Analyze the harmonic structure of a given jazz composition, identifying and explaining key chord functions, voice leading, and modulations.

Analyzing the harmonic structure of a jazz composition involves understanding the function of each chord within the context of the key, examining how the voices move between chords (voice leading), and identifying any modulations (shifts in key). This process involves both a vertical understanding (the chords themselves) and a horizontal understanding (how they move in relation to each other).

Let's take a simplified analysis of a common jazz standard, "Fly Me to the Moon," which is frequently played in the key of C major, as an example to explain how to identify these key musical elements. The song uses a common 32-bar AABA form.

In the A section, the opening progression is a classic example of a ii-V-I in C major: Dm7 - G7 - CMaj7. Here, Dm7 functions as the ii chord (subdominant), G7 is the V chord (dominant), and CMaj7 is the I chord (tonic). This progression is the core of tonal music. The Dm7 provides a subtle departure from the tonic C and establishes the dominant as a pull towards the tonic. The G7 is the dominant chord that strongly resolves to the tonic CMaj7, creating a sense of resolution. The following chords will usually move to Am7, then D7 resolving to G7, and then back to the tonic CMaj7. These chord changes create a smooth, balanced and familiar sound, based on diatonic harmony of the key of C.

Voice leading within this A section of "Fly Me to the Moon" generally follows the rules of good voice leading principles. For example, in the transition from Dm7 to G7, the third of the Dm7 (F) tends to move up a half step to the third of the G7 (B), creating a smooth leading tone. Common tones, such as G, are sustained between chords, providing further continuity. Also, the resolution of the seventh of the G7 (F) down to the third of the CMaj7 (E) contributes to a good voice leading. This approach helps the individual voices to move in a stepwise manner, enhancing the clarity and smoothness of the harmonic progression. The bass line also contributes to the voice leading, usually moving in a step-wise motion, creating a more flowing sound. These simple but effective movements support the smooth flow of the song.

The B section, the bridge, introduces harmonic contrast. In "Fly Me to the Moon", the bridge shifts to the key of A minor, the relative minor key of C major. This is done using a common ii-V-I in A minor, which would be Bm7b5-E7-Am7. However, the bridge doesn't stay there, and then it continues with a progression of chords that move back into C major. The specific chords of this section are often Am7 - D7 - G7 - Cmaj7. This is an example of a temporary modulation to the relative minor. A modulation implies a shift of the tonal center or the tonic. These chords create a harmonic journey that eventually leads the music back to the original key of C major, effectively setting up the return of the A section. This is a very common method for creating contrast within a song, by temporarily leaving the established key and then returning to it. The bridge section contrasts the main A section by being in a minor tonality, usually providing a melancholic contrast to the main section.

The return to the A section provides a return to the original tonic and chord progressions. These chord changes reinforce the main key and harmonic framework of the song. This makes the structure of the song easily predictable. The chord changes and the movements are always resolved effectively, creating an easy and familiar sound. Overall, the harmonic structure of "Fly Me to the Moon" is very typical for most standards. It uses mostly diatonic chords, good voice leading, smooth transitions, and a temporary modulation in the bridge. All these components blend together to form an effective and pleasing harmonic structure.

In summary, analyzing a jazz composition involves looking at the chord function (how chords operate within the key), examining the voice leading (how individual voices connect chords), and identifying modulations (shifts in the tonal center). Understanding these components provides a full insight into the harmonic language of a piece of music. By applying these steps to a variety of different jazz tunes, one can greatly improve their understanding of musical language, which then allows one to perform, arrange, compose, and improvise more effectively.