Harold Galper was born in Salem, Massachusetts on April 18, 1938 and started piano lessons at six. He went to Berklee on a scholarship in 1955 and studied there until 1958, taking technique from Margaret Chaloff, the Boston teacher known to two generations of pianists as Madame Chaloff, and spending his nights in the city's clubs. He hung around Herb Pomeroy's room, the Stable, until they let him sit in, and he ended up as its house pianist and later as house pianist at Connelly's and at Lennie's on the Turnpike. The players he learned the music from on those bandstands were Jaki Byard, Alan Dawson and Sam Rivers, and he worked in Pomeroy's band. His first appearance on record is a Berklee student anthology, Jazz in the Classroom, cut for the school's own label in 1958.

He moved to New York in 1963 and was working almost immediately. Chet Baker took him on for about three years and recorded three of his tunes, "This Is the Thing", "Pamela's Passion" and "Mr. B"; Galper is the pianist on the whole of the Colpix album released as The Most Important Jazz Album of 1964/65, where he also arranged and wrote two pieces, and one of three pianists on the Limelight date Baby Breeze. He accompanied singers for a living in the same years, working with Joe Williams, Anita O'Day, Chris Connor and Dakota Staton, and he took the piano chair on Sam Rivers's Blue Note quartet album A New Conception, recorded on October 11, 1966 with Herbie Lewis on bass and a young drummer named Steve Ellington, who would become the pivot of Galper's own band twenty-four years later. In June 1970 he was the pianist in the Hutcherson-Land Quintet at the Ljubljana festival, a performance that survives as "Mana Mercury" on two documentary LPs, and in 1969 he played on and arranged three tracks of Randy Brecker's Solid State debut Score.

That session began the most consequential of his associations. Randy and Michael Brecker are the front line of the two loud, electric records Galper made for Bob Shad's Mainstream label at the start of the 1970s, The Guerilla Band (August 1971) and Wild Bird (1972), both of them built around his Fender Rhodes and both of them a long way from the acoustic trio work he is now remembered for. A third Mainstream album, Inner Journey (1973), reversed course completely: acoustic piano, all seven pieces his own, with Dave Holland on bass and Bill Goodwin on drums. Between the two he spent a year with Stan Getz from 1972, and in 1973 he replaced George Duke in the Cannonball Adderley Quintet and stayed until 1975. He is on three Adderley albums for Fantasy, Inside Straight, Love, Sex, and the Zodiac and Pyramid, and on Nat Adderley's Double Exposure, and the band played a great deal of his writing: eight of his compositions are spread across those three Fantasy records. One of them, "Leo: Rosebud", reached a second audience twenty-four years later when A Tribe Called Quest sampled it on "Steppin' It Up".

A National Endowment for the Arts grant in the mid-1970s let him put together the Hal Galper Quintet, with the Brecker brothers again, Wayne Dockery on bass and Billy Hart on drums. It opened at Sweet Basil in Greenwich Village and made four albums, Reach Out! for SteepleChase in November 1976, the live Speak With a Single Voice and Redux '78 from two nights at Rosy's in New Orleans in February 1978, and a Berlin concert from November 1977 that sat in a vault for forty-four years before Origin issued it in 2021. Around the quintet he cut two of his most admired records for Enja: Now Hear This (February 15, 1977), a quartet with Terumasa Hino, Cecil McBee and Tony Williams, and Ivory Forest (Ludwigsburg, October and November 1979), where the guitarist is John Scofield and the drummer Adam Nussbaum. The three had recorded together the previous year on Scofield's Rough House. He also made a duo record with Lee Konitz, Windows, in New York in January 1975.

From 1980 he held the piano chair in Phil Woods's band, a job he kept for a decade and which produced the largest single block of sideman work in his catalogue, some fourteen albums. The group was a quartet with Steve Gilmore and Bill Goodwin when he joined, won a Grammy for the Village Vanguard recording At the Vanguard, and became a quintet when Tom Harrell joined the front line. His own leader dates in that decade were fewer and quieter: a trio night in Melbourne in January 1982 with Rufus Reid and Victor Lewis that BlackHawk released as Naturally, the standards album Dreamsville with Gilmore and Goodwin in 1986, a Stockholm session with the Swedish clarinettist Putte Wickman the same year, and Portrait for Concord in February 1989 with Ray Drummond and Hart, its sleeve notes written by Nat Hentoff.

He left Woods in August 1990 to run a trio of his own, and for the next nine years it was on the road half of every year. Steve Ellington was the drummer throughout; Todd Coolman took the bass chair first, and Jeff Johnson eventually became the permanent replacement. That band recorded Invitation to a Concert, Tippin', Live at Vartan Jazz and Fugue State, and expanded to take in the tenor saxophonist Jerry Bergonzi on Just Us, Rebop and the quintet album Let's Call This That. A solo recital for Concord's Maybeck Recital Hall series in July 1990 and a solo Toronto broadcast issued by the Italian label Philology round out the decade. From the mid-2000s his working group was a second trio, with Johnson and the Seattle drummer John Bishop, and it became the vehicle for the idea that occupied the rest of his life: a rubato conception in which the trio plays loose with tempo, harmony and form without abandoning the tune. Seven Origin albums document it, from Furious Rubato (2006) to The Zone: Live at the Yardbird Suite, taped in Edmonton in November 2016. Two outliers stand apart from it, Art-Work, recorded live at William Paterson University in February 2008 with the John Coltrane alumni Reggie Workman and Rashied Ali, and a 2016 festival set in Pennsylvania fronting a band of conservatory students he called the Youngbloods.

Teaching mattered to him as much as playing. He was a charter faculty member of the New School for Jazz and Contemporary Music when it opened in 1986 and was still auditioning students there thirty years later, and he served on the faculty of the Conservatory of Music at Purchase College for fourteen years until he retired in 2014. His article on the psychology of stage fright, first published in the Jazz Educators Journal, has been reprinted four times, and he wrote two books that are standard equipment for a working improviser: Forward Motion: From Bach to Bebop (2003), issued as the first interactive jazz e-book with more than three hundred playable examples, and The Touring Musician (2007), which is about the small-business end of the job rather than the music. He kept teaching through YouTube and social media into his eighties. In November 2024 he announced that he was stepping back from performing to concentrate on writing, and he passed away at his home in Cochecton, New York on July 18, 2025, at eighty-seven. He is survived by Lillyan Peditto, his partner of more than forty years.

Galper was a bebop pianist by training and a restless one by temperament, and the tension between those two facts is the whole story of his playing. The technical foundation came from Madame Chaloff in Boston, whose approach to weight and touch he credited for the singing, unhurried sound he kept even at speed, and the vocabulary came from the bandstands of the late 1950s, where he learned the music from Jaki Byard and Herb Pomeroy rather than from a classroom. What unsettled him was Ornette Coleman: he told Cadence that he could not play the way he played later without the intervening years of bebop groundwork, but that the first Coleman record he heard set the direction. The synthesis arrived late, in the Origin trio records after 2006, where the group treats tempo, harmony and even form as elastic and the tune survives anyway, a practice he simply called rubato. His most durable idea, though, is pedagogical. Forward Motion argues that jazz phrasing resolves forward, onto the strong beats ahead rather than the barline behind, and it reframes bebop line-building as an inherited technique rather than a mystery. It has become a standard text, and Dave Liebman wrote its foreword. DownBeat called him an underrated master of his craft; the guitarist Yotam Silberstein, one of many former students, called him one of the best teachers he ever had.