BEETHOVEN's “KREUTZER” SONATA an ANALYSIS a Thesis

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BEETHOVEN’S “KREUTZER” SONATA

AN ANALYSIS

A Thesis

Presented to

The Graduate Faculty of The University of Akron

In Partial Fulfillment

of the Requirements for the Degree

Master of Music – Theory

Eya Setsu

May, 2021

BEETHOVEN’S “KREUTZER” SONATA

AN ANALYSIS

Eya Setsu

Thesis

Approved: Accepted:

______Advisor Department Chair Dr. James Wilding Dr. Marc Reed

______Committee Member Dean of the College Dr. Robert Brownlow Dr. Joe Urgo

______Committee Member Dean of the Graduate School (name) Dr. Chand Midha

______Committee Member Date (name)

______Committee Member (name)

ABSTRACT

This thesis takes an in-depth theoretical look at all three movements of

Beethoven’s Violin Sonata No. 9, Op. 47. Every movement was analyzed using three different lenses: formal, harmonic, and motivic. The first and third movements are in sonata-allegro form. As a result, the formal analysis was most important here in order to understand how Beethoven used the form and any moments where he deviated from it. The second movement is in the form of a theme and variations, resulting in a comparative motivic analysis to understand how exactly Beethoven molded each variation. As the variations progressed, the theme became more difficult to discern.

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DEDICATION

To J.C.C., for being on the phone with me for much of the time that I was completing this thesis. Your love, patience, and endless wit has brought such humorous light to my life throughout this tumultuous year.

To A.M.S., for giving me every reality check I have ever needed to choose to continue this career path. You fought for me when I did not want to, and I could not be more grateful for your tough love.

To my parents, for giving me the support and the space to make my own decisions, which ultimately led to the publication of this thesis, and the chance to grab new opportunities I never saw coming.

ACKNOWLEDGEMENTS

First, I would like to thank my advisor, Dr. James Wilding, for his patience, reassurance, and understanding as I worked on my thesis. His guidance and continued support have given me “food for thought” as I honed my analysis skills through this research.

Second, I would like to thank my graduate advisor, Dr. Guy Bordo, for sharing the opportunity to complete a second master’s degree at the University of Akron and making it possible for me to continue my studies with assistantship.

Third, I would like to thank Dr. Robert Brownlow for agreeing to be on my committee and for taking the time to read through my thesis.

TABLE OF CONTENTS

Page

LIST OF FIGURES ...... viii

LIST OF TABLES ...... x

CHAPTER

I. OVERALL STRUCTURE ...... 1

II. TONAL ANALYSIS OF I. ADAGIO SOSTENUTO – PRESTO ...... 2

Exposition ...... 2

Development ...... 8

Recapitulation ...... 12

Coda ...... 15

III. TONAL ANALYSIS OF II. ANDANTE CON VARIAZIONI ...... 18

Theme ...... 18

Variation I—Rhythmic Variation in the Piano ...... 20

Variation II—Rhythmic Variation in the Violin ...... 26

Variation III—F minor ...... 30

Variation IV—F Major ...... 36

IV. TONAL ANALYSIS OF III. FINALE – PRESTO...... 43

Exposition ...... 43

Development ...... 48

Recapitulation ...... 49

Coda ...... 50

BIBLIOGRAPHY ...... 51

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LIST OF FIGURES

Figure Page

2.1 Semitone motivic cell ...... 3

2.2 Expansion of the semitone cell in D minor ...... 4

2.3 The secondary theme and its expansion ...... 6

2.4 Original eighth note figure at m. 118 and its following transposition ...... 7

2.5 Beginning of the development ...... 8

2.6 Measure 234-236 ...... 9

2.7 Newly added third descent in the violin ...... 10

2.8 Extension of the closing theme in the violin part ...... 10

2.9 Inverted motive in the piano ...... 11

2.10 Climax of the development section ...... 12

2.11 Piano takes the primary theme first in the recap ...... 13

2.12 Building the expectation of A minor and subverting it ...... 14

2.13 Chromatic sequencing of material into Coda ...... 15

2.14 New melodic fragment that is being traded off ...... 16

2.15 New melodic fragment outlining A minor triad ...... 17

3.1 Comparison between the A theme (measure 1 vs. measure 28) ...... 19

3.2 Shared thematic material (mm. 109-111) ...... 30

3.3 Measure 117 outlines material from measure 36 ...... 31

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3.4 Piano condenses the rhythm in measure 119 ...... 32

3.5 Comparison of the A section ending in Variation IV ...... 37-38

4.1 Start of the primary theme (m. 1) ...... 45

4.2 Secondary Theme (m. 62) ...... 46

4.3 Tertiary theme (m. 100) ...... 47

LIST OF TABLES

Table Page

2.1 General sonata form diagram of the first movement ...... 2

3.1 Form layout of the second movement ...... 18

3.2 Side-by-side comparison (A Section vs. Variation I) ...... 22

3.3 Side-by-side comparison (B Section vs. Variation I) ...... 25

3.4 Side-by-side comparison (Theme vs. Variation II) ...... 29

3.5 Side-by-side comparison (Theme vs. Variation III) ...... 34-35

3.6 Side-by-side comparison (Theme vs. Variation IV) ...... 41-42

4.1 Form layout of the third movement ...... 43

4.2 Form layout of the exposition...... 44

4.3 Form layout of the recapitulation ...... 49

CHAPTER I

OVERALL STRUCTURE

Beethoven’s Sonata for Violin and Piano No. 9, Op. 47 consists of three movements. The first movement, Adagio sostenuto – Presto, is in sonata-allegro form with an overall tonality of A minor. However, it frequently uses mode mixture, so A major is also heavily present throughout this movement. The second movement, Andante con variazioni, is set up in a theme and variations form in F major with the exception of one variation in F minor. The final movement, Presto, is back in sonata-allegro form, but in joyous A major. Overall, Beethoven maintains the usual structure of a three-movement sonata, while drastically expanding the sections within each movement.

