-137. It frequently happens in the case of Bartók that the page numbering, provided by the staff at the New York Bartók Archive, does not necessarily coincide with the actual order of composition (or the original state of the source as it arrived at the Archive); more often than not, such a numbering was made according to a brief inspection of the source and with reference to the final form of the piece. 30 The only exception among the Forty-Four Duos is no. 23, "Farewell to the Bride" which was written on the lower space on pp. 16 and 22. These pages, despite their non-continuous numbering, might have constituted a single bifolio, thus Bartók succeeded in effectively using the blank space. For another interpretation of the paper structure, see ITO, Barutôku, 135-137. The situation is similar to the case of Mikrokosmos, almost all of whose pieces were also drafted one after another. of later possible revisions, often a single staff between the systems and free space in the margins. Thus, the initially extended staves suggest that, when drafting the canon, he anticipated that the remaining space might not be enough to finish the piece. It is also remarkable that the canon is somewhat more densely notated, especially in the last system, than the prelude. So, the compositional process might have been the following: Bartók drafted the entire prelude on page 6, leaving blank space for the possible later addition of a second section, perhaps the canon or something else. After completing another piece on page 7, he returned to the composition of the canon on page 6 (chronological relationship between the genesis of the canon and no. 31 can, however, differ but, at least, the completion of no. 31 must have been prior to that of the canon), and finished the draft on page 7.
Second, Bartók repeatedly revised the conclusion of the prelude (which can also be considered a bridge section to the canon). Example 4 shows only the earliest and the latest from among the different layers appearing over one another in the draft, as it is not always possible to distinguish chronological layers when multiple corrections took place. (Note that the first and the second violin were originally exchanged after m. 27.) 31 The prelude originally ended with F 2 , which could have led seamlessly to E 2 at the beginning of the canon. (The first and the second violin parts were later exchanged in this passage so both F 2 and E 2 were still assigned to the second violin in the draft.) Bartók, however, later significantly revised the last measures and introduced the restatement of the initial perfect fourth downward leap motif, B 1 -FY 2 , which rounds off the prelude more elegantly than the F 2 .
It is uncertain whether these revisions had been made before Bartók started working on the canon or rather only later. The open ending with F 2 cannot be excluded, as some pieces of the Forty-Four Duos (e.g. nos. 5 and 29) have similar endings on another degree than the tonic. Neither can the fact that the prelude has a simple double bar line instead of final bar line guarantee that the piece was considered incomplete, as Bartók did not always use the final bar line to mark the end of a composition.
Third, this extensive series of revisions in the prelude is in sharp contrast to the composition of the canon, which was apparently directly drafted on paper almost without hesitation. It is known that Bartók more often than not sketched complicated contrapuntal sections in pencil, probably due to the special difficulty of contrapuntal writing. 32 The lack of such sketches in pencil does not necessarily mean that they never existed; it is possible for several reasons that sketches made on separate sheets might have been lost. In this case, it is highly probable that he could have tried out the music on the piano so that he could then directly notate the canon. Finding possible two-part combinations in canon does not necessarily require working-out on paper, in comparison with, for instance, writing a four-part fugue. It is of course possible that 31 It is quite interesting to observe that the original notation might have been more logical than the published version, concerning the voice leading: BX 2 in measure 26 was actually resolved to B 2 in m. 27. Sections with similar voice leading can frequently be found in the Twenty-Seven Two-and Three-Part Choruses (BB 111a), and his friend, Zoltán Kodály even gave some advice on them but Bartók did not always accept his proposals; see Miklós SZABÓ, "Kodály széljegyzetei Bartók kórusműveihez" [Kodály's notes on the margin to Bartók's choruses], Muzsika 38/9-10 (1995), 27-33 and 16-22. It may suggest that, for Bartók, strict voice leading was not the primary issue, in contrast, for instance, to musical or pedagogical concerns. 32 László SOMFAI, Béla Bartók: Composition, Concept, and Autograph Sources (Berkeley: University of California Press, 1996), 78-80. Bartók, after completing the prelude, might have decided to write a canon but put it aside for a whilepossibly due to the difficulty in finding appropriate combinationsand this might be why he returned to it only later.

