"La Fiesta," "Someday My Prince Will Come," and "Olé"

A couple of days ago I was driving home from teaching, and turned on KCSM, our Bay Area jazz station. Miles' recording of "Someday My Prince Will Come" was playing, and I tuned in just in time for John Coltrane's solo. The first notes in the solo are pretty much exactly the beginning of the second theme in Chick Corea's "La Fiesta." I had never noticed that before.

Here's the Miles recording on Youtube. Coltrane's solo starts at about 5:50.

Here's a transcription of the solo, scrolling while the music plays. (Sorry I can't just post these videos here - apparently Sony has blocked any access except viewing them directly on Youtube.)

Here's Chick Corea's tune. The second theme (the part in question) starts at 1:45:

Both tunes are in 3/4 time, and the chord progressions are the same for four measures. The Miles recording was done in 1961; "La Fiesta" was recorded in 1972. It seems pretty clear that Corea got some initial inspiration from the Miles/Coltrane recording. 

As you might expect, I was not the first person to notice this. Here's a discussion from 2003; check out the first comment from Mike Fitzgerald (fourth comment from the top), with some very good information on this question. The comments also point out the similarity of the first theme of La Fiesta to the Coltrane tune "Olé" (recorded in 1961 also). Coltrane's "Olé" definitely uses the same chord progression as the first theme in "La Fiesta," but as Fitzgerald points out (quoting Lewis Porter's Coltrane bio), the progression was not original with Coltrane. 

The song "El Vito" is a likely source, both for "Olé" and for the first theme of "La Fiesta":