Bob Dylan has been much in the press lately thanks to the release of the six-CD box set, The Basement Tapes Complete and of The New Basement Tapes, on which Elvis Costello, T-Bone Burnett and company try to do for Dylan’s leftover 1967 lyrics what Billy Bragg and Wilco did for Woody Guthrie’s leftovers on Mermaid Avenue.

Dylan himself, however, has declined to acknowledge the excitement. At nearly every 2014 show, he has performed the same 19 songs in the same order, and not one of them originated in The Basement Tapes sessions (though his first encore number on the 2014 tour, “Blowin’ in the Wind,” was re-recorded during those sessions).

When Dylan played Washington’s Constitution Hall just before Thanksgiving, however, the songwriting sensibility of The Basement Tapes was much in evidence, even if the actual songs weren’t. Of the 19 songs, 14 were from 1997 or later, a period in which the singer has relied on the same free-floating stanzas that he experimented with in 1967-68 and then largely abandoned until 1989’s Oh Mercy.

Since 1940, most American songwriting has been linear, meaning that the first stanza has to come before the second stanza and the third after the second, as if telling a story with a beginning, middle and end. This approach can’t be beat for constructing a narrative or developing a theme, and most songs are written this way.

But there’s another, older songwriting tradition, especially on the old blues, hillbilly and gospel records that Dylan loved, where the stanzas can be scrambled without affecting the meaning very much. This mix-and-match approach was the result of singers grabbing the best stanzas from a favorite song, discarding the rest and adding a few new verses of their own. Or taking verses from several pre-existing songs and attaching them all to a generic blues, waltz or ballad melody. It was as if each song were a greatest-hits collection of pre-existing stanzas.

With this approach, neither the order nor the origin of the verses mattered much; what was important was the punchline of each stanza and cumulative effect the combined verses created. With some lines from this songwriter, some lines from that songwriter and some lines by the performer, all filtered through a distinctive voice, the result was a fusion of group consciousness and individual consciousness, a blend that created its own distinctive thrill.

A good example is Blind Lemon Jefferson’s “One Kind Favor,” a song that Dylan recorded as “Please See That My Grave Is Kept Clean” on his very first album and recorded again under its original title during The Basement Tapes sessions. It doesn’t really matter who wrote which verse or which one you sing first: the one about the broom sweeping, the one about the church bell tolling or the one about the silver spade digging. From any source or in any order, the song is going to have the same chilling anticipation of inevitable death.

Nor does it matter how much of the words and music Dylan invented and how much he “borrowed” for “Wild Wolf,” the greatest unbootlegged revelation of the box set. He might have scrambled the verses about living in a frontier town with canine wolves outside the stockade walls and human wolves inside, and they would have been just as evocative in their well-earned paranoia.

Nor does it matter with “Things Have Changed,” the 2000 song that began Dylan’s Constitution Hall show. The first line is “borrowed” from Woody Guthrie (“A worried man with a worried mind”); other lines paraphrase the Doors (“People are crazy and times are strange”), Bo Diddley (“I walked 40 miles of bad road”) and Ray Charles (“You can’t win with a losing hand”). Each verse describes a different example of social dysfunction inducing the same response from the singer, “I used to care, but things change,” and it wouldn’t matter in what order the examples were offered. The echoes of other songwriters and the free-floating stanzas don’t dilute the number; they give it a timelessness that redoubles the impact.

When early blues and hillbilly musicians shoved floating verses together, the juxtapositions were sometimes jarring. Instead of smoothing over such collisions, as pop craftsmen might, these early singers savored such dislocation and used it to introduce surrealism into the songs. Animals talk; machines works miracles; people fly and grow tails; years grow and distances shrink. This obviously appealed to Dylan, and during The Basement Tapes sessions he described himself as drinking a bottle of bread, riding into town on a ferris wheel and talking in meows and moos.

Dylan has returned to such fabulist writing on his 21st century songs. At Constitution Hall, for example, he described the “Early Roman Kings” in sharkskin suits, top hats and tails nailing spikes into railroad tracks and their own coffins. Also from the 2012 album Tempest were “Scarlet Town,” an imaginary village of palm trees, marble slabs, chilly hills, seven wonders and whiskey wars, and “Pay in Blood,” whose narrator has drugs in his pocket, poker cards in his hand, an attack dog on a leash and a cudgel behind his back.

For the free-floating-stanza approach to work, the music has to be loose enough to accommodate verses from various sources and with different numbers of syllables. At the same time the playing has to acquire enough forward momentum to pull the song across the implied ellipsis dots (...) where the missing explanations might be. It takes an exceptional group of players to strike the right balance between flexibility and propulsion, but Dylan’s current band has all the right instincts.

At Constitution Hall, the longstanding group of bassist Tony Garnier, pedal steel guitarist Donnie Herron, drummer George Recile and guitarists Charlie Sexton and Stu Kimball implied a kind of 12/8 time signature. This allowed them to follow their lead singer as he shifted between duplet and triplet phrasing without losing the overall forward motion.

After two songs standing at a mic stand without a guitar (he never touched a guitar all night), Dylan sat down at a baby grand piano for “Beyond Here Lies Nothing.” Sporting a loose white suit, a flat-brimmed white hat and a pencil-thin mustache, he played the two-fisted, lower-register chords that cued the groove for this rumbling, uptempo blues about an oasis of love in a city of broken cars. Recile’s triplet fills with the brushes lent a push-and-pull Latin tinge to the proceedings.

