In the New York music season now ending, I did not hear a better performance than one from Hilary Hahn: The young violinist played Bach’s Sonata No. 2 in A minor, instructively and transcendently. In fact, I’m not sure I heard a performance as good.

Her latest CD gives us, not Bach, but the Violin Concerto by Sibelius and the Violin Concerto by Schoenberg. (The label is Deutsche Grammophon.) Collaborating with Ms. Hahn are the conductor Esa-Pekka Salonen and the Swedish Radio Symphony Orchestra. And this is a seriously good disc.

The Sibelius is a summit of violin playing, and Ms. Hahn stands on it triumphantly. She begins the concerto in eerie, otherworldly fashion, drawing you in. And Mr. Salonen and his forces are right with her. As she continues, Ms. Hahn is incisive and exacting. At the same time, she is not punctilious or clinical. She is always musical.

And — if you can accept this peculiar statement — she is icy without being cold.

Seldom is the Sibelius Concerto played with such clarity. Ms. Hahn applies the values of Bach and Mozart. Her performance may be too clean for some — but others will find her kind of precision thrilling.

Tempos throughout are just: unrushed and arresting. And parts of the concerto practically make your heart stop. There are moments in the slow movement that are so beautiful, they almost ache. Of course, Sibelius gets some credit for this, too.

The last movement is not at all fast — which follows the composer’s marking: Allegro, ma non tanto — but it is bristling. And the music kind of bites you as it goes along. Ms. Hahn’s playing in this movement, and the others, too, is Heifetzian.

Mr. Salonen brings out interesting things in the score, appearing to have some fun with it. And he is neither brusque nor dismissive, as he has been known to be. He allows for ample beauty and sense.

No one can be in love with every measure of this performance. There are points at which I myself desire just a little more abandon, and just a little less control. But no measure is stupid or ill-considered, that’s for sure.

And I’ll tell you something personal: I listened to Ms. Hahn in the Sibelius right before I went to bed — or wanted to go to bed. So penetrating and almost freaky was this playing, it disturbed me, making it hard to sleep. I continued to hear the performance in my head.

How about the Schoenberg Concerto? It is very rarely played, and Ms. Hahn — with her partners — does it full justice. The concerto is brainy, virtuosic, and, to many ears, beautiful. You could call it tailor-made for Ms. Hahn.

The liner notes tell us that Heifetz found this impossible to play. “Schoenberg need not have been surprised; Heifetz dwelt in a kingdom of traditional violin technique, while Schoenberg was pioneering in new compositional styles.”

Oh, please: There wasn’t a thing on earth Heifetz couldn’t play — “traditional technique” my eye. My suspicion is that he didn’t like the concerto very much, or in any case didn’t care to play it — and for that reason said it was impossible.

Hilary Hahn is young, yes — 28. But she has long been a great violinist. And it might as well be acknowledged now, for it surely will later, when it’s perfectly safe.

* * *

Nigel Kennedy is not just a violinist — he is a persona. He has spiky hair, funky clothes, and a performing calendar that includes rock and jazz. Some years ago, we read that he was dropping the “Nigel” and going with just “Kennedy.” But the full name seems in operation now.

He goes in for political gestures too. Of all the countries in the world, he boycotts one, evidently considering it uniquely evil. (Three guesses which country it is: It is a little slice of the Middle East.)

The cover of his new album (from the Opendisc label) shows him in silhouette, tramping through the woods — or in a field bordering woods — with his violin case. Where’s he going? Rehearsal? The back cover shows him walking along with poles, a backpack, and a rugby shirt. No violin case.

He plays the Beethoven Concerto and the Mozart Concerto No. 4, and does so with the Polish Chamber Orchestra. Conducting? Mr. Kennedy himself, which in Mozart is not so unusual — though it should be — but in the Beethoven is highly unusual.

Unfortunately, the Beethoven Concerto does not go well. Mr. Kennedy’s sound is not good — cramped, for one thing — and his intonation is iffy. (It is somewhat surprising to hear this on a recording, which can be endlessly doctored.) Much of Mr. Kennedy’s playing is stiff and effortful. And the concerto has too much of that “period”-style punch, rendering it choppy and trite.

The Rondo, however, shows an interesting spirit. And Mr. Kennedy fashions his own cadenza, which recalls the first movement and makes use of the orchestra (or some of it). This cadenza is unexpected, inventive, and fun.

He does his own cadenzas in the Mozart, too — one in each of the three movements. And the first one is … what? Jazzy, bluegrassy, New Agey, psychedelic. Kind of drugged-out, or blissed-out. You know those recordings of whale sounds? I thought of that. And Mr. Kennedy again has the orchestra playing along with him (or is it a synthesizer?).

What’s more, a certain recording technique is in use: Mr. Kennedy and his friends sound like they’re playing in a bathroom or something. I’m not sure they could achieve their desired effect in a concert hall. And the cadenza does not really match Mozart or his concerto.

But, you know? I liked it, rather a lot. Listened to it more than once.

The slow movement’s cadenza features more of the same, but is not as successful. It’s pretentious, I believe. And the final cadenza suffers from some blandness.

Mr. Kennedy fills this disc out with a Stéphane Grappelli act: his own arrangement of “Creepin’ Out,” a piece by Horace Silver (of “hard bop” fame). In fact, Mr. Kennedy, as a youngster, played with Grappelli, the late jazz violinist. And he does a fine job with his jazzy funk here.