Béla Bartók's Sonatina for piano (1915) is a fascinating and appealing work, eminently suitable as an introduction to Bartók's larger works. An early composition, it provides an excellent preview of Bartók's mature oeuvre by revealing his meticulous organizational thinking, his solid grounding in classical theory, and his incorporating of folk elements into the core of his compositional style. At the college level, pianists find the Sonatina attractive and challenging to play, yet not overly difficult. Analysts discover in it a wealth of material for study from intermediate through graduate level.
This paper presents a theoretical analysis of the Sonatina from several viewpoints—Schenkerian, motivic, modal, and symmetrical. Yet the discussion proceeds as an exploration of questions and observations of a hypothetical performer, listener, or music historian. Through this approach, the essay embraces the theme that theoretical analysis, valuable enough in its own right, can be enriched deeply by establishing its relevance to other facets of music. In College Music Symposium 2000, Barbara English Maris advises us to "[h]elp students put together the specialized parts of music study, learning how knowledge of music history, music theory, and music performance strengthen each other."1 Michael Rogers remarks that "[diverse] orientations within music theory . . . [can] be folded gracefully into the natural habits of music study."2 George Houle cites Putnam Aldrich's question "What is the fundamental idea of this piece?" as "tak[ing] his students through a rich and varied process of insights that could transform a mental image of the composition."3 In this article, Béla Bartók's Sonatina provides a forum for exploring many fascinating aspects of composition by one of the twentieth century's greatest masters, and for bringing to life the musical personality of the composer.
Bartók states in his autobiography:
I began writing piano music when I was nine years old and made my first public appearance as a 'composer' and pianist [at age ten] . . . before I was eighteen I had acquired a fairly thorough knowledge of music from Bach to Brahms . . . came to Budapest . . . and at the Academy of Music was considered . . . a first-class pianist . . . It was the time of a new national movement in Hungary, which also took hold of art and music . . . When this movement reached me, it drew my attention to studying Hungarian folk music . . . The outcome of these studies was of decisive influence upon my work, because it freed me from the tyrannical rule of the major and minor keys. The greater part of the collected treasure, and the more valuable part, was in old ecclesiastical or old Greek modes, or based on more primitive (pentatonic) scales, and the melodies were full of most free and varied rhythmic phrases and changes of tempi . . . It became clear to me that the old modes, which had been forgotten in our music, had lost nothing of their vigour. Their new employment made new rhythmic combinations possible. This new way of using the diatonic scale brought freedom from the rigid use of the major and minor keys, and eventually led 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.4
Written during Bartók's early years of folk music collection, the Sonatina was originally conceived as a group of dances for piano.5 Its themes, five in all, are traditional Rumanian folk melodies whose transcriptions and titles in Bartók's handwriting are reproduced in Benjamin Suchoff's edition of Piano Music of Béla Bartók.6 Analysis reveals that the Sonatina is far from being a loose collection of five dances; rather, it displays a unified diatonic structure organized by tonality, motive and symmetry that stem from both classical and folk sources. Let us begin by approaching the Sonatina from the performer/listener's viewpoint. Its attractiveness comes from its catchy tunes, their lively accompaniments, and the rustic flavor of the music. It also poses some puzzles. For example, is the first movement finished, or does it end with a half cadence leading onward? Does the last movement finish with a full- or half cadence; if a half cadence, how can this be the end of the Sonatina? Why do the phrase endings of principal themes in the first and last movements feel inconclusive? What should the performer "do" with repetitious passages such as the middle section of the first movement? How is the Sonatina different from the many wonderful settings of individual folk melodies in Bartók's collections For Children? These and other intriguing questions guide the ensuing discussion.
Students in any music appreciation, history or theory class will expect a piece entitled "Sonatina" to have three movements in fast-slow-fast order, and see their expectations confirmed. They will also perceive three clear, simple classical forms. The first movement, Bagpipers, is in ABA form; the second, Bear Dance, presents a single repeated melody; and the third, Finale, is in AB form with a coda restating both themes. But students will also probably expect a piece labeled "Sonatina" to display such classical necessaries as developments, recapitulations, and "correct" keys for "textbook" events. These aren't here, at least at the surface level, because the themes are all quotations of authentic folk melodies. Is Bartók just being casual with his title? To the contrary, analysis of the Sonatina reveals a tonal organization that is clearly characteristic of a classical sonatina. The structure offers a fine example of the underlying tonal plan and background-level connections in classical works that supersede the surface appearance of themes.
Schenkerian reductive techniques provide an excellent view of the Sonatina's tonal design. Example 1 shows a voice-leading graph of the complete work, and its corresponding principal features are labeled in the score at the end of this paper. In overview, the three movements function together as a tonal unit creating one structure in the key of D major. The basic scalar outline, the "fundamental line," descends 
-
-
-
in the first movement (with an intervening retardation of , interruption, and restatement of the descent); is retarded in V in the second movement; tonic is reestablished in the third movement by an octave scalar ascent; and descends to 
at the end of the Sonatina.