CHAPTER II

TONAL ANALYSIS OF I. ADAGIO SOSTENUTO – PRESTO

Exposition

Beethoven writes his first movement to be in complete sonata-allegro form.

Not only does it have an exposition, development, and recapitulation in standard sonata-allegro form, but also an introduction and a coda laid out in the following format:

Introduction Exposition Development Recapitulation Coda

mm. mm. mm. mm. mm.

1-18 19-193 194-313 314-517 518-599

Table 2.1 General sonata form diagram of the first movement.

Although the introduction is short relative to the other sections, it is crucial in that it highlights the two foundational techniques of this movement: modal mixture and the half step motivic cell. The violin begins in A major and is quickly rejected by the piano entrance at measure 5. The pianist initially begins with an A major chord, but follows that with a iv chord. This rejection is the first instance of modal mixture and destabilizes A major immediately. Starting in measure 7, a series of tonicizations further destabilize the key.

While the piano part presents the first instance of modal mixture, both parts present the first instance of the semitone motivic cell at measure 13. The violin ascends from a C-sharp to a D and then descends from a C-natural to a B. The right

Figure 2.1. Semitone motivic cell. hand of the piano follows this contour while the left hand has an inverted contour.

It descends by a semitone before ascending a whole tone. Therefore, it does not quite line up with what the violin and the right hand are intending to do. Instead of placing these two pairs of notes on downbeats, Beethoven puts them off the beat to continue the destabilization that was started by the modal mixture earlier. The sense of unease has not gone away, but is now added to with the persistence of the semitone. In measure 16, both parts repeat the semitone one additional time as if to emphasize the importance of this cell before Beethoven begins to work with it. It could be considered the first time that the cell has been expanded. Harmonically,

Beethoven is playing around with D minor, especially in the piano part. This diverts

3 the attention away from A minor without completely establishing a new key, letting the unease continue.

Figure 2.2. Expansion of the semitone cell in D minor.

The exposition and the first theme begin at the Presto in the pickup to measure 19 with two pairs of semitones spaced further apart. The violin moves from an E to an F-natural before leaping down to an A and a G-sharp. The contour is exactly the same as the original semitone cell, but spacing the pairs a minor 6th instead of a minor 2nd makes it more subtle to the listener. As a result, the start of the primary theme is based on the semitone cell.

The key signature now indicates a more prominent shift to A minor, but

Beethoven subverts the expectation of the tonic by continuing with D minor that was left unresolved at the end of the introduction. He follows it with a V chord before landing on i to affirm A minor. Despite moving from the dominant to the tonic, it does not feel like a cadence. The violin part is not finished with the primary theme when this harmonic motion occurs. Instead, it carries on its momentum to the actual first cadence of the exposition. Beethoven subverts expectations once more by placing an authentic cadence confirming C major. The cadence doesn’t feel

4 too out of place because of its relation as the relative major of A minor. Starting in the pickup to measure 28, the piano now takes the primary theme before the violin joins in the latter half. The harmonic motion is the same as before except that the piano confirms C major with a sweeping arpeggiation gesture.

In measure 37, Beethoven takes the first part of the primary theme (E to F- natural) and sequences it by continuing to ascend by semitones until reaching the first truly convincing cadence in A minor at measure 45. From there, he writes a series of bariolages in the violin part. The piano then picks up these ideas as both instruments attempt to outdo each other. A minor is well established during this section because the bariolages alternate between the tonic and dominant. The interjections between both parts as well as the constant alternating prevent this section from creating further cadences.

Starting in measure 61, he uses chromatic sequencing to move the section forward towards E minor, which is established in measure 69. Again, Beethoven uses the semitone relationship between the D-sharp and E to build an abrupt, new melodic idea. This further emphasizes E minor due to the constant presence of the leading tone being resolved on top of the arpeggiating nature of the piano in B major, the dominant. As the section progresses, the B major arpeggios become the most important harmonic function to lead into the secondary theme, which begins in measure 91.

The secondary theme is more chorale-like in nature compared to the declamatory primary theme. The agitative nature of the preceding eighth note runs is suddenly silenced by the dolce, whole-note melody. E major is established in the

5 piano, while the violin uses the semitone of G-sharp and A to build a new 4-bar idea.

The first iteration of this idea moves from G-sharp to A, back to G-sharp, and down to F-sharp. The immediate response to this iteration is to expand the first semitone

Figure 2.3. The secondary theme and its expansion. to a minor third. As a result, the first G-sharp now leaps to a B before descending to the A. When the piano takes over the melody, it does so in E minor (G to A to G to F- sharp) before ending the section on a D dominant 7th chord held by a fermata. In this particular instance, Beethoven does not seem to care for a proper cadence, but uses the pause in momentum with the fermata to question the tonality of this section.

The dominant 7th resolves to G, and the music moves sequentially back to E minor. The violin continues using the semitone to help develop shorter musical ideas, while reflecting the changing harmony. This is especially obvious with the eighth note gesture from measure 118 to 120. The eighth note gesture gets transposed as the music returns to E minor.

Figure 2.4. Original eighth note figure at m. 118 and its following transposition.

In addition, the violin continues interjecting by holding its high E’s unlike before where they were octave E quarter notes. These interjections help to tonicize

A minor for a few measures before cadencing at measure 144.

The closing zone in E minor begins in measure 144 with a theme based on the half-step motive in the piano. The motive was originally presented as a pair of sixteenth notes in the exposition, but has now been transformed into an eighth tied to a half note and dotted quarter note. The violin takes the theme over in measure

156 and elongates the cadence. At measure 176, the material from measure 117 returns to provide cadential material in E minor. At the close of the exposition,

Beethoven moves to A minor—the same key, which was subtly established at the

Presto—to retransition back to the opening.

Development

The development begins with the closing theme in F major starting in the pickup to measure 194 in the piano. The violin picks up this theme in G minor in

Figure 2.5. Beginning of the development. measure 202. The function of modulation is rather balanced between both parts.

