Short answer, and I WILL be ostracized for saying this, NO!
A composition comes out of the intellect, imagination and emotion of the composer. How do you teach THAT? How can you tell someone else what they are imagining?
But you can teach students techniques of composition, the tonal/rhythymic building blocks of different styles, the creation of mood through not just tone and rhythm, but also timbre, tempo, articulation, range and dynamics.
How do you learn these techniques? By playing and listening to the music of others, and analyzing what the composers are doing.
For instance, I have always had a strong emotional response to Barber's Adagio for Strings. I sat down with the score to study the key, chord progressions, phrasing, etc. I kept thinking "there is nothing really remarkable here, WHY do I have such a strong emotional response to this music?" I focused in more on exactly where I had my strongest reaction, listening to the music and studying the score. Finally, I realized my reaction was the strongest where the violins were playing their highest pitches at a ff level in the piece. The volume combined with the physical tension of playing that high on the strings, followed by a dramatic pause, would bring me to tears every time. While this realization explained my response at that point in the music, I also had to consider how Barber masterfully led up to this point in the music, and then away from it to the end.
Too often, analysis in music lessons and classes means "what key, what chords?" To understand composition, we need to know those parameters, but even moreso we need to ask "What is the mood? How did the composer use rhythm, tempo, articulation, dynamics, texture, etc. to achieve this mood?"
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