It is significant that Phil Lesh, who has died aged 84, claimed that one of his earliest memories was of being stunned by hearing Brahms’s Symphony No 1. Lesh became renowned as the bassist with the Grateful Dead, but his classical training and wide-ranging musical tastes ensured that his playing stretched far beyond the traditional narrow confines of the bass guitar in rock music.

The Grateful Dead, formed in San Francisco in 1965, pioneered their own brand of improvisational music, and Lesh’s playing was imaginative enough to enable them to roam freely from rock, blues and country through sprawling jams. Even their most ardent fans acknowledged that their concerts could be hit-and-miss affairs, as the band waited for inspiration. But when it did, the results were unforgettable.

Their live performances are preserved in numerous official recordings and on countless bootleg tapes, but Live/Dead (1969) and the box-set So Many Roads (1965-1995) offer examples of the band stretching out at length, with Lesh’s extended introduction to Dark Star on the former a trademark moment. His eloquent, contrapuntal basslines were as distinctive and vital to the band’s sound as Jerry Garcia’s lead guitar.

Lesh helped write several of the Dead’s best known songs. His most personal piece is Box of Rain (from the 1970 album American Beauty), a melancholy ode to his dying father on which he sang lead vocal, with lyrics by Robert Hunter. But he also scored songwriting credits on the Dead’s on-the-road odyssey Truckin’ and Cumberland Blues.

He co-wrote and sang on Unbroken Chain and Pride of Cucamonga from the album From the Mars Hotel (1974), put a funk-like stamp on Passenger from Terrapin Station (1977), and was one of the masterminds behind St Stephen, an early favourite at Grateful Dead concerts.

Born in Berkeley, California, Phil was the son of Frank, an amateur musician who owned a small business, and his wife, Barbara (nee Chapman). He was often looked after by his maternal grandmother, Jewel “Bobbie” Chapman, a music lover who kept the radio tuned to classical stations. As Phil wrote in his autobiography Searching for the Sound: My Life With the Grateful Dead (2005): “I was awakened to the power of music early in life through the magic of radio broadcasts and by listening to my father play, from memory, his favourite tunes on the piano.” Lesh began learning the violin, and played with Berkeley’s Young People’s Symphony Orchestra.

At 14 he switched to the trumpet, then transferred from El Cerrito high school to Berkeley high school to study harmony. He became interested in free jazz and the classical avant garde and, after short stints at San Francisco State College and the College of San Mateo, enrolled at UC Berkeley.

However, he again dropped out in favour of studying with the Italian experimental composer Luciano Berio at Mills College in Oakland (among his classmates was the future star of minimalism, Steve Reich). Lesh created several of his own compositions and tried some writing with Reich.

In 1965 he met Garcia, at the time better known as a bluegrass banjo player than an electric guitarist, and who was performing with his band the Warlocks at a pizza parlour in Menlo Park in San Francisco’s Bay Area. Lesh would recall being struck how “music with that kind of directness and simplicity could deliver an aesthetic and emotional payoff comparable to that of the greatest operatic or symphonic works”.

The story goes that Garcia immediately informed Lesh that he was the band’s new bass player, to which Lesh replied: “Why not?” Soon afterwards the group changed its name to the Grateful Dead. Perhaps uninhibited because he had never previously played bass, Lesh approached the instrument in the same spirit as other 1960s innovators such as Jack Bruce of Cream, John Entwistle of the Who, and Jack Casady of Jefferson Airplane.

The Dead’s colourful career ended with the death of Garcia in 1995, a year after they had been inducted into the Rock and Roll Hall of Fame. But the band members had frequently branched out into projects outside the band, and continued to do so.

In 1975 Lesh had combined with the electronics specialist Ned Lagin and various California-based musicians on the experimental album Seastones. In 1998 he joined his fellow Dead survivors Bob Weir and Mickey Hart, and the sometime Dead keyboard player Bruce Hornsby, in the Other Ones, who later renamed themselves the Dead.

The same year Lesh, who had been suffering from chronic hepatitis C, had a liver transplant. Fully recovered, he then worked with his own outfit, Phil Lesh and Friends. This had enjoyed a brief incarnation in 1994 when it featured Garcia, but from 1999 became a rotating group of musicians that included members of Phish, Little