Williams has had some bad years. She said 2008 was so rough for Paramore, she later chose not to move into a house with those numbers in the address. She called 2015 “the worst year. And I’m pretty sure we won a Grammy that year.” (It was best rock song, for “Ain’t It Fun,” and it sits on a shelf in her living room next to a stack of Shel Silverstein books.)

That was the year Williams briefly quit Paramore — privately, not publicly — leaving the guitarist Taylor York as the only member. The band’s entire career has been marked by a series of high-drama lineup changes that kept the group in gossip columns, as fans argued over the shifts and whether it mattered that Williams is technically the only member with her name on the Atlantic contract. Because she was initially recruited to the label alone and insisted on playing in her band, anxieties about what it would mean to “go solo” were particularly pointed.

The year 2015 was also when Williams put her engagement on hold. Her tumultuous near decade with the New Found Glory guitarist Chad Gilbert ended in 2017, the year after they married. Paramore stayed on the road until the following September, and Williams’s first few months back home were some of her darkest.

When she returned from the therapy retreat, her vital, beloved grandmother fell and suffered a head injury that permanently affected her memory. A distraught Williams sat down with Paramore’s touring bassist Joey Howard and wrote “Leave It Alone,” about the inevitability of loss. (They went on to write seven more “Petals” songs together.) She’d spent a bunch of money setting up Pro Tools and a recording rig and planned to learn to produce her own music to pass the time, but gravitated instead to York’s home studio.

York, 30, one of the childhood friends who has been a bedrock of Paramore since 2007 and helped the band’s sound evolve, became her “Petals” co-pilot and producer, sculpting an aesthetic far from the group’s crunchy guitars and the bouncy new wave of “After Laughter.” Taking their place were intricate and ominous layers, neck-snapping funk, dizzying industrial electro, glitter-pop reveries. Williams’s glorious, flexible voice, which sometimes strains to be heard atop her band, is in the foreground.