More than just sonic shards exploding in your face, free jazz can be intricate yet mellow, graced with not just ferocity but also shifting, nuanced light and shadow. Even its hallmark jagged lines, angular rhythms and dissonant harmonies can be balanced with delicate phrasing and, yes, lovely passages drenched in kaleidoscopic colors, patterns and textures. At least it can be all these things and more in the challenging, abstract sonic world created by Kris Davis, a 27-year-old, New York-based pianist/composer and her tightly interactive quartet, which plays Friday at 8:30 and 10 p.m. at Firehouse 12, New Haven’s haven for progressive music. Backed by her working band of five years, Davis will be accompanied by tenor saxophonist Tony Malaby, bassist Eivind Opsvik and drummer Jeff Davis, her husband. A native of Vancouver, Canada, Davis studied classical piano through the Royal Conservatory of Music and received her bachelor’s degree from the University of Toronto before relocating to New York City and studying composition with the prominent pianist/composer Jim McNeely. As an indication of her open-ended approach to composition and improvisation, Davis cites multiple influences from both jazz and classical music. These range from Thelonious Monk and Paul Bley (a fellow experimental, Canadian-born pianist/composer) to the Hungarian composer Gyorgy Ligeti (including his innovative use of shifting blocks of sound and tone color) to the exquisite, enigmatic piano music of the Russian composer, pianist and mystic, Aleksandr Scriabin. On her most recent and second CD, “The Slightest Shift” (Fresh Sound New Talent), she and her three regular collaborators (the same contingent as the Firehouse 12 date) engage in tightly interactive musical conversation. Her debut album, “Life Span,” was released in 2004, also on Fresh Sound. Abstract but spirited, the quartet’s running conversation-sometimes rooted in two, three or four overlapping voices-explores a wide range of colors, textures and emotional moods from turbulence to serenity. Critic Ben Waltzer best sums up Davis’s fundamental aesthetic as being “jargon free improvising, and a harmonic approach that reached beyond boundaries without sacrificing coherence.” More than merely just loathing jargon, Davis strives for creating bold new directions that have an inherent logic all their own. Or as she explains while speaking of what she learned from studying with a great mentor like McNeely: “We worked a lot on exercises in which voice-leading determined the chord qualities in a given progression, rather than say, using stock chord progressions as a basis for improvisation. Basically, he helped me think in less predictable ways,” she says. Among her new album’s eight original pieces, “35 Cents” is, quite typically, rooted in conversation that builds momentum like a locomotive, even sometimes reeling on its tracks with tricky Ornette Coleman-like twists and turns. Saxophone and piano continuously complement each other by commenting on and expanding on what the other says. Davis’s “Morning Stretches” is mournful and mysterious, its brooding, almost requiem-like mood underscored by the bowed bass parts. “Jack’s Song” sounds soft and refined, almost as if you’re overhearing other voices from other rooms, a nice contrasting element of delicacy among the current of edgy, free-flowing lines. Throughout, there’s a continuous stream of statement and counterstatement, a synthesis of thesis and antithesis yielding an extemporaneous meeting of the minds generating surprising results. And the four-way conversations are expressed in a language rooted in a different sort of syntax in which even punctuation marks don’t fall where you might think they would. Obviously, Davis more than achieves her stated goal of unpredictability. At the same time, however, she quite mercifully avoids the elitist pitfalls and pratfalls of making music so archly arcane that only other like-minded musicians could bear listening to it.