A friend of mine, fellow jazz critic Lee Jeske, discovered in an interesting way how music exists in a cultural context. While vacationing in India a few years ago, he ran into a local music fan who was very curious about one particular point: How is it, he wanted to know, that there could be an American blues singer named Taj Mahal?

I was thinking about that recently when I watched Marion Cotillard in her Oscar-winning turn as Edith Piaf in “La Vie en Rose.” With no disrespect to the late singer, every time I hear Piaf sing her signature song, I can’t help but think how much more I enjoy Louis Armstrong’s version. To some, that would make me guilty of cultural imperialism. Not long ago, the American domination of media was hardly worthy of the term “exchange”; we send our music and films to other countries while absorbing and assimilating everyone else’s.

In early 2008, however, two new jazz releases have shown that intercultural musical give-and-take can indeed be a two-way street: producer Bob Belden’s “Miles From India” (4Q / Times Square) and trombonist Conrad Herwig’s “The Latin Side of Wayne Shorter” (Half Note Records). The latter serves as a complement to a concert at Zankel Hall this Wednesday in which the San Francisco Jazz Collective will reinterpret Mr. Shorter’s music.

Conceptually, “Miles From India” grew out of the observation that Miles Davis, in his electronics-driven experimental music of the early 1970s, created a fusion not merely of jazz and rock but of American and international music. Mr. Belden, who produced Sony’s recent compilation of this material (“The Complete On The Corner Sessions”) observed that Davis employed Indian musicians on several occasions, most famously the tabla player Badal Roy. Davis’s eclecticism inspired something of an odyssey for Mr. Belden, who has now assembled a double-CD set of compositions by and associated with the legendary trumpeter and jazz icon, as reimagined by a combination of contemporary Indian and American musicians (not least of whom is Mr. Roy himself).

If the word “fusion” had several meanings in Davis’s music, the term “crossover” can be taken to mean many more things here: Mr. Belden’s intent is to cross not only continents and cultures, but generations as well, uniting veteran players from Davis’s own groups — such as the brilliant alto saxist Gary Bartz, bassist Ron Carter, and drummer Jimmy Cobb — with contemporary players hailing from both America and India. Two key players are the saxophonist Rudresh Mahanthappa, long acknowledged as a master at playing jazz with an Indian accent, and the trumpeter Wallace Roney, who has frequently been cast as a stand-in for Davis, even by the trumpeter himself in his own lifetime.

While I was listening to “Miles From India” recently, I thought for a moment that Mr. Belden had licensed an old track of Davis and remixed it with a newly recorded ensemble backdrop when Mr. Roney soloed on “Miles Runs the Voodoo Down.” What makes the project immediately interesting is that Davis was not generally a composer who worked in recognizable song forms (like Duke Ellington) or with short, immediately identifiable melodies (like Thelonious Monk). In fact, only a few of Davis’s compositions are immediately recognizable jazz standards — two of which, “All Blues” and “So What,” originated on his 1959 album “Kind of Blue,” a fact that goes a long way toward explaining why that album is his most popular. With “Miles From India,” Mr. Belden is not merely setting recognizable tunes to new rhythms or playing them on new instruments, but readdressing the mixing and mastering process that Davis and his producer, Teo Macero (who died a few weeks ago), perfected.

Mr. Belden has recaptured the grooves and the overall feel of 11 Miles-centric works with a mostly new cast of players who speak with an entirely different accent. It feels like a modern adaptation of “Twelfth Night” or “The Tempest,” in which the characters wash ashore in an entirely new country. For instance, on Davis’s groundbreaking modal waltz “All Blues,” the sitarist, Ravi Chary, now takes both the introduction and the main melody before the two altoists, Messrs. Bartz and Mahanthappa, more or less walk off with the whole show.

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Another selection from “Miles From India,” “Spanish Key,” is an interesting choice, since Mr. Belden is adding yet a fourth language to Davis’s original mixture of jazz, rock, and Latin elements. Similarly, it could be said that on “The Latin Side of Wayne Shorter,” the trombonist-arranger Conrad Herwig is, in fact, transposing eight Wayne Shorter classics into a Spanish key. Overall, it’s a much simpler approach, yet no less meaningful than the one featured on “Miles From India.” On the Miles album, the results are so densely multilayered that they probably couldn’t be performed live, whereas “The Latin Side of Wayne Shorter” was actually recorded live at the Blue Note.

Mr. Herwig and fellow arranger (and trumpeter) Brian Lynch concentrate on some of Mr. Shorter’s more directly melodic pieces, such as “Ping Pong,” which was originally recorded by Mr. Shorter with the Jazz Messengers. On Mr. Shorter’s Argentine-styled “The Gaucho,” the group makes it even more Latin than the composer himself intended. The most thoroughly reworked tune, though, is Mr. Shorter’s most famous, “Footprints,” which has been taken out of 6/4 time and restructured according to dance rhythms that make said footprints sound like part of the instruction chart for a lesson in mambo or samba.

Even though the idea of “Miles From India” is weighed down with concept and theory, it’s still essentially highly musical, swinging, and fun, and even though “The Latin Side of Wayne Shorter” is driven by a much simpler idea, it’s no less intellectually satisfying. Both are more than enough to warm my old, culturally imperialistic heart.

wfriedwald@nysun.com