On the album, Rivers is joined by members of the Rivbea All-star Orchestra: saxophonists Greg Osby, Steve Coleman, Chico Freeman, Gary Thomas, and Hamiet Bluiett, trumpeters Baikida Carroll, James Zollar, Ralph Alessi, and Ravi Best, trombonists Art Baron, Joseph Bowie, and Ray Anderson, baritone horn player Joseph Daley, tubist Bob Stewart, bassist Doug Mathews, and drummer Anthony Cole.

"[1] Bill Shoemaker of JazzTimes stated that Rivers's "current work has a more vibrant edge than 99.9% of the music now glutting the market," and commented: "Rivers' avant-icon status obscures the fact that his sensibility is pan-stylistic, and that, more often than not, the dense clusters and jarring voicings of his orchestra works are in the service of setting up tangy funk, Latin, and swing grooves for soloists.

"[9] The authors of The Penguin Guide to Jazz Recordings awarded Inspiration a full 4 stars, and noted "the sheer originality of Rivers's concept: that he can mould an orchestra of highly individual performers so that it sounds like the expression of a single, idiosyncratic imagination.

"[5] Author Gary Giddins stated that the album "brims with the exhilaration exclusive to the form," and wrote: "The music is wonderfully schizoid; the dense voicings are dissonant, but the riffs and pithy solos are downright toasty.

"[10] A writer for Mother Jones commented: "Imagine funk idol Maceo Parker falling under the sway of abstract expressionism, and you have an idea of how Rivers' new album combines aggressive dissonance, tricky rhythms, and unconventional grooves... At 77, Rivers has produced an album that any audacious young avant-gardiste would envy.