Example 1. Voice-leading graph of complete Sonatina.
While producing such a graph is beyond the capacity of most undergraduate students, understanding its basic information is not. Much Schenkerian thinking is quite intuitive, sometimes even prompting comments from beginners that it seems so obvious. Necessary background includes some grasp of basic counterpoint, of reduction/prolongation concepts, and of outlining at either an intuitive or a more scholarly level, all of which intermediate college students typically have. Example 2 shows the thinking process that gradually reduces the foreground "surface" level of the score through a middle level of outline to a basic background summary.
Example 2. Foreground, middleground and background graphs of first movement, A section.
In mm. 1-20, the A section of the first movement, the melody begins after a four-measure broken-chord ostinato introduction that establishes tonic. The tune's most obvious note, the first one and the one that others circle around and return to, is A, scale degree . Then passing-tone 
() moves on to 
() in m. 7, which is circled around and returned to in similar fashion.7 Here the melody repeatedly leads from () through E () to D () in mm. 8-12. Thus the outline of the folk melody is --
(prolonged)--, as seen in the fore- and middleground graphs of Example 2. But why do the graphs show A-- in white notes and the descents through E-D in black notes (indicating levels of greater and lesser structural importance in Schenkerian notation)? In mm. 8-12, an interpretive problem arises: The repeated melodic s all arrive on E, which is always ornamented with grace notes and lengthened, but then always move on to a quick merely perfunctory D. The repeated, accented, lengthened Es seem intuitively important; on the other hand, the tonic Ds appear only in rhythmically weak positions and are either not harmonized at all or are supported with the IV chord instead of I. Does the melodic structure end inconclusively on E () or conclusively on D ()? Should the performer help us through this quandary by clarifying the tonic D endings (with, for example, a decrescendo or phrase articulation)? After all, this is a folk melody that perhaps doesn't fulfill our classical expectations of a cadence. We gain new perspective on our problem when the melody repeats in m. 13. At the end of the whole A section, in m. 20, Bartók chooses to harmonize E () with a big accented half cadence on V, and avoids a final descent to and a tonic chord. It seems, then, that he intends E () rather than D () as the long-range structural goal. Thus the background outline of the whole A section presents an unfinished --- descent of the fundamental line, supported by I-V harmonic motion, as shown in the background graph of Example 2. With this insight, the performer may now confidently enjoy the many ornamented arrivals on active E, moving onward through the tonic non-endings in mm. 8-12 and 16-20 to the dramatic half cadence in m. 20.
And what of the accompaniment? It is repetitious and ostinato-like. Is repetition its most important feature, thus allowing the more interesting melody to shine? If so, then why do its "thumb" notes change to form a new melody? If this thumb melody is important, why does it occur on the rhythmically weak off-beats? Furthermore, why does the repeated chord of the ostinato feature the dissonance D-E rather than, for example, a consonant open fifth more charcteristic of drum-like ostinato patterns in classical music? A notion of basic counterpoint is helpful in answering these questions. In this A section of the first movement, the bass D pedal point and the persistent E-D chord that accompany the melody provide it with contrapuntal support. D continuously defines tonic, and the E-D pair alternately create consonances with notes of the melody's fundamental line (E-D are transferred to the bass clef and represented as separate rather than simultaneous pitches in the middle- and background graphs). The thumb notes of the left hand accompaniment create consonant counterpoint with melody notes, seen most clearly in the middleground graph. Yet rhythmic displacement creates numerous surface dissonances that belie the consonant underpinnings, as seen by annotations in the score corresponding to notes in the graphs. Bartók charmingly captures the flavor of folk music and its "out of tune" rustic character by meticulously acknowledging classical norms of counterpoint, yet intentionally misaligning them.
The B section of the first movement presents a new folk tune beginning on the melodic E where the A section left off. Only now E is comfortable triad tone in the key of C major rather than unfinished of D. (In Schenkerian terms, this is called a "retardation:" an active tone temporarily becomes stable). A succession of descents from E through D to the new tonic C (--) presents cadences on I in mm. 23, 26, 30, and 37. The performer will wonder again if each phrase should be "finished." The question arises here because each time the next phrase starts rhythmically "too soon", with no pause or long note to denote an ending. The many short phrases all seem stuck on E, and the last, at m. 38 ff., gets so trapped that it just can't get beyond E to finish the phrase. Is this an unfortunate directionless melody, a quotation of folk material that can't be altered? Couldn't Bartók have picked a different melody? To the contrary, hovering on E is precisely the point; prolongation makes the E more important. With analysis as a guide, the performer can now justify enjoying, dawdling, dancing over the many versions of E. The accompaniment that supports it with numerous cadences in local C major suddenly presents a surprising 
minor harmony in m. 39 that jolts the music into a new direction. There the initial mezzo-forte diminishes to pianissimo in m. 43, and rhythmic motion ceases. Then in m. 44 the E octave pedal point regains its rhythmic energy, the opening ostinato, and a deeply descending bass that passes through the dominant A (as in a classical dominant preparation) on its way back to tonic D. A triumphant restart of the original melody in m. 50 is the reward, and the whole A section repeats.
