To grasp fully what it means for certain popular musicians to remain popular decades after their birth, you have to calculate the conversion from normal human time to pop-star time. Life expectancy in the United States today is 78.88 years. A pop singer, however, can reasonably hope to survive as a figure of some prominence in the music marketplace for about a year and a half, the typical duration of the life cycle from rising unknown to new face to celebrity to fading star to judge on America’s Got Talent. A singer can expect to enjoy stardom for approximately 1.9 percent of the lifetime of a regular person; and while human life expectancy grows each year, the ever-accelerating pace of hype and ever-diminishing span of audience attention conspire to continue reducing the half-life of famousness.

America’s ongoing fascination with two singers born 100 years ago, Billie Holiday and Frank Sinatra, is extraordinary and speaks to the unique power of their images as artists, their myths, and—above all, I think—their music. After all, Holiday and Sinatra were hardly the only singers born in 1915. The blues great Muddy Waters, born McKinley Morganfield, may have had the same birth year, though the records for poor African-American families in and around his probable birthplace in Issaquena County, Mississippi, are scandalously incomplete. (Waters himself, at various times, gave 1913 and 1915 as the year of his birth.) Wynonie Harris, the proto-rock R&B howler, was born in 1915, and so were Alice Faye, Ginny Simms, Billy Daniels, “Honeyboy” Edwards, Dorothy Dell, Midge Williams, and a great many more.

Alice Faye? Yes—well, she was one of the top box-office attractions in the country in 1939, when Billie Holiday was just beginning to achieve mainstream success. Ginny Simms? Oh, sure—she made 11 movies before Sinatra appeared in his breakthrough film, From Here to Eternity, in 1953. Billy Daniels, in 1952, was among the first African-­American entertainers to have his own national television show, produced in what would later become the Ed Sullivan Theater.

Unlike most of the other singers who arrived in the same time frame, as well as countless pop vocalists and musicians who came and went over the nine decades to follow, Billie Holiday and Frank Sinatra are still solidly grounded in the public consciousness—­if anything, too solidly. Our collective conceptions of them both, ­reinforced by years of replays of a handful of their best-known recordings and regurgitation of the same stories about their robust private lives in books and magazine articles, have served to freeze Holiday and Sinatra in our minds as “icons,” symbols of use for worship or ridicule, but ill suited to serious consideration: Holiday, the drug-ravaged ex-prostitute who croaked her songs in pain; Sinatra, the mobbed-up, Jack-chugging swinger who chewed up life and spit it out. The fact that they were musicians—and great ones, committed to producing creative work that endures as a consequence of their mastery and originality—­seems almost incidental now.

In the months leading up to 2015 and over the course of this year, the machinery of centennial celebration has brought more attention to Holiday and Sinatra than they have had since their deaths—Holiday, at 44 in 1959, of complications from liver disease; Sinatra, at 82 in 1998, of a heart attack. (The movie version of the Holiday myth, Lady Sings the Blues, produced by Jay Weston, James White, and Motown founder Berry Gordy in 1972, celebrated its star, Diana Ross, more than its ostensible subject.) In 2014, Audra McDonald appeared to critical praise as Holiday in the one-woman theater piece with music Lady Day at Emerson’s Bar & Grill. This year, the jazz singers Cassandra Wilson and José James have released a pair of tributes to Holiday on CD: Wilson’s Coming Forth by Day, an ambitious reconsideration of Holiday material with musicians including T-Bone Burnett and members of the Yeah Yeah Yeahs and the Bad Seeds; and James’s Yesterday I Had the Blues, a more conventional album of respectful, meaty jazz performances, featuring pianist Jason Moran. The biographer and critic John Szwed, author of a superb book about another influential child of 1915, the folklorist Alan Lomax, has published a sober rumination on Holiday’s importance, Billie Holiday: The Musician and the Myth. And the two labels with the largest holdings of Holiday recordings, Columbia II and Verve, have both put together centennial-edition collections of her tracks, too, of course.

In honor of Sinatra’s centennial, the documentarian Alex Gibney, the maker of smart earlier films about Enron and the WikiLeaks scandal, produced a serious HBO biography that managed, almost miraculously, neither to romanticize Sinatra as the capo of stars nor to sensationalize the macho hedonism of his Rat Pack days. Jazz at Lincoln Center hosted a “Sinatra at 100” concert with the pianist Monty Alexander, who in his teens was a protégé of Sinatra, and the singer Kurt Elling, who has been touring the country (and spots in Europe) with his own tribute, “Elling Swings Sinatra.” The centennial has brought at least three new Sinatra books: a compact collection of poetic riffs on Sinatra by David Lehman, Sinatra’s Century: One Hundred Notes on the Man and His World; a coffee-table book assembled from materials in the Sinatra family archive, Sinatra 100; and Sinatra: The Chairman, the concluding volume of James Kaplan’s breezy two-part biography. And in the recordings that make the most lucid argument for Sinatra’s importance, there’s a judiciously curated new collection of four CDs, Ultimate Sinatra, bringing together Sinatra’s music on all three of the major labels he recorded for (Columbia, Capitol, and the company he started himself, Reprise) between 1939 and 1993.

