Born in Portland, Oregon, Aldwell's early musical training was in Texas and at the Cincinnati Conservatory of Music. He then received undergraduate and graduate degrees from the Juilliard School, where he studied piano with Adele Marcus. He studied theory privately with Carl Schacter, with whom he later co-authored the music theory textbook Harmony and Voice Leading.

Aldwell joined the faculty of Philadelphia's Curtis Institute as a theory teacher in 1971, and also taught piano at the Mannes College of Music in New York.

He received an Ingram Merrill Foundation grant for analysis and performance of Bach's keyboard music and made his New York debut performing Book I of the The Well-Tempered Clavier. He gave many recitals devoted to Bach, and was scheduled to give an all-Bach recital in February 2007 at Philadelphia's Benjamin Franklin Hall.

A 1987 review in the New York Times of a Bach performance described him as "an unusual artist who knows how to transmute scholarship into passionate performance."

Aldwell's recordings include both books of The Well Tempered Clavier, the Goldberg Variations, and the French Suites, as well as works by Hindemith and Faur_. Classical Music