Willman was a vanguard creator and influential exponent of twentieth-century contemporary music.
As chairman of the music department at the University of Wyoming, he is credited with rapidly expanding music arts within the institution.
He led the development of a more comprehensive Music Department for aspiring academicians and professionals in performance, composition, education, and musicology.
Between 1940 and 1950, enrollment in the Music Department quadrupled.
Willman was founder of the Wyoming Music Teachers Association; and—with Wyoming businessman and composer George William Hufsmith, Jr.
(1924–2002), and Casper conductor Ernest Gilbert Hagen (1913–2000)—Willman was co-founder of the Grand Teton Music Festival in 1962.