A.k.a "Fly Right", a.k.a "Iambic Pentameter", a.k.a. "Volcano"
Though usually associated with Thelonious Monk, "Epistrophy" (originally "Fly Right") is co-credited to Kenny Clarke, who explained its origins thus*: "One night Charlie [Christian] and I were at the Douglas Hotel on St Nicholas Avenue visiting a friend who was a dancer and played the ukulele. I fooled around with the uke and then Charlie took it out of my hand. "Look, Kenny," he said, "you can make all the chords you want to on this if you just stretch your fingers right." He showed me, handed back the uke, and I started experimenting. I got an idea that sounded good, went upstairs to my room in the same hotel, and wrote it down. Later on Joe Guy showed the tune to Cootie Williams, and Cootie had Bob MacRae make an arrangement. I called it 'Fly Right', and Cootie used to broadcast it from the Savoy Ballroom".
Other sources state that Clarke wrote the main melodic theme, while the chords were written by Monk, who copyrighted the tune on June 2, 1941. It became the closing number of each set at Minton's Playhouse during that period. The later title is assumed to derive from the English term "epistrophe", defined as "the repetition of a word at the end of successive clauses or sentences" and originating from from the Greek epistrophē, from epistrephein "to turn around" (Oxford Dictionary).
First recording was by Cootie Williams and his Orchestra (firmly in the swing idiom) on April 1, 1942 (but only released in the mid-1960s), under the original title. Clarke recorded it as "Epistrophy" with his 52nd Street Boys on September 5, 1946. Monk first recorded it on July 2, 1948 (at the "Wizard of the Vibes" sessions, with Milt Jackson) and subsequently on almost all his live albums. Clarke later rearranged "Epistrophy" as a modest drum feature under the titles "Iambic Pentameter" (in France with Hubert Fol and his Be-Bop Minstrels, October 29, 1949) and "Volcano" (on "Klook's Clique", February 6, 1956; and "Kenny Clarke, Francy Boland And The Band - Live At Ronnie's, Vol. 1", February 26, 1969).
Note: According to Clarke, "Rhythm-A-Ning", another composition attributed to Monk (and recorded by him in 1957) was also originally devised by Charlie Christian at the Minton's sessions. It can be heard at any rate (after a typically electrifying Christian guitar solo) at the back end of the tune on the Newman mid-1941 recordings (issued on the 1970s LP "Trumpet Battle at Minton's), starting here.
*Source: Ira Gitler, quoting an interview in "Inside Jazz"