Speaking of successors to Dewey, I should have mentioned Leonard B. Meyer and his Emotion and Meaning in Music (1956) and Music, the Arts and Ideas (1967). Thanks to Strange Magic who has mentioned Meyer and his work in a number of threads here. Meyer's work is dense and slow going, but thoughtful and interesting.
Though he is more concerned with a critical history of aesthetics rather than philosophy, at least directly, and discusses the arts generally rather than focusing solely on music, I highly recommend Walter Jackson Bate's From Classic to Romantic: Premises of Taste in Eighteenth-century England (1946).
Finally, though he certainly is more a musicologist and historian than an aesthetic philosopher, Charles Rosen's method of analysis, as in The Classical Style, The Romantic Generation and Arnold Schoenberg, his approach certainly reflects a philosophical approach based, imo, in the pragmatism of Dewey et al.
All of these writers have to deal with questions like, What is music, and what is its purpose? at least indirectly, to establish their own premises.