051218-ZY075-肖箐-英普-Frontiers in Art Research.docx American Journal of Art and Communication Vol.7,Issue 6;November-December-2022; 1252 Columbia Rd NW, Washington DC, United States https://topjournals.org/index.php/AJAC; mail: topacademicjournals@gmail.com 1 | American Journal of Art and Communication | https://topjournals.org/index.php/AJAC UNDERSTANDING THE COMPLEXITY OF BEETHOVEN'S PIANO SONATA NO.15 THROUGH SCHENKERIAN ANALYSIS Jane Elizabeth Doe and Maria Sofia Garcia University of Miami, Miami, Florida, 33124, United States Abstract: This paper uses Schenkerian analysis to explore the Beethoven Piano Sonata No.15 in D Major, Opus 28, focusing on the exposition sections of the first movement. Schenkerian theory is an analytical method developed by Austrian composer and theorist Heinrich Schenker. This theory can provide a deeper understanding of a piece's musical content by revealing its underlying structure. The relationship between theory and performance will be discussed to provide a more comprehensive analysis. This paper also demonstrates how Schenkerian analysis can illuminate the characteristics of Beethoven's music and influence how we hear his music. Through this analysis, we can better understand this work and appreciate its complexity. Keywords: Schenkerian analysis, Beethoven Piano Sonata No.15, Exposition, D Major, Opus 28 1. Introduction Analyzing a musical composition provides profound insight into its structure and other components. This paper will use Schenkerian analysis to explore the Beethoven Piano Sonata No.15 in D Major, Opus 28, concentrating on the exposition sections of the first movement. Schenkerian theory [1] is an analytical method developed by Austrian composer and theorist Heinrich Schenker. This theory can provide a deeper understanding of a piece’s musical content. The relationship between theory and performance will be discussed to provide a more comprehensive analysis. Also, this paper demonstrates how this analytical method can illuminate the characteristics of Beethoven’s music and influence how we hear his music. Through this analysis, we can better understand this work and appreciate its complexity. Ludwig van Beethoven was a German composer and pianist born in 1770 and died in 1827. He is widely considered one of the most influential composers of all time, with his works usually regarded as spanning the Classical and Romantic eras. During his lifetime, Beethoven composed thirty-two piano sonatas, of which this is the fifteenth. Beethoven’s composition time is separated into three periods; this work, created in 1802, is known as the “Pastoral” and belongs to his last piano sonata from the early period. Researchers have been fascinated by applying Schenkerian theory[2] to Beethoven’s piano sonata for many years. They used various methodologies to investigate the problem, the most prominent of which was a mix of music theory and analysis centered on harmony, progression, prolongation, and structure. 2. Thematic Development and Harmonic Progression Firstly, the form of the first movement in this piece is a sonata form, which includes three parts: exposition, development, and recapitulation. Here is the chart demonstrating the structure of the exposition part in the first movement.Here is the chart demonstrating the structure of the exposition part in the first movement in Table 1. The exposition is the opening portion of the sonata form and is regarded as one of the most essential components of the structure. The exposition section includes two themes: primary and secondary theme. The primary theme is in the key of D major, and creates a lyrical and flowing melody, while the secondary theme is mailto:topacademicjournals@gmail.com American Journal of Art and Communication Vol.7,Issue 6;November-December-2022; 1252 Columbia Rd NW, Washington DC, United States https://topjournals.org/index.php/AJAC; mail: topacademicjournals@gmail.com 2 | American Journal of Art and Communication | https://topjournals.org/index.php/AJAC modulation to A major; the secondary theme is the contrasting part, using different materials from the primary theme; the second theme is more forceful. As the exposition progresses, Beethoven introduces several transitional passages that help to modulate the key from D major to A major. The connecting episode uses different textures, changing the harmony and using different melodic materials. They help to create a sense of tension and anticipation leading up to the arrival of the second theme in A major. The initial theme includes two sections; each section has two phrases, each ending in a cadence. The second theme is developed in the exposition, with melody variations and accompaniment changes. Beethoven introduces a closing theme, which ends the exposition. Overall, the exhibition of Beethoven’s piano sonata Op.28 is an expert display of thematic development and harmonic progression. Beethoven used various gestures and textures to create a sense of unity and coherence throughout the section while introducing contrasting material to keep the listener engaged. The first and second themes connect the episode and coda to create a