Soprano saxophonist Chris Jonas has played in Cecil Taylor’s large New York ensemble and William Parker’s Little Huey Creative Music Orchestra, and over the past four years he’s graduated from studying for his master’s under Anthony Braxton to working in Braxton’s groups and coconducting his recent collaboration with the Slovenian National Radio Orchestra. Like his mentors, Jonas cultivates a fluid relationship in his music between spontaneous gestures and planned ones; elaborately scored structures and dense improvisations can coexist within an album-length composition, sometimes as contrasting elements and sometimes as simultaneous events. His second disc with a band he calls the Sun Spits Cherries, The Vermilion (on Assif Tsahar and Susie Ibarra’s Hopscotch label), is representative of this approach. The music is a multilayered field of parallel, overlapping planes; Jonas, trombonists Joe Fiedler and Chris Washburne, percussionist Andrew Barker, and guest pianist Myra Melford articulate stark, angular arrangements full of contrasting textures and timbres. Jonas often uses an “entry schedule,” meaning that the components of a given piece drop in and out or change character according to a timetable, and a single musician’s role might be continually reconfigured, from foreground to background or from rhythmic to melodic. Energetic, tightly knotted solos sometimes emerge from the spaces within or between composed lines–or else suddenly appear, framed by silence, when all accompaniment falls away. Jonas has never played in Chicago, and seems bent on making up for lost time with this visit: on Sunday afternoon he’ll lead nine members of the Chicago Improvisors Group through a new piece at the Green Mill, and on Tuesday night at the Empty Bottle he’ll rejoin three of those nine–trombonist Jeb Bishop, cornetist Todd Margasak, and drummer Adam Vida–for a more intimate examination of the musical ideas developed on Sunday. Also on Tuesday, Bishop’s wonderful trio with bassist Kent Kessler and drummer Tim Mulvenna makes its return. Sunday, April 1, 2 PM, Green Mill, 4802 N. Broadway; 773-878-5552. Tuesday, April 3, 10 PM, Empty Bottle, 1035 N. Western; 773-276-3600.