It’s not all about Boston Calling this weekend, though that makes up the bulk of local concert action. There’s even a Gillette Stadium show on Friday with English singer-songwriter Ed Sheeran, charming his largely age 15-25 demographic with his brave solo tour-de-force that incorporates vocal and guitar looping.  Not so unusual, but certainly so for a stadium setting. Madonna hits the opposite end of the spectrum, as the matured Material Girl (above) brings her army of nattily attired dancers and musicians to TD Garden on Saturday. Her lavish Rebel Heart tour includes a cross-shaped ramp on the floor, a fair share of pole dancing, 2.5 million Swarovski crystals on Madonna’s costumes alone, and a mix of hits and rarities.

Boston Calling nonetheless kicks in on City Hall Plaza with beautiful fall weather, starting Friday night with a pleasant pairing of Icelandic folk-pop band Of Monsters and Men and spirited folk-rockers the Avett Brothers.  Saturday looks most interesting during the late afternoon with a stretch of ironic jammer Stephen Malkmus & the Jicks (who also play the Sinclair on Friday), smooth country outlaw Sturgill Simpson and sardonic folk-rock chameleon Father John Misty (who just covered Ryan Adams’ take on Taylor Swift’s 1989, but in the style of the Velvet Underground). Saturday night gets more electronic with Chromeo and Chvrches before alt-J faces the sprawling plaza. I like alt-J’s oblique trip-pop on record but have found their shows a bit underwhelming. Still, it won’t hurt to expand the British band’s light show to the kaleidoscopic designs that grace the face of City Hall to make Boston Calling a cool experience at night. Along those lines, Boston Calling finally closes with a bang on Sunday thanks to the last trifecta of folky English dark horse Ben Howard, Irish folk-rock darling Hozier and soulful rockers Alabama Shakes, fronted by the dynamic Brittany Howard. Again, that alone stands as a great concert bill. You can jump to my recent chat with Shakes drummer Steve Johnson. And here are BC set times.

If jazz is more your style, there’s also the Beantown Jazz Festival, making a free multi-stage street fair out of Columbus Avenue on Saturday afternoon, with a range of acts including R&B singer Ledisi, saxophonist Javon Jackson with drummer Jimmy Cobb (who played on Miles Davis’ iconic Kind of Blue) and the Mosaic Project led by Grammy-winning drummer and Beantown artistic director Teri Lyne Carrington. Here’s the Beantown Jazz schedule. And up in Newbury, Buffalo Tom also caps Saturday afternoon at the American Music and Harvest Festival at Spencer-Peirce-Little Farm. On the folk singer-songwriter side, Greg Brown plays Somerville’s Arts at the Armory on Saturday, while Peter Mulvey returns to his old stomping grounds on Sunday with a free 12-hour concert on the street outside Club Passim in Harvard Square, from 9 a.m. to 9 p.m., with a 15-minute break every hour. And Canadian post-rock ensemble Godspeed You! Black Emperor gets darkly cinematic on Sunday at the Paradise Rock Club.

Looking ahead into next week, my top picks would be soul-folk vocalist Lianne La Havas at Royale on Monday and textural guitar-rockers Built to Spill at Brighton Music Hall for a three-night stand starting Tuesday.