A note to those who feel, not without merit, that popular culture is getting so stiflingly politically correct and even “woke” that it is being strangled to death: In 1989, when I published my book “Jazz Singing,” I used the term “canary” in reference to female big band vocalists. Frankly, I was then astonished that many reviewers took umbrage at that term, calling it — and me along with it — chauvinistic and even sexist.  

As it happened, all of the editors and proofreaders who worked on the manuscript were women, and none of them objected. All of the critics who took me to task were male. Therefore I feel vindicated, a lifetime later, now that a new project celebrating the legacies of the great female jazz singers is being called “Flying High: Big Band Canaries Who Soared.”

The project is from producer Suzanne Roche of Jazz at the Ballroom, a performance series and production organization based at San Francisco, working with a pianist and singer, Champian Fulton. It is a clear indication that female singers have reclaimed the term as something affirmative, the same way that various racial and ethnic groups have reclaimed various terms and made them into something worth celebrating.

“Flying High” had its New York premiere at the Triad last year and has since played Birdland several times, mostly recently last week. It also tours around the country, with several dates in Northern California on the schedule, and a new album has just been released on both vinyl and CD. 

The line-up in New York last week was Ms. Fulton along with the formidable Ekep Nkwelle and an excellent young Australian singer new to me, Olivia Chindamo. The album features six different singers following the lead of Ms. Fulton, who also serves as accompanist and musical director.  

The six range in experience, with the most senior being Carmen Bradford, who has been singing with the Count Basie orchestra for almost 40 years — and who really shines on an authoritative reading of “Lullaby of the Leaves,” including the verse, a song, coincidentally, composed by a woman. The youngest would probably be Ms. Nkwelle, though, to my disappointment, she isn’t on the album.

Although the title indicates an emphasis on major singers of the 1930s and ’40s and their early work with the legendary big bands, the program itself is much more casual — it’s a very loose mandate overall. The program varies from specific recreations of iconic female singer arrangements to songs simply associated with great singers to anything anybody feels like singing.

Ms. Fulton herself came up with a rather brilliant homage to Ella Fitzgerald. There are plenty of contemporary singers who, perhaps unwisely, try to recreate Fitzgerald’s scat masterpieces, but Ms. Fulton uses as her point of departure Fitzgerald’s rarely performed mid-1970s arrangement of “The Man I Love.” 

She starts out of tempo — leaning into the song’s classical connections — and soon shifts into 4/4 swingtime for a chorus or so; in the coda, she changes lanes again, this time into a funky backbeat, over which she interjects a few spoken exhortations about waiting for her man.

Indeed, all of the singers are so good here that it’s hard to single any of them out: a name new to me, Gretje Angell, has been working on the West Coast, according to Ricky Riccardi’s helpful liner notes, and comes through with a suitably bluesy, understated take on “Why Don’t You Do Right” and fairy glides over Ms. Fulton’s block chords on “You Belong to Me.” 

Vanessa Perea, who has been heard around New York as half of the duo The Ladybugs, is more introspectively intimate on “Secret Love” but outgoing and swinging on “The One I Love (Belongs to Somebody Else)” with bassist Neal Miner and drummer Fukushi Tainaka. (Bonus, here is a really excellent performance by Ms. Perea of an overlooked number from the Nat King Cole songbook.)  

Still, it’s Ms. Fulton’s show throughout, and she even attracts attention even when she’s not supposed to be pulling focus, as in her expert accompaniment behind Jane Monheit on “I Only Have Eyes For You,” which has drummer Charles Ruggiero playing “Poinciana”-style mallets. She also adds sparkling Erroll Garner-isms behind Ms. Chindamo’s very original and very engaging take on Peggy Lee’s “I Don’t Know Enough About You.”  

“Flying High: Big Band Canaries Who Soared” pivots around a very loose theme but ultimately a very worthy one, serving to remind us what an amazing contribution female singers have made to this music — both then and now.