Movement 1: Allegro moderato, G major, 3/4 time, Sonata Form

The overall form of the movement is a very standard sonata form. The opening theme begins with a motive consisting of a quarter note with a trill and a three-note descending figure.

Musical Example 1: Opening Theme

Similar to this opening theme, several main melodies within the movement contain a motive of about one measure, ascending then descending within a narrow range, giving the whole a sense of unity (Musical Example 2: Secondary theme group, measures 72ff.; Musical Example 3: Closing theme, measures 84ff.).

Musical Example 2: Secondary theme group, measures 89-73

Musical Example 3: Secondary theme group, measures 84-88

Exposition

The piano and violin alternately present the thematic melody or melodic motive, treating them in a concertante manner. On the other hand, in the passage beginning at measure 10 (based on the main motive from measure 5), the piano and violin move in unison.

Musical Example 4: Theme group, measures 7-12

Sections where each voice aligns with the same rhythm or motive often coincide with formal junctures (measures 38ff.: both piano voices; measures 55ff.; measure 79: piano and violin). These commonalities, alongside the commonality of melodic motives, contribute to the overall unity of the piece. Furthermore, the point where the relationship between the two instruments, such as melodic voice and accompaniment voice, is dissolved and transformed into a homogeneous texture, not only highlights formal divisions but also suggests a consideration to avoid monotony.

The tonality of the exposition is conventional, with the main theme group in the tonic key of G major and the secondary theme group (measures 40ff., Musical Example 5) in the dominant key of D major. However, Beethoven's ingenuity in tonality can be seen in the secondary theme group, which is not exclusively in D major but modulates to B-flat major (the flat VI key) from a deceptive cadence in D major (measures 61ff.).

Musical Example 5: Beginning of secondary theme group, measures 40-44

Development Section

Using material from the exposition's closing theme, transitional modulations occur from D major, which concludes the exposition, following the descending bass line to F major (measures 98ff.), B-flat major (measures 104ff.), and E major (measures 111ff.), though the major or minor mode remains undefined. E major becomes definitive only when the piano's bass line ceases its descent and the motive changes to one derived from the secondary theme group (measure 116).

Subsequently, modulation continues through the circle of fifths towards the tonic dominant. Harmonically, the recapitulation from measure 142 is prepared by the sustained dominant of G major (measures 131ff.), and motivically, by the trill of the movement's opening theme melody presented by the violin and piano. Furthermore, at the conclusion of the development section (measures 132ff.), both hands of the piano and the violin align with the same rhythm or motive. This commonality of rhythm and motive between the two parts at formal divisions is consistent with the exposition, reinforcing the inference that a unified structure was intended.

Recapitulation

In the opening theme, contrary to the exposition, the piano part initially carries the melodic voice. The modulation to E-flat major (the flat VI key of G major) in the transition section (measures 151ff.) recalls the connection to the modulation in the secondary theme group.

The coda begins at measure 239, based on the main theme with trills. After the theme is briefly presented in C major, the subdominant key of the movement's tonic G major, a G minor diminished seventh chord is strummed, and the trilled motive from the beginning of the theme is exchanged between the violin and piano, accompanied by arpeggios in the piano's right hand. When the tonic key of G major is reintroduced (measures 255ff.), as the motive is further truncated, the entry intervals become more urgent, and the dynamics also intensify. Both parts ascend with increasing momentum in sixteenth notes for the first time in the movement, seemingly entering the conclusion of the movement with florid trills (measure 267). However, the music immediately reverts to its initial tranquil character, concluding quietly with a perfect authentic cadence at measure 171, leading into the coda. In the coda, based on the main theme, the violin and piano ascend rapidly in the final three measures, closing the piece with a forte.

Movement 2: Adagio espressivo, E-flat major, 2/4 time, Lied Form

This is a lyrical movement with a cantabile melody featuring many ornamental passages reminiscent of coloratura in vocal music. The espressivo (expressively) marking, indicating the desired character, is partly conveyed through concrete instructions such as abundant pedal markings and frequently fluctuating dynamics.

An unusual choice for the movement's key is E-flat major (three flats) compared to the work's tonic key of G major (one sharp). Ullrich Scheideler interprets this key choice in relation to C minor, the relative key of the expected subdominant C major, and points out its connection to the modulations to E-flat major in the first movement, the third movement's Trio, and the fourth movement's interlude (measures 164ff.) (1). Furthermore, the arrival at G-sharp major (six flats) in the transition section (measure 26) and the alternation of chords in the coda (discussed later) reveal Beethoven's broad perspective in his skillful handling of tonality and harmonic structure.

Section A (measures 1-20) consists of two parts: a theme played solo by the piano and a section where the violin carries the melodic voice. Measures 9-11 are a remnant of the piano solo theme, but since the three-note descending melody in measure 8 becomes the melodic material for the subsequent violin, this section bridges the first and second halves of Section A in terms of both instrumentation and melody. The latter half modulates to A-flat major.

Simultaneously with the A-flat major cadence, the music enters the transition section. Here, modulations unfold with the piano part's intricate thirty-second note figures and a steady rhythm of eighth notes. The prolongation of the dominant from measure 31, foreshadowing the return to the movement's tonic key while avoiding direct resolution to the tonic, also demonstrates an ingenuity in harmonic color.

