Recently I heard a smooth jazz trumpet star “do” Miles Davis. He captured Miles’s distinctive muted tone, getting every note right, and, more surprisingly, even the spaces between. The trouble was that he left out everything that made Miles Miles: the vocalized inflections, the expression, the distortions, the bent notes and tones. What he played was so colorless and without character that I was left to ponder the distinctions between homage, parody, and just plain-old theft.

The distinctions are particularly important because just about everybody is honoring Miles Davis these days, and they will continue to do so for a while: In time for what would have been his 81st birthday this month, there have been live celebrations (such as the “Four Generations of Miles” package at Iridium) and a new album in his memory by his longtime bassist, Ron Carter. There also are at least two new books, including “Dark Magus” (Backbeat Books), a memoir by Davis’s son Gregory, and a worthy overview of his career and music, “It’s About That Time: Miles Davis On and Off Record” (Oxford University Press), by Richard Cook.

On Friday and Saturday, Jazz at Lincoln Center mounted the most ambitious salute this season: “The Many Moods of Miles” was a two-concert series in which four well-known trumpeters — Ryan Kisor, Terrence Blanchard, Nicholas Payton, and Wallace Roney — evoked four distinct eras of Davis’s music. Thankfully, all of them fared better than our smooth, unnamed friend.

Without making a point of it, both nights opened with a re-creation, though not necessarily a strict one, and closed with a more free interpretation of Miles’s music. Friday began with Mr. Kisor, of the Jazz at Lincoln Center Orchestra, in an energetic performance that covered Davis’s bebop years in the late 1940s and early ’50s. In a program that could have been named for Davis’s Prestige album, “Collector’s Items,” Mr. Kisor and the alto saxist Sherman Irby showed that there are a lot of overlooked gems in Davis’s much-explored canon, notably 1947’s “Milestones” — a bright bopper that anticipated the birth of the cool and was the first tune Davis recorded under his own name — and one of his earliest trademark slow ballads, J. J. Johnson’s “Enigma.” Driven by drummer Willie Jones III, Mr. Kisor played with more of a pure power approach, sounding more like Clifford Brown instead of mimicking Miles.

Mr. Payton opened the second night with music by Davis’s second great quintet of the mid-’60s. For a starting point, he wisely used the repertoire of Davis’s European concerts from the fall of 1967, which gave him the chance to play a wide range of music going back 10 years from that point.

Mr. Payton’s co-star on tenor saxophone was a young woman named Sophie Faught, whom he discovered recently at Indiana University; more than anyone else in the four bands, she came closest to the musician whose considerable shoes she was filling — in fact, I’ve never heard another saxist sound so much like Wayne Shorter. Mr. Payton and Ms. Faught were especially ace on the tenor-trumpet exchange that opens the 1960 “No Blues” and appropriately agitated on Mr. Shorter’s “Agitation.”

Mr. Payton ended with a piece that Davis almost never played live: “Circle in the Round,” recorded in 1967, but not released until a decade later, was Davis’s first experiment with an electric guitar, a steady drone played here by Mike Moreno. True to its title, it’s an engagingly spherical melodic line with no beginning or end, though Mr. Payton’s version was considerably tighter than Davis’s 30-minute studio track.

This was a prophetic lead-in for the second set, in which bassistcomposer Marcus Miller led two other former Davis sidemen, including drummer Lenny White (who played on “Bitches Brew”) and Wallace Roney, who is one of few trumpeters to share a stage with the Dark Magus. The septet played on a collage of funk and rock riffs from the early ’70s that was engaging, but it’s hard to distinguish one tune from another in this period — it’s more about the jamming than the melodies. The group sounded better when it played an actual tune, Cyndi Lauper’s “Time After Time,” which Davis covered in one of his few classic ballads from the later years.

The highlight of the four sets was the first night closer: Mr. Blanchard’s recasting of the music of the Miles-Coltrane period of the late 1950s. Mr. Blanchard, an accomplished composer, did something fairly common in electronic music that I’ve rarely heard done live or acoustically: He played direct quotations of famous Miles phrases, reproduced nearly exactly as if they were sampled, but spaced out and worked into new groupings in a distinctly Miles-ish manner. The set reached an apogee in a thoughtful collage of three tunes from the “Porgy and Bess” album — “Buzzard Song,” “Bess, You Is My Woman Now,” and “Gone.” It was a thoughtful application of the concept of jazz repertory; in Mr. Blanchard’s view, this is how the tunes might have sounded had Davis played them live with the quintet.

During his set, Mr. Blanchard shared an anecdote about playing in the Jazz Messengers 25 years ago. Whenever his trumpet solos got too abstract or ambitious, leader Art Blakey would bring him back into line by barking, “Play the melody! You’re not Miles Davis!”

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During the Marcus Miller-Wallace Roney set, I was thinking about how Richard Cook, in his new book “It’s About That Time,” wisely divides Davis’s electric period into two phases: the early ’70s, when the trumpeter played jazz with rock and avant-garde components, and the ’80s, when he tried to make pop records in which his trumpet was the only jazz element. “It’s About That Time” is the first general volume on Davis since John Szwed’s “So What” from 2002 (this decade has seen no less than three books on Miles’s electric period alone).

Considering its scope, “About That Time” is a fast and breezy read. It focuses on what the author regards as Davis’s 12 most essential albums, but also considers virtually every recording the trumpeter ever made, live or in-studio, legitimately released or otherwise. Mr. Cook goes through the 1940s fairly quickly, arguing that Davis wasn’t much of a bebopper; he also finds hardly anything to get excited about in the ’80s, when Davis couldn’t seem to get much of a handle on anything. Mr. Cook’s strength is wittily showing, with lots of fresh observations, how Davis’s music was a continual journey. Rather than perfect one approach and stay there for a while before moving on to the next challenge, Davis never stopped evolving. It was both his blessing and his curse.

wfriedwald@nysun.com