From EMI Classics comes a most curious disc: Gabriela Montero’s “Bach and Beyond.” Ms. Montero is a Venezuelan pianist, and some readers may remember her for her stint with the New York Philharmonic last March. She played Rachmaninoff’s Rhapsody on a Theme by Paganini and did so impressively: with intelligence, technical skill, and flair.

She is a big improviser, Ms. Montero, and her Bach album is a display of her improvisation — that’s the “Beyond.” In an interview tucked in the CD booklet, Ms. Montero says, “I have been improvising since my hands first touched the keyboard when I was just eight months old, but for many years I kept this aspect of my playing secret.” No more. It was her friend Martha Argerich, she says, who encouraged her to go public. (Ms. Argerich, as you know, is the mercurial Argentinian pianist.)

In this same interview, Ms. Montero says that, “whenever I play a concerto, I invariably invite the audience to suggest a melody for improvisation by way of an encore.” That could be fun.

Her new album contains 12 themes of Bach, played with. The first cut — and that is the word — is “Jesu, Joy of Man’s Desiring.” When it starts out, you think this will be a lovely piano transcription, à la Myra Hess’s. But no: Ms. Montero soon gets divergent and funky. She will do the same with all the other cuts. The Presto of the Italian Concerto is a syncopated romp. When you hear the Air in G, you think you are tango-ing. “Sheep May Safely Graze” is sort of a woozy waltz. A D-minor invention brings hot Latin jazz. And so on.

This album may at first be off-putting, because Ms. Montero is tampering with a master — adulterating him. There is a “mustache on the Mona Lisa” aspect here. But eventually she wins you over, or at least she did me. And, improvisations aside, she’s a good pianist — a good player.

One question to be asked is: Are these really improvisations — thought up at the keyboard — or did Ms. Montero do a little preparing? Did she just plop herself down at the Abbey Road Studios and play whatever happened to come out — or was there some forethought? Only her hairdresser knows for sure.

Speaking of hairdressing, Ms. Montero is a fetching woman, and her record company takes full advantage of that fact, with come-hither photos. I guess I can’t blame them for their marketing. And I believe they have a winner of an album.

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Mozart’s “Zaide” has had an exceptionally good year, and that is understandable: We are in Mozart’s 250th anniversary year, and even the obscure is being performed, including this opera. Last month,”Zaide” was put on at both our own Mostly Mozart Festival and the Salzburg Festival. Though Mostly Mozart’s “Zaide” was directed by Peter Sellars, I can pretty much guarantee that Salzburg’s out-weirded him.

“Zaide” is a “singspiel” — a German “singing play” — composed in 1779–80. It is a “Turkish” opera, much like Mozart’s “Abduction from the Seraglio,” composed in 1781–82. Like the latter opera, “Zaide” has a character named Osmin, along with a pasha (sultan, actually).

A new recording comes now from Deutsche Harmonia Mundi, and it is led by the conductor Nikolaus Harnoncourt, tireless exponent of Mozart and others. This recording is live, and Mr. Harnoncourt himself is lively, and full of commitment.

He has with him the Concentus Musicus Wien, which he founded more than half a century ago. It may be the mother of all period-instruments groups. In “Zaide,” they play grittily and usually incisively, if not with great refinement. (They’re not supposed to do refinement, really.) And, I tell you this, when they play forte, they can make a terrible racket.

Mr. Harnoncourt also has an excellent cast of singers (who use their own original instruments). When he needs a tenor, he almost always turns to Michael Schade, proving that this conductor is no dummy: Mr. Schade is a supreme singer, particularly in Mozart. And in the title role is Diana Damrau, the marvelous German soprano whose voice is an acrobat. (This is also a soprano loaded with personality, which flavors her singing.)

Another cast member of note is Florian Boesch, a baritone who sings smoothly, engagingly, and — much to be appreciated — on pitch.

The original spoken dialogue for “Zaide” was lost, so must be filled in by others. And doing the filling in for this performance is Tobias Moretti, an Austrian best known as an actor. Indeed, he does the narrating here, too.

No one would claim that “Zaide” represents Mozart at his best, but it is a Mozart opera after all, containing much music worth knowing. How could it be otherwise?

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I wonder if you like an encore album — an album of encores — as much as I do. Do you remember Alicia de Larrocha’s (all-Spanish)? It is still available, in the Decca Legends line. Encore albums usually come from pianists and singers, but the Emerson String Quartet made one too (Deutsche Grammophon), and it is diverse, distinguished, and thrilling. Anyone who says he doesn’t like short bites just may be fibbing.

The latest to make an encore album is Leif Ove Andsnes, the Norwegian pianist. Called “Horizons,” the album has 22 tracks, nicely chosen. As you might expect, Mr. Andsnes plays Scandinavian encores (Sibelius, Grieg), but also Spanish ones (Albéniz, Mompou). And there are several offbeat ones, such as George Antheil’s bracing Toccata No. 2.

As usual, Mr. Andsnes plays with clarity, logic, and some coolness. And he is clean, clean, clean — indeed, he may be our most uncluttered pianist. Sometimes you might like a speck more feeling, but Mr. Andsnes usually provides enough (barely). A Bach-Busoni chorale prelude is rendered with a measured solemnity that is just right. And how about a Shostakovich polka? It is zany, severe, off-kilter, methodical, perfect.