There’s a reason McCoy Tyner, who is appearing this week at the Blue Note with his trio and special guest Pharoah Sanders, was the perfect pianist for John Coltrane: He has an amazing sense of harmony and relishes beautiful, complex chords, yet he also knows when to play with the utmost simplicity and never wastes a note.

Mr. Tyner’s sound is rooted in modal and bop traditions, and he is also a master interpreter of the Great American Songbook. Yet he was adventurous enough to follow Coltrane in his musical adventures around the globe to Africa and India and even into outer space. He can caress the keyboard in a warm, lyrical fashion, like a lover (or like Bill Evans), or he can jab at it with rhythmic punches and punctuations as if he were mad at it (or like Horace Silver). With his reptilian gaze and incredible ears, he doesn’t seem to miss anything.

In 1965, when Coltrane was gradually moving beyond his Classic Quartet, which he had led for the past five years with Mr. Tyner (the sole surviving member) as his co-pilot, the first musician he added to his working band was Mr. Sanders. Coltrane included both Mr. Tyner and Mr. Sanders on his long-form works “Ascension” and “Meditations.” By the end of that year, as Coltrane became ever more firmly focused on avant-garde music, Mr. Tyner, who had come to feel he was no longer part of Coltrane’s journey, left the ensemble and the Classic Quartet was no more. Mr. Sanders, however, continued to play with Coltrane until the end of the legend’s short life.

Mr. Tyner and Mr. Sanders have performed together on only a handful of occasions since then; thus their appearance together at the Blue Note, on the occasion of the 80th anniversary of Coltrane’s birth, is a major reunion. Coltrane’s spirit certainly pervaded the second set of the opening night Tuesday. Even the opening two tunes, which were composed by Mr. Tyner after Coltrane’s death, seemed infused by his spirit: “Manalyuca” from Mr. Tyner’s 2003 “Land of the Giants,” which was played by the trio alone (with Charnett Moffett on bass and Eric Kamau Gravatt on drums) and the 1973 “Walk Spirit Talk Spirit.”

The first Coltrane tune performed was the tenorist-composer’s most famous ballad, “Naima,” dedicated to his first wife. Mr. Sanders, clad in his usual African-style shirt, looked, as always, as much like a holy man as a musician. He has always struck me as the Coltrane acolyte who has done the most to extend the spiritual legacy of the man sometimes described as “The Jazz Messiah.” Coming from Mr. Sanders’s horn, “Naima” sounded more like a prayer than a love song, as if he were dispensing blessings to the crowd. Later, when Mr. Tyner called “Say It” from the Classic Quartet’s masterpiece album “Ballads,” it could have been called “Pray It.”

I have heard Mr. Sanders play standards only rarely, but he and Mr. Tyner essayed this Frank Loesser tune so movingly — as a duo without bass or drums — that I would love to hear them tackle a whole album of duets on standards.

The quartet also essayed “Lazy Bird,” an early bop number (from “Blue Train”) out of Coltrane’s sheets-of-sound period; I have never heard Mr. Sanders work in this idiom, but he showed that he was clearly doing something before he became Coltrane’s partner in postmodernism. More in Mr. Sanders’s native idiom was “Afro Blue,” in which Mr. Tyner, no dummy he, took the opening melody for himself but left the first improvisation to Mr. Sanders, who played it with a buzzy echo — as if there were more than one spirit in his horn.

Surprisingly, this climactic number was itself climaxed by a bass solo from Mr. Moffett, who played by tapping the strings with his bow, creating a strikingly percussive, wholly original sound that made the tune, not to mention the whole evening, both much more “Afro” and much more blue.

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For most of her 81 years, Elaine Stritch has been an actress on Broadway and in films and television. For the last five years, most of her live appearances have been as herself: first in the 2002 “Elaine Stritch at Liberty,” then last year in her first cabaret appearance, “Elaine Stritch at Home at the Carlyle” (referring to how she actually resides at the hotel, three flights above the café), and now in “Elaine Stritch at Home at the Carlyle … Again.” It says something about the breadth and scope of her career (she first hit Broadway 60 years ago in a long-forgotten 1946 play called “Loco”) that she is still able to assemble nearly five hours of autobiographical anecdotes, songs, and observations without ever repeating herself.

Even in her prime, Ms. Stritch never had a big or particularly beautiful voice, and she has considerably less of one now. Yet when she starts to sing, she shows that there’s a lot more to putting over a song, to embodying a lyric through a character (and vice versa) than just hitting notes; she’s the polar opposite of every contestant on “American Idol.”

At the Carlyle, when Ms. Stritch opens with “The Life of the Party” it’s as if she’s performing with a virtual lampshade on her head, and she is similarly upbeat without being the least bit naive on “Comes Once in a Lifetime.” She intermingles song and personality to a remarkable degree on two Rodgers and Hart classics, “You Took Advantage of Me,” in which she weaves a narrative of how Rodgers broke with his own tradition in encouraging her to reinterpret the song as a bluesy belter. On “To Keep My Love Alive” she makes a grand show of trying to remember — and engaging the audience in the process — all 15 luckless knights that are swiftly dispatched by the murderous heroine.

This latter tune, one of Lorenz Hart’s final works, shows that Ms. Stritch can be just as funny when singing as when telling a joke or a story. She gets the biggest laughs, however, when, absolutely dead straight, she delivers the entire “Theme From ‘The Sopranos’ (Woke Up This Mornin’),” rap effects and all.

One of Ms. Stritch’s more surprising turns is “The Ladies Who Lunch” (her signature tune from “Company”). In “Company” she sang it touchingly reflexively, referring to the ladies in the third person but actually describing the character she was playing. Contrastingly, at the Carlyle she sang it with pure extroversion, without any hint of irony or reflection. But she also took “Song on the Sand” (from “La Cage Aux Folles”) a rather lachrymose, overdone number that few would regard as one of Jerry Herman’s best, and suddenly made it seem incredibly touching. Indeed, Ms. Stritch does such an amazing job at using her songs as windows into her soul, letting us all see straight inside of her, that the spoken portions of her show are almost beside the point.