Saxophonist Sarah Hughes. (Diriki Rice)

D.C. alto saxophonist Sarah Hughes named her Sunday night trio gig at Twins Jazz “Calling All Voices.” Out of context, it’s a seemingly inspirational title. But it did have a context. “Toward the end of the set, I want anyone in the audience to be welcome to come up and join us for some improvising,” Hughes explained from her perch at stage left. “Listen to us carefully, and if you think you can fit in with us, please come on up!” That made it even more inspirational — certainly one of the most inspiring nights of music this reviewer has witnessed.

Hughes, with bassist Tarus Mateen and drummer Tyler Leak alongside, had a more traditional performance to take care of first. They began with a version of “Stella by Starlight,” reharmonized nearly beyond recognition. As such it was impossible to tell how long she stayed with it, because it began an uninterrupted 30 minutes of quickly and constantly changing music. What was here an incantatory ballad, Mateen strumming darkly (and getting a surprising wood sound from his electric bass) and Leak busily comping with mallets, there became a pointed alto-sax declamation, Hughes overblowing some skronks and Mateen creating an alluring vamp in mixed meter. There were at least nine distinct sections, though they were universally haunting, thanks in great part to Hughes’s plaintive vibrato and bluesy passing phrases, both of which recurred throughout.

After a second, much shorter original tune — a pretty, spartan ballad called “I Hope I Dream of You” — came the headline event. It was even less predictable than promised: The first volunteer was a middle-aged man who introduced himself as Ted Jacobsen, boasting a Louis Armstrong vocal impression. Shortly afterward came a pianist (introduced as Errol) and a clarinetist (Alisha Coleman), and they were off, Hughes getting the room humming in a harmony that she then picked up on alto — as did Jacobsen, who fragmented his Armstrong impression into disjointed chunks of “Hello Dolly” and “When the Saints Go Marching In” (with a morsel of “Rockin’ Chair”).

Soon, Hughes and Coleman fell into a gentle call-and-response with Jacobsen scatting and Mateen developing into a harmonic structure based on the note Hughes had begun humming in (B-flat). As Leak brought it to a shuffle beat, two new improvisers joined: trombonist Shannon Gunn, brandishing a Harmon mute, and a baritone saxophonist identified as “Jack.” When they all got moving together, it became increasingly clear that Jacobsen was the center of the action — the bass and drums accentuated him, the horns played fills in and around his singing and scatting; as it drew to a close, he simply groaned repeatedly, and the trombone, baritone, and piano all gave different interpretations of an echo. Spontaneity and creativity never felt more at home, and alive, with each other.