Kraft was born in Chicago, Illinois. He was awarded two Anton Seidl Fellowships at Columbia University, graduating with a bachelor's degree cum laude in 1951 and a master's degree in 1954. He studied composition with Jack Beeson and Henry Cowell, orchestration with Henry Brant, percussion with Morris Goldenberg, timpani from Saul Goodman, and conducting with Rudolph Thomas and Fritz Zweig. During his years in New York, Kraft was also active as a freelance musician and had the privilege of working with some of the most well-known musicians of the mid-twentieth century. Kraft thoroughly enjoyed doing freelance work. Among his gigs, he played as an extra percussionist for the Metropolitan Opera and played percussion and conducted for Ondine. In 1954, Kraft joined the Dallas Symphony. After only one season there, he moved to Los Angeles.
He took a position with the Los Angeles Philharmonic beginning in the 1955/56 season. He spent 25 years in the orchestra, the first eight as a member of the percussion section, and the remaining 17 as principal timpanist. Kraft was also the assistant conductor of the orchestra for three seasons under Zubin Mehta. From 1981 to 1985, Kraft was the Composer-in-Residence for the orchestra, during which time he was also responsible for the founding and directing of the Philharmonic’s New Music Group. During his early years in Los Angeles, he organized and directed the Los Angeles Percussion Ensemble, a group which played a vital part in premieres and recordings of works by such renowned composers as Ginastera, Harrison, Krenek, Stravinsky, Varèse, and many others. As percussion soloist, he performed the American premieres of Stockhausen’s Zyklus and Boulez’s Le marteau sans maître, in addition to recording Histoire du soldat under Stravinsky’s direction. He has also composed film soundtracks, including the scores to Psychic Killer, Avalanche, Bill, and Fire and Ice. He served as chairman of the composition department and holder of the Corwin Chair at the University of California, Santa Barbara until he retired in June 2002.
In the 1960s and 1970s, most of Kraft's compositions were serial, while in the 1980s he incorporated jazz rhythms and impressionist harmonies. Although percussion works feature prominently in his catalog, in 1996–1998 he concentrated on composing his first opera, Red Azalea.
Recordings
Compact discs completely devoted to Kraft’s music can be found on Harmonia Mundi, CRI, Cambria, Crystal, Albany, and Nonesuch labels. Other works can be found on GM, Crystal, London Decca, Townhall, EMI, and Neuma. Recent works include Brazen, commissioned by the San Francisco Symphony Orchestra; Quintessence Revisited and Concerto for Four Percussion Soloists and Symphonic Wind Ensemble, premiered and recorded by the New England Conservatory Wind Ensemble, Frank Battisti conducting. His 'Encounter' solo series has been recorded multiple time on all appropriate instruments. On Encounters he worked with guitarist John Schneider. Encounters II showcases unique techniques for tuba such as multi-phonics double pedal range. In 2010, the Los Angeles Philharmonic released a recording on DG Concerts of the Timpani Concerto No. 1 featuring Joseph Pereira as soloist with John Adams conducting.