“He never went away,” said Bob Dylan in an interview with AARP magazine timed to help promote Dylan’s own recent homage to Sinatra and his tradition: Shadows in the Night, an album of Tin Pan Alley standards softly crooned with grandfatherly devotion. “All those other things that we thought were here to stay, they did go away. But he never did.”

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Many of the recordings of Billie Holiday and Frank Sinatra must sound irredeemably old-fashioned or weird to listeners weaned on contemporary pop, alternative rock, hip-hop, and other musical genres of recent vintage. Both singers were acutely attuned to the lyrical content of the songs they sang, and no degree of due admiration for the wordsmithing of such master lyricists as Oscar Hammerstein II and Johnny Mercer can obscure the fact that some of the presumptions at work in their songs are artifacts of their time. The attitude toward gender in, say, Rodgers and Hammerstein’s “Soliloquy,” with its noble-sounding but demeaning conception of girls as delicate little objects in need of male protection, or Arlen and Mercer’s “Blues in the Night”—“A woman’s a two-face / A worrisome thing who will leave you to sing / The blues in the night”—is unsettling today, and made all the more so in Sinatra’s recordings by the conviction in his voice.

In Holiday’s work, the feeling of deep vulnerability in her voice can be mistaken for an expression of hopelessness, and that becomes tricky when thought of as a statement on African-American womanhood. Among the attributes that give Holiday’s singing its veracity is its fragility, a quality present as early as 1935, when Holiday, at age 19, sang the mournful blues lament “Saddest Tale” in Symphony in Black, a film short centered on Duke Ellington. “My man’s gone / I feel so alone,” Holiday murmured, collapsed on the street. “He didn’t treat me fair / It’s more than I can bear.” As her health declined, rapidly and inescapably over the course of her abbreviated life, Holiday’s voice grew more brittle and thin, and she employed its technical weaknesses for emotional effect. By the time of her final recordings—particularly the last album released during her lifetime, Lady in Satin—every song sounded anguished, and the myth of Holiday as a tragic figure, a symbol of black womanhood as a condition of hopeless victimization, was set.

This is a myth that Szwed, building on the incisive work of the Holiday scholars Farah Jasmine Griffin and Robert G. O’Meally, challenges fervently. As Szwed, Griffin, and O’Meally have all pointed out, Holiday was fiercely willful and independent-minded in both her professional and personal life—hardly a victim, if frequently the prey of predatory law enforcement and the institutional inequity under which all African-Americans suffered in her era. Holiday fought all of that, and her singing was the sound of her survival, for as long she could stand, looking smart and stately in her long fur coat.

There’s a quality in some of Sinatra’s music, particularly the punchy big-band records he made with the arrangers Nelson Riddle and Billy May in the 1950s and early ’60s, that is no doubt off-putting to contemporary listeners. For one thing, 21st-century ears are unaccustomed to the chromatic harmony in the orchestrations, and the sound of horn sections today carries associations with reruns of cheesy old TV cop shows, casino lounge acts, karaoke, and the near-­impersonations of Sinatra that limited talents such as Michael Bublé and Seth MacFarlane perform for no purpose I can discern. The cocksure exaltation in some of Sinatra’s hardest-swinging tracks, like “I’ve Got You Under My Skin” (from Songs for Swingin’ Lovers, arranged by Riddle) and “Blue Moon” (from Sinatra’s Swingin’ Session!!!, also arranged by Riddle) can come across as little more than midcentury male swagger.

Worse, to my ears, is in the sneering indifference that Sinatra could not help but exude when suffering through the recording of Top 40 pop material of the ’60s and ’70s that was beneath his abilities and standards, such as “Leaving on a Jet Plane,” “Close to You,” and “Winchester Cathedral.” You can even hear a hint of this dismissive languor in one of his biggest hits of the ’60s, “Strangers in the Night.” He despised the song for its pandering simplemindedness and resented having to sing it. Yet, contortedly, he did so for the label he founded. There were strains of self-torture in this work more convoluted than anything Billie Holiday recorded.

Sinatra had not always sounded so arrogant. This is not easy to fathom today, yet he first made his name as an artist whose delicacy and sensitivity were seen as shockingly, even dangerously, transgressive. In a three-part series of profiles of Sinatra published in The New Yorker in 1946, E.J. Kahn Jr. quotes a critic of Sinatra “who thinks much about these things” as finding Sinatra’s “style very dangerous to our morale, for it is passive, luxurious, and ends up not with a bang but a whimper.” The implication was that Sinatra, as a singer, was not enough of a man.

