Good things come in threes.

Fred Hersch Trio: Live in Europe (Palmetto)

Brad Mehldau Trio: Seymour Reads the Constitution! (Nonesuch)

Bill McHenry Trio: Ben Estrada La Nit (Fresh Sound/New Talent)

By Steve Feeney

Though each disc has a single designated leader, three new jazz releases tap into the magic of equilateral improvisation.

Fred Hersch has maintained his place as one of the top pianists in jazz for a very long time. He has called Live in Europe, his latest release, “the best trio recording we’ve yet made.” I wouldn’t argue with that, although his earlier work provides strong competition.

Bassist John Hebert and drummer Eric McPherson, both of whom have been with the 62-year-old pianist for nearly a decade, complete the unit.

At least half the tunes on this new disc have been recorded by Hersch in various settings over the years. Like Bill Evans, who I can’t help but think of when listening to Hersch, he always digs ever deeper into his repertoire to discover new veins of inspiration.

Two Wayne Shorter tunes, which the pianist has been performing in tandem since at least 2003 (see Live at the Village Vanguard), are state-of-the art studies in advanced interplay. “Miyako” floats on a harmonic wave of gentle counterpoint, with Hersch’ s left and right hands telling each other the story of the lovely young girl (Shorter’s daughter) of the title. Hebert and McPherson are not only there for support, but expand on the unfolding variations; they bring a complicating dramatic engagement to what is minimal thematic material.

As “Miyako” drifts to its end, McPherson almost immediately begins to solo on the uptempo “Black Nile.” Hersch and Hebert sound the catchy theme and take it on a rhythmic walk along the banks of a post-bop river. Hersch’s solo supplys a series of mature variations born of living with the tune for quite a spell. When the threesome hit the final statement of the head, the inclination (at least of this listener) is to quickly punch the replay button. There’s obviously a lot more to discover in this zesty performance.

A pair of Thelonious Monk tunes bookend the disc: “We See” ambles along with playfully updated complications, though the original is never lost sight of. Hersch’s solo performance of “Blue Monk” has him embellishing the tune with plenty of historical references as well as a pure exuberance of spirit that both pianists share.

Three new Hersch compositions are dedications. “Bristol Fog (for John Taylor)” evokes the late British pianist’s impeccable touch, but in a melancholy key — the piece is suggestive of times long gone but remembered. Hebert is given some solo space here, and he refracts the melody in such a way that Hersch’s reentry into the piece is trampolined into more elevated realms.

“Newklypso” honors Sonny Rollins with a visit to the saxophonist’s classic musical excursions into the Caribbean. McPherson syncopates the pianist’s dance-inspired turns before taking a solo that further breaks down rhythmic standardization. Writer Tom Piazza is honored with “The Big Easy,” a bluesy reverie that reminds me of the gently deconstructive work of Hersch’s former student Brad Mehldau.

Since leaving the tutelage of Hersch, the 47-year-old Mehldau has done his bit to revitalize the traditional piano/bass/drums trio format by incorporating strains of late minimalism and post-Beatles pop. His distinctive work often evinces a loose, fugue-like churn supported by a relentless rumble from his longstanding bandmates Larry Grenadier on bass and Jeff Ballard on drums.

Mehldau’s latest, the provocatively titled Seymour Reads the Constitution!, features all of the above ingredients. And it is his best album in a while.

The title piece, a Mehldau original, suggests a vision of a hapless character trying to catch up on his law studies as he strolls along a lonely path. The melody generates a genial irony, assisted by the repetition of Grenadier and Ballard, who give the piece a familiar Mehldau Trio lope. The pianist offers enough variations to suggest that Seymour’s journey may be sad, perhaps pathetic, but not futile.

Paul McCartney’s “Great Day,” as might be expected, is more upbeat, with Ballard incessantly tapping out a quick beat. Grenadier’s solo is playfully funky, and the leader’s re-entry sets up an infectious swirl, a sonic signature of this band.

Brian Wilson’s “Friends” waltzes along nicely, a fine exercise in amiable charm. Mehldau’s right hand sticks to the dance melody, adding just a frill or two, while a brushes-to-sticks solo by Ballard adds welcome comment.

Mehldau’s ambitious “Ten Tune” possesses the relentless, formal rigor of chamber jazz. A lurching tempo makes way for an extended, rhapsodic solo from the leader.

Finally, a newly minted trio is out with a disc entitled Ben Entrada La Nit. The album sports the advantage of having two of its three members hail from my home state of Maine, though they’ve gone on to traverse the planet.

Led by tenor saxophonist Bill McHenry, a Blue Hill native, and featuring Machias’ own RJ Miller on drums, the formidable Bill McHenry Trio is completed by Eric Revis, one of the best upright bass players in circulation (hear any of his own recent discs for ample proof).

The tenor sax/bass/drums configuration inevitably calls to mind the epochal trio recordings of Sonny Rollins from over a half-century ago. The reference is more than apt because the 46-year-old McHenry, though a cooler head than Rollins, knows (and can exercise) the power of the big horn.

Reportedly, these 2015 recordings (three live cuts and four in studio, all recorded in Spain) represent the first time these three had played together. You can hear whiffs  of that uncertainty, but you can also hear a good amount of unvarnished, in the moment, jazz. Five tunes by the leader, one by Revis, and one classic make for a heady program.

McHenry’s title tune introduces his slightly flat, dry tone. You almost feel as if you are in touch with the interior contours of his horn as he works, methodically, through langourous phrasing on his way to generating some extraordinary moments.

About halfway through the 13-minute-plus track, the saxophonist takes off on a Coltrane-esque flight that rockets into pure expressiveness. The segment passes far too quickly. But the effect is riveting enough to convince any skeptics of the man’s range. McHenry definitely ought to step in from the chill more often.

Revis audibly scats along throughout the performance and adds a thick and rich solo, while Miller taps and shuffles behind the proceedings before he contributes his own, delightfully energized, solo.

Revis’ tune “The Elephant” starts off with an ostinato and a bit of vocal communication among the players. This is unquestionably a tune that is still evolving.  Mysterious clatter from Miller sets the stage for the leader to enter a modal realm where one in invited to imagine large, soulful animals are wandering the endless plain.

The bassist walks along on McHenry’s post-bop-ish “John Daniel,” another Rollins reference point to these ears. And the threesome finishes with gentle lyricism on the classic “Mean to Me,” Miller’s brushes propelling the take-off for a reflective flight home.

Much of Ben Entrada La Nit seems to be about three guys enjoying creating pleasant moments, but the players go well beyond that when, as with the Hersch and Mehldau units, they create spellbindingly warm and inviting triangular spaces.

Steve Feeney is a Maine native and attended schools in Maine, New Hampshire and Massachusetts. He has a Master of Arts Degree in American and New England Studies from the University of Southern Maine. He began reviewing music on a freelance basis for the Portland Press Herald/Maine Sunday Telegram in 1995. He was later asked to also review theater and dance. Recently, he has added BroadwayWorld.com as an outlet and is pleased to now contribute to Arts Fuse.