When the violin enters in measure 202, the piano is harmonically using the B-flat from F major as a common tone to move to G minor and then on to E-flat major. The violin helps the modulation by focusing on the half-step relationship whereas the piano uses an eighth note arpeggio figure to modulate. Both parts then trade off these two motives with each other to help cloak the modulations. For example, the violin now takes over the eighth note arpeggio figure in measure 210 while the piano switches to the augmented half-step motive.

The development is also very technical for the violin part so audiences are more likely to focus on that without realizing Beethoven is bringing them to a new key area every few bars. In measure 226, the piano takes over with the running eighth notes in the key area of F minor before breaking it down and holding on to B-

8 flat in measure 234 via octave jumps. The violin begins a broken third run in the same measure. This particular run is very awkward in the left hand of the violin because it is difficult to articulate the notes clearly with the proper intonation. As a result, the listener will automatically find comfort in the B-flat that the piano is pausing on.

Figure 2.6. Measure 234-236.

In measure 237, the piano resumes the arpeggio eighth notes and seems to dwell in A-flat minor before moving back to F minor in measure 246. The right hand of the piano helps to reaffirm this new tonal center by including F-naturals which are displaced by an octave. The development moves through A-flat major in measure 250 while further distorting the half-step motive in the violin part. Not only is it rhythmically augmented, but a third descent is added at the end of the motive to increase the tension.

Figure 2.7. Newly added third descent in the violin.

In measure 258, Beethoven states the closing theme in D-flat major and extends the end for several measures. He eventually cadences in F minor in measure 270. This extension is followed by tonic-dominant alternations (measure

270 to 273). The left hand of the piano ate measure 270 takes the extension and

Figure 2.8. Extension of the closing theme in the violin part. inverts it. Instead of two descending seconds, this motive ascends by the same intervals. It then falls to the first note of the pattern, which can be a descent of a major third or minor third depending on the note. Beethoven then uses this pattern sequentially. He repeats this process in C minor from measure 278 to 281. These techniques are used once more in G minor in measure 286.

Figure 2.9. Inverted motive in the piano.

Between measure 294 to 299, the piano plays eighth note octaves to help modulate back to A minor. The intensity of the section is mirrored by the violin part, which has also begun to use eighth notes to build momentum. One could argue that measure 297 is the most important climax of the development. Looking at the intervallic structure of the eighth note run, it becomes clear that this is based on the inverted motive. Measure 295 begins with the two ascents of a major second followed by a return to the open E. Measure 296 begins with an ascent of a major second followed by a minor second and a descent back to the A. The three measures afterwards diverge from this pattern to emphasize the change from ascending melodic minor to descending melodic minor. In measure 300, the dominant pedal point is established, which is prolonged until the end of the development.

Figure 2.10. Climax of the development section.

Recapitulation

The start of the recapitulation picks up the harmonic motion from the very end of the development. The key of A major is immediately established in measure

314 with the arpeggios in the violin part. This arpeggio figure was already present in the piano part at the very end of the development, but has now become highlighted in the foreground. The piano part begins with the half-step motive again to emphasize A major while the violin uses chromaticism until the half cadence at measure 323. Measures 324 to 326 dwell on the half-step motive once more over a

G minor triad, functioning as the subdominant. The piano takes the lead and moves onwards to the primary theme, which is then picked up by the violin. In the exposition (measures 19 to 36), the primary theme was originally introduced by the

12 violin and then picked up by the piano. In the recapitulation, the roles are reversed—the piano reintroduces the primary theme then the violin takes it from there. Harmonically, this leads to end an authentic cadence on F major as opposed to C major in measure 335.

Figure 2.11. Piano takes the primary theme first in the recap.

Following the primary theme is a transition built on the half-step motive.

This transition also begins with the piano this time instead of the violin like in the exposition. The beginning of this idea (pickup to measure 337) is harmonically based on G minor. It could be understood that this transition connects to the previous G minor triad (measure 324-326). Unlike the exposition which has two clear iterations of the primary theme in succession, the recapitulation breaks them up with a nine-measure transition. It ends by establishing A minor and bringing back the primary theme for the second time in measure 345. The second cadence occurs in measure 353, which is also an authentic cadence on C major, much like the exposition. The difference is that the piano does not have a sweeping C major arpeggio gesture this time around. Instead, a short transition occurs leads to a

13 cadence in A minor in measure 366, which corresponds to measure 45. Once again,

Beethoven employs the use of a bariolage in the violin part that gets picked up by the piano. Starting in measure 366, Beethoven is harmonically flipping from tonic to dominant to maintain A minor.

In measure 382, a transition begins corresponding to measure 61 in the exposition. The music goes differently in measure 389 in order to remain in A minor rather than modulate to E minor. The secondary theme returns in A major at measure 412. Starting in measure 428, the switches back to the parallel minor.

However, Beethoven subverts the expectation of the audience by ending the section on a G-dominant 7th chord at measure 437, just as he had done at measure 116.

Figure 2.12. Building the expectation of A minor and subverting it.

This lays the groundwork for bringing back the closing material in A minor as opposed to E minor in the exposition. The music quickly moves from C major and towards A minor briefly before spiraling away harmonically as before.

The closing theme returns in measure 465 and corresponds to the exposition until measure 510. At the end of the exposition, this material was used to lead into the repeat back to the start of the exposition as well as into the development. In the

14 case of the recapitulation, Beethoven chose to chromatically sequence this material, resulting in a harmonic motion into B-flat major through an authentic cadence at measure 517.

Figure 2.13. Chromatic sequencing of material into Coda

Coda

After establishing B-flat major, Beethoven has the piano take on the eight note runs from the violin in this new tonal center in measure 518. This effectively starts the coda of the first movement. Beethoven treats this section much like other transitional sections. He chromatically sequences the eighth note runs again in the piano to arrive on the dominant of A minor in measure 529. The violin is holding out a B-flat and D, assuming the role of a pedal point for the piano to move against.

