The idiosyncratic voicings and subtly shaded chords of Chicago guitarist Dave Onderdonk don’t pulsate off the bandstand–at least not like the emotionally charged, vocally inflected melodies of local guitar heroes such as John McLean and Bobby Broom. So despite the fact that he’s been playing in town longer than either McLean or Broom, Onderdonk remains less well-known to the jazz public. I find it more telling, though, that other Chicago musicians–from bassist Ken Haebich and saxist Jim Gailloreto, who host a weekly anything-goes collaboration called the Ken & Jim Show, to vocalist Kurt Elling and guitarist Fareed Haque–so often call on Onderdonk to supply his jazz-folk textures, rhythmic bite, and specifically guitaristic lyricism to their own projects. Avoiding the hornlike, melismatic melodies favored by so many players, he phrases his solos to emphasize the gracefully percussive character of a plucked string–and even his single-note lines manifest the impressive harmonic knowledge at his fingertips. Equally at home on classical and steel-string guitars, Onderdonk brings the personality of those acoustic instruments to his occasional turn on an electric. (The best document of his technique is a mid-90s Southport album, Loose Contact, with drummer Mark Walker.) Onderdonk writes some great tunes too, but because he rarely leads a band, they rarely find a stage. He’ll rectify that situation this Sunday afternoon, when he plays a set of his own music with an excellent trio comprising bassist Larry Kohut and drummer Tim Davis–part of the second concert presented by the newly formed Chicago Jazz Composers Collective. The brainchild of vibist Kathy Kelly, the CJCC hopes to provide a regular showcase for new music by the city’s less outre improvisers; Kelly’s own quintet plays the second half of this month’s show. Sunday, December 16, 2 PM, Green Mill, 4802 N. Broadway; 773-878-5552.