: What are the main elements of classical music composition? I've come up with the following as the components of music composition and theory: Counterpoint Harmony (chords and triads) Music forms and development (sonata,

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Yes, you're on the right track. If you haven't already, you will also want to get into the principles of accepted Music Notation, the pracrtice of Orchestration, and a view of the History of Classical Music as it covers the evolution of style through the various recognized periods.

In addition to a textbook type of source for information about Music Theory, as Todd Wilcox mentions in his comment to your question, you will probably also benefit from general reading in the subject, such as is found in reviews of recorded music (the British magazine Gramophone is particularly good at this) and books or articles that analyze well-known classical pieces. (Penguin has several good ones.)

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Some other points to consider are :

Melody: ie a 'good tune' especially for musical theatre/light opera forms and even in more academic styles there is the concept of the 'theme or motif' ie a recognisable tune associated with a particular mood or character. And this is the bedrock of pop music.
Orchestration : the ability to allocate specific groups of instruments to particular parts of a score to create an overall mood to the sound.
Structure : how a piece of music begins develops and ends be it a three act structure in opera or a intro/verse/chorus in a pop song