Big band album of the year? It’s too early to say, but the first-ever live recording by the superlative Bill Holman Band has earned front-runner status for that honor and will surely be hard to trump. Holman, an acknowledged master in the realm of writing and arranging for large ensembles, already has one Grammy Award in the trophy case (for Brilliant Corners, his ingenious adaptation of the music of Thelonious Monk), and could soon have another if NARAS members lay aside any unreasonable biases and vote with their ears.

The Holman Band was taped last September during Stratospheric, the Los Angeles Jazz Institute’s four-day homage to high-note trumpet monarch Maynard Ferguson. I was among those in the audience that day, and the album I’m savoring as this is being written easily transcends my memory of the performance. I knew it was good, but not that good. When parceling out praise, the hardest task is to decide where to begin.

Let’s start with the band itself, as without it there would be no music to assess. To begin with, Holman’s charts, which frequently call upon the various sections to perform implausible acrobatics, are no mere stroll in the park. They’re not written for novices, nor does Holman employ any. Faced with his incredibly demanding arrangements, the ensemble cruises through them without the least trace of wariness or indecision. Brass and reeds are razor-sharp, the rhythm section never less than indispensable. Even more to the point, everyone swings, on every number and at every tempo. Beyond his role as a team player, each member of Holman’s band is a sharp and resourceful improviser. How good are they? Well, the amazing Carl Saunders is in the trumpet section, and he doesn’t solo once! With Bob Summers and Ron Stout on either side of him, he doesn’t have to, and can focus on leading the others, which he does with alacrity and style. Soloists aren’t listed in the booklet, but that’s unnecessary, as Holman identifies them clearly, sometimes more than once.

Holman composed five of the eight selections, and each one is a gem-like showpiece, as are his splendid arrangements of Lennon / McCartney’s “A Day in the Life,” Bird’s “Donna Lee” and Frank Rosolino’s “Blue Daniel.” “Donna Lee” and “Zoot ‘n Al,” Holman’s snappy salute to the peerless Sims / Cohn tenor tandem, are the obligatory chops-busters, but even when easing back on the throttle, as on “Blue Daniel,” “Bebop Love Song” or “Woodrow,” his affectionate bow to Woody Herman, Holman makes certain the band toes the mark by interspersing the strenuous arpeggios and split-second contrapuntal exchanges that are the hallmark of his elaborate modus operandi.

“Woodrow,” closely bound to Herman’s longtime theme, “Blue Flame,” is a snappy shuffle that accommodates swaggering solos by Summers, pianist Christian Jacob and tenor Ray Herrmann who is featured again, with trombonist Andy Martin, on the breezy “Day in the Life.” Another Holman original, the lively and aptly named “Bary Me Not,” is a showcase for baritone saxophonist Bob Efford, while the fleet and lovely “Donna Lee” is further enhanced by Jacob, tenor Doug Webb and valve trombonist Bob Enevoldsen who plays with a happy spirit reminiscent of Cy Touff, the irrepressible bass trumpeter in Herman’s Third Herd.

Stout and alto Bruce Babad help cheer up “Blue Daniel,” and Martin, Summers and Webb share the stage on the playful “Press One,” written by Holman to express his frustration with the catch-all directive given to callers by today’s automated phone systems. The soulful “Bebop Love Song,” with ad-libs to match by Webb, Enevoldsen and bassist Joel Hamilton, leads to the high-octane finale on which Webb and Herrmann, sitting in admirably for Zoot and Al (or Al and Zoot), scamper through and around the changes with reckless abandon while drummer Kevin Kanner shows why Holman chose him to be the band’s resident bombardier, succeeding such renowned timekeepers as Mel Lewis, Jeff Hamilton and Bob Leatherbarrow.