This article goes on my list of first-rate Parker scholarship: Four Studies of Charlie Parker's Compositional Processes, by Henry Martin, published in the July 2018 issue of the journal "Music Theory Online."
Martin studies four Parker compositions that show some evidence of Parker's compositional processes. His article covers the tunes and issues below, in considerable detail:
"Ornithology" has been credited to Benny Harris, to Parker, or to a collaboration of the two. The end of the song was changed (for the better) in later Parker performances. Martin considers the lineage of melodic motives used in the tune as they occur in earlier recordings by Harris, Parker, and others. In the end, it's not possible to positively ascribe authorship to one or the other, though it would seem most likely that Harris wrote the tune, basing the beginning on one of Parker's licks, which in turn derives from Lester Young. The revised ending seems to have definitely come from Parker.
"My Little Suede Shoes" is a combination and reworking of two c.1950 French pop songs, "Le Petit Cireur Noir" and "Pedro Gomez." I discussed this in a previous post, but Martin presents much more detail. Parker's compositional process here consisted of altering and combining the two songs into a coherent and melodically satisfying new tune.
With "Red Cross" and "Blues (Fast)," we have the opportunity to observe Parker reworking tunes during recording sessions. Parker changes the melodies over the course of subsequent takes, until a final satisfactory result is reached. Martin examines the development of each tune in detail.
Going beyond the discussion of Parker's composition process in these four pieces, Martin considers the question of what exactly "composition" means in a jazz context, proposing a wider definition of the term, including instances of what one might otherwise consider improvisation. It's an interesting question; to me it immediately brings up the issue of what can be copyrighted. Martin has the good sense to stop short of this difficult, thorny question.
Anyone interested in Bird scholarship really should check out this article; a brief review can't do it justice. Just click the link at the beginning of this post.