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Alan was born in the Ironbound District in Newark, New Jersey. He started on alto saxophone, but switched to trumpet after graduating from high school. He attended Howard University but soon rebelled against the ultra-conservative atmosphere and dropped out (he later attended and graduated from New York University (NYU)). He played his first professional gigs with a local bebop big band called the Jackie Bland Band (other members included his brother Wayne, trombonist Grachan Moncur III, and pianist Walter Davis, Jr.). He was very much a bebop player in his early years, but soon gravitated towards free jazz, and with the exception of six months he spent in a US Army Band, continued to play in that style for the rest of his career.
He recorded two albums as a leader: Orgasm (1968) and Tes Esat (1971) (both were out of print for many years until re-issued by Verve Records in 2004 and 2005 respectively). He also recorded five albums with saxophonist Archie Shepp (1965–1970), including the classic, Four for Trane, two albums with Marion Brown (1965–1966), one album with Alan Silva (1970), and made an appearance on one of his brother's albums (The All Seeing Eye in 1965). Several of these albums feature his unusual compositions, his most famous being "Mephistopheles".
In the mid-1960s Alan moved to Europe, leading his own avant-garde gigs in Geneva and Paris. His style of free jazz sometimes proved to be too far-out for European audiences (his brother remembered that Alan's gigs in Europe would often end with him responding to the crowd's boos by yelling, "You're not ready for me yet!") but he generally found European audiences more receptive than those in the U.S. Eventually he moved back to the States, where he taught briefly at Bennington College but otherwise faded into obscurity. He died of a ruptured aorta in L.A. in 1987, at age 56, shortly after becoming engaged to Ruth Ann Hancock, a cousin of Herbie Hancock.
Alan's playing is comparable to Don Cherry, but with a more aggressive, anarchic bent. His own albums feature his groups functioning as a unit, rather than focusing on his own virtuosity (or lack thereof). Reportedly, his musical style is much like he was personally: deep and intellectual, but intentionally strange (his childhood nickname was "Doc Strange").
- 1968: Orgasm (Verve Records) - with Charlie Haden, Gato Barbieri, Reggie Johnson, Muhammad Ali, Rashied Ali
- 1971: Tes Esat (America Records) - with Gary Windo, Johnny Dyani, Rene Augustus
With Archie Shepp
- Four for Trane (1964)
- Archie Shepp and the Full Moon Ensemble (1970)
- Pitchin Can (1970)
- Doodlin' (1970)
- Coral Rock (1973)
With Wayne Shorter
- The All Seeing Eye (1965)
With Marion Brown
- Marion Brown Quartet (1965)
- Juba-Lee (1966)
With François Tusques
- Intercommunal Music (1971)
With Alan Silva
- Seasons (1970)