The Music of the Ainur is the music of Arda, of creation, of all existence. Arda was made for the Children of Illuvatar, which are exclusively Elf and Man. However, if the Music embodies all that was, is, and will be, then the Dwarves should be in the Music too. It's generally assumed the Valar do not know how to create that which they had not already seen.
So how do the Dwarves fit into the Music? Were their creation already foreseen? Did Illuvatar already see it coming in Aule's music? What place do they have in the Music?