Rudy Vallee, who in the late 1920s had been an early idol of the microphone age, murmured his songs more quietly than Sinatra and had vocal limitations that made his music sound tenuous and thin. He was commonly derided as effete, though he exploited that fact as part of his comically bookish college-boy image. Vallee used the sexual ambiguity of his singing as a joke.

Bing Crosby, the great innovator of jazz-pop singing whom Sinatra idolized and emulated in many ways, was more musically sophisticated than Vallee and sang with a coolness, an evident casualness, that made his singing sound confidently, almost diffidently, offhanded. He parceled his emotions in his music—a discreetly placed glissando, an occasional trill—from a distance. The low-key naturalism of his delivery came across accurately as restraint rather than weakness.

Sinatra added unabashed sentimentality and male vulnerability to the conversational naturalism and coolness that Vallee and Crosby had introduced to mainstream popular music in the microphone age. These qualities, working in conjunction with aspects of Sinatra’s extramusical image at the time, made him awfully suspicious to parents of his young fans (and other protectors of what no one had yet started calling “heteronormativity”). The gossip columnists and the comedians who helped shape public opinion defined Sinatra as much by his skinniness as by his singing. (In a Looney Tunes short from the mid-1940s, Swooner Crooner, a character based on Sinatra is so thin he all but disappears behind his microphone stand, and in another cartoon from the same period, the Sinatra figure is so frail he needs to be pushed around in a wheelchair by an orderly.) After America entered the war, Sinatra’s exemption from military service (4-F for a perforated eardrum, diagnosed in his second visit to the draft board, after he was initially classified 1-A) only fed his reputation for unmanliness—or at best, a funny new kind of manhood. In 1945, a song about him was published, with the lyric “Dear Mr. Sinatra you’re so tender and sweet and so fine.” I once interviewed the pianist Joe Bushkin, who played with Sinatra dozens of times after their apprenticeship with Tommy Dorsey, and we talked about the codes of machismo in pop music of the 1940s. “They didn’t know what to make of him,” Bushkin said. “They thought you were light on your feet if you gave half a shit about beauty.”

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Sinatra came to full maturity as an artist in the early ’50s, partly by absorbing the influence of Billie Holiday, whom he had begun studying years earlier. As Sinatra explained to Ebony magazine in 1958, a year before Holiday’s death, “It is Billie Holiday, whom I first heard on 52nd Street…who was and still remains the greatest single musical influence on me. It has been a warm and wonderful influence and I am very proud to acknowledge it. Lady Day is unquestionably the most important influence on American popular singing in the last 20 years. With a few exceptions, every major pop singer in the U.S. during her generation has been touched in some way by her genius.”

Holiday professed to have imparted little to Sinatra. In a few brief comments on the matter to the gossip columnist Earl Wilson, Holiday said, “Listen darling, I didn’t teach Frank anything. I told him about notes at the end he should bend, and later he said I inspired him. Bending those notes—that’s all I helped Frankie with.” The technique to which Holiday refers, the effect of sliding a tone downward into the flat range, suggests sadness or despair—the note descends, and along with it, the feeling. Holiday used it freely, Sinatra sparingly but effectively on ballads such as “Yesterdays” on his Sinatra & Strings album, arranged by Don Costa in the manner of Axel Stordahl, a specialist in lush orchestral settings who worked extensively with Sinatra in the ’40s.

Sinatra’s manner of learning a new song was to read the lyrics, typed out on paper like the manuscript of a poem, before he heard the music. He would read the words aloud, as if they were speech, to absorb the meaning and enable the language to flow from his tongue like conversation. Sinatra was a disciplined musician with excellent intonation, remarkable breath control (especially in the first 15 years or so of his career, before his smoking habit tightened his lungs), an appealing sound (a well-varied and expertly controlled mix of tones from his chest, throat, and head), and a masterly way with mouth and tongue effects (such as holding notes on the nasal consonants “m” and “n,” for their resonance, instead of emphasizing the vowels as many singers do). But it was his attention to lyrics and naturalistic phrases—attributes he shared with Holiday and may well have learned from studying her—that made his singing, like hers, especially compelling.

What Holiday and Sinatra shared as singers involved technique, for sure, but also transcended it. The innovation they both enacted was a profound one. They absorbed their material deeply with close attention to the lyrical content, and they communicated the meaning so naturally and emotively that they made popular singing feel like an expressive, rather than an interpretive, art. Internalizing the material and then singing almost as if they were whispering confidences, one on one to people listening alone in their rooms with radios or record players, Holiday and Sinatra made popular music something personal. When they sang, the lyrics sounded like their own words, rather than the work of professional tunesmiths. They collapsed the wall between singer and songwriter by sounding like neither, but rather like people opening their hearts and minds. That, I think, is why the music of Holiday and Sinatra, or at least the best of it, endures. Beneath its jazzy musical beauty, there’s the timeless eloquence of truth.