Joan Armatrading isn’t the household name she deserves to be (at least, not in the U.S.), but her sweepingly idiosyncratic melodies and personal lyrics bear the markings of a true original. At its best, Armatrading’s work leaves us just a bit off guard, rooting our senses in the familiar pop/R&B base she has always favored while confronting us with the strange and unknowable. Much of her continuing appeal lies in the feeling that we’ve never quite figured her out; and, while we may not like everything she does, invariably we keep listening.

Without question this is true of Into the Blues, Armatrading’s first album of new material since 2003’s Lovers Speak. It opens with “A Woman in Love,” an odd, synth-driven churner that has every reason to sound dated but somehow, through its overarching musicality, doesn’t. The puckish “Secular Songs,” in which Armatrading imagines a church where congregants sing “French love songs,” is hauntingly beautiful, while “Into the Blues” balances tough piano and sweet Caribbean-influenced choruses to magnificent effect. “Mama Papa,” in which the St. Kitts native recalls her loving upbringing in the U.K., offsets the disc’s brasher moments with tender sincerity.

Armatrading is famously private, dodging any questions that threaten to approach her romantic life, but the playful “Liza” will give fans lots to ponder. We haven’t had much opportunity (have we had any?) to hear a female-to-female romantic song in contemporary blues, and Armatrading’s incorporation of a classic guitar shuffle only reminds us that blues, like any other music, is a living, changeable presence, open to reinvention. True to form, this singular artist upholds conventions while challenging them: It’s the kind of blues album only Joan Armatrading could make.

Hopefully Armatrading will spotlight portions of Into the Blues, along with classic older numbers (“Down to Zero,” “Love and Affection”), during her appearance Tuesday evening at the World Financial Plaza, part of the excellent (and free) River to River Festival. It’s a rare opportunity to experience this inventive performer in the kind of warm, atmospheric environment she deserves.

June 12, River to River Festival, WFC Plaza, Battery Park City, 7, free.