One of the most exquisite recent recordings I know – recent, as in the last five years – is the Frenchsonata album made by Midori, the (one-named) violinist, and Robert Mc-Donald, the pianist who is her regular collaborator. (The album is on Sony.) The contents are the Poulenc sonata, the Debussy sonata, and Saint-Saens’s first sonata. The album is jewel-like, and its principal qualities are probably tastefulness and musicality. (Of course, tastefulness is a function of musicality.)

This duo – Midori and Mr. McDonald – began their recital at Carnegie Hall on Tuesday night with the Debussy sonata. It was, yes, tasteful and musical. Midori gave us a sonata in watercolor, truly impressionistic, and not quite of this world. Her sensitivity is extreme. She sang where she should have, she insinuated where she should have. Interestingly, she imparted to this work a sense of play – even when the music was relatively somber.

The second movement is marked “Fantasque et leger” – whimsical and light – and it was just so. Throughout the sonata, Midori kept her focus, and Mr. McDonald proved, as usual, a superb partner: His was a mature Debussy, not too timid, but clean, straightforward, and aware. It is comforting, as well as satisfying, to be in the presence of two real musicians.

Midori followed with a work she commissioned, from Michael Hersch, an American composer in his 30s. Mr. Hersch has enjoyed great success, his music played frequently, the critics complimentary.

His work for Midori is “the wreckage of flowers: 21 Pieces After Poems and Prose of Czeslaw Milosz.” (Milosz, you recall, died just four months ago.) These fragments from Milosz were listed in the Carnegie Hall program. (Sample: “Starry skies go out.”) If you didn’t like Mr. Hersch’s music, you could always read the words.

I myself had trouble discerning connections between the music – the 21 pieces – and the words. Perhaps it was easier for others, and the composer himself surely views the music and words as obviously corresponding. Mr. Hersch has written a work of severity and bleakness, containing elements common in music today, especially American music: Sounds jump out at you, as in a haunted house; a grim landscape is traversed, or simply beheld, or quaked at. The work develops in some ways, although a sameness prevails. (Call it continuity instead, if you like.) Toward the end, there is an interesting and moving elegiac “piece.”

In any event, Mr. Hersch’s commissioner did well by him, displaying maximum control and sympathy. The same is true of her pianist, Mr. McDonald.

And if I may break from music for one second, to say something about that great man, Milosz, and another great man, Jian-li Yang: The latter is a scholar, democrat, and Tiananmen Square leader, who is now in some Chinese dungeon. I had the privilege of meeting him once, and I asked whether there was anything written that described the condition in which he and his fellows found themselves. “Yes” he said: “‘The Captive Mind’ [a Milosz masterpiece].”

After intermission, Midori turned to Janáček, whose 150th birthday we are celebrating . . . and celebrating (you know music and anniversaries). But Janáček’s violin sonata is one of the most beautiful things he ever wrote, and Midori allowed it its full glory. In the opening movement, she was rather dark and gypsy-like – also a little decorous. One can play this music more freely, but then, one would not be Midori. The second movement – Ballada – was really beautiful, songful and simple. Indeed, it was angelic (with Mr. McDonald providing some fluttering of wings). The third movement was rightly rough and rambunctious, and the final movement – an Adagio – built to a satisfying conclusion.

The program itself concluded with the Brahms D-minor sonata, and here Midori was, again, Midori: You can imagine bigger, bolder Brahms. More Brahmsian Brahms, if you will. But Midori was not un-Brahmsian: She was clean and correct, yet sufficiently Romantic. That great slow movement was noble and affecting. The closing movement – Presto agitato – was, yes, agitated, and also sweeping and masterly. To say it once more: Midori and Robert McDonald are two real musicians, and if you can’t endorse every measure they play, you can appreciate it.

For an encore, we had Efrem Zimbalist’s transcription of Carl Engel’s “Sea-Shell.” So lovely. And Midori ended it with a superbly executed long, rapid trill. The hall was rapt.

I myself will end with a side note: While onstage, at various points, the violinist engaged in some very lengthy tunings-up. Perhaps they cannot be avoided. But it would be pleasant – and help the effect of the recital – if they could.