The big bands may never have died, but the jump bands–those smaller, looser, roadhouse-rockin’ groups that presaged the advent of rhythm and blues–certainly did. Except for Louis Jordan, the Savoy Sultans, and one or two others, the jump bands were obsolete by the early 50s. So the modern presence of the Cheathams’ little big band, which is based in San Diego, is all the more surprising–as is its recent commercial success. Jimmy plays the bass trombone, Jeannie sings from her seat at the piano, and the music sits steady in the middle of jazz, blues, and soul; best of all, the band includes some certifiable jazz legends. (Most notable are Red Callendar, the Los Angeles bassist who tutored the young Charles Mingus, and the female trumpeter Clora Bryant.) Later this summer, Joe Segal plans to bring in Jay McShann, perhaps the last authentic Kansas City bandleader–but McShann hasn’t led anything much larger than a trio for about 40 years. If he did, chances are it would sound a good deal like the Sweet Baby Blues Band, which has the determination and the right people to make the Showcase jump like KayCee used to. Tonight through Sunday, Joe Segal’s Jazz Showcase, Blackstone Hotel, 636 S. Michigan; 427-4300.