Saxophonist James Carter.

One of the jazz world’s more interesting players is the Detroit-born saxophonist, bandleader and composer James Carter, who made a big splash in the classical world a couple years back with his performance and then recording of Roberto Sierra’s Concerto for Saxophones.

One of the reasons for its success was that it spotlighted a performer of tremendous technical accomplishment who is also one of great range. Carter is usually categorized as a “post-bop” saxophonist, but he seems to follow in the same line laid out by John Coltrane and Ornette Coleman, two ferocious theorists who had no fear about pursuing their ideas to their logical end, no matter how untraditional they ended up sounding.

Carter appears Thursday night with his organ trio — organist Gerard Gibbs and drummer Leonard King — in the Community Arts series at the Coral Gables United Church of Christ. There is any number of recorded live performances of this trio on the Internet, and they showcase a nimble, forceful, tremendously energetic threesome that sounds comfortable in whatever style of tune they choose to take on.

One of the unsung stories of jazz has been the rise over the past 30 years of a generation of players who treat the music with a kind of reverence and respect that has revitalized the tradition in the manner of the greatest performers of the past. Musicians such as Carter, Wynton Marsalis, Terence Blanchard, Esperanza Spalding and others have resisted the “smooth jazz” path, in which a sweet cream of 1970s and 1980s pop styles is ladled over a light jazz base, as a hybrid that comes out of the pop rather than the jazz world.

These performers and composers prefer to do things in a way that honors classic craftsmanship, using the established instruments and the jazz canon, seeing what new things can be made from them, and writing their own works in a manner congruent with that tradition. The result is that not only is there a great deal of exciting, uncompromising music to be heard, but it also reminds the listener of a fine corpus of recent jazz that should get more attention. (I remember seeing Spalding in a concert in Lake Worth before her first Grammy, and afterward I spent some time reacquainting myself with the music of Wayne Shorter, which Spalding loves and plays in concert.)

Many fine jazz musicians call South Florida home, and the season always brings a few big names through for aficionados. But getting to see the James Carter trio in the thick of a South Florida summer is a bracing invitation to what’s happening in jazz these days, and it should help concertgoers burn off some of their July doldrums.

Here’s a performance by the trio in May, recorded at a festival honoring the music of the great Belgian Gypsy guitarist Django Reinhardt.

The James Carter Organ Trio appears at 8 p.m. Thursday in the Community Arts series. Tickets range from $30-$50. Call 305-448-7421, ext. 120, or visit www.communityartsprogram.org.