Saturday night at Zeitgeist Gallery in Inman Square, saxophonist Joe Giardullo and multi-instrumentalist Joe McPhee continued a musical dialogue they’ve been conducting for more than 12 years. They’ve released one duet album, Specific Gravity (Boxholder), and they share woodwind duties on releases by Giardullo’s quartet and McPhee’s two-horns/two-basses Bluette. Giardullo’s hard, bright tone and sharp analytical approach contrasts with McPhee’s darker, fatter sonority and more sensual, even lyrical, style. But their rapport and common sense of development allows them to blend their sounds and styles into some of the most unified free improvisation around these days.

Giardullo, who played soprano sax all night, began with quick little pecked notes that McPhee accompanied with taps on the mouthpiece of his flügelhorn. Giardullo’s spare notes elongated into continuous tones, then broke apart into keypad taps as McPhee began a series of broad, airy sounds that evolved into floating melody. These complementary textures set the tone for the four improvisations that made up their set.

McPhee’s switch to soprano underlined their rapport. He laid out a deep-pile carpet of long tones down which Giardullo sent prancing staccato notes; they swept up into high, mournful sounds that suggested the weeping of birds; they layered sounds that billowed like clouds and wrapped their lines together like coiling plant tendrils. Throughout, they displayed an uncanny knack for simultaneously changing direction. Each passage had such a discernible beginning, middle, and end that the music resembled a continuous series of individual compositions more than one long improvisation.

They incorporated some jazz standards into the last two pieces. The third number featured a series of allusions to and variations on Monk’s "Evidence." McPhee opened the final offering with a beautiful rendition of Ellington’s "Come Sunday"; that gave way to a tumultuous Giardullo solo and a concluding duet that blended the melody with free improvisation. This ability to meld contrasting aspects of jazz and improvised music was the hallmark of the performance.

The opening duo of pianist Steve Lantner and cellist Dan Levin combined modern classical and free-jazz elements into graceful, cliché-free improvisations.