Every great music festival has a few of those moments. If you’re a music lover, you know them well. You desperately want to catch two — maybe even three or four — spectacular billings at the same time, on different stages.

But since humans haven’t yet cracked on-the-spot mitosis, one has to make tough decisions about whom to catch, when, and for how long. The Hyde Park Jazz Festival is replete with these small agonies, which says a lot about its primo programming. This year’s festival, running Sept.

28-29, welcomes trumpeter Ambrose Akinmusire (11 p.m. Sept.

28 at Rockefeller Memorial Chapel), saxophonist Immanuel Wilkins (7:15 p.m. Sept.

28 at Logan Center Performance Hall), pianist Craig Taborn (in a trio with cellist Tomeka Reid and drummer Ches Smith , 5:15 p.m. Sept.

28 at Logan Center Performance Hall), a Billy Higgins tribute by drummer Willie Jones III and trumpeter Jeremy Pelt (8 p.m. Sept.

28 at the Wagner Stage on the Midway) and nearly 30 other acts. It all sprawls across a setting overflowing with jazz history. Hyde Park, as well as surrounding Woodlawn, Kenwood, Bronzeville, Washington Park and Englewood, were crucibles for the genre, from big band stages that welcomed Louis Armstrong to the ongoing sonic forays of the Association for the Advancement of Creative Musicians and Sun Ra Arkestra.

“The beauty of programming a festival here is that there are so many trajectories embedded in the history of this music that have emanated from the South Side,�.