During their commercial peak in the 1960s, the songs of Burt Bacharach (who died today at 94) and lyricist Hal David were so commercially successful and ubiquitous that they were often categorized as schmaltz — their lush, rich sound, easy melodies and gentle tempos conjured visions of ascot-and-sunglasses Bel Air poolside parties for the very rich, like the ones in the early scenes of the contemporaneous film “The Graduate.”

Yet part of Bacharach’s brilliance was in that deceptive simplicity: His songs are extremely musically sophisticated, complex and often downright weird, combining a world of influences — from jazz and classical to bossa nova and westerns — along with startling yet seemingly smooth key and time-signature changes, unusual voicings and more.

But for all that, to countless millions of ears it’s simply beautiful music — art and ability and human spirit at its peak, the same thrill one gets when watching a gymnast or ballerina or downhill skier so talented they make it look like anyone can do it. When Rupert Everett somehow leads a singalong of Bacharach and David’s “I Say a Little Prayer” at Cameron Diaz’s’ rehearsal dinner in the 1997 film “My Best Friend’s Wedding,” some suspension of disbelief is required — it’s a really, really difficult song to sing, both melodically and rhythmically.

Bacharach’s songs — the most classic of which were written with David — have been covered by thousands of people, from the Beatles (on their first album, no less), Barbra Streisand and Neil Diamond to psychedelic rockers Love to Isaac Hayes and new wave one-hit wonders Naked Eyes, and were originally performed by a battery of top-shelf singers from the Carpenters and the Drifters to Dusty Springfield and their ultimate interpreter, Dionne Warwick. Her arch, crisp delivery and formidable ability were a perfect match for Bacharach’s easy-sounding but deeply challenging melodies and high-class arrangements, and he and David reached even further beyond convention as they began to tailor songs for her.

Born in 1928, Bacharach’s musical sensibilities were formed decades before his songs became ubiquitous, and his first hits in the 1950s were very much of their time, with swooning string arrangements, doo-wop-inspired vocals and even whistling. Yet his brilliance began to emerge in the early 1960s and reached full bloom throughout the decade, largely in his and David’s work with Warwick and Springfield. His songs’ deceptive simplicity in many ways has only been rivaled by that of ABBA, another act whose image, accessibility and lyrics often overshadowed the brilliance and sophistication of their music.

An exceptionally gifted pianist and a sumptuous arranger, Bacharach wrote a mind-boggling number of classics and narrowing them down to a dozen best is a fool’s errand — even the briefest comprehensive “greatest hits” collections have around 50, and he wrote more than 100 with David alone and even more with others across a 70-plus-year career. What follows below aren’t necessarily his biggest hits or his best songs or even his many perfect pop songs (except for one at the end), but rather 12 stellar examples, among many, that illustrate his genius.

Dionne Warwick “Anyone Who Had a Heart” (1963) — In many ways, this is where the magic really begins: with Warwick’s first hit and the bridge between Bacharach’s early work and his peak period. It’s is an unusual and challenging song, starting off almost deadpan, lingering on one chord before the lilting backing vocals and sweeping orchestra join in. The song’s time signature is all over the map, moving from 4/4 to 5/4 to 7/8 at the end — “That’s just the way I felt it,” Bacharach is quoted as saying.

Dusty Springfield “Wishin’ and Hopin’” (1964) — Originally recorded by Warwick in 1962 in a nearly identical arrangement, Springfield’s version is the definitive one for reasons that are difficult to pin down: Both are obviously world-class singers, but here Springfield’s vocal has a bit more command and power than Warwick’s. It’s a remarkable song either way (despite lyrics that are horrifically sexist, even without 60 years hindsight), with a smooth, mellifluous melody delivered over a rhythm that is downright lurching, stop-starting or changing tempo every few bars.  

Dusty Springfield “I Just Don’t Know What to Do With Myself” (1964) — Another song first recorded in 1962 (by Chuck Jackson and, later, Tommy Hunt) this version reached No. 3 in the U.K. and out-Spectors Phil Spector, with a regal opening fanfare of French horns, a soaring string arrangement and booming drums creating an even more dramatic setting for Springfield’s powerhouse vocal. Later, the song also showed an unexpected-at-the-time sentimental side of Elvis Costello, who released a live version in 1977 at the peak of his angry-young-punk days — and would collaborate with Bacharach nearly 20 years later on the “Painted From Memory” album, which comes out in an expanded reissue next month — as well as Jack White, who covered it with the White Stripes in 2003.

Sandie Shaw “Always Something There to Remind Me” (1965) — An ultimate breakup song, Shaw lays in the cut on the verses, delivering the song’s complex, latticework-like melody, but bursts open on the chorus as the elaborate arrangement booms behind her. The verses’ melody snakes over a jazzy, even more complicated shuffling rhythm that new wave duo Naked Eyes simplified dramatically on their 1983 hit version.

