Describe the relationship between melody and harmony in a given piece of classical music, and demonstrate how the melody is either supported or challenged by the underlying harmonic structure.

The relationship between melody and harmony in classical music is a dynamic interplay where one either supports or challenges the other, creating a cohesive and expressive musical experience. Melody, a succession of musical tones perceived as a single line, and harmony, the combination of simultaneously sounding musical tones, are interdependent forces in shaping the overall character and emotional content of a piece. The way a composer manipulates this relationship is essential in determining the musical narrative.

When harmony supports a melody, the chord progression underlying the melody provides a sense of stability and reinforcement. The harmonic structure follows the melody closely, usually aligning with the contour and rhythmic phrasing of the melody. This can enhance its lyrical quality, giving the listener a sense of fulfillment and resolution. Typically, this occurs when the melody notes are part of the underlying chord, creating consonance and a natural flow. When the melody moves to a note that is not part of the underlying chord, it will resolve to a consonance on the next chord change. In a diatonic progression, the harmonic support comes from chords based on the main scale of the melody. When a melody is accompanied by very stable and consonant harmonies, the melody is supported in the most direct way.

On the other hand, when harmony challenges a melody, the underlying chords might introduce dissonance, unexpected modulations, or a sense of instability. This tension can create a sense of unease, anticipation, or dramatic contrast. The melody might contain non-chord tones or may move in ways that create harmonic conflict, and then the harmony may not resolve in a way that one would expect, leaving the listener in a state of tension. This approach of challenging the melody is an effective tool for creating dramatic shifts in character.

Here are some specific examples demonstrating these relationships:

1. Supporting Harmony: A classic example of supporting harmony is the opening of Mozart's "Eine kleine Nachtmusik." The main melody is very clear and diatonic and it is accompanied by simple and functional harmonies. The harmony and the melody share a key, and the chords that support it are consonant and are closely aligned with its contour. The harmonic progression moves smoothly and predictably, reinforcing the melody's lyrical and joyful character. The harmony does not challenge the melody in any way, and therefore is supportive in nature. The harmonic rhythm is relatively slow, with changes occurring at a regular pace that aligns with the phrasing of the melody, which makes it seem very stable and provides a very pleasant feeling to the listener.

2. Challenging Harmony: An example of a more challenging relationship can be found in the development section of a Beethoven sonata. Let's take the first movement of Beethoven's Piano Sonata No. 14 "Moonlight Sonata," where the main melody in the exposition is quite consonant, but in the development section, the same melody is used but in more unstable harmonic contexts. The melody itself remains relatively unchanged, but the harmony underlying it becomes more dissonant and unpredictable, with frequent modulations to distant keys. This harmonic instability creates a sense of unease and intensifies the feeling of conflict that is being expressed in the development. The use of dissonant chords makes the melody stand out in a way that is quite different from the exposition. This challenging of the melody creates a sense of dramatic tension. The tension is eventually resolved in the recapitulation, where the melody is presented again with a stable and consonant harmonic backing.

3. Melody as a Harmonic Challenge: In some cases, the melody itself might introduce dissonance that the harmony then must react to. In a passage from Wagner’s opera “Tristan und Isolde,” the melody often presents itself with chromatic notes that are outside of the prevailing harmony, creating a sense of yearning, desire, and instability. The harmony in this context is used to reflect the uncertainty and emotional turmoil of the characters. The melody challenges the harmonic boundaries, and it is not always in accordance with the harmony, but it is not always in dissonance with it either, and this creates a mix of instability and consonance that is highly expressive. The unresolved dissonances in both the melody and harmony are very characteristic of Wagner's harmonic language, and the lack of resolution creates a sense of tension.

4. Contrasting Harmony and Melody: In some cases the melody and harmony contrast each other, such as in a piece by Bach, where the melody might be simple and diatonic but the underlying harmonies may include many non-chord tones, passing notes and suspensions, creating a rich and contrapuntal texture. The melody floats above the harmony while the harmony still provides a clear underlying structure. The tension between these elements is what creates the musical interest.

In summary, the relationship between melody and harmony in classical music can range from one of complete support and stability, where the harmony reinforces the melody, to one of challenge and tension, where the harmony creates an unstable and often dramatic effect. The composer’s manipulation of this relationship is a key factor in shaping the overall expressive character of the piece, and the way the composer treats this relationship is key to their unique sound. Understanding how harmony supports or challenges a melody helps in appreciating the dynamic interplay between these two fundamental elements of musical composition.