Measure 533 is a rather important moment in the piece because it is the first time that a tutti section occurs. All three voices are playing the primary theme an octave apart, insisting on its importance to the listener. The chromatic sequence that follows starting on measure 537 is also done in the same manner. This moment in the piece is one of the most intense because the audience has no choice, but to be hit over the head with the strongest iteration of the primary theme and affirmation of A

15 minor at measure 547. The violin and piano begin to diverge at this point and trade off a new melodic fragment. After this intense moment of unity, both parts return to a texture that is more “at-home” for the listener. The piano has the melodic fragment measures 547 to 548 before the violin takes over an octave higher.

Overall, this moment is harmonically in A minor.

Figure 2.14. New melodic fragment that is being traded off.

One of the more interesting parts about the coda is how quickly it seems to wind down. A clear example of this is measure 559 in the violin part. Previously, eighth note runs were done with separate bows with an occasional slur here and there, suggesting very crisp bow articulation. This helps the notes speak individually and provides the clarity that is necessary for a musician’s intended phrasing. In measure 559, the eighth note run is now slurred one bar at a time.

Combined with the lower register of the G string, the timbre is now significantly more muddled than before. This allows another melodic fragment to shine through in the piano part, starting in measure 559. The melodic fragment is comprised of C-

E-C-A and is bounced around from the right hand to the left until measure 572. This motive outlines an A minor triad to solidify the tonality once again. The violin picks

16 up on the motive, but in a diminutive form—the half notes are now shortened to quarter notes—in measure 571.

Figure 2.15. New melodic fragment outlining A minor triad.

Beethoven signals the beginning of the end of the coda with two cadences.

The first one occurs in measure 577 and is an authentic cadence settling on B-flat major. This is immediately followed by a cadence moving from a D minor triad to an

A minor triad. Between the two cadences, the first feels more final while the second feels more uneasy. After this, the violin has a fiery eighth note run that repeats three times and confirms A minor. The piano counters with its own eighth note run with its contrasting contour. In measure 593, the violin finally lets the run unravel all the way down to the low A as the piano continues its own unravelling, which is followed by an authentic cadence.

CHAPTER III

TONAL ANALYSIS OF II. ANDANTE CON VARIAZIONI

The second movement of Beethoven’s Kreutzer Sonata is in the form of a theme and variations based in F major. There are four variations, each with their own unique characteristic. The first variation focuses on rhythmic variation in the piano with the use of triplets. The second employs rhythmic variation in the violin part, using 32nd groupings. The most unique feature of the third variation is that it is the only variation in F minor, the parallel minor of the overall key of the movement.

The fourth and final variation plays with the musical texture with its frequent use of embellishments, such as trills and various rhythmic groupings. It is also the longest variation of the movement.

Theme Variation I Variation II Variation III Variation IV

mm. 1-54 mm. 55-81 mm. 82-108 mm. 109-135 mm. 136-235

Table 3.1. Form layout of the second movement.

Theme

The theme is in rounded binary form (A-B-A). The A section consists of a phrase that is presented in the piano, followed by the violin repeating it. This is considered a written-out repeat with each iteration of the theme being eight

18 measures long with the total section being 16 measures long. Beethoven gives a small nod to the half-step motive from the first measure. Instead of having the motive ascend from E to F, he has it descend before quickly moving on to new material. Because the theme begins and ends on F major, this section is tonally closed.

The B section attempts to gain a foothold in measure 17 and establish a new idea for 11 measures. Based on the number of measures within each section, it appears that Beethoven has created a theme that is asymmetrical in nature. The B theme begins in the piano, much like its A counterpart, as it modulates from F major to C major. Therefore, the B theme is tonally open.

C major is important because it seamlessly brings back the A section in the home key in measure 28. The melody is also brought back in the violin part, joining

Figure 3.1. Comparison between the A theme (measure 1 vs. measure 28). the piano an octave above. The A section is stated once (measure 28 to 35), followed by a written out repeat of B-A in measure 36 to 46 and 47 to 54.

Variation I—Rhythmic Variation in the Piano

Variation I is entirely focused on rhythmic variation in the piano. The violin part is minimal at best and acts as the accompaniment. The only rhythms it uses are sixteenth note triplets and eighth notes as it lightly outlines the harmony above the piano. By having such a sparse texture in this variation, Beethoven focuses the audience on the piano’s rhythmic variation.

In terms of the rhythmic range, the piano also uses sixteenth note triplets and eighth notes as well as quarter notes, dotted sixteenths, and thirty-second notes. The rhythmic variety provides better contrast against the violin by allowing the piano part to seem like it is pausing on a note while the violin continues the rhythmic motion. Since the violin is high in register, it makes it difficult for it not to stand out against the piano. The violin part is marked as sempre piano with rhythmic simplicity due to its accompaniment function. The piano is the main feature, and this is attributed to its greater in dynamics and rhythm as well as being the only part to work with the theme.

The beginning of the variation quotes the first two measures of the A section note-for-note to reinforce the connection to the previous musical material. While this occurs, the left hand in the piano is establishing the new rhythmic motive

(sixteenth triplets) as well as F major by using the tonic and dominant chords. This is exactly the same way that the A section began harmonically. At measure 57,

Beethoven re-works the rest of the A section using triplet sixteenth notes. Each note from the original A section in measure 10 is now expanded as sixteenth note triplets with octave jumps. On the first half of the second beat, a C is added beneath the

20 highest E to help fill the root of the harmony, which is a dominant 7th chord. That C is kept there in the second half of beat two as well. Since each sixteenth note triplet covers the duration of one eighth note, the variation neither augmented nor diminished the harmonic rhythm.

In measure 58, Beethoven chose to shorten the F-sharp and augment the G that follows it. The original rhythm (measure 11) has the F-sharp at a quarter note and the following G as an eighth note. Instead, the duration of the F-sharp was shortened to one eighth note and the G was expanded to a quarter note. This effectively changed the rhythm to match that of the first two measures of the theme

(eighth-quarter-eighth). With each measure, Beethoven gets more and more bold in varying the theme. Measure 59 not only expands the original rhythm of the dotted- quarter note A (measure 12), but also shortens the F to a third of its original value.

This allows him to fill the distance between the A, F, and D (the start of the next measure) with passing tones to distort the original idea. The passing tone of E is continued on the downbeat of measure 60 before moving to D and B-flat like in the original A section. Here the D and B-flat is shortened to allow for continued descent from the A all the way down to the F.