CANON: MUSICAL ANALYSIS
The contrapuntal difficulty results from the quite extraordinary idea of combining three different kinds of canons on the same theme (Example 5). While the dux always begins on E 2 , each comes starts on a different degree (G 1 , A 1 , then B 1 ) and at a different temporal distance (one, two, and three quarter-notes later). Writing a canon in unison can be considered a basic study in counterpoint; however, inventing a theme that can simultaneously be appropriate for different vertical and horizontal relationships is quite a challenge. It is true, however, that Bartók did not "invent" the theme but essentially "discovered" possibilities of contrapuntal combinations inherent in an existing folk tune. While singing an existing (folk) tune in canon in unison can be considered a popular practice in Europe and can easily be done, 33 exploiting complex contrapuntal possibilities in an existing melody can be a difficult task. It cannot be established for sure how much time Bartók devoted to working out the canon, but it is easy to imagine that he was proud of this contrapuntal achievement.
One may suspect that Bartók ended up with merely tolerable sonorities when using the monadic folk song in strict canon and thereby superimposing the melody on itself while shifted in time. Combining all the intervals in different temporal distances (as Bartók might have done), we can indeed get some "acceptable" sonorities (to Bartókian ears)namely, canons beginning with B, A, GY, G, and FY (although for a canon in the distance of two quarter-notes, only the A as a starting note is acceptable, as otherwise the sequential motives in measures 6-7 of the original folk song would result in unusual parallel intervals, such as perfect fifth, major seventh, and minor seventh). A closer examination of the intervallic relationship between two voices (as well as their evolution in the compositional draft), however, eventually discloses his unique contrapuntal style, thus it can be concluded that he very consciously chose exactly these combinations to work out this canon. 34 Clear evidence of Bartók's conscious efforts can be found in the draft of the third canon. Contrary to the previous two canons, Bartók here slightly modified the original folk tune (see Examples 6-8), but in two different ways. First, he had already changed the circling figure (B 1 -CY 2 -D 2 -B 1 as well as FY 1 -GY 1 -A 1 -FY 1 ) to different ascending scales (B 1 -CY 2 -D 2 -E 2 as well as FY 1 -GY 1 -A 1 -B 1 ) when he drafted. Secondly, in three instances, he revised the notes derived from the original folk tune: the characteristic note repetition at the beginning of the motives G 1 -G 1 -FY 1 -E 1 and D 1 -D 1 -CY 1 -B were revised to simple diatonically descending scales A 1 -G 1 -FY 1 -E 1 , and E 1 -D 1 -CY 1 -B (omitting the characteristic stomping gestures of the first two notes). All The contrapuntal style, to be discussed below, does not need to be generally applicable to Bartók's other compositions. It has been observed that Bartók occasionally invented some particular "tailor-made theory" for individual compositionsas Somfai wrote on the unusual texture of the opening of the Second Piano Concerto, "Bartók a rá jellemző rendszer-fabrikáló kedvvel látott hozzá, hogy külön kis 'összhangzattant' teremtsen e speciális anyaghoz, konszonanciákkal és különböző módon disszonáns feszültségekkel." [Bartók, with his characteristic tendency to establish a system, started by producing a little "Theory of Harmony" for this special material including consonances and dissonances with varying tensions.], see SOMFAI, "Statikai tervezés," 211. these changes appear to be made in order to avoid dissonances. 35 However, we have to distinguish between prior and posterior changes to the draft, which may give us hints as to what Bartók might have considered "acceptable" and "avoidable" dissonances. The revision of the quarter note E 1 into two eighth notes D 1 -E 1 in measure 22 deserves special attention. In the draft, the distribution of the notes looks somewhat like this: Thus, it is very likely that Bartók originally wrote an E 1 but then added another note D 1 in front of the E 1 , as well as a beam over them. However, the unlikely idea that he originally planned the D 1 -E 1 eighth note dyad but merely failed to write them with precise vertical adjustment should not be ruled out.
It seems that while consecutive seconds A 1 /G 1 and G 1 /FY 1 in measure 22 should be at any rate avoided (thus Bartók already notated B 1 in the draft instead of FY 1 ), unprepared dissonances, A 1 / G in measure 22 and G 1 /D 1 in measure 23, which resolve into B 1 /G 1 and FY 1 /D 1 , respectively, might have been considered acceptable but they still were later revised.
These revisions are quite interesting, because there are a lot of unprepared dissonances in this canon. Would there be any specific reasons to leave or avoid such dissonances? We shall put aside this question for the moment and instead continue examining how Bartók dealt with consonances and dissonances in the piece.