While the obvious surface form of Bagpipers shows an ABA arrangement and two independent folk themes, a more subtle background study reveals that this material has been carefully poured into a classical tonal mold. Original material in the tonic key (A section), a tonal departure (B section), a dominant preparation (mm. 44-49), and a restatement in the tonic key (A section again) are characteristic of the classical rounded binary form. The movement's ending, however, is a surprising half cadence. Unlike a tonic ending and a finished fundamental line that has arrived at a full close on scale degree , the dramatic unfinished pause on at the end of Bagpipers carries a sense of expectancy. The performer will want to hold the listener's attention through the break between movements. At this point, a composer of the classical era might indicate "attacca."
The second movement, Bear Dance, provides a balance between the outer two movements mirroring that of the B section within the first movement. Bear Dance transforms active (E) now into stable triad tone in the minor dominant key, A minor, as summarized in Example 1. The simple folk melody forms a period: An antecedent-consequent pair of phrases descend from to , then to (mm. 1-4); then an answering antecedent-consequent pair ascend to and end first on , then on (mm. 5-8). The melody appears first with bass accompaniment, then repeats in a lower register with accompanying chords above, then repeats the last phrase yet again with higher treble chords. By itself, the second movement is a charming setting of a simple tune, grumbling in an awkwardly low register characteristic of a folk-traditional bear dance. If it were a single piece, the performer might choose to define the eight-measure melody conclusively, then to focus on the different "vocal" characteristics of the repetitions, leaving the accompaniment far in the background. But in context, new ideas emerge. The outline of Bear Dance displays the same ---- as did the A theme of the first movement (see Example 2, fore- and middleground graphs of mm. 5-12). In addition, it now becomes clear that the treble chords do more than just accompany; they too reiterate the same ---- outline (see score and Example 1). On yet further consideration, it seems that this movement functions as a classical development section: Its melodic outline is the same as the first movement's A theme, now in a new key; it develops that outline first as a new melody in mm. 1-8, then as a bass line in mm. 9-20, and yet again as the soprano voice of the accompanying treble chords in mm. 17-20. Its initial foreground motive E--E-D reworks the opening E-
-E-D motive of the first movement's B theme (compare II: m. 1 with I: m. 21). Furthermore its final cadence on A provides the dominant preparation that will lead back to tonic. The performer might feel initially that this movement seems too short and too simple for a Sonatina, and that he must "do" something with it. What can be "done" in addition to playing it for its own sake, is to clarify the ---- structure, especially emphasizing the grace notes, trills and accents in the melody that stress C (), and to bring out, albeit quietly, the soprano line of the treble chords to reveal their ---- outline. Then waiting expectantly on the last chord will again hold the listener's attention for an attacca start of the third movement.
Finale of course supplies the last piece in a typical three-movement sonatina design. But if we consider that the second movement supplies the Sonatina's development and dominant preparation, and continues attacca, is there any sense in which we could view the third movement as a recapitulation in a unified structure? Finale's opening four-measure octave D drone immediately reestablishes tonic and recalls the introductory four-measure ostinato of the first movement. The accompaniment continues the drone overlayed by a "thumb melody" that creates counterpoint with the main tune, as in Bagpipers. Yet the A and B themes of the first movement don't reappear literally, as would be expected in a classical recapitulation; rather, Finale presents two more authentic Rumanian folk melodies. Of the hundreds of folk melodies Bartók collected, why did he select these particular two? Careful examination shows a remarkable similarity in pitch content and contours between the themes of Bagpipers and Finale, as shown in Example 3. The A themes of both movements commence with a scalar four-note ascent, a turn, and a neighbor tone ascending to ; then answer with diverging tetrachords centered on , and a - descent. The B themes are both built on repetitious ornamented versions of a -- double-neighbor figure. Although the surface melodies differ, their middleground designs are nearly identical. Thus the themes of Finale recapitulate the themes of Bagpipers quite successfully. Bartók has again ingeniously poured his folk themes into a classical mold.
Example 3. Comparison of A and B themes in first and third movements.
Finale poses further questions. Why does the key change to G (with a G key signature) in the middle, at m. 37? Does the Sonatina end on a half cadence in G or on a full cadence in D? To solve these puzzles, we must examine the background structure. The movement's melodic outline ascends a full octave D scale in two portions that divide it into equal tetrachords D-G and A-D, marked with brackets in Example 1.8 The A section of Finale, mm. 1-36, establishes a --- tetrachord (D-E--G). Each of its three consecutive statements is answered by a subsequent descent of the same tetrachord (which descent might be interpreted locally as finishing a ---- line that continues from the final A of Bear Dance). The most obvious harmonic feature of the section is a tonic D pedal point. Tonic harmony supports the beginning and ending of each tetrachord statement, and left-hand thumb notes support individual tones as seen in Example 1 and the score. Yet this passage seems tonally ambivalent. The IV chord that supports of each tetrachord (mm. 6, 8, 14, 16, 25, and 27) tricks us into hearing the passage locally as a dominant D pedal point in support of tonic G. Bartók subordinates G to D by placing the G chords in inversions, but we are nevertheless drawn toward G as a new tonic. (In retrospect, we may now see that Bartók prepared this tonal ambivalence in the first movement with rhythmically weak cadences on IV in mm. 9-10 of the Sonatina's initial melodic phrase, further evidence of this movement's recapitulation function.)
