Welcome to “The Month in Live Jazz,” a column highlighting five outstanding performances from the past month on stages across New York City.

Honoring an Icon

‘TRIBUTE TO GERI ALLEN’ Tishman Auditorium at the New School, Jan. 15

Geri Allen, who died last year, was one of jazz’s great sense-makers of the past 35 years — a splintered and confusing time in the music, by any account. But she will be remembered mostly for her luminescent attack as a pianist, her way of guiding a band, and pushing it toward a breakthrough.

To open this tribute concert, a video of Allen performing played on a screen high above the stage, and slowly, the pianist Craig Taborn joined in, offering scattered, bright-hued flights in duet with the recording. He is one of the major inheritors of Allen’s influence, a player who can be abstract and rhythmic and crisp all at once. His playing implied what the rest of the evening guaranteed: that Allen’s impact will continue to ripple throughout almost every pocket of the jazz world.

Organized by the drummer Terri Lyne Carrington and presented as part of Winter Jazzfest, this concert was not a simple rehashing of Allen’s repertoire. A quartet featuring Ms. Carrington, the alto saxophonist Tia Fuller, the pianist Kris Davis and the bassist Linda May Han Oh played a sharp but untethered rendition of “Miss Ann,” by Eric Dolphy, who was the subject of Allen’s master’s thesis. Later, the TEN Trio — Ms. Carrington, the bassist Esperanza Spalding and the trumpeter and pianist Nicholas Payton — played two tunes with a tightly wound urgency, the driving “RTG” and the spacious “Unconditional Love.” Ms. Carrington and Ms. Spalding used to play with Allen; after her death, they joined with Mr. Payton. The new trio has quickly developed a rapport, and its performance was a highlight.