Analysing Bartók's music, a possible approach could be to examine every simultaneous sonority and consider each as having independent statussomewhat similarly to what von der Nüll did in his doctoral dissertation. 36 While he identified many independent chords (highly dissonant ones not necessarily followed by a resolution) in, for instance, Fourteen Bagatelles no. 10, Bartók rather thought that the framework of the music is far simpler than it appears (Example 9). 37 Thus, following Bartók's manner, we can ignore many of the dissonances as passing notes or escape notes (both accented, though; see Example 10). The succession of unusual intervals (major seventh and major ninth) in measure 3 can be considered a combination of a leaping auxiliary note (E 2 ) with what can be interpreted as either embellished stepwise motion (F 1 to G 1 ) or authentic bass movement (D 1 to G 1 ).
Dissonances handled in an unusual manner can be found in measure 6, where the expected resolution of a dissonance happens simultaneously with another melodic motion. While G 1 in the upper part in measure 6 moves to FY 1 , the upper major third of D 1 , this D 1 moves to BX without waiting for the resolution in the upper part. Similar phenomena can be observed in measures 8 and 14 (in the former, FY 1 /C 1 dyad moves to E 1 /BX in parallel, instead of the expected resolution to E 1 /C 1 , and in the latter, G 1 /D 1 contrarily moves to FY 1 /E 1 , instead of FY 1 /D 1 ). This elusive form of resolution is, of course, not calculated; in fact, what Bartók actually did was to write a strict canon by incorporating an existing folk tune, which made it impossible for him to considerably change the melody. Nevertheless, this unconventional musical effect can offer a key to interpreting a secret programmatic concept that may lie behind the music. coincidental that Bach was probably one of Bartók's artistic ideals at that time. 38 A unique feature of the Goldberg Variations is that its every third variation (except for the last one, a quodlibet) is a canon, and the interval between the two canonic voices gradually widens from unison to ninth. Furthermore, the quodlibet is a skillful contrapuntal combination of German folk melodies. One has to recall that Hungarian folk music seemed not to offer many contrapuntal possibilities. As Bartók stated in the already quoted article, "The Folk Songs of Hungary," -"we did not find much contrapuntal inspiration in our peasant music." 39 Thus, it could appear an adventurous endeavour to exploit hitherto unknown contrapuntal possibilities of Hungarian folk songs.

A CANON AS A COMPOSITIONAL CHALLENGE
Example 9. Von der Nüll, Béla Bartók: Ein Beitrag zur Morphologie der neuen Musik, 6 Example 10. 44 Duos no. 37 "Prelude and Canon," Canon, mm. 1-8 38 To Edwin von der Nüll's question ("Why do you make so little use of counterpoint which is so heavily used by all other modern composers?") in 1928, Bartók answered that "In my youth my ideal of beauty was not so much the style of Bach or Mozart as that of Beethoven . . . [I]n the last few years I have also been engrossed in music from the pre-Bach period, and I believe traces of this can be found, for example, in the Piano Concerto and in the Nine Little Piano Pieces." cf. Edwin von der NÜLL, "A Change in Style," in Bartók and His World, ed. by Péter LAKI (Princeton, NJ: Princeton University Press, 1995), 276-277. This answer only indirectly refers to Bach (as well as his music), and Bartók indeed extended his repertoire to works by composers other than Bach. Nevertheless, one should not miss that allusions to Bach can often be found in Bartók's compositions, namely the above-mentioned Nine Little Piano Pieces (the title of the first four pieces, "Four Dialogues" may refer to "Vier Duette" BWV 802-805 in Clavier-Übung III; the opening of Cantata profana (BB 100, 1930) unmistakably refers to the St. Matthew Passion, and so on). For Bach's role in Bartók's youth, see VIKÁRIUS, "Bartók's Late Adventures," 404-405. 39 English translation quoted from VIKÁRIUS, "Bartók's Late Adventures," 403.
It is also significant that writing canons with an original folk song falls outside the usual categories of folk song arrangement discussed by Bartók in his articles. In spring 1931, somewhat earlier than the composition of the Forty-Four Duos, Bartók mentioned the following in a paper now known under the title "The Influence of Peasant Music on Modern Music": Two main types can be distinguished among [folk song arrangements].
In the one case accompaniment, introductory and concluding phrases are of secondary importance, and they only serve as an ornamental setting for the precious stone: the peasant melody.