With the lower D-G (-) tetrachord thoroughly established, a quick ascent of the upper tetrachord -
-
-
ushers in the B section at m. 36. Numerous foreground tetrachords ascend and descend to and from A (), shown by brackets in the score. The new folk theme of the B section is supported by extended trills that generate consonances with melodic pitches (functioning like the E-D chords in the first movement's ostinato). Surprisingly to a classicist, a new key signature appears here in mid-movement, that of G major. The ambivalence noted earlier is further reinforced by the fact that the new melody, by itself clearly in G, is accompanied by strong concentration on tonic D as the initial and longest-sustained tone of the melody, by the trill on D, by accents marked on recurring Ds in the bass, and by the added soprano D pedal point in mm. 75-81. Do these Ds, often paired with 
s in the melody, function as dominant-seventh chords in support of G, or does G function as a strongly-supported subdominant in the original key of D? Another puzzle: What single pitch attracts the most attention throughout the whole B section? Even the most intuitive listener will perceive that A, as the accented final note of each melodic phrase, is shocking because of its obvious "unfinished" quality. (Scale degree is indeed the final note of the folk melody.9 The classically trained performer must avoid the intuitive temptation to treat it as a - upbeat to the start of the next phrase.) After five melodic cadences on A in quick succession (mm. 40, 44, 46, 48, and 50), the melody is transposed and the accompanying trill moves up to high a2 in m. 52 and to the highest pitch of the entire Sonatina, a3 in m. 59. The trilling reiterated As occupy the busiest, loudest, highest, and central portion of the entire movement. Even the background harmonic support for the section moves to A in m. 53 (see Example 1). The performer, in the context of an independent setting such as one in For Children, might well choose to relegate all of these As quietly to the background; the melody seems obviously to be the main feature. But in a larger context, we see that A carries special significance. In this case, a thoughtful performer might, to the contrary, exaggerate the rustically awkward endings on A of the melodic phrases and the insistent "A-ness" of the whole passage. In a structural sense, A, the dominant in the Sonatina's governing key of D, is the featured pitch of this entire central section of the movement, yet Bartók cleverly works it into the tug-of-war between G and D.
Eliding the ending of the B section, a long scale begins on bass A in m. 80. The huge scale encompasses fourteen measures and proceeds ultimately from scale degree through to 
in a higher octave (a2-b2-
3) in mm. 84-86, then through to 
in a lower octave (a-b-
1) in mm. 90-91, and at last to in the "correct" register (d2) in m. 93. Far from being mere accompaniment, this scale marks the structural coda and completes the ascent of the movement's upper tetrachord A-B--D.10 The surface coda, in m. 84 as marked by editor Benjamin Suchoff, begins part-way up the long ascending scale where three thoughtfully stated ascending tetrachords in mm. 84-93 recall earlier material. Each tetrachord restates the opening theme of Finale; the first also recalls the initial melodic pitches of Bagpipers (a2-b2-2); each summarizes the important perfect-fourth interval; and each is followed by an expectant pause. The performer might well exaggerate the pauses, rather than "smooth over" the awkward silences, leaving time for reflection. The most tantalizing pause of all is on leading-tone in m. 91; here the performer can tease the listener with Bartók's accent, staccato ending, forte dynamic level and sostenuto molto tempo, into urgently expecting resolution to tonic D. The long-anticipated D arrives in m. 93, and is swept up in a joyful repeated whirling - - pattern that lasts five measures. With harmonic support formed by overlapping descending chromatic scales in two voices, the spinning motion's culminating D () at m. 97 repeats over an alto restatement of Finale's B theme, and at last tonic support arrives at m. 102 with a clear bass V-I. All of the melodic and supporting harmonic elements involved in this complicated whirling pattern seem again intentionally misaligned to create surface dissonances that capture a delightful rustic character.