In the recapitulation of Section A (measures 38ff.), the part carrying the melodic voice changes from the beginning of the movement. While the accompanimental figuration and the harmonic structure of measures 12-14 are preserved in the latter half of Section A, the melody is altered except for the opening three-note descent. Furthermore, measures 15ff. are omitted, and measures 49-51 are varied and repeated, leading into the coda.

In the coda (measures 54ff.), dissonant chords such as major chords, diminished seventh chords, and augmented sixth chords alternate over a tonic pedal point, and stability is not achieved until near the end of the movement, along with the dynamics. Once the harmonic fluctuation and rhythm settle, the piano's tremolo prevents musical stasis, and the violin's leading tone, C-sharp, prepares the transition to the Scherzo.

Movement 3: Scherzo Allegro, G minor, 3/4 time

Trio E-flat major, 3/4 time

The Scherzo proper consists of two 16-measure sections (8+8). In both, the piano first presents the main voice, and the violin repeats it. The basic rhythmic motive is also the same. During the repetition, the upper voice of the piano part is struck on weak beats, giving more rhythmic drive.

The Trio section is also simple, like the Scherzo proper, and there are many commonalities between them. For example, similar to the Scherzo proper, one part presents the melody, and another part repeats it. The eight-bar melodic structure is also common to the Scherzo. While maintaining these structural commonalities, Beethoven contrasts the Scherzo and Trio in the following ways: for instance, in contrast to the rhythmic Scherzo proper, legato is dominant in the Trio section. Furthermore, the order of parts carrying the main melodic voice is reversed from the Scherzo proper, with the violin part leading in the Trio section. Moreover, the voices do not merely alternate between two parts; from measure 20, imitation occurs in the order of violin, piano upper voice, and piano lower voice. The expansion of the upper register to B-flat in the three-line octave can also be considered a factor in contrasting the Scherzo proper and the Trio.

After the recapitulation of the Scherzo proper, the music modulates to G major in the coda. The Scherzo theme is briefly presented. In the coda, the section corresponding to measures 7-8 of the theme is modified to resemble measures 23-24, which is likely a change to achieve a perfect authentic cadence on the tonic.

Movement 4: Poco Allegretto, G major, 2/4 time, Variation Form

This movement consists of a theme, eight variations, and a coda. In the first and second halves of the 32-measure (16+16) theme, the piano part carries the main melody solo for the first eight measures, after which the melody is repeated an octave higher, accompanied by parallel octaves in the violin part. The latter half of the theme modulates to B major, a third relationship to the tonic key of G major.

The skeletal notes of the theme melody are preserved in each variation. Variations 1-3 (measures 33-112) are, as is common in variation forms, progressively subdivide the basic note values into shorter durations.

Variation 4 (measures 113-144) marks a sudden shift from the texture of Variations 1-3, which clearly separated melodic and accompanimental voices. It is constructed from the alternation of two contrasting measures: rhythmic chords and descending scales.

Variation 5 (measures 145ff.) changes to Adagio and 6/8 time, with virtuosic and ornamental passages woven primarily by the piano. The part carrying the main voice changes every half-phrase, and there is no repetition of the theme's eight-measure phrases. The end of Variation 5, instead of cadencing on the G major tonic chord, prolongs the dominant (measures 160ff.), transitioning into an interlude that leads to Variation 6. The modulation to E-flat major in the interlude (measures 164ff.), based on the original form of the theme melody, and its connection to other movements, is also noted by Scheideler, as mentioned earlier.

Returning to G major, Variation 6 (measures 174-206) accelerates to Allegro, and with sf (sforzando) on the beat and staccato accompaniment, the music progresses with great vitality, in stark contrast to Variation 5. While some interpretations consider measures 206-217 as part of Variation 6, it would be more appropriate to consider this section as a transition, as it cadences on the tonic chord at measure 206 as per the theme's original form, and subsequently, both the motive and harmonic progression change abruptly.

In the subsequent seventh variation in G minor, although the opening part of the theme melody is indeed

“varied,” and imitated from the lower voice to the upper voice, there is no melodic variation in the latter half of the theme, and the tonality also changes fluidly from measure 234 to C minor, E-flat major, D major, and G major, giving it a strong transitional character rather than a classical, complete variation.

In the final variation from measure 246, with a more propulsive arpeggio accompaniment than the theme's piano part, the theme melody is played in its original form, and immediately upon the theme's conclusion, a powerful unison passage signals the beginning of the coda. Both parts then successively ascend to the highest d4 in the movement, like a concerto solo part, forming a climax. The structure where the tempo slows down at the end of the movement, a part of the theme melody appears, the motive gradually shortens and fragments, becoming more urgent, and then the movement concludes again at a rapid tempo, is common in final movements of multi-movement works, as seen in, for example, String Quartet Op. 18 No. 2. Furthermore, the point where each part alternately carries the ascending passage in the coda and the ascent to g3 on the piano's octave arpeggio at the end of the movement are common with the first movement, but it is more appropriate to consider this as one of the common techniques for movement endings rather than an intentional inter-movement connection.

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1

Ullrich Scheideler, “Sonaten für Violine und Klavier,” in Beethovens Kammermusik, ed. by Friedrich Geiger and Martina Sichardt, Beethoven-Handbuch, vol. 3, Laaber: Laaber-Verlag, 2014, p. 50.