The Fastbacks work very hard at being what they are — a group that hasn’t left the garage in 20 years, a band that saw grunge come and go without ever getting called up to the majors. “The Day That Didn’t Exist,” the band’s 10th full-length, details 24 hours in a fictional day filled with quintessentially Fastbackian moments: fitful ruminations on freedom (“Defy’s Gravity”), happiness (“One More Hour”) and despair (“What’s the Use?”); melodies perky enough to overshadow tales of calamity (“Have You Had Enough?”); guitar riffs that suggest the world began the day God created the Buzzcocks (all 14 songs).

It should be mentioned that guitarist Kurt Bloch, who’s a guy, writes the Fastbacks’ songs, and that bassist Kim Warnick, who’s not a guy, sings the bulk of them. Don’t mistake the arrangement for something more than it is. Bloch is no Babyface; his songs have never suggested a willingness to wear someone else’s shoes. Warnick, with the occasional backup of guitarist Lulu Gargiulo (also not a guy), fleshes out Bloch’s everyperson tales in a way that he never could. As a singer, Warnick is a Peppermint Patty with a hacking cough. But when she leans into a melody like the one in “I Was Stolen,” a melody so full of its own energy that drummer Mike Musburger has no choice but to try to hammer it in place, she sends it into the clouds.

What’s new in the Fastbacks’ garage? Nothing, except for the fact that the Fastbacks are still there, recording and surviving the passage of time the only way they know how: doing this.

June Carter Cash, Johnny’s wife and a musical legend in her own right, appears more the gracious hostess than the main attraction, even though tonight, that’s exactly what she is. The early evening event is to honor June upon the release of “Press On,” her first solo record in more than 25 years. June will play for the invited guests later on, and if she’s nervous at the prospect of performing on her own instead of in support of her husband, which is what she’s done mostly since the couple married over 30 years ago, she doesn’t show it.

June’s there at the front door of her home, urging guests to go inside and take a look around. Built along the banks of Old Hickory Lake, next door to the lot where the late Roy Orbison used to live, the place practically creeks with history. It’s crowded with hand-carved, dark wood furniture that the couple’s imported from all over the world. Portraits of Cash family members share wall space with gold records and priceless photos: Johnny chatting up Prince Charles. Waylon Jennings looking young and a little tipsy. Carl Perkins recording in the studio back in the day.

As I reach the bottom of one set of stairs, a man extends his hand to introduce himself: “I’m Tommy Cash, Johnny’s brother.” Just beyond Tommy is a table adorned with a collection of acoustic instruments, a few of which, I’m told, were used by the original Carter Family, the first family of American folk music, progenitors of modern country music and the family Johnny joined when he married June. Around the corner, through a hallway and down some more stairs is the lakeside room where Johnny hosted his legendary “guitar pulls” in the late ’60s and early ’70s. The events were informal, star-studded jams at which, as Johnny writes in his ’97 autobiography, “Kris Kristofferson sang ‘Me and Bobby McGee’ for the first time … and Joni Mitchell ‘Both Sides Now.’ Graham Nash sang ‘Marrakesh Express’ and Shel Silverstein ‘A Boy Named Sue.’ Bob Dylan let us hear ‘Lay Lady Lay.’”

There are bold-faced names in the flesh as well — George Jones(!), Naomi Judd, Jane Seymour(!), Diane Ladd — but the event feels more like a wedding than a star-studded gala. “Entertainment Tonight” is on hand, but for the most part, the camera hands inconspicuously keep their gear at the rear of the tent where everyone gathers to eat and watch June perform.

A lot of people talk about how June and Johnny have made them feel like family. With a plate full of fried green tomatoes and slices of roast pork, I sit next to Laura Weber, the young violinist/multi-instrumentalist who’s playing in June’s band. Laura’s parents, Pat and Sharon, came in from Oregon for the occasion. The parents flew into Nashville a few days ago, but they’ve spent most of their time at the compound helping the Cashes, whom they’d never met before, prepare for the evening’s festivities. They seem at ease among all the celebs, local and otherwise; neither parent flinches when Nashville songwriter Tom T. Hall ducks in to flirt and joke with their daughter.

But still, reverence is hard to disguise. Pat’s eyes beam when he tells me that June is allowing Laura to play a vintage guitar that was a favorite of Maybelle Carter, June’s mom and an original Carter Family member. Dad knows that the instrument could likely have been used to help create the music his daughter has devoted her life to playing. Later on in the meal, Sharon tells me that she read an article recently — she doesn’t remember where — in which a musician was quoted comparing Johnny Cash to Abe Lincoln. At first she thought the comparison seemed silly, “but now,” she says, “I think that it sounds about right.”

The evening proceeds with a casualness that befits the album that occasioned it. “Press On” is an unbound, rustic-sounding collection of Carter Family nuggets (“Diamonds in the Rough,” “Will the Circle Be Unbroken”), classic June Carter originals (“Ring of Fire”) and quirky new numbers (“Tiffany Anastasia Lowe”); the playing is sharp, but the overall effect is loose, like a front-porch jam, complete with giggles and miscues.