colorful and complex musical tapestry. As a Schenkerian music theory analysis researcher, it is fascinating to delve deeper into the inner progression of this section and uncover the intricate relationships between the various musical elements. Table 1:Music Form Exposition Measure Structure Tonality Primary Theme 1-39 Binary Form (Section A+ Section B) D Major Connecting Episode 40-90 Part I (40-62), Part II (6376), Part III (77-90) A Major, E Major, F-Sharp Minor, A Major, E Major, F-Sharp Minor, A Major, F-Sharp minor, A Major. Secondary Theme 90-135 A Major Coda 135-159 A Major Passage 159-163 A Major The exposition section of the first movement is characterized by a clear tonal structure[3] that is established with critical relationships. The primary key of the movement is D major, which is introduced in the opening measures and uses the tonic note of the pedal point to emphasize the tonic function. However, Beethoven also incorporates several secondary keys, which create tension and contrast within the tonal structure of the movement. One of the most significant things of connecting episode, this part changes the tonality frequently, using the F sharp minor, A major, and E major, using these relative and close keys to emphasize the function and transition naturally to the second theme. Beethoven also uses the key of D major in the exposition's closing theme, which serves as a transitional key between the second key of the upcoming development section. The interaction between various keys is another critical feature of tonality in Beethoven’s piano sonata opening movement. Throughout the exposition section, Beethoven employs key relationships to create tension and release. The link between F sharp minor and A major is a critical relationship in the connecting episode part, taking the bridge function. As mentioned above in the transition portion, the modulation establishes this link. Harmonic progression is a fundamental aspect of music theory, and it plays a crucial role in sonata form analysis. In Beethoven’ s piano sonata Op.28, the first movement’s exposition section is an excellent example of harmonic progression, particularly the tonic-dominant relationship. The tonic-dominant-tonic progression is one of the essential harmonic relationships in tonal music, and it is used extensively in the sonata form. In the first movement’s exposition section, the dominant-tonic progression creates tension and release, a hallmark of the sonata form. He mailto:topacademicjournals@gmail.com American Journal of Art and Communication Vol.7,Issue 6;November-December-2022; 1252 Columbia Rd NW, Washington DC, United States https://topjournals.org/index.php/AJAC; mail: topacademicjournals@gmail.com 3 | American Journal of Art and Communication | https://topjournals.org/index.php/AJAC uses this progression to build anticipation and create a sense of resolution, an essential aspect of the sonata form. In this part, Beethoven used the secondary chord, making tension in the progression of music; on the other hand, he used the sequence to create music and used the tonic pedal point and repeat note and motive split all techniques to create. The harmonic and melodic variations found in this piece of the first movement in the exposition refine the structural elements of the piece. Using Schenkerian analysis, it is possible to identify the specific harmonic and melodic variations used to develop and refine the musical ideas presented in the piece. These abundant music textures include modulations, non-diatonic chords, secondary chords, and chromatic passing tones, embellishment notes. All these techniques serve to develop further the musical ideas presented in the exposition part. The colorful harmonica found in this piece is primarily used to create a sense of tension and movement. The most common gestures of harmonic variation used in this piece are modulations. Through modulations, Beethoven can change the tonal center of the music and create a sense of tension and movement. These harmonic variations help to refine the structural elements of the piece. Harmonic progression in music relies heavily on chordal motion. The chordal motion is essential in the first movement exposition and contributes to the piece’s overall structure. A sequence, a recurring musical pattern at a new pitch level, is one of the most prevalent types of chordal motion. The composer borrowed sequences from the exposition in this passage. From measure forty to measure fifty-five, he used the fifth degree of sequence to create different tonality; the connecting episode used the new materials and combined them with the harmonic sequence to the composer, making the music full of tension. The employment of the pedal point is another crucial aspect of chordal motion. A pedal point is a note maintained as the other voices move around it. Throughout the exposition, Beethoven uses pedal points in various ways to create tension and release into harmony. 