The final structural gesture of the Sonatina comes in m. 103. Here (E), left at the half cadence of the first movement, is at last retrieved and resolved to (D) in the "obligatory register" (in Schenkerian terms, the unique register in which the fundamental line occurs). The final five measures thrice harmonize scale degrees - with V-I chords, confirming the tonic D and completing the fundamental line of the entire Sonatina. With the structural significance of the entire Sonatina's fundamental line in view, and conscious of the E left unresolved as /V at the end of the first movement, the performer may now declare triumphantly the finality of E-D (-) by means of strong V-I support. In these final five measures Bartók also includes Gs in the tonic chords of mm. 102-105 and resolves them through triplet tenor motion to , as in a traditional 4-3 suspension, thus clarifying G's subservience to the reigning key of D. In too small a context, especially to Western listeners, the ending of the Sonatina might seem inconclusive. Is it a half cadence in G? If so, what comes next? Has Bartók made a mistake? To the contrary, through background structural design as well as through surface details, he at last resolves the G-D ambivalence in favor of D tonic, and indeed finishes the Sonatina with a strong full cadence.11, 12
The foregoing Schenkerian view reveals the Sonatina's classical design. Yet classical tonality is only one of several interrelated organizing features to be seen in this work. Bartók also establishes the reigning key of D by several non-traditional means, one of which is motive. We have already noticed a variety of situations where decisions were made regarding onward motion or delay, accentuation or resolution, dissonance or consonance; now in overview, we can see that many of these situations involved two particular pitches, E and D. Bartók consistently provides motivic unity throughout the piece by pairing these two pitches, E and D. Their dissonance together and their resolution as active to stable govern much of the music's sonority and direction. The E-D pair appears in many guises, listed below and circled in the score: in the opening ostinato, in melodic surface motives, as locally active tones, as middleground connectors, and ultimately as the final pitch pair resolving the fundamental line. Their pervasive presence provides a tonal magnet for the whole Sonatina.
E-D motivic pairings:
I mm. 1-4 Accented E, discordant with D-A ostinato introduction. mm. 5-7, 13-15 E-D in melody's "alto voice." mm. 8-12, 16-18 E-D cadential melodic motive. mm. 5-20 D-E chordal ostinato accompaniment throughout A section. mm. 20, 65-66 D-E cadential melody notes, ending on active mm. 21-41 E-D initial melodic motive repeated frequently in B section. mm. 20-21 E transformed from mm. 39-44 E returned gradually to original function as I-II I: m. 66 - II: m. 1 E transformed from II mm. 1, 3, 9, 11 E-D opening motive of melody. II-III II: m. 1- III: m. 1 E ( III mm. 5, 13, 24 Melody of A section starts with D-E activation. mm.12, 20, 31-36 Melody of A section closes with E-D resolution. mm. 38-51, 68-75 Continuous E-D trill accompanies melody in outer portions of B section. mm. 53-64 Melody in parallel sixths reiterates E-D pair in central portion of B section. I-end I: m. 66 - III: m. 103 E (
In addition to classical and motivic organization, elements that derive specifically from folk music govern much of the Sonatina's structure. Music history students learn that Bartók and a number of his contemporaries incorporated folk music into their compositions. Obvious examples show direct quotation of folk music in much twentieth century literature. In Bartók's case, however, folk influence runs deeper. He, for instance, methodically collected folk melodies and transcribed them with scientific care, becoming acknowledged as the first ethnomusicologist. The Sonatina shows even further absorpton of elements of folk music into his compositional thinking. Beyond the direct quotation of authentic Rumanian melodies, what else may we see herein? In a 1928 lecture, Bartók says that
we find in the music of Eastern Europe the most incredible variety in the leading of the melodic lines, as well as of available tonal modes. . . . In the majority of these tonal modes the fifth degree in general does not play that dominant part which we can observe in the case of the fifth degree of the major or minor scale. . . . A further peculiarity of these old melodies is to be found in the frequent occurrences of the skip of a perfect fourth. . . . The frequent repetition of this remarkable skip occasioned the construction of the simplest fourth-chord.13
The perfect fourth in Western classical terms is problematic. It is a dissonant interval in traditional counterpoint that must be resolved, or hidden among the upper voices of a triadic structure. A Schenkerian fundamental line spanning a fourth (either --- or ---) is highly unlikely: cannot function as a starting point because it is not a member of the tonic triad; and the upward resolution - denies the natural tendency of lines to descend toward tonic. Yet in Eastern European folk music, the fourth occurs commonly. Elliott Antokoletz explains:
The frequent melodic skips of a perfect fourth in the old Hungarian folk melodies were a significant source for Bartók's melodic and harmonic inventions . . . [construction of the fourth-chord] transforms the diatonic modes into symmetrical pitch constructions. . . . In traditional tonal music, composers worked according to a system in which the octave was divided into unequal parts. The fundamental division was derived from the perfect fifth, which served as the basis of harmonic root function and as the primary structural interval of major and minor triads. In turn, the perfect fifth of the triad was unequally divided into major and minor thirds. In contrast, the pitch relations in Bartók's music are primarily based on the principle of equal subdivision of the octave into the complex of interval cycles. . . . the interval cycles and derivative symmetrical segments have an important function in the large-scale structure.14
In the Sonatina, Bartók features the fourth extensively. It is immediately obvious in the opening ostinato, whose structure establishes a tonic D pedal point, the dominant A, and the motivic E-D pair: of the many possible voicings of this basic pitch material, Bartók chooses a vertical structure built in fourths, E-A-D superposed over the tonic D pedal point. At a deeper level, the fourth controls the Sonatina's tonal structure. The fundamental line of the first movement descends a perfect fourth A-E. The fundamental line of the third movement divides the octave scale into two ascending tetrachords, D-G and A-D. The final ascending A-D fourth of the coda answers the first movement's descending A-E fourth. The penultimate tonic chord is spelled D-G-A-D, reiterating vertically the two perfect fourths that govern the Finale, and recalling the fourth-chord structure of the opening Bagpipers ostinato. In the Sonatina Bartók treats the perfect fourth, derived from folk sources, with structural significance on equal footing with the tonic-dominant pillars of classical theory.
