The categories of Latin jazz and Afro-Cuban music are convenient fictions, a way to collect and identify a lot of great, important music. But they can also sadly limit listeners' attention to and awareness of music that has roots in those traditions but expands out in unexpected, nontraditional directions.

Take Cuban pianist Aruàn Ortiz, who has been a major figure in jazz since his arrival in America early this century. The clave is there in his playing, as he pointed out recently across a Zoom connection from Europe, where he was on tour with bassist Brad Jones and (alternately) drummers John Betsch and Jeff Ballard. But Ortiz is a true modernist; when he plays, it often becomes an opportunity to worry a succinct idea through myriad variations, or explore how many harmonic relationships he can develop out of simple material. That makes for a style of playing that is elegant, sinuous, capable of both introspection and energetic extroversion. An Ortiz solo can be a slender path like a river, or a triumphant arch, like a mountain.

"I work with the melody of rhythm a lot, like building rhythms I generated with lines, and then make them fit into an architecture of style," Ortiz says. He also looks back to his country of origin: "Of course, coming from Cuba, I have a natural approach to rhythm... but not in the way of creating patterns," he adds. That is (he explains), he does not create repeated sections as in Afro-Cuban music. Instead, it's "the way to generate a kind of language...where everything is very liquid and it could disintegrate. The elasticity of rhythm for me is very fascinating, and how you could build layers of different micro-rhythmic cells."

In a historical sense, this is classic modernism, reaching back to older ideas and using them in a new context, and when it comes to jazz and spontaneous music-making, these elements (many of which can be found in Medieval European music) become new each time Ortiz builds something with them. "When you hear all of them, you hear one or two things happening, but it's just like little cells that are one on top of another, and that is another approach to polyphony."

Ortiz' flexible and distinctive personal voice balances rhythm, melody and especially harmony, the foundation of his modernism. He learned the fundamentals from Charlie Banacos, a pianist and teacher with influential harmonic concepts that have become staples at leading jazz schools like Berklee College of Music, the New England Conservatory, and the New School; however, he has developed them in his own way.

"My creative process," he says, "let's put it this way: I've started moving away from the tonal center, and then to organize intervals. It could be based on combinations of intervals, like pitch collections. So you have a group of pitches, three or four, and I find a relation with all intervallic organizations. Then I go as far as I can to try to move through a path, and organizing it allows me to go back to the center."

He also credits pianist, composer and bandleader Muhal Richard Abrams and reed player Don Byron. The former showed him "compositional rhythm-how to combine harmony, rhythm, and melody at the same time." From the latter, with whom he made the excellent duo recording Random Dances and (A)tonalities, he learned ways to integrate his harmonic studies with the range of jazz and jazz-related traditions that Byron brings to the table.

His discography as a leader includes Live in Zurich with Jones and drummer Chad Taylor, Inside Rhythmic Falls with drummer Andrew Cyrille-who Ortiz describes as "a poet of colors" - and percussionist Mauricio Herrera, and most recently, Serranías: Sketchbook for Piano Trio, with Jones and Betsch (all albums are on the Swiss Intakt label).

Ortiz has also been an invaluable member of other groups, especially saxophonist James Brandon Lewis' Molecular Quartet, where he shows how powerful his playing can be, and also how comfortable he is playing with stacked harmonies, while always ready to choose freedom as the destination away from the center.

The pianist always plays with a sense of purpose and meaning: there's intention behind each note. His concepts may organize how an individual piece of music works, but also seem to be fundamentally a way of expressing his own voice. "I'm not looking for consonance or dissonance," he explains. "I'm looking for a release of tension. I'm looking for different parameters when I play and compose, like if you have emptiness and you can have activity, so you have something very fast, very slow.

"In a way, that creates an arc, a gesture. I work with a lot of gestures, and if I play something very atonal or dense, I tend to empty that. I create a sense that you're going somewhere, that you're moving in a sort of cycle. I always focus first on the design of it; here's how I know that the pieces are moving in the clear way. All those parameters are always present when I play-that's why I love to improvise and to ...

Three distinctive approaches to post-bop piano from Aruán Ortiz, Alexander Hawkins and Marie Krüttli

Three piano albums from Swiss label Intakt that offer three distinctive takes on post-bop freedom. Most rooted in main-stream post-bop- though highly individual nonetheless is Aruán Ortiz's Serranías. Alexander Hawkins radically recon-ceives the jazz piano trio, while Marie Krüttli offers lyrical free improvisation.

British pianist Alexander Hawkins's trio features Neil Charles (bass) and Stephen Davis (drums). It was formed in 2012, and as Bill Shoemaker's sleevenotes argue, continues to stretch the jazz piano trio's horizons. Jazz grooves predominate, but they're given abstract colourings often taken from free improv and contemporary composition. The edgy "Sarabande Celestial" is only remotely related to the stately baroque dance, with pungent lines and stabbing chords against subdued but eerie electronics. "Unlimited Growth Increases The Divide" is a slow ballad, more lyrical than dirge-like. "Fuga, The Fast One" has increasingly furious piano over a thunderous bass pedal point. "Canon Celestial" is free piano and bass against mechanically ticking drums. A stellar release.

Marie Krüttli comes from French-speaking Switzerland. She began as a classical pianist, but got interested in jazz. Transparence is her first solo album. As she explains in an online interview - Google translated from French - "Silence and space are necessary for improvised music. This allows inspiration to come to us". She cites Craig Taborn and Jason Moran as influences, but on this evidence, they're closer to jazz than she is. The Bösendorfer piano she plays is a less common choice of instrument, but she likes its warmth.

In other projects Krüttli uses electronic effects, but the textures here are purely acoustic. There are some prepara-tions on "Departure", she placed an old key in the piano, inducing shimmering and rattling effects. The sublimely slow "Exploration" is freely but lyrically ruminative, with prominent use of the sustain pedal. Throughout, the playing is open, lucid and plangent, an outstanding example of melodic free improv.

Aruán Ortiz, from Santiago de Cuba, is a leading presence in New York avant jazz, whose work has its roots in Cuban tradition. Serranías, an impressive trio album with bassist Brad Jones and veteran drummer John Betsch, marks the pianist's 50th birthday. Its Cuban toques, rumba and Afro-Haitian influences colour post-bop jazz. Montunos a kind of ostinato or vamp - are a motif.

The album highlight is a hugely exciting interpretation - or rather, deconstruction of bebop anthem "Shaw 'Nuff" by Charlie Parker and Dizzy Gillespie. The classic misterioso opening vamp is extended to three minutes, followed by a theme statement that soon lurches almost into atonality. "Memorias Del Monte" has a rapid motoric theme that becomes increasingly fragmented and free. The haunting and very slow "Lullaby For The End Times" is rather reminiscent of Charlie Haden's composition "Silence". While David Virelles is for me the most outstanding of a remarkable group of Cuban pianists - also including Gonzalo Rubalcaba, Chucho Valdés, Hilario Durán - Ortiz runs him close. A challenging and very rewarding listen.