3. Exploring Tonal Hierarchy and Linear Progressions Schenkerian[4] music theory involves the concept of tonal hierarchy. Schenkerian analysis tries to identify a composition’s “Ustaz” (fundamental structure) or underlying structure. The underlying structure of the music is the tonal hierarchy, which is established by the composer’s usage of various musical components. The Ustaz in Beethoven’s Piano Sonata No.15 in D Major, Opus 28, is set by the piece’s opening tonic. This tonic is bolstered and sustained by harmonic progressions, melodic motives, and other tonal organizing aspects. The tonic sounds increasingly solid and secure throughout the piece using these devices. In the sonata’s first movement, for example, the Ustaz is established by using a tonic pedal in the left hand, which provides a strong foundation for the rest of the music. Additionally, the first movement’s cadences are built upon this tonic pedal, further reinforcing its importance. When analyzing Beethoven’s Piano Sonata’s exposition section, it is critical to consider the piece’s form and periodic structure. The exposition is structured like a sonata, with an initial theme, a transition, a second subject, and a conclusion. This structure is distinguished by periodic phrases, which create a sense of symmetry and balance within the music in section A in the primary theme, and the second phrase in section A is a non-symmetry phrase. Cadential phrases are also used extensively in the sonata’s exposition part. These sentences bring each component of the form to a close and resolution. A half cadence, for example, is employed in the opening theme to provide a sense of pause before the transition part. The second theme then ends with a beautiful realistic cadence, ending the passage. These cadences are a vital feature of the sonata form, contributing to the piece’s overall structure and cohesion. Voice leading[5] is an essential aspect of Schenkerian analysis, as it helps to understand the relationship between the individual voice within a musical composition. In the exposition section of Beethoven’s Piano Sonata’s first movement, the voice leading plays a crucial role in the piece’s motivic development and linear mailto:topacademicjournals@gmail.com American Journal of Art and Communication Vol.7,Issue 6;November-December-2022; 1252 Columbia Rd NW, Washington DC, United States https://topjournals.org/index.php/AJAC; mail: topacademicjournals@gmail.com 4 | American Journal of Art and Communication | https://topjournals.org/index.php/AJAC progression. Using Schenkeian analysis, we can identify the underlying harmonic structure and how the melodic and contrapuntal lines of the composition shape it. One of the most prominent features of the voice leading in the exposition section is the use of motivic development. The dissonant suspensions play a vital role in the music's progression, such as from 4-3; but Beethoven used the parallel of the sixth interval frequently. This technique involves taking a short melodic or rhythmic motif and transforming it throughout the composition. In Beethoven’s Piano Sonata’s first movement, the opening motive is repeated and develops throughout the exposition section, creating a sense of unity and coherence in the piece. Additionally, the voice leading helps to emphasize the harmonic progression, highlighting the tonal relations between the different chords and creating a sense of tension and resolution. In Schenkerian music theory, intervallic relationships play a crucial role in analyzing the structure and organization of a musical composition. The intervals of thirds, fourths, fifths, and sixths are significant, as they are often used to create harmonic and melodic connections between different parts of a piece. At the beginning of this piece, the composer uses parallel sixth continuously, making progression smooth and convenient. By examining these intervallic relationships in this piece's middle ground and foreground, we can gain insight into the composer's use of harmony and melody in seminal work. The primary theme of this piece in the opening phrase used a cluster of motives and gestures based on a descending D major scale. These motives and gestures are then developed and expanded into longer phrases characterized by a rising and falling melodic contour. The terms are structured in a way that creates tension and release, leading to the pivotal moment of the theme. The flowing shape of the composition is simple yet effective, conveying a sense of stability and resolution that is characteristic of Beethoven's music. In the primary theme of the sonata, the descending scale motive is used as the basis for the music, while the rising and falling gestures create a sense of motion and development. The use of motives and gestures, combined with the melodic contour, creates a cohesive and unified structure characteristic of Beethoven's music. In addition to the melodic contour, the use of motives and gestures is another vital aspect of the melodic structure in Beethoven's music. Motives are short musical ideas repeated throughout a piece, while gestures are more significant musical ideas developed and expanded over time. In the primary theme of the sonata, the descending scale motive is used as the basis for the theme, while the rising and falling gestures create a sense of motion and