It’s not enough to make list after list. The Turning the Tables project seeks to suggest alternatives to the traditional popular music canon, and to do more than that, too: to stimulate conversation about how hierarchies emerge and endure. This year, Turning the Tables considers how women and non-binary artists are shaping music in our moment, from the pop mainstream to the sinecures of jazz and contemporary classical music. Our list of the 200 Greatest Songs By Women+ offers a soundtrack to a new century. This series of essays takes on another task.

The 25 arguments writers make in these pieces challenge the usual definitions of influence. Some rethink the building legacies of popular artists; others celebrate those who create within subcultures, their innovations rippling outward over time. As always, women forge new pathways in sound; today, they also make waves under the surface of culture by confronting, in their music, the increased fluidity of “woman” itself. What is a woman? It’s a timeless question on the surface, but one deeply engaged with whatever historical moment in which it is asked. Our 25 Most Influential Women Musicians of the 21st Century illuminate its complexities. —Ann Powers

Classical music has a gatekeeping problem, and much of that can be traced through the word “great.”

I don’t mean great as in “that was great,” the kind of thing you’d say as you walk out of the concert and pull out your phone to find somewhere for post-concert cocktails on Yelp. I mean Great as in Great Composers, the set of dead white guys whose Great Works manspread across the programming of most symphony orchestras, opera companies and other classical music-presenting institutions in the country that don’t exclusively focus on new music.

Don’t get me wrong. Most of these works are in the canon because they are actually pretty great. They’ve been fascinating us, pulling our heartstrings and making us hum along for centuries. But if the major selling point of classical music is how objectively Great it is or how Great the composers are, Greatness becomes insidious: effectively meaningless, but unchangeable, almost impossible to fight. Being sold Greatness is now what audiences expect. It belongs only to the past, so it’s antithetical to welcoming or nurturing composers and listeners of the present and future, especially if they don’t buy into that lineage of Greatness.

Missy Mazzoli, 38, is trying to tear down the gates for new composers and listeners. She’s a prominent figure in new music; she has three operas to her name with librettist Royce Vavrek, including the vicious Breaking the Waves — an adaptation of the controversial 1996 Lars von Trier film — and the dry, spooky Proving Up, based on Karen Russell’s ghost story set on the 19th-century prairie. Her work engages with stories about human beings and the oft-fraught relationships between them. None of her main characters is someone you would aspire to be or, conversely, an irredeemable monster (except one, in Proving Up, who actually is a monster). But all are complex and fully realized. In the case of Breaking the Waves, Mazzoli’s act of adapting a story hinging on a woman’s trauma feels especially prescient in a time when it’s still common for such stories to be told by all-male creative teams.

Her resumé also includes a handful of composer residencies with institutions like the Chicago Symphony Orchestra and the forward-thinking Opera Philadelphia, and two heady recordings with her all-female band Victoire, which she assembled to perform her own music.

“Band” isn’t a word that typically applies to classical ensembles, but it’s really the only accurate descriptor of Victoire, in which Mazzoli plays keyboards. Anything else would be slapping a label on it that doesn’t fit. Its second album of Mazzoli’s music, Vespers for a New Dark Age, turns poems by contemporary poet Matthew Zapruder into searing songs of secular prayer, with propulsive drumming by Wilco’s Glenn Kotche and production by Victoire member and synth wizard Lorna Dune. It feels like it belongs to no genre and many genres at once. It’s been called everything from “ravishing, unsettling…from the chamber-operatic to the electronic and semiabstract” to “an engrossing classical-electronic-vocal epic” to a “suite for singers, chamber ensemble and electronics” — that last clear-cut description nonetheless makes it sound drier and less friendly than it is. When I try to think of what to call it, anything I come up with either sounds too generic or detracts from the simplicity I hear in its core. But it moves; it’s old, new, borrowed and blue. I’d play it for people who would never go to a classical concert.