Measure 61 is the most distorted alteration of a measure from the A section.

The descent from the F to the E followed by the ascent to the high C is condensed into the duration of one eighth note. F and E are repeated at the beginning of each sixteenth note triplet in this measure while the following note is chromatically altered. This bypasses the G that was originally found in measure 16 before ending the phrase on the F right above middle C (F4). It is important to note that

Beethoven used a repeat after this eight-bar phrase because there is no need for this melody to be passed on to the violin. This repeat also allows the A section of

Variation I to be the same length as that in the Theme. Though the rhythms are vastly more complex this time around, the form has not changed.

Original A Section Variation I

m. 11 m. 57

m. 12 m. 58

m. 13 m. 59

m. 14 m. 60

m. 15 m. 61

m. 16 m. 62

Table 3.2. Side-by-side comparison (A Section vs. Variation I).

The B section begins in the pickup to measure 63. The piano uses the exact notes from the original B section as the first note in every triplet grouping for most of this section. Because of this, the contour of the melody is kept the same. The rhythmic variation makes the melody slightly more ambiguous to the audience’s ears because each melodic note is disrupted with sixteenth notes in between. It is important to note that the fourth beat of measure 65 is the first instance where the melodic note is not on the downbeat, but rather in the middle of the triplet. This slight deviation from the established variation hints that there is more to come. In measure 68 and 69, Beethoven decides to use the original rhythmic value of eighth notes from the B theme. The difference is that all the notes are doubled in octaves with the exception of the first C-natural, which is supported by an E below (minor

6th relation). In addition, Beethoven deviates the contour compared to measure 41.

Instead of descending to the G a perfect fourth below, the C ascends a perfect 5th and continues its ascent to the rest of the notes. It is only the contour between the first two notes of the measure that are inverted, resulting in a linear ascent to the high F.

After having a brief moment for the audience to breathe and reconnect with the melody, Beethoven returns to triplet sixteenth notes in measure 70 to 73. The melodic notes remain on the downbeat, but now the triplets consist of octave displacements. This continues to distort the contour of the melody, so it becomes muddled to the audience again. Because the notes are still kept the same to the original melody, there is a sense of something being vaguely familiar. In measure

73, Beethoven displaces the notes of the melody from the downbeat to the middle of the triplet grouping. On the first beat, he holds the D over from the previous

23 measure before moving to the C on the next sixteenth note. The rest of the measure uses a sixteenth note rest on the downbeat to create a syncopated feel. Texturally, the right begins to be more chordal in nature before the reprise of the A section.

The reprise of the A section only has one slight difference in the right hand.

The triplet sixteenth note octaves are now double-stop octaves with a C. For example, individual E’s are now replaced by a double stop of E and C. This is most apparent in the first two beats of measure 76. The first A section within this variation strictly has octaves without double-stops. Other than that, the rhythmic variation and the ornamental trills are the same as the first A section.

Original B Section Variation I

m. 36 m. 63

m. 37 m. 64

mm. 38-39 mm. 65-66

mm. 40-41 mm. 67-68

m. 42 m. 69

mm. 43-44 mm. 70-71

mm. 45-46 mm. 72-73

Table 3.3. Side-by-side comparison (B Section vs. Variation I).

Variation II—Rhythmic Variation in the Violin

While the violin had a very minimal role in the Variation I, it now takes on the primary role in Variation II. Beethoven heightens the rhythmic variation further by using four 32nd notes for every eighth note beat. With the exception of the final note in both A sections, thirty-second notes are being played constantly by the violin while the piano outlines the harmony in sixteenth notes. In terms of articulation, the melody is much more staccato in nature, which changes the overall feel of the variation compared to the smooth original theme. The formal structure of A-B-A still remains. The A section remains tonally closed, like in the Theme and Variation

I, on the tonic (F Major).

Unlike Variation I which stays close to the original theme, Variation II immediately begins with rhythmic variation from the very first pickup beat. For the most part, the rhythmic duration of the notes reflects that of the original rhythm in the theme. The difference is that Beethoven offsets the note from the theme by one

32nd note. In the instance of the pickup to measure 82, the original note of the melody (F) is preceded by a perfect fourth jump from a C. The F remains for the duration of four 32nd notes, which is equivalent to the eighth note in the original.

Choosing to have it be offset by one 32nd note creates a distorted, syncopated melody. At the start of measure 82, the F drops down by a half-step to the E for the last three 32nd notes, which reflects the original half-step descent from the F to the E as an eighth note. The E remains for the next two groupings of 32nd notes, but they are broken up by a D-sharp on the first note of every 32nd grouping. In the moment,

26 the D-sharp acts as a leading tone to the E and emphasizing it further. The following

D is preceded by a descent of a minor third from an F.

At measure 88, Beethoven changes it up a little bit by using F-E-C, which is reminiscent of the original theme at measure 15. Instead of staying true to the original rhythmic value of two sixteenth notes and an eighth, the rhythm changes to two thirty-second notes for the F and E followed by a scale up to the C for the last two thirty-second notes of the measure. The scale link replaces the duration of the

Es originally seen in measure 15. The sixteenth note E and the quarter G found after the high C in measure 15 are omitted in Variation II. The melody sits on the high C as it is played for one full beat before descending a perfect 5th to the F at the end of the A theme.

The B section begins using the same rhythmic variation with the displacement of the chromatic leading tone into the melodic note. Variation II has the melody up an octave compared to measure 36 to 38. The rhythmic duration is still roughly the same with the exception of the G in measure 92, which is the focus for one and a half beats. In the original theme, the G lasts for one full beat. At measure 93, Beethoven finally puts the notes of the melody on the downbeat and replaces the chromatic leading tones with an octave displacement right after the first 32nd note. This is another moment for the audience to recognize a familiar melody without it being too obvious. In measure 94, some of it gets distorted. In measure 40, the F to D is done with a rhythm of a dotted eighth-sixteenth. Variation

II does not adhere to the original rhythmic duration for either note. The F is the focus for the third grouping in the measure, but the final grouping (or final eighth

27 note beat) alternates between F and D. There does not seem to be a clear landing point for the D to be emphasized within that last eighth note beat. This could resemble the fact that the D in the original melody only lasts for one 16th note, so

Beethoven did not need to bring attention to it. After that, the variation returns to offsetting the melodic notes with a chromatic leading tone up until measure 97.