development. The use of motives and gestures, combined with the melodic contour, creates a cohesive and unified structure that is characteristic of s music; Beethoven used the motive split to create music, the same melody in the different registers to development and use the same materials to repeat again and again, letting music full of tension. Linear progression [6] is an essential element of Schenkerian music theory, which focuses on the voice leading between two or more voices. It is a way of understanding how music progresses through time and relates to a piece’s tonality. In this piece, the linear progression of the first movement’s exposition is crucial to understanding its structure. The exposition starts with a presentation of the secondary chord to the dominant harmonies after the single tonic note, followed by the subdominant to go to the dominant and tonic. The prominent structure of the primary theme progresses in the vital function, emphasizing the tonality of D major, just using different chords, and changing the register, making the colorful melody layers. Melodic contour refers to the shape of a melody represented graphically. It is an essential aspect of music analysis because it provides insights into a piece’s structure and emotional content. In this piece’s first movement, the exposition part’s melodic contour is created by a falling and rising pattern. The use of stepwise motion and sequential repetition of harmonic and melodic patterns characterize the secondary theme's linear progressions. The initial phase of the secondary theme begins with a descending stepwise motion in the melody, accompanied by a harmonic progression that moves from the dominant to the tonic. This mailto:topacademicjournals@gmail.com American Journal of Art and Communication Vol.7,Issue 6;November-December-2022; 1252 Columbia Rd NW, Washington DC, United States https://topjournals.org/index.php/AJAC; mail: topacademicjournals@gmail.com 5 | American Journal of Art and Communication | https://topjournals.org/index.php/AJAC harmonic progression is repeated sequentially, with the melody moving up and down stepwise, creating a sense of continuity and coherence in the musical structure. Using linear progressions in the secondary theme also highlights the significance of harmonic repetition and variation in Schenkerian analysis. The repetition of the dominant-to-tonic harmonic progression in the secondary theme provides a framework for the development and variation of the harmonic and melodic material in the subsequent sections of the composition. The linear progressions, therefore, serve as a foundation for the overall harmonic and structural organization of the Beethoven piano sonata no.15 in D major, emphasizing the composer's proficiency in form and structure in his music. Heinrich Schenker emphasizes the idea of fundamental structure in his theory. This theory believes that all structures of tonal music around a fundamental tone are the tonic note of a particular key. This graph simplifies the music into essential elements, highlighting the underlying harmonic and melodic structures. The fundamental structure is a hierarchy of musical events, with the most important events occurring at the top of the graph and the less critical events occurring further down. A piece of music's fundamental structure is used as a blueprint overview for the entire work. It provides a framework for understanding the relationships between different music sections and how they fit together to create a coherent whole. In the context of the Beethoven piano sonata no.15 in D major, the structure of the first part of connecting episode is fundamental in the connecting episode of the exposition section. This episode serves as a bridge between the primary and secondary themes, and its function is to modulate the key to the secondary theme. The fundamental structure of this episode reveals the underlying harmonic and melodic structures that allow this modulation to occur. The fundamental structure of the first part in the connecting episode in this piece, emphasis from tonic to the dominant and tonic, through the use of modulation in the different keys, such as A and E major, figure that begins on the dominant to solve to the tonic, though by looking the graphic about this passages, the majority of the fundamental structure is from tonic to dominant and solve to the tonic or the movement from dominant to the tonic. Interestingly, the same materials repeat again and again but are written in different registers; the last time, changing some notes and then letting the music listened to is close to the tonic in E Major, and this figure is repeated several times; This creates a sense of tension and release. 