Tom Jones “What’s New Pussycat?” (1965) — Okay, this novelty song is pretty ridiculous, but its brilliance lies in the way the arrangement embraces that ridiculousness: Underpinned by a bass drum, and with a tuba honking the part that ordinarily would be played by the bass, it’s got accordions, a guitar that sounds like a banjo, some weird calliope-like keyboard and a blaring horn section. It’s absolutely hilarious, but whatever — it worked, peaking at No. 3 in U.S. in July of 1965, behind the Rolling Stones’ “Satisfaction” and another masterpiece of absurdity, Herman’s Hermits’ “I’m Henry VIII, I Am.” (Inevitably, a modified version of the song soundtracked a long-running Purina Cat Chow TV commercial.)

Cilla Black “Alfie” (1966) — One of Bacharach’s most famous songs had an unpromising start: Written for the Michael Caine film of the same name, it was turned down by Sandie Shaw and initially rejected by Black, who recalled telling her manager Brian Epstein (yes, also the Beatles’ manager), “‘I can’t do this. For a start — Alfie? You call your dog Alfie!’” But she changed her mind after Bacharach agreed to fly to London and not only play piano but write the song’s lush orchestral arrangement, which was helmed by Beatles producer George Martin. This epic became a classic and has been covered literally hundreds of times.

Burt Bacharach “Nikki” (1966) — Named after Bacharach’s daughter with Angie Dickinson, this version is perhaps his ultimate instrumental, with a playful coronet melody and celestial strings in the background — not surprisingly, it was the theme for ABC’s “Movie of the Week” for many years. However, the song now has a bittersweet edge: Nikki herself, who suffered from Asperger’s Syndrome, died by her own hand in 2007.

Herb Alpert & the Tijuana Brass “Casino Royale” (1967) — Many of Bacharach’s great works were instrumental, and this definitively 1967 song — performed and produced by Alpert but written and arranged by Bacharach — bears many of the hallmarks of his sound, particularly a sumptuous melody underpinned by a complicated, ever-changing rhythm. It’s the kind of song that will eternally summon cliché visions of a carefree drive along a coastal highway, the wind blowing in a beautiful companion’s hair…

Jackie Trent “Make It Easy on Yourself” (1967) — While the song was one of Bacharach’s first major hits, as recorded by Jerry Butler in 1962, this version is a stellar example of the sound that became one of his trademarks: a big singer and big orchestra, offset by a trebly electric bass. Unusually, it begins with the chorus — in itself not an innovation, but with the chorus initially played instrumentally by the orchestra and the vocalist first heard on the payoff line, “Because breaking up is so very hard to do,” a lyrical sleight of hand that leaves the listener subconsciously wondering what came before.

Dionne Warwick “Do You Know the Way to San Jose?” (1968) — This classic, possibly quintessential song by the Bacharach-David-Warwick triumvirate begins as oddly as any hit song in history: With a four count from the bass and a bass drum, followed by a lilting “Woah-woah woah-woah woah-woah woah-woah-woah” that is then repeated before the song’s indelible, jazzy melody kicks in. The magic lies in the seeming effortlessness of the melody and Warwick’s delivery, but her vocal skips up and down the scale and floats above the shuffling, stop-start rhythm that was a trademark of many Bacharach’s best songs.

Aretha Franklin “I Say a Little Prayer” (1968) — Originally recorded by Warwick in 1967, it’s safe to say that Aretha’s version of this song about a woman’s concern for her man fighting in the Vietnam war is the definitive one, her peerless voice soaring over the song’s complicated chorus, delivered by the Sweet Inspirations (featuring Cissy Houston, who is not only Whitney’s mother but replaced Warwick, her niece, in the group). Like many of Bacharach’s great songs, the time signature careens all over the place, from 4/4 to 10/4 and back, climbing to 11/4 on the chorus — which is why the scene from “My Best Friend’s Wedding” mentioned above is so hard to imagine taking place in real life. (Warwick’s original, produced by Bacharach and David, shows the brilliant liberties Frankin and the Sweet Inspirations took with the melody.)

Dionne Warwick “Promises, Promises” (1968) — One of Bacharach’s jazziest melodies and certainly one of his most complex and unpredictable — and as always, Warwick’s range, phrasing and breath control are more than up to the challenge. The song, the title track of Bacharach and David’s first and only Broadway musical, would be a vocalist’s triathlon even without the hard stops required for a repeated word beginning with “P” — and after all the intricate rises and falls and half-steps required for the verses, she has to belt and hold a series of four increasingly higher notes on the chorus. Not for the faint of voice.

BONUS: Dionne Warwick “I’ll Never Fall in Love Again” (1969) — While not as musically complex as many of the songs listed above, this may be Bacharach’s most perfect pop song, its effortless melody complimenting Warwick’s faux-nonchalant delivery of Hal David’s sour-grapes lyric (“What do you get when you kiss a guy?/ You get enough germs to catch pneumonia”), which are designed to be unconvincing. The song, also from “Promises, Promises,” was written quickly after Bacharach was in the hospital with the above-referenced pneumonia after producer David Mamet raged for another love song for the musical; consequently, Bacharach later said it was the fastest song he’d ever written. Driven by his piano, it fades out with him elaborating beautifully on what may be his most timeless melody — unforgettable, as if it were always there, but he was the one who found it.