Original Variation II

mm. 9-10

mm. 82-83

mm. 84-86 mm. 11-13

Mm. 15-16

Mm. 87-89

mm. 90-92

Mm. 36-38

mm. 39-40 mm. 93-94

Table 3.4. Side-by-side comparison (Theme vs. Variation II).

Variation III—F minor

Of all the variations in this movement, this is the only one that is uniquely in the parallel minor. The previous two variations had very clear roles for each instrument, but now they are working together in a manner similar to their roles in the Theme. For instance, the piano begins the section with a variation of the F to E descent from the Theme. Instead of it seamlessly moving into the rest of the thematic material. Beethoven lets it derail chromatically for the duration of an eighth note while the violin picks up the thematic material based on the D to C descent in the pickup to measure 110. At this point, both the violin and piano are playing a variation of measures 10 and 11 of the original theme, just spaced out an octave apart.

Figure 3.2. Shared thematic material (mm. 109-111).

Measure 112 marks another point of departure from the Theme. Originally, the melodic material consisted of an F-sharp, G, and G-sharp. In the minor variation, this material is transposed up a minor third. The resulting notes became A, B-flat, and B to maintain the same intervallic structure. Harmonically, the variation begins on a dominant pedal, which is the same as the theme.

In measure 115 to 116, the melodic material is loosely based on the material in measure 7 to 8 and15 to 16. The key indicators of this are the tied over E in measure 115, and the G to the F descent in measure 116. The G to F descent helps close the A section with a perfect authentic cadence in F minor. Therefore, the section is tonally closed, reflecting the same harmonic motion in the A section of the

Theme.

The B section begins in F minor with the piano filling in the main line chromatically. The notes that highlight this are A-flat, G, C, A-flat, and F. While these notes are originally eighth notes, they are now sixteenth notes that do not

Figure 3.3. Measure 117 outlines material from measure 36. necessarily fall on an eighth note beat. Changing the rhythm allows for Beethoven to fill the beat with chromatic passing tones to obscure the harmony and destabilize the F minor feel. This is especially obvious on the second beat of measure 117 with an F major triad due to the raised third scale degree (Picardy third). The A-natural could be considered a passing tone to the A-flat that follows it. However, the placement of the A-natural on the downbeat suggests that it could be a slight hint at modal mixture, which was reminiscent of the first movement.

The violin uses the pickup to measure 118 to reference the A to G descent, but does not continue to strongly reference any material from the Theme. Instead, it seems to merely help the piano outline specific notes while using chromatic lines in between each note. The A to G was especially important to the beginning of the B section, so it would make sense that the violin reiterated this. It could also be considered that the G in the violin is refers to the downbeat of measure 17 and 37.

The C, A-flat, and F are in the piano part in the form of sixteenth notes with chromatic filler. The melodic material has now been split between the two parts unevenly. The piano takes the material from measure 18 and 38 and condenses the rhythm to consist of a sixteenth note, three syncopated eighth notes, and one

Figure 3.4. Piano condenses the rhythm in measure 119. final sixteenth note. This is compared to the original rhythm of an eighth note, syncopated quarter note, and eighth note. While the piano uses the B-natural and G in its original order, the violin chromatically dances around B-natural. It starts with an octave drop while chromatically moving away from it and returning to B-natural.

In measure 120, the piano continues using passing tones to circle around E,

D, C, and D from the Theme. Measure 21 uses D as a neighbor tone between the Es on the first and second beats before continuing to the F to D descent. Originally, the rhythm is a dotted eighth note with a sixteenth, but it has been condensed into a

32 dotted sixteenth and a thirty second note. The C in the right hand that ends the phrase is used to lead into the violin part, which takes up the G, A, and B-natural from measure 41. In the Theme, each instrument had the A or B section for its entire duration (usually 8 bars) before being repeated by the other instrument. In

Variation III, the instruments are essentially cutting each other off and taking snippets of the larger theme. The violin only takes a snippet of the B section for one and a half measures before the piano takes it up again in the second half of measure

123.

The piano continues the B section by filling it in with chromatic neighbor tones. The violin joins the piano in measure 126 and is written an octave above before leading into the final A section at measure 189.

Original Theme Variation III

m. 31

m. 112

mm. 15-16 m. 114-116

m. 36

m. 117

m. 37

m. 118

m. 38

m. 119

mm. 39-40

mm. 120-121

m. 122 m. 41

m. 42 m. 123

Table 3.5. Side-by-side comparison (Theme vs. Variation III).

Variation IV—F Major

The fourth and final variation returns to F major to round out the movement harmonically. It is also the longest of the variations. The best way to characterize

Variation IV is that it is entirely based on creating an ornamental texture using the notes from the theme as the melodic outline. The melodic outline is filled in by trills or what can be considered “written out” trills, such as thirty-second note passages.

Because of this, the themes are the most obscure compared to the previous variations.

Like Variation III, Variation IV begins with a perfect fourth ascent from C to F.

After the F is established, the ornamented A theme begins in the right hand of the piano from measure 136 to 143. In measure 136 to 138, Beethoven maintains the original rhythm of the theme by highlighting the notes and filling the rhythm with ornaments and eventually a sextuplet grouping built on thirty-second notes. In measure 139, the rhythmic integrity from the theme becomes offset slightly. The F- sharp originally lasted for a full quarter note followed by two eighth notes (G and G- sharp). However, the F-sharp lasts for the duration of one eighth note filled in by a sextuplet group while the following G a quarter note embellished with a trill. This measure is usually followed by a measure with an A that descends a minor third to an F-natural. Instead, Beethoven changes both the rhythmic duration from the theme as well as the contour. The A now ascends a minor sixth to an F-natural that alternates with an E in a sixty-fourth note passage. The ornamentation completely takes over the A section from measure 141 to 143. The only note that is clear from the original theme is the high D in measure 141. Afterwards, a chromatic sextuplet

36 line takes over before ascending to the F, marking the end of the piano’s turn with this ornamented A section.