4. Schenkerian Graphical Analysis In addition, this graph demonstrates that the Schenkerian analysis uses Beethoven's piano sonata No. 15 in D major's exposition part of the primary theme in Figure 1 and 2. The middle ground and foreground of this piece are essential elements of the piece. The middle ground refers to the intermediate level of harmonic organization between the structural bass and the melody. It includes the contrapuntal lines not as prominent as the melody but still contribute to the music's overall texture. The foreground, on the other hand, is the superior level of harmonic organization. It is where this graphic presents the melody and other essential musical elements to explain. In the exposition part of this piece's primary theme, the characteristics of the middle ground are used with counterpoint. The contrapuntal lines create a sense of tension and release that supports the melody. The middle ground also includes the harmonic progressions that connect the different phrases of the melody. In this section, Beethoven uses a mixture of simple and complex harmonies to create a sense of forward momentum. mailto:topacademicjournals@gmail.com American Journal of Art and Communication Vol.7,Issue 6;November-December-2022; 1252 Columbia Rd NW, Washington DC, United States https://topjournals.org/index.php/AJAC; mail: topacademicjournals@gmail.com 6 | American Journal of Art and Communication | https://topjournals.org/index.php/AJAC Figure 1: Schenkerian Analysis Graphic Part I Figure 2: Schenkerian Analysis Graphic Part II 5. Exploring the Middle Ground and Foreground: Rhythmic and Melodic Elements The foreground of the exposition is part of the primary theme of Beethoven's piano sonata no.15 in D major's characteristics by the unique and charming melody. The melody is presented in the right hand and by the left- hand accompaniment. When playing this part, you should focus on the balance between the different parts, letting mailto:topacademicjournals@gmail.com American Journal of Art and Communication Vol.7,Issue 6;November-December-2022; 1252 Columbia Rd NW, Washington DC, United States https://topjournals.org/index.php/AJAC; mail: topacademicjournals@gmail.com 7 | American Journal of Art and Communication | https://topjournals.org/index.php/AJAC the listener understand the line and layers and the basic progression of this piece. The melody is simple yet elegant, characterized by repetition and variation. The repetition of the melody creates a sense of familiarity, while the variation adds interest and complexity to the music. The rhythm plays a vital role in the Schenkerian music analysis. In the exposition section of Beethoven's Piano Sonata No. 15 in D major, the main theme displays various rhythmic characteristics, including syncopation and hemiola. Syncopation refers to the displacement of accents from the expected strong beats of the meter to weaker beats or off-beats. In this sonata, Beethoven employs syncopation in the primary theme to create a sense of tension and instability. By shifting the emphasis away from the expected strong beats, Beethoven creates a sense of rhythmic unpredictability that adds to the overall drama of the piece. In addition to syncopation, Beethoven uses hemiola as the exposition's main theme. Hemiola is a rhythmic device that juxtaposes two different rhythmic groupings. In this sonata, Beethoven uses hemiola to create a sense of rhythmic tension and contrast. Specifically, he alternates between groupings of three and two beats, creating a sense of rhythmic instability and asymmetry. This rhythmic contrast helps to emphasize the melodic and harmonic aspects of the theme, highlighting the tension between stability and instability that characterizes the piece. 6. Conclusion In conclusion, Schenkerian analysis provides a valuable tool for understanding the intricate workings of Beethoven's Piano Sonata No.15 in D major. Closely examining the piece's exposition section has identified critical structural elements such as the primary and secondary themes and their associated harmonies and voice leading. Furthermore, Schenkerian analysis has allowed us to delve deeper into the piece's underlying tonal structure, revealing the intricate interplay between different levels of harmonic organization. By examining the relationships between individual pitches and their function within larger harmonic structures, we have gained a more nuanced understanding of Beethoven's compositional technique and the expressive qualities of the music. Ultimately, applying Schenkerian analysis to Beethoven's Piano Sonata No.15 has shed new light on the piece and the broader field of music theory and analysis. As we explore the intricacies of tonal organization and the insights gained through this analysis will prove invaluable for future generations of scholars and performers. References Beach, David. “Schenkerian Theory”, Music Theory Spectrum Vol. 11 no. 1 (1989):3-14. https:// www.jstor.org/stable/745943. Brown, Matthew. Explaining Tonality: Schenkerian Theory and Beyond. Rochester, Ny, University of Rochester Press, 2006. Forte, Allean and Gilbert, Steven. Introduction to Schenkerian Analysis. New York: Norton, 1982. [4] Pankhurst, Tom. Schenker Guide: A Brief Handbook and Website for Schenkerian Analysis. New York and London: Routledge, 2008. Schenker, Heinrich, et al. The Masterwork in Music: Volume I, 1925. New York: Dover Publications, INC, 2014. mailto:topacademicjournals@gmail.com https://www.jstor.org/stable/745943 https://www.jstor.org/stable/745943 https://www.jstor.org/stable/745943