In the lecture cited above, Bartók further explains that in "pentatonic scales [of Eastern European folk music] the third, fifth and seventh are of equal rank and importance; since the second degree and the major seventh are missing, the trite dominant-tonic cadence . . . is not possible."15 Antokoletz elaborates that "[a] special property of the minor-seventh chord is its symmetrical intervallic construction—half of the chord intervallically mirrors the other half . . ."16 The dominant-function chords in the Sonatina are often of the minor-seventh variety. Let us consider some "problematic" instances. For example, in mm. 44-49 of the first movement, is the A--E-G chord a dominant? It clearly behaves like a dominant harmony in that it is built on V and leads strongly to the I chord at m. 50 and the return of the A section; yet the obvious presence of rather than classically crucial leading-tone is stressed repeatedly. We have seen that the middle movement functions as a classical development and dominant preparation for the recapitulation in Finale; yet its key is A minor, not major. And most problematic of all is the final cadence, in mm. 103-107. Here again, Bartók spells the minor-seventh chord on A rather than the classical dominant that would include leading-tone . This minor dominant chord is the source of ambivalence between two possible interpretations of the final cadence: traditional II7 - V in the key of G and V7 - I in the key of D are identical except for versus . Bartók uses both and freely throughout the piece, and juxtaposes them especially significantly in several places. The opening of the Sonatina immediately features the highest note of the melody as , yet its accompaniment features . The key area of the B section in the first movement is C major, but minor is the attention-getting chord in m. 39 that suddenly changes the context of the principal melodic pitch E.17 In the coda of the last movement, the long scale ascending from bass A incorporates both and : it reaches its highest pinnacle on in m. 86, yet it prepares the arrival of tonic through leading-tone in mm. 91-92. The spinning soprano - - motive of mm. 92-97 uses , yet the adjacent alto restatement of the B section's melody in mm. 97-102 uses . The shift between and provides a background motive throughout the Sonatina. The stems from folk sources, and the leading-tone from classical practice. Rather than settling the argument in favor of one or the other, Bartók brazenly juxtaposes them.
The symmetry stemming from folk sources, as seen in the symmetrical tetrachord division of the octave and the minor-seventh chord, extends to many other aspects of the Sonatina. Bartók provides myriad symmetrical pitch patterns and symmetrical segments of form, as listed in the following table, balancing contrasts of above/below, vertical/horizontal, upward/downward, backward/forward, before/after. Has the symmetry found naturally in Eastern European folk music worked its way into the core of Bartók's thinking? This is a rhetorical question with no clear answer; yet there seem too many symmetries to be merely coincidental.
Symmetries:
I mm. 1-4 Opening treble chord provides motivic E-D (e1-d2), spaced a perfect fourth below and above dominant A (a1). mm. 8, 12, 16, 20 Melodic neighbor tones mm. 21-23 Alto neighbor tones surround central G by half steps.
m. 44 "Dominant-seventh" chord A- mm. 21-37 Principal melody tone E ( ) surround tonic D by whole steps.
whole mvt. ABA form of entire movement is symmetrical. mm. 5-20, 50-66 Accompaniments of the two phrases of the A section are reversed in restatement of A. II mm. 1, 3 Melodic neighbor tones mm. 4, 8 Melodic neighbor tones B and G surround cadential A by whole steps. whole mvt. Bear Dance melody appears first in soprano, providing fundamental line; then in bass, providing fundamental bass structure. I-II B section of first movement alternates cadences on C major and A minor, with C predominating. Second movement alternates cadences on A minor and C major, with A predominating. I-II Fundamental line A-E of first movement is reversed E-A in second movement. III mm. 4-36 Melody of A section first ascends, then descends D-G tetrachord. mm. 5-12, 13-19 Accompanying tenor line becomes bass line, above and below central D pedal point. mm. 1-36, 80-102 Fundamental line of third movement is ascending octave scale divided into two equal tetrachords D-G, A-D. These comprise first and last sections of three-part (A-B-Coda) movement. mm. 36-81 (36-50, 51-66, 66-81) B section is divided into three parts: outer two provide D trill below melody in key of G; central part provides A trill above same melody in key of D. Focal tones G and A are perfect fourths above and below tonic D. mm. 103-104 "Dominant-seventh" chord A-G- mm. 103-104 Resolving "tonic" chord spelled D-G-A-D is vertical representation of the two horizontal tetrachords of third movement's scalar line. I-III Fundamental line of first movement is descending perfect fourth A-E. It is balanced by third movement coda's ascending perfect fourth A-D. I/II-III Fundamental line of combined first and second movements forms octave scalar descent A-A. It is answered by octave scalar ascent D-D in third movement.
