Jenny Scheinman is about as successful as you can be and still be eccentric. This is a jazz/Americana/world music violinist who plays in nearly every possible context and—oh, yeah—with multi-million-selling Norah Jones. But maybe calling Ms. Scheinman eccentric is just a way of saying that she’s real: really talented, really musical, really independent. She plays swinging modern jazz, Django/Grappelli-styled swing, Balkan music, free jazz, Latin music, out-chamber music, you name it. She’s all over the place, so: does she really know where her heart is at?

12 Songs says: You betcha.

This is not Ms. Scheinman’s first recording, but it sounds like a defining one. It manages to be both wide-ranging in style and focused in sound. Although the music moves from calypso to free jazz to dirge, the superb band assembled here brings a consistent sound and approach. Ms. Scheinman’s frequent employer, guitarist Bill Frisell, plays with his usual blend of understated melody and nervy atmosphere. Ron Miles (cornet) and Doug Weiselman (clarinet) fill out the “front line” with the leader’s fiddle, each adding a distinctive flavor that seamlessly blends on the ensemble passages. The rhythm section (Rachelle Garniez on accordion, claviola, and piano, Tim Luntzel’s bass, and Dan Rieser on drums) is consistently sympathetic. The band tackles everything but never feels out of balance or inauthentic.

Take “Antenna” as an example. Mr. Frisell and the rhythm section start things off so that you sense the moody track is going to be an exercise in stinging Frisell-y guitarism. But within eight bars, a composed melody played by the violin and clarinet enters, moving into the tune’s foreground. Mr. Miles’ cornet creeps into the tune as well but without the showiness we associate with brass, and so the elegant balance of all the septet’s colors is maintained. Ms. Scheinman’s improvised solo lacks the virtuosic flash of bop, yet it seems to have the lyrical bent and sense of interactive atmosphere we associate with, say, the Bill Evans Trio. The ensemble’s return feels utterly consonant with the improvisation—a rare feat that too few jazz musicians bother even to attempt.

Many of the tracks on 12 Songs have a theatrical sound. The opener, “The Frog Threw Back His Head and Laughed”, moves with a quiet backbeat and a desirous-of-lyrics melody, creating an immediate, seductive mood. The solos (Ms. Scheinman, Mr. Frisell, and Mr. Miles) all seem spoken—like desolate but funny monologues in a tune by Samuel Beckett. “Song of the Open Road” is the best kind of soundtrack: a musical analogue to motion, gliding forward on cymbals and sustain. “Moe Hawk” feels like a march for an army of ants—the rhythm section taking tiny steps as Ms. Scheinman skitters and slides the fingerboard, then a melody enters that bounces like an unusually limber overweight boy. “Sleeping in the Aquifer” and “The Buoy Song” are both essays in ballad time, tone poems that come off like watercolor landscapes or gradual sunrises through fog.

There is also, however, a distinct sense of dance to this recording. “Suza”, “Little Calypso”, and “Satelite” all trade in world music folk melodies that seem like refugees from wonderful weddings you only wish you could attend. And this is what the band does so well—move from brooding to fun, from chamber hall to dance hall, from carefully composed to devilishly playful without seeming schizophrenic or splintered. Consistency and diversity in one fell stroke—that sounds like some sort of American ideal.

My favorite track on 12 Songs is the “praise hymn” for Albert Ayler, “Albert”. Ayler was an elusive figure in ‘60s free jazz—a musician of harsh sound but great melody. Ms. Scheinman has composed a tune that uses two very Aylerian conceits—building melody from a repeated element and slowly building intensity—yet sounds so unlike Albert in its gentle lyricism, absent the anguished cry of forty years ago. Again, musical sleight of hand: a gentle sliver of Ayler, a band capable of virtually anything that never loses its identity.

For all its strengths, 12 Songs lacks a moment of climax or explosion. The last track, “June 21” slowly dissolves in a bell-like wash of Frisell-ian sound. And perhaps too many other songs are similarly easygoing or lyrical. I itch for a taste of the skitter and slash that Ms. Scheinman is capable of. (Check her out on Bill Frisell’s Richter 858 recording for electric guitar and string trio.)

But this seems like quibbling. 12 Songs is a brilliant example of what a jazz career can be in 2005—eclectic yet singular, and very very lovely.