It is the other way round in the second case: the melody only serves as a "motto" while that which is built round it is of real importance. All shades of transition are possible between these two extremes and sometimes it is not even possible to decide which of the elements is predominant in any given case. But in every case it is of the greatest importance that the musical qualities of the setting should be derived from the musical qualities of the melody, from such characteristics as are contained in it openly or covertly, so that melody and all additions create the impression of complete unity. 40 In strict canons, the melody is combined with the same melody, thus, there are no essential differences between the melody and the accompaniment. Consequently, in a certain sense, the composition of canon may enable the composer to achieve the "complete unity" as everything grows from a single material. 41

CONCEALED VILLAGE SCENE
Such an interpretation may essentially ignore, however, the concluding part of the piece, which no longer continues the strict canonic writing and dissolves into something like a real turmoil (see Example 11). It is Bartók's favourite strategy to prepare the conclusion with fragmentary motives, and numerous examples can easily be found for example in Mikrokosmos pieces, such as nos. 103, 138, or 146. One could argue that in no. 37 of the Forty-Four Duos all the elements used in measures 25ff. are derived from the original folk tune. However, does such a seemingly superfluously detailed analysis make sense at all?
An examination of the original folk tune may offer, however, an extraordinary answer to this question, and make possible a comprehensive interpretation built on the elements examined so far.
Let us first look at the text of the folk tune: This folksong belongs to a type called párosító (in English: "Match-making" song), "[whose text] names a girl and a boy whom the village[r]s know to be, or suspect of being, in love with one another." 43 In this case, Fáni is a girl and Pali Bosnyák is a boy, thus, the two voices of the canon can be interpreted as two peonies symbolising a young pair. The music reveals, however, that something goes wrong. As is mentioned above, while the interval between the dux and the comes becomes narrower, from the major sixth to the perfect fourth, the temporal relationship eventually becomes larger, from a quarter note to three quarter notes. It also deserves attention that the above-mentioned "elusive resolution" may also imply a kind of "discord" or disagreement between the two "characters." Nevertheless, there could still be a kind of reconciliation brought about by the revision in the third canon, which reduced the number of unprepared dissonances.
Thus, the extraordinary canon, which could be an adventurous experiment in counterpoint by Bartók, could possibly be related to what we may call a secret programme of the piece. This interpretation can be supported by the original phonograph recording. 44 It should be clear that the informant, while largely keeping the tempo in the first stanza, gradually accelerates and then she is no longer able to normally sing the last stanza (thus "she bursts out laughing," as Bartók remarked on the transcription). Obviously, this was not intentional. Probably due to the personal involvement with the people mentioned in the song, she could not suppress her amusement. (We can also hear on the recording that several other girls were present listening to the song who then also joined in her laughter.) Still, it is quite interesting that the acceleration can also be found in Bartók's arrangement, and the music is also interrupted by something which can possibly be interpreted as a musical depiction of "laughter" since the original folk tune disintegrates and only fragments of it can still be heard.
There is indeed a similar "laughter" phrase at the conclusion of the third piece from Four Hungarian Folksongs for mixed choir (BB 99, 1930), "Finding a Husband" (see Example 12). The folk song used in this chorus does not belong to the párosító type, but the content of the text of the folk song is also related to match-making, and so the similarity might not be accidental. Here the musical similarity is striking, as asymmetric short rhythmic figures move in inversion.
In these two sections, the actual meaning of the "laughter" can, however, differ. While in "Finding a Husband" the harmony is a stable G-major and the rhythmic figure in the middle voices essentially embellishes the G-major triad (thus, implies some kind of concordance), in "Prelude and Canon" there is no unambiguous consonant harmony: the harmonic frame is established by the A 1 /D 1 fifth and voices in contrary motion result in ever new dissonances. If we imagine this section as the depiction of "laughter" while the "two protagonists" are still playing their role, it can be interpreted that although one "character" catches up with the other, the conflict between them is still not completely resolved. The reconciliation can only happen in the last measures, where both violins play in unison in a long note value.

CONCLUSION
In the present paper, more than one interpretation of "Prelude and Canon," Forty-Four Duos no. 37 has been considered. From the analytical point of view, this piece can be regarded as a contrapuntal masterpiece, demonstrating Bartók's compositional dexterity. One may even contemplate that it was Bartók's main intention to represent a logical contrapuntal structure within a miniature piece. Indeed, a pursuit of a kind of order is an intriguing task and such an interpretation might be the only way to sufficiently acknowledge the impressive musical coherence the composer achieved with intellectual power in the composition.