The plan for the concert was to perform the entire album, but the script gets tossed at the outset. The first standing ovation comes a good hour before the music even starts, when Johnny takes the stage to say a few words. His illness is evident mostly in his face, which is swollen and red. The only time the singer alludes to his health is when he thanks the Lord for allowing him to stand, if only for today, on his own two feet. Otherwise, he talks of June and the love they share. “Her time has come now,” he proclaims, his voice still deep as ever. “This album, ‘Press On,’ is just a small bit of what she has to offer.”

June, dressed in a smart suit and high heels, her hair pulled loosely back, professes to be embarrassed by the attention, but she thanks Johnny for his remarks all the same. After instructing everyone to get something to eat, she walks off. When she returns to the stage over an hour later, she does so with her autoharp in hand and playfully asks, after noticing how much of her legs become exposed when she sits on her stool, if anyone has a safety pin that she can borrow.

Johnny looks on from the front row as June introduces her first song, explaining how she wrote it, a long time ago, after waking up in the middle of the night and telling herself, “I think I’m in love with a wild man.” She looks at Johnny. “I was frightened of him. I wasn’t going to tell him I was in love with him. And I wasn’t going to tell anyone else either.”

Then she plays “Ring of Fire.” The way Johnny immortalized it, the song chronicled a man’s unsteady relationship with wildness and his inability to break free from it. June reclaims the song, seizing its perspective and flipping it around. In the hands of June and her band, “Ring of Fire” is a rickety, swaying folk ballad. As she sings, “burns, burns, burns,” you can hear the voice of a girl who long ago fell for a guy who trashed hotel rooms for the hell of it. The kind of guy who’d borrow your car, wrap it around a tree and never apologize.

Johnny’s visibly moved as he joins his wife to perform onstage. The man may be ailing, but he can still play a guitar and sing, and he introduces “The Far Side Banks of Jordan” by offering up a bit of its history. Twenty-five years ago, he brought the tune with him from Nashville to Jamaica. “This is going to be our song,” he told his wife. And so they play it. They’re voices aren’t perfect together, never have been; June’s is hillbilly sweet and high where Johnny’s is earthbound and famously, immovably low. The point is that the song is theirs, and they’re still singing it. When the tune’s over, Johnny takes June’s hand. He kisses it, considers it for a second, and then gives it a bite. Then he walks off the stage and out of the tent. He never returns. Abe Lincoln all the way.

June’s group is a touch under-rehearsed. At one point, John Carter, the only child of June and Johnny, the co-producer of “Press On” and a member of the band, shuffles a bunch of papers and announces, “We lost the lyrics!” “Oh I know it,” his mom replies, and the band launches into “Losin’ You.”

The mishaps only underscore the informality of the event. When June wants to locate one of her daughters, she simply cries out, “Where are you Rose?” (In the distance: “I’m over here Mama.”) Before singing “Tiffany Anastasia Lowe,” June calls up the granddaughter who inspired her to write it. Tiffany, as her grandmother points out, is young and quite striking; apparently she was or is being courted by a certain maverick film director. On the record, the song is an oddity. Here, it makes sense. Tiffany can only laugh as her grandma sings, “Tiffany run find an earthquake girl/Go jump in a crack/Just don’t let Quentin Tarantino find out where you’re at/’Cause Quentin Tarantino makes the strangest movies that I’ve ever seen.”

The crowd is as loose as the band by the time the encore rolls around. June’s set her autoharp down and taken the mike. She pumps her arms like a preacher, unleashing “Will the Circle Be Unbroken,” arguably the most immortal of all the Carter Family songs. The tent feels like a church as the crowd sings along from their seats. The applause lasts long after the spiritual winds down. No one cries out for Johnny. It was June’s show, and this time, Johnny was her guest.

Folds’ real growth on “Messner” is musical. He’s no longer interested, as he once was, in proving to punk snobs that a piano man can front a power trio. “Narcolepsy,” the opening track on “Messner,” is the most outrageous Folds tune to date. It’s a five-minute-plus opus worthy of Queen, replete with strings, drums that tumble in like flash floods and enough musical costume changes to suggest that the band wrote the song in movements.

Nothing else on the record is as audacious as “Narcolepsy,” but the song does set the tone for the rest of the album. Folds spent the bulk of his first two records, “Ben Folds Five” (1995) and “Whatever & Ever Amen” (1997), turning gripes into melodic, guitar-free stomps; on “Messner,” he mixes up the formula. Arty rhythm shifts slow the headlong surge of “Army” before it’s recharged by a brass section. On “Don’t Change Your Plans,” Folds throws melodies against a suite of Bacharach strings. “Regrets,” which starts, “I thought about sitting on the floor in second grade,” sounds like a Steely Dan tune grafted onto an outtake from “The Wall.”

“Messner’s” sundry celebrations of ’70s-era radio cheese aren’t terribly surprising, given that Ben Folds Five prefer to poke fun at hipsters rather than court their attention. Folds isn’t interested in irony, and his band marches through these flamboyant arrangements with nary an apology or a wink. The singer’s worries are the same as they were two long albums ago; it’s the music that Folds uses to air those worries that’s changed. Adulthood can’t be far off.