Similar to how the melodic themes were presented in the theme, the violin takes Variation IV’s A theme in a written-out repeat. At measure 148, it diverges from the piano’s iteration by having the A ascend to a C before chromatically descending to a D. Instead of copying the same chromatic line as the piano, the violin ascends to a B-flat before ending its version of the A theme with the E-G-F ending. This suggests that perhaps both parts have complimentary versions of the ornamented A section. The ending of the violin’s iteration suggests that perhaps it is the one to mark the end of the A section and the start of the B section.

(Piano, mm. 140-143)

(Violin, mm. 148-150)

Figure 3.5. Comparison of the A section ending in Variation IV.

Harmonically, the A section largely relies on alternating between the tonic and dominant as well as an ascending broken octave line to help move the piece forward. The broken octaves are found in the pizzicato of the violin at measure 140 to 141 and later in the left hand of the piano from measure 147 to 150. The cadence in measure 150 ends on a perfect authentic cadence in F major, rendering the A section as tonally closed, just like the theme.

The B section begins in the pickup to measure 152 with the piano using a chromatic neighbor tone ornamentation of the A to G descent, which was originally found in measure 36. Instead of having one singular instrument establish the ornamented B section, Beethoven has the violin and the piano split the melody. The best way I can describe this is that it is similar to the use of hocket in medieval music. After the piano gets the A to G descent, the violin takes the C to A descent.

The piano barely hints at the F before pairing it with the adjacent G in measure 153.

This interplay between instruments is very brief because Beethoven decides to give the notes in measure 38 to the piano in measure 154 while the violin moves towards a pizzicato line in measure 156. The use of three sixteenth note Cs in this measure seems to hint at a reference to the first variation, in which the violin part was primarily focused on triplet Cs. Instead of trading off the ornamented melody every

38 other beat, it is elongated into measures. The piano ornaments the original B melody from measure 155 to 156, but the violin pizzicato takes over for the next five measures. The piano takes over again to lead variation back to another A section.

The B section is similar to the A section in that alternating between the tonic and the dominant is still important. There are some uses of secondary dominants as well, such as in measure 154. The piano uses a dominant pedal point as part of the chromatic lines in the left hand. The reason this is such an effective pedal point is due to the fact that C is always occurring on the downbeat starting in measure 157 all the way to measure 161. This gives the sense of a pedal point while also immediately juxtaposing it with a heavily chromatic line that is best perceived as an ornament to the C. This pedal point leads to a first inversion F major chord. The chromatic line makes the movement from V to I not as obvious for an authentic cadence. The B and A sections repeat with variants at measure 171 and 182.

The section from measure 190 to 196 is functioning as a transitional section prior to the coda. The texture is suddenly very sparse with the violin entering towards the latter half and very minimal melodic material. Harmonically,

Beethoven is modulating from F major to G minor. This is most evident in the authentic cadence found between measure 192 to 193, which moves from a D dominant 7th chord to G minor. The fermata that immediately follows is a G dominant 7th chord.

After listening to it repeatedly, there seem to be two impressions of this particular moment. The first is that it can be understood as an homage to the previous minor variation because of the insistence of G minor. The second is that

39 the juxtaposition of G minor followed by G major hints to the use of mode mixture.

This could be a very brief homage to the frequent use of mode mixture in the first movement of the sonata. Regardless of which impression appeals to the listener,

Beethoven specifically chose G major for its secondary dominant function. As a result, a C major chord is set up as the dominant of F for the start of the coda.

The coda section is best described as an expanded cadence in F major, which explains why the section begins on the dominant and winds its way to the tonic at the end of piece. It also hints at previous variations throughout the section. For example, the start of the coda uses the sixteenth note triplet motive, which was the most prominent feature of Variation I. In measure 218, the ornamental rhythms

(64th notes) and the trills return, referencing the beginning of Variation IV. The material starting in measure 226 is a reference to the B material of the original theme and lasts briefly before continuing on to a perfect authentic cadence reaffirming F major.

Theme Variation IV

mm. 9-11

mm. 136-138

mm. 12-13

mm. 139-140

m. 36 m. 152

m. 37

m. 153

m. 38

m. 154

mm. 39-40

mm. 155-156

Table 3.6. Side-by-side comparison (Theme vs. Variation IV).

CHAPTER IV

TONAL ANALYSIS OF III. FINALE – PRESTO

The third and final movement of Beethoven’s Kreutzer Sonata is in sonata- allegro form. Both the exposition and the recapitulation contain two larger sections

(A and B). The A sections contains the primary and secondary themes with the transition in between. The B section contains the closing zone as well as some A section material to act as a retransition back to the repeat or development. As per usual, the development plays around with the thematic material that was presented in the exposition before moving to the recapitulation followed by the coda. As a result, the overall chart is as follows:

Exposition Development Recapitulation Coda

mm. 1-177 mm. 178-290 mm. 291-454 mm. 455-539

Table 4.1. Form layout of the third movement.

Exposition

The previous movement established F major as the home key, which is why the A major chord at the beginning of the third final movement is so jarring. It is especially disruptive because it is a fortissimo chord that interrupts the previous pianissimo mood. In terms of harmonic relation, A major is the major III chord of F

43 minor. The chord in conjunction with significant dynamic contrast is highly effective at establishing the start of something new.

A B

mm. 1-126 mm. 127-176

Primary Transition Secondary Tertiary Closing Retransition

Theme mm. 28-61 Theme Theme Zone mm. 152-176

mm. 1-27 mm. 62-99 mm. 100- mm. 127-

126 151

Table 4.2. Form layout of the exposition.

As outlined in the chart above, the A section contains three distinct areas.

The primary theme lasts from measure 1 to 61, which begins in A major and ends on the dominant (E major). However, there are some brief moments of modulation.

