Was it Buddha — or Grasshopper on “Kung Fu” — who said, “It is a poor teacher whose pupils do not surpass him”? I wouldn’t go so far as to say that Mark Murphy, who is certainly the most celebrated teacher of the art of singing jazz, has been outdone by his illustrious student, Kurt Elling — nothing like it. Rather, the disciple (who turns 40 this fall) has perfected his own thing, which is as valid and wonderful as anything that he has gleaned from his inspirations, while, at the same time, the master (who turned 75 on Wednesday) is still the master.

As it happens, both Messrs. Murphy and Elling have new albums out: Mr. Murphy’s “Love Is What Stays” was just released by Verve in Germany (an American release is likely) and Mr. Elling’s “Night Moves” was released by Concord. Mr. Murphy is currently celebrating his birthday and launching the “Sing Into Spring Festival” this week at Dizzy’s at Jazz at Lincoln Center (which continues until April 16), and Mr. Elling did a week at the Blue Note last month.

As a teacher, Mr. Murphy’s primary lesson is not “do what I do,” but rather, “find your own way into the music and be yourself.” Even had he never taught a single lesson directly, he has shown several generations of younger artists what to do by inspiration. Mr. Murphy is the founding father of today’s gender-crossing eclectics and experimentalists (for example, one of the ballad highlights of the new set is a song by Johnny Cash). Mr. Murphy was among the first to show that jazz singing does not begin with a melody and a set of chord changes but rather with a set of possibilities.

What this native New Yorker has done lately is get all international on us: His quartet at DCCC is a veritable United Nations, starting with the excellent young Russian pianist Misha Piatigorsky, the Austrian bassist Hans Glawischnig, the Cuban drummer Ernesto Simpson, and the Israeli percussionist Gilad. He is singing a lot of Brazilian music at Dizzy’s (Gillespie, the founder of Latin jazz, would have doubtless approved); with two show-stopping percussionists such as Messrs. Simpson and Gilad on the bandstand, it would be a waste not to. Even some of the American standards that he includes are reconfigured in the bossa beat — like his fast samba version of “You Go to My Head” (partly inspired, one imagines, by Judy Garland’s cha-cha-cha treatment from Carnegie Hall). Mr. Murphy, thankfully, is well aware that there are other bossas beyond the short list of very-overdone hits by Carlos Jobim, such as Ivan Lins’s irresistibly rhythmic “Madalena,” and the gently seductive “Bolero de Sata,” which he learned from Ellis Regina (the latter is represented by a video of Mr. Murphy on YouTube).

His standout ballad at Dizzy’s at the late show Tuesday was a stunning, Miles Davis-influenced reading of “Once Upon A Summertime,” which he makes sound less waltzy and minor than the way Michel Legrand wrote it. Mr. Murphy has apparently decided that club gigs are perfect for up-tempo, party-type numbers, particularly bossas and montunos, but albums, contrastingly, are a better bet for slow introspective love songs. The climax of the new CD is a devastatingly reflective “Did I Ever Really Live,” with lyrics by the funnyman Allan Sherman. Another ballad highlight at Dizzy’s is “Like a Lover”; coincidentally, in her show at the Café Carlyle on the opposite side of Central Park, Jane Monheit is also singing this Dori Caymi-Alan and Marilyn Bergman collaboration. While she renders the melody beautifully, it’s Mr. Murphy who really makes us believe that the velvet moon could somehow share your pillow or that the river wind could actually sigh and ripple its fingers through your hair. Or even my hair, and I’m as bald as an eagle.

Mr. Elling also includes some Brazilian rhythms on “Night Moves,” as on his original “And We Will Fly,” and intermingled in one of two Sinatra-specific medleys, “If You Never Come to Me” and “Change Partners,” both titles being from the classic 1967 Sinatra-Jobim album. He also weaves a new lyric to Keith Jarrett’s “Leaving Again” into the Blue Eyes signature “In The Wee Small Hours” and, finally, returns to Cole Porter in “Well Did You Evah?” a bonus track in which Mr. Elling and fellow funster John Pizzarelli joshingly update the Sinatra-Bing Crosby duet from “High Society.” Mr. Elling casually tosses two classic ballad solos by Dexter Gordon into the mix on “Where Are You?” and “Body And Soul.” Yet the comparatively young singer has arrived, in his own way, at the realization that pure eclecticism is not an end unto itself. In his six Blue Note albums (1995—2003), Mr. Elling often seemed to be frantically moving in every direction at once, and even though he stirs an eclectic brew here, the overall result is much more tightly focused.

Still, the most moving performance here is a classic Elling mashup; where Mr. Murphy is international, Mr. Elling is inspirational. He starts with the Duke Ellington gem, “I Like the Sunrise,” which was written as an epilogue to the 1949 “The Liberian Suite,” an optimistic work predicting a bright future for the African-American people. Mr. Elling has retooled “Sunrise” as a prayer, expanding the purview to include all of humanity — especially those who make music and art. To achieve this, he has thrown in a set of variations from another of his heroes, the Chicago tenor legend Von Freeman (though without replicating Mr. Freeman’s distinctive and occasionally flat intonation), to which he has added lyrics adapted from the medieval Islamic poet Rumi. The connection between the three is one that only Mr. Elling could have made.

Mr. Elling is perhaps the first to realize that both Rumi and Ellington, in surprisingly similar ways, both made the point that music is a key element in one’s personal relationship with God — and that art is a way of achieving a higher spiritual consciousness. But then, obviously, Mr. Murphy has known that all along.

Until March 18 (33 W. 60th St. at Broadway, 212-258-9800).