Fred Hersch and esperanza spalding
‘Alive at the Village Vanguard’ (Palmetto Records)

Fats Waller in 1939 wrote a song called, “You Can’t Have Your Cake and Eat It.” That seems like a truism, but is it really?

The artist who raises that question is esperanza spalding, who eschews capital letters when it comes to her name. In 2011, she won her first of what is so far five Grammys, for Best New Artist. Over the course of a career that’s about 15 years along, she’s released eight albums as a leader, all of her brand of contemporary jazz, showcasing her talents as composer as well as bassist and vocalist. As a musical conservative I’ve always yearned to hear her do an album of standards — now that would be like having my cake and eating it, too.

Well, that long-awaited cake has now arrived from the baker, and it’s tastier than anything I could have wished for. In October 2016, Ms. spalding teamed up with the veteran pianist Fred Hersch, one of the most creative keyboardists of our time, for a run at the Village Vanguard. Samples from three of those nights give us the eight marvelous tracks of the new album, “Alive at the Village Vanguard.” To celebrate, Mr. Hersch and Ms. spalding have been reconvening at the Vanguard this week; the shows have been sold out for months in advance.

The intermingling of speech and song in a jazz context has been explored by the late Mark Murphy, and continues to be done by Sheila Jordan and Kurt Elling. As Mr. Hersch has demonstrated, jazz improvisation essentially takes two interlinked approaches: melodic (think Louis Armstrong) and harmonic (think Charlie Parker). Ms. spalding’s treatment of these mostly well-known lyrics introduces a new idea: elaborating on the inner meaning of the ideas and attitudes underlying these classic songs, what she described at the start of the Thursday show as the “subtext.”

Considering that the Gershwin Brothers’ “But Not For Me” is more than 90 years old, both the text and the subtext hold up very well indeed. Ms. spalding’s elaborations are essentially two-fold: She remarks on the text itself, admitting that she can’t quite relate to the allusions to old English that were intended as deliberately quaint and archaic in 1930, and of the reference to gray skies in Russian plays, she sings, “I haven’t seen too many, but they say that Russian plays go for gray skies, all right.” 

She weaves this all into a commentary about her own life and relationships, “What a sad case I seem to be … you’d think that just by living long enough, you’d wind up next to someone who you could share romantic feelings for.”

“My Little Suede Shoes,” which Mr. Hersch has also recorded in duos with guitarist Bill Frisell and vocalist Nancy King, is a Pan-American instrumental, part calypso part rhumba, introduced by Charlie Parker in 1951. It’s been recorded hundreds of times, but there’s no official lyric.  Thus, the Hersch-spalding interpretation is all subtext and no actual text.  Mr. Hersch starts by plucking on a string inside the piano case, hammering a staccato repeated pattern as Ms. spalding enters scatting, then talking.  

“It’s not lost on us that it’s a Saturday night,” she says, “and you have generously or foolishly chosen to spend that night in a jazz club, sitting cramped behind a table. Bless you.” She goes on to instruct the crowd: “Imagine you’re dancing in an old Whitney Houston music video … with your suede shoes on, and you know when you have suede shoes on, you can do no wrong.” 

“Evidence” and “Dream of Monk” are a two-part reflection on the legacy of Thelonious Monk, the second being a Hersch original that, he tells us, came to him in a rather elaborate dream, and is not to be confused with the jazz icon’s own “Monk’s Dream.” Even without the title or Mr. Hersch’s lyrics, anyone listening could instantly spot the inspiration for “Dream of Monk,” those jagged rhythms and unexpected chromaticisms — not least because it ends with a quote from “Ruby My Dear.”  

“Evidence” doesn’t use the lyric by Jon Hendricks but rather is pure scatting combined with highly ingenious variations from Mr. Hersch, who ends his solo by allowing the underlying source material, the 1929 song “Just You, Just Me,” to shine through.

“Girl Talk” is one of the duo’s most remarkable creations. Even within a few years of the song’s introduction in 1965, Bobby Troup’s lyric to Neal Hefti’s melody was already being dismissed as, at the very least, chauvinistic. Yet Ms. spalding postulates that the words are not necessarily sexist, but actually secret messages from the frontlines of the gender equality wars. If she’s taking requests, I want to hear what she and Mr. Hersch might do with Burt Bacharach and Hal David’s “Wives and Lovers”; clearly, that’s also crammed with codes from the feminist underground.

The Hersch-spalding “Girl Talk” makes you laugh and makes you think, but they save their two biggest heartbreakers for the end: Jule Styne’s “Some Other Time” (written for Sinatra, as distinct from the more famous “On The Town” show tune) and “A Wish,” a beautiful song with a melody by Mr. Hersch and a lyric by Norma Winstone, the British singer. There’s an acute contrast between these straightforward ballads and the talkier numbers. Ms. spalding actually doesn’t need extra words or improvised verbiage to illuminate the subtext here; she brings it all forward — all the interior meetings as well the surface-y ones.  

I’ll take another slice of that cake anytime. These two have got their little suede shoes on, and they can do no wrong.