The foregoing Schenkerian, motivic and symmetrical views reveal the Sonatina's clearly diatonic tonal structure. But what of the many chromatic pitches throughout the piece? Might the chromaticism function structurally, perhaps foreshadowing the twelve-tone technique of composition evolving in the early twentieth century? Is there a logic to the chromaticism in the Sonatina? Bartók explains that
our peasant music, naturally, is invariably tonal, if not always in the sense that the inflexible major and minor system is tonal. (An 'atonal' folk music, in my opinion, is unthinkable.) Since depend upon a tonal basis of this kind in [my] creative work, it is quite self-evident that [my] 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.18
In the Sonatina, several sources of chromaticism pertain, none of which is twelve-tone. Some chromatic pitches stem from the modal folk melodies that Bartók quotes. For example, the D scale of the first folk melody in Bagpipers combines Ionian, Lydian and Mixolydian modes (using , , and respectively).19 Within that initial melody, both and 
occur.20 The Dorian mode of Bear Dance pits against the local key signature of no sharps or flats. Many accidentals not directly quoting folk melodies follow classical theoretical tendencies, with raised pitches resolving upward, and lowered pitches resolving downward. For example, in mm. 24-25 of the first movement resolves up to A while resolves down to G, and in mm. 30-31 of the third movement resolves up to D while 
resolves down to A. Often conflicting accidentals are intentionally juxtaposed, as with the and in m. 21 of Bagpipers, enhancing the rustic charm of the Sonatina. The chromaticism that abounds throughout the Sonatina does not govern structure as it would in a twelve-tone piece, but rather, richly colors the diatonic framework.
In conclusion, study of Bartók's Sonatina reveals meticulously detailed organization at many levels. The piece provides a wonderfully accessible window into the mind of one of the twentieth century's greatest musical geniuses. Students may glean insight into Bartók's thinking whether motivated by performance, history, or theory questions. The Sonatina's melodic charm and brevity (four minutes) make it attractive and less daunting for study than Bartók's later and more complex works, yet it foreshadows much of his mature compositional style. At the most accessible level it presents five Rumanian dances grouped together into three movements in easily graspable surface forms. At a deeper level, its design presents a unified diatonic structure beginning and ending on tonic D, with intervening departures to related keys, and returns to tonic prepared by the dominant A. Within this classical framework, motivic unity emerges in the consistent pairing of pitches E-D, whose dissonance and resolution as - define tonic. On a par with the classical design is a symmetrical design stemming from Eastern European folk music. Particularly, the interval of a perfect fourth and its consequent division of the octave into equal halves, and the symmetrical construction of the minor-seventh chord exert strong influence over the Sonatina's tonal structure. Example 4 illustrates the symmetrical interrelationships among the various tonal design features.
Example 4. Symmetries of tonal structure in complete Sonatina.
The piece begins and ends on chordal structures that establish tonic D, dominant A, the fourth, and the D-E pair; the first two movements together outline a descending full octave scale on dominant A, answered by an ascending full octave scale on tonic D in the last movement; the initial pitches of movements II and III reiterate the E-D pair; symmetrical tetrachords A-E in the first movement and A-D in the coda move in opposite directions from the classical pillar, dominant A, reaching the motivic E-D pair at their ends. The many disparate structural elements of the Sonatina are masterfully coordinated. Within the highly organized diatonic framework lies a wealth of chromaticism.
Béla Bartók's Sonatina for piano is a delightful piece, whether approached from the viewpoint of the casual listener, performer, or scholar. Perhaps foremost, it presents an attractive, easily listenable and playable setting of five rollicking, rustic Rumanian peasant dances. At a more intellectual level, it displays a tapestry of intricate design whose diverse threads are woven together into a rich musical fabric. Bartók says:
The Hungarian peasants, as well as the other peasant populations of pre-war Hungary, such as the Slovaks and Rumanians, possess an incredibly large musical treasure in their folk music. . . . It was material which, on the one hand, could turn into short compositions by providing melodies with accompaniments, while on the other hand could draw original inspiration from the same music . . .21
In the Sonatina Bartók does both, by presenting five Rumanian peasant dances with accompaniments, and by pouring them into a mold that is shaped by the original inspiration he draws from folk music as well as by his classical training. His meticulous attention to the myriad interconnected compositional details provides a wonderful playground for those who delight in puzzle-solving, and a model of excellence for aspiring young musicians. Biographer Agatha Fassett quotes Bartók's wife as saying "for him only the entire truth is the real truth, every tiny detail is important to the whole; you see, that is what the truth is made of, in life, and in art too."22
1Barbara English Maris, "Redefining Success: Perspectives on the Education of Performers," College Music Symposium 40 (2000): 16.