For example, there are hints of G minor in measures 18 to 25. There are also hints of F-sharp major in measure 50 to 60 are especially prominent due to the left hand of the piano alternating between B and A-sharp, which is used as the dominant of the dominant in E major.

Figure 4.1. Start of the primary theme (m. 1).

The violin has the primary theme for eight bars, which is accompanied by the piano until it gets its own iteration a fourth up on F-sharp. The roles reverse between the two instruments at this point before unraveling in an eighth note run.

The imitative nature of the eighth note run between parts lends itself to modulations and tonicizations very well. Starting in measure 57, both the violin and the piano have the same part octaves apart to insist on the B to A-sharp relation before diverging at measure 62. This can be understood as the end of the transition towards the secondary theme.

The secondary theme is based off the rhythmic motive from the primary theme (quarter note followed by an eighth note), but adds a dotted half note to end the motive. Instead of hinting at modulations, the secondary theme remains steadfast in E major. When the piano takes the melody, the melodic and

45 accompaniment roles reverse again. Rhythmically, both parts come together again briefly before transitioning to the tertiary/third theme.

Figure 4.2. Secondary Theme (m. 62).

The tertiary theme continues the key of E major that was established earlier.

It is best characterized as the most lyrical of the three themes due to the heavy use of slurs in both the piano and violin parts. The frequent use of D-sharps also hints at its function as prolonging the dominant. Between the two parts, the piano is the most active because it uses the D-sharp to set up a deceptive cadence of V7 to vi in E major that leads into the B section. The dominant 7th chord on B is the final measure of the tertiary theme. While the audience may expect the dominant 7th chord to resolve to the tonic, Beethoven substitutes it with a vi chord on C-sharp to signal the beginning of the closing zone (B section).

Figure 4.3. Tertiary theme (m. 100).

Compared to the A section, the B section is shorter and categorized by changes in the time signature. The switch to 2/4 maintained the overall feel of two large pulses per measure while also creating the illusion that the piece is slowing down. The rhythm went from constant eighth notes to half notes and quarter notes followed by an interjecting 6/8 measure. The tempo itself does not change until the ritardando in measure 142. The B section is still overall in E major and sets up a B major dominant chord from measure 148 to 151. Beethoven realizes expectations by resolving it to an E major chord in measure 152.

Measure 152 is the start of the retransition section. The rhythmic motive from the primary and secondary themes returns, which is helpful in hinting at the repeat of the exposition. The retransition also functions as dominant prolongation that resolves to A major in the first ending, finally returning to the home key the audience yearned for.

Development

The development section begins in the second ending with an A minor chord due to the immediate presence of C-naturals in both the piano and violin. This is an example of mode mixture, an homage to the first movement. It also immediately begins referencing the three themes from the A section. In measure 177 to 185, the primary theme makes an appearance after being transposed to A minor in the violin.

The secondary theme homage begins in measure 186 and starts out in the relative major (C major). However, it quickly modulates through the circle of fifths until it reaches an F-sharp dominant 7th chord in 206. The motive is then used freely as the music continues the modulation through the circle of fifths until it reaches F major at measure 214.

In measure 230, the texture becomes more imitative in nature as the piano and violin interject each other with the main rhythmic motive (quarter note followed by an eighth). They converge onto the same rhythm at measure 246 to arrive on a dominant pedal with a half-step alteration of E to F. This pedal is interrupted by a lyrical section starting at measure 255 that becomes more imitative in nature again. In measure 287, Beethoven uses a C-sharp pedal in the violin while having the piano reiterate the other members of a C-sharp dominant 7th chord, meaning that Beethoven wants to use this chord to move to another key area.

Recapitulation

A B

mm. 291-403 mm. 404-488

Primary Transition Secondary Tertiary Closing Retransition

Theme mm. 313- Theme Theme Zone mm. 429-488

mm. 291- 338 mm. 339- mm. 378- mm. 404-

312 376 403 428

Table 4.3. Form layout of the recapitulation.

Like the name of the section suggests, the recapitulation is structured very similarly to the exposition with the three smaller themes of the A section. However, it starts in the wrong key of F-sharp minor. Originally, the exposition started in A major, but the recapitulation is now in the key that has a submediant relation (vi).

The submediant has essentially replaced the tonic. Then, the primary theme moves through B minor and makes its way towards A major by measure 313. The transition beginning in measure 313 alters its course in measure 323 to remain in the tonic. In the case of the recapitulation, the material is being used to reaffirm the tonic (A major) when the secondary theme arrives instead of affirming the dominant (E major). The tertiary theme continues the key of its preceding theme just like in the exposition. The difference is that it continues to assert the tonic instead of the dominant. This section leads into the B section with the exact same harmonic motion from V7 to vi.

The B section is still in A major overall. It also uses the same changes in time signatures as before as well as the dominant prolongation. The retransition reprises its role of modulating up a perfect 4th, this time to D minor for the start of the coda at measure 455.

Coda

Beethoven ends the piece with a short coda that includes fragments of the primary, secondary, and tertiary themes. The fragments of the primary and tertiary themes build to a deceptive cadence in measure 489 and the Adagio statement of the motive. Once the coda reaches the final Tempo I marking in measure 501, the harmony is decorated with chromatic passing tones until it begins prolonging the tonic in measure 517. A tonic prolongation is exactly what is expected at this point of the coda, and Beethoven uses the secondary theme fragment from measure 525 to conclude the piece.

BIBLIOGRAPHY

1. Beethoven, Ludwig van. Sonaten für Klavier und Violine: Bande II. München, Germany: G. Henle Verlag, 1978.

2. Hepokoski, James A. and Warren Darcy. Elements of Sonata Theory: Norms, Types, and Deformations In the Late-Eighteenth-Century Sonata. New York, NY: Oxford University Press, 2006. https://hdl-handle- net.ezproxy.uakron.edu:2443/2027/heb.06334. EPUB.

3. Rosen, Charles. Sonata Forms. New York, NY: W.W. Norton and Company, 1988.