It feels surreal to interview Billy Corgan in a Chicago bar where a handful of ‘90s groups like Nirvana, Weezer and, yes, his own Smashing Pumpkins, are sprinkled into the mix of current indie rock playing on the jukebox.

It’s a backdrop reminder of the legacy Corgan has been wrestling since the early chapters of Smashing Pumpkins ended almost 15 years ago with the bitter disbanding of the band’s original lineup. Anyone who has followed all the ensuing twists in Corgan’s career--and he’ll be the first to tell you that few fans have--knows that Smashing Pumpkins never stopped being a vehicle for the frontman’s output.

On Tuesday the band releases a new album, “Monuments to an Elegy.” It’s the latest installment in a music cycle titled “Teargarden By Kaleidyscope,” which is expected to conclude next year with the release of another album.

All that might sound impenetrable to someone whose knowledge of the band doesn’t go much deeper than “Mellon Collie and the Infinite Sadness” (which recently got a deluxe reissue, along with the group’s other ‘90s albums). So, the bottom line on “Monuments” is that it’s Corgan’s most direct collection of songs in years. Hazy pop and flashes of prog rock fold into a signature Smashing Pumpkins sound, including throbbing waves of aggressive guitars and the nasal cry of Corgan’s vocals.

On the day before Thanksgiving, in the bar near a theater where he would later play a sold-out show, Corgan drank iced tea as he talked about his new music, the book he’s writing, and his unlikely bro-ship with Mötley Crüe’s Tommy Lee, who played drums on “Monuments to an Elegy.”