2Michael Rogers, "How Much and How Little Has Changed? Evolution in Theory Teaching," College Music Symposium 40 (2000): 114.
3George Houle, "Performance: The Profession and Preparation for It," College Music Symposium 40 (2000): 11.
4Benjamin Suchoff, ed., Béla Bartók Essays (Lincoln: University of Nebraska Press, 1976), 408-410.
5Benjamin Suchoff, ed., Piano Music of Béla Bartók, Series II (New York: Dover Publications, Inc., 1981), xxiv.
6Suchoff, Piano Music, xxiv-xxv.
7Schenkerian analysis normally operates within diatonic scales. Here scale degree , , stems from the modal folk melody being quoted. Further discussion follows later in this paper.
8In Schenkerian terms, a rising fundamental line is problematic. David Neumeyer suggests that a complete rising line ------- does not exist, due to the needlessly long distance traveled to resolve lower scale degrees upward rather than downward to tonic. He offers several examples of convincing --- lines, however, which are similar to the tetrachord segments in Bartók's Sonatina. David Neumeyer, "The Ascending Urlinie," Journal of Music Theory 31 (Fall 1987): 275-303.
9Bartók's transcription of the quoted Rumanian folk melody shows that it ends on scale degree without ever resolving to . (Suchoff, Piano Music, xxv.) János Kárpáti states that "the final notes of [Rumanian melodies] . . . are relatively high and consequently lack a sense of cadence. This explains why Western listeners often find colinde unfinished, as if they had been left open." János Kárpáti, "Piano Works of the War Years," in Malcolm Gillies, ed., The Bartók Companion (Portland, Oregon: Amadeus Press, 1994), 148-149.
10Benjamin Suchoff's edition of the score indicates a double-bar and the word "coda" in parentheses at m. 84. Bartók's manuscript, however, shown in facsimile in the introduction of the Suchoff edition, has neither the double-bar nor the word "coda" and, perhaps significantly, begins a new line of score with the scale beginning on bass A in m. 80, as if to indicate the start of a new section. (Suchoff, Piano Music, Score p. 150 and Introduction.)
11The performer would be well served to examine Bartók's handwritten version of the last six measures, shown in facsimile in the introduction of the Suchoff edition (Piano Music). The manuscript does not indicate the slurs from G to G that appear in the edited version, thus implying more clarity in the G- resolutions; and the bass D on the downbeat of the penultimate measure in the manuscript is restruck rather than tied, thus clarifying the tonic arrival.
12With regard to the key signature, which changes to that of G major in m. 37 and remains there to the end rather than returning to that of tonic D, one may reflect on Bartók's comments in 1945 regarding his 1908 Bagatelles: "The first one bears a key signature of four sharps . . . in the upper staff and of four flats . . . in the lower one. This half-serious, half-jesting procedure was used to demonstrate the absurdity of key signatures in certain kinds of contemporary music. After carrying the key signature principle ad absurdum in the first piece, I dropped its use in all the other Bagatelles and in most of my following works as well." Suchoff, Essays, 432-433.
13Suchoff, Essays, 333-336.
14Elliott Antokoletz, The Music of Béla Bartók: A Study of Tonality and Progression in Twentieth-Century Music (Berkeley: University of California Press, 1984), 51 and 67-69.
15Suchoff, Essays, 334.
16Antokoletz, 29.
17Examination of an earlier sketch of Bagpipers, in facsimile in the Suchoff edition (Piano Music, Introduction), shows the V chord of the half cadence retained as the new I chord in the B section. Bartók has changed his mind in composing the Sonatina and retained scale degree , the head-tone of the new melodic descent, as the common tone linking the two keys, creating instead a new tonic of .
18Suchoff, Essays, 338-339.
19This pitch collection, D-E---A-B--D, or its transposition, appears in many of Bartók's works. It is referred to as a "hybrid-Lydian scale" by Elliott Antokoletz (Antokoletz, 135-137), as an "acoustic" or "Bartókian" scale by János Kárpáti (Gillies, 148-149), and as the "acoustic (overtone) scale" by Ernö Lendvai. Lendvai's discussion claims that the overtone scale is a reordering of the pitches found naturally in the first four octaves of the overtone sequence. Ernö Lendvai, Béla Bartók: An analysis of his music (London: Kahn & Averill, 1971), 67ff.
20Regarding the presence of both and as scale degree , János Kárpáti explains that a "characteristic feature that is easily recognizable is the faltering quality of certain degrees of the scale. Bartók, when analysing Romanian folk music, always pointed out this phenomenon, most probably since he considered it to be an important element of his own compositional technique." Gillies, 149.
21Suchoff, Essays, 331-332.
22Agatha Fassett, Béla Bartók's American Years: The Naked Face of Genius (Cambridge, Massachusetts: The Riverside Press, 1958), 134.