I began listening to the singer and songwriter Valerie June last fall, at a time when the relentlessness of the Presidential campaign season was pushing me toward new sounds—or, as in the case of June, something new spun out of old materials. I had seen her album “Pushin’ Against a Stone” filed in at least three different sections of a local record store (“Jazz,” “Soul / R. & B.,” “Rock”). However categorized, it was a kind of music I might have ignored at a different time: I go through weeks where I barely listen to anything without a voice that isn’t Auto-Tuned, glossed, or coarsened during postproduction. But I wanted to hear a stranger’s voice. I found June’s voice so untroubled. I was drawn to the way her music edged into different, old-timey genres, cohering around a belief that the American songwriting tradition was common ground. June’s utopian vision of what she described as “organic moonshine roots music” felt a little out of step with the hectic, angry urgency of the land that had produced it.

June grew up in western Tennessee, a part of the state often described as a meeting point between different musical traditions: blues, gospel, Appalachian folk. As a child, in the eighties, she often tagged along with her father, a local promoter specializing in gospel and R. & B., as he put up posters around town. In her late teens, she moved to Memphis, where she began trying to assimilate these disparate influences in the funky, jam-happy rock band Bella Sun, which she formed with her then husband, Michael Joyner.

She self-released a series of home-recorded solo albums, which sound like attempts to find the right vehicle for her versatile, radiant voice. She found one in 2013, with “Pushin’ Against a Stone.” That album was produced by the Black Keys’ Dan Auerbach, who gave it the sonic equivalent of a vintage-looking Instagram filter. June ranges effortlessly from girl-group sprightliness to bluesy lament, from the garage-rock-tinged slow dance of the title cut to “Wanna Be On Your Mind,” which aims for the spacey atmospherics of a seventies soul gem. “Houston’s a hard town / New York’s not for mine / Every town I drift through / I just can’t unwind,” she sings over the campfire strums of “Tennessee Time,” which ultimately finds her venturing back to her home state.

June’s new album, “The Order of Time,” is a moodier affair, lacking some of the sparkly edge of her major-label début. She sounds imperious on raucous numbers like “Got Soul” and “Shake Down.” The latter track was released as the album’s lead single and features backing vocals by her father, who died in November. It is a riot of handclaps, saloon piano, and crackling guitars, as June beckons everyone to have as much fun as she and her band are having.

But I kept listening to “The Order of Time” because of its slower, more patient turns. I was captivated by the album’s ethereal slowness, its almost psychedelic wandering. In the past few months, I’ve grown enamored with the leisurely calm of certain songs of hers. They linger on the textures of everyday life: coming and going, the possibilities of love and loss, the passage of time, the engine of ambition.

I kept returning, in particular, to “The Front Door,” which describes the final minutes of a spent relationship. There’s a feeling of stillness as it rises from the quiet, with June mumbling and whispering, like she’s hiding her words behind the light churn of organ and the glimmer of pedal-steel guitar. She eases into the arrangement, then repeats the final lines, over and over, and they begin to stand on their own: “Bound, / Farewell, I’m bound / To leave you / Waiting by / The front door.”

On “Astral Plane,” a delightfully coy ballad, she sings with a confident innocence, dancing toward “other worlds” and wondering what keeps her anchored in this one. There’s something humble and intimate in the moments when her mesmerizing voice seems to dissolve into the ambience around her. “If I should fall so deep / May it be with you,” she sings on “With You,” gently seesawing along with a twee acoustic guitar line and a modest string section. There’s a tranquillity that seems elusive, aspirational.

We judge a song to be good or bad because of our own systems of taste, but we find a deeper comfort in something because of coincidences of timing. Maybe it speaks to something that vexes us, or finds language where words previously seemed futile. I suppose the question is a personal one: whether you turn to music to understand the world or find in it an escape, a reminder that life goes on. “The Order of Time” is best in moments of peaceful restraint, when June good-naturedly investigates those around her, testing when to hold back and when to uncoil her sweet, chalky voice; when to sing along with the rest of the band’s melody and when to stray and strut from it. “In search for the grasses green,” she sings on “Long Lonely Road,” her words melting into a delicious hum. She knows when quiet is enough. It feels like a model for being.