o10, that soundtrack is a bit confusing. The link you provided doesn't include Monk or any of his songs. In the bio, "Thelonious Monk, The Life and Times of an American Original" there is discussion about Monk avoiding signing the contract for the score until the very last minute. When he finally signed and went to the studio to record the music he only did a few of his existing compositions rather than write anything new. The exception was his solo performance of the old hymn, "We'll Understand it Better, By and By". Most of the music furnished to Vadim for the film was done in those same sessions by Blakey and the Jazz Messengers.
I've never seen the film but the title and credits in your link leave me wondering.
I've never seen the film but the title and credits in your link leave me wondering.