According to the voluminous notes her label sent to critics, the cast of characters on Tori Amos’s new album includes “Santa (SanaTORIum),” who is “sexual but not at all interested in vulgarity”; “Clyde (CliTORIdes),” an artist who “appreciates beauty and the story within”; “Pip (ExpiraTORIal),” who “has close ties to a CIA analyst”; and plain old “Tori (Terra–TORIes),” whose “name suggests there are many Toris and with this group of women she allows them all to come in and help her explore her many identities.” In other words: Women’s studies majors, start your senior theses.

Only Amos could come up with a record this maddeningly self–important, this wigged out — and this good. For 15 years, she’s explored lust, love, motherhood, sexual violence and other heady topics with an infuriating mix of lyrical abstruseness, New Age mysticism and pure artsy–fartsy pretension. And time and again, her ingenious music has carried the day. If you wish, you can ponder the runes of this latest concept album. (Quoth the press release: “American Doll Posse is the dismembered feminine re–membered.”) Or you can luxuriate in its riches: bruising hard–rock stomps (“Body and Soul,” “Teenage Hustling”), lush, syncopated ballads (“Beauty of Speed”), skittering gypsy jazz (“Velvet Revolution”).

Texturally, it’s a middle ground between her searing early album Under the Pink and the sun–dappled 2005 The Beekeeper. Songs like “Big Wheel” no longer rely on the eccentric dynamic shifts that sometimes felt imposed on earlier songs. But some things haven’t changed: Amos remains one of pop’s most dedicated, and scariest, sexual provocateurs, a fierce fighter in the battle of the sexes, whose come–ons (“I am a M–I–L–F, don’ you forget”) usually sound like threats. Whether or not this album re–members the dismembered fem­inine, one thing’s for sure. Tori — and Santa, Clyde and Pip — are not broads you should mess with.

Download: “Girl Disappearing,” “Big Wheel”