Blackwood was born in Indianapolis, Indiana. He studied piano in Indianapolis and was doing solo appearances at the age of 14 with the Indianapolis Symphony Orchestra. After studies at many places (including Yale University, where he earned his Master of Arts degree) in the United States, he went to Paris to study from 1954 to 1956.
For forty years, from 1958 to 1997, Blackwood taught at the University of Chicago, most of the time with the title of Professor.
His initial compositions were not particularly unconventional, but in 1981 he shifted to a new style. For these pieces, he used microtonality to create unusual scales.
He is known for his book, The Structure of Recognizable Diatonic Tunings, published 1986