“Love Sick” was given a reggae feel; “Early Roman Kings” became a Chicago blues stomp. “Forgetful Heart” had a lilting string-band arrangement with Dylan on harmonica, Herron on fiddle, Recile on mallets and Garnier on bowed bass. “Blowin’ in the Wind” was transformed from folk anthem to lightly swinging hillbilly gospel. “Simple Twist of Fate” acquired a supple swing that encouraged Dylan to rewrite the lyrics: “You should have met me back in ’58; we could have avoided this simple twist of fate.” And because he was singing the same songs with the same band every night, Dylan no longer lost track of the melody or the lyrics and sang with more confidence than he has in decades.

With their loose-limbed swagger and melting pot of various roots musics, the current road band is taking its cue from The Band, especially as it played on The Basement Tapes sessions. On May 17, 1966, guitarist Robbie Robertson, bassist Rick Danko, pianist Richard Manuel and organist Garth Hudson (Mickey Jones of TV’s Home Improvement fame had replaced the absconded Levon Helm on drums) had backed Dylan in Manchester, England, during the legendary “Judas!” show preserved as the Live 1966 album. It still stands as one of the most manic, confrontational rock ‘n’ roll albums ever recorded.

Six weeks later, on July 29, the rear wheel on Dylan’s Bonneville motorcycle locked up on a back road near Woodstock, New York, and threw the rider over the handlebars onto the asphalt which cracked his collarbone and concussed his head. It also provided an excuse for the burnt-out singer to cancel the rest of his scheduled tour as well as his contracts for a book and a TV special. Instead he holed up with his wife and children in Byrdcliffe, their new house in Woodstock. He saw almost no one and played almost no music, though he couldn’t stop himself for scribbling down lyrics as the autumn of 1966 turned into winter. Those scribbles included the 24 songs turned over to T-Bone Burnett in 2013 for The New Basement Tapes project.

By February, Dylan decided he needed some collaborators if he were going to forge a new musical path, and because Robertson, Danko, Manuel and Hudson were already being paid a retainer, he asked them to come up to Woodstock to create some demo tapes that he could send to his publisher. At first they worked in the Red Room at Byrdcliffe, but eventually they moved to Big Pink, the ranch house with garish siding that Danko had rented in nearby West Saugerties. In the basement garage, Hudson set up a makeshift studio, and the five men would gather there two or three times a week from mid-afternoon to mid-evening to play some songs—both old and new. In the fall, Helm returned from self-imposed exile and joined the proceedings.

Sometimes Dylan would call out old songs he remembered—everything from Hank Williams’ “My Bucket’s Got a Hole in It” to Curtis Mayfield’s “People Get Ready,” from Brendan Behan’s “The Auld Triangle” to John Lee Hooker’s “Tupelo.” Sometimes he would hand out lyrics fresh from his Olivetti typewriter with a vague instructions as to melody and rhythm. Steeped in the sound of those older songs, the musicians would cobble together some similar music for the first-draft lyrics. Hudson would turn on his reel-to-reel tape recorder and capture the result.

It was an unusual songwriting process, and much of the pleasure of plowing through all 138 tracks on the six-CD box set is listening in as that procedure unfolds, yielding fragmentary throwaways such as “I’m Guilty of Loving You” and “Gonna Get You Now,” but also such enduring classics as “I Shall Be Released,” “Tears of Rage” and “Wild Wolf.” You can hear how the new songs echo the old and how The Band’s bar-band gamesmanship could turn any half-forgotten oldie or any half-written new composition into an utterly relaxed and inviting finished song.

It’s that easygoing playfulness that’s missing from The New Basement Tapes album. My Morning Jacket’s Jim James and Mumford and Sons’ Marcus Mumford are notorious for their melodramatic earnestness, and that proves antithetical to Dylan’s carefree, down-to-earth lyrics. Songs such as “Down on the Bottom” and “Quick as a Flash,” with music and lead vocals by James, or “When I Get My Hands on You” and “Stranger,” with music and lead vocals by Mumford, are so overstated that they sound more like a U2 tribute band from Ohio than a complement to The Basement Tapes.

I’ve never liked Dawes, but the band’s lead singer Taylor Goldsmith turns in the best moments on The New Basement Tapes. Dylan was going for the collectively sourced flavor of old folk and blues songs, and Goldsmith’s understated restraint on songs such as “Liberty Street” and “Kansas City” helps the lyrics achieve this. Elvis Costello displays the best rhythmic instincts of this ad hoc band assembled by producer T-Bone Burnett. His tongue-twisting spitting of triplets and eighth notes on songs such as “Married to My Hack” and “Six Months in Kansas City” suggest that he’s been listening closely to Dylan’s current road band.

The Carolina Chocolate Drops’ Rhiannon Giddens is the group’s best singer (James has the best voice, but that’s not the same as being the best singer) and she shows it off on many-verse folk ballads such as “Spanish Mary” and “Duncan and Jimmy.” But even the Costello and Giddens tracks suffer from an overly ornate production that is out of sync with the material. The whole project represents a missed opportunity.

The final encore of Dylan’s show at Constitution Hall sounded a lot more like The Band’s Basement Tapes than these so-called New Basement Tapes. Dylan followed “Blowin’ in the Wind” with his only true cover of the night, an old song that sounded like an old Celtic ballad, pleading for a lover not to leave, laced with steel guitar and drum mallets. The fact that the song, “Stay with Me,” came not from an Appalachian field recording but from a 1965 Frank Sinatra album, merely proved Dylan’s ecumenical tastes and his ability to alchemize any material into the timeless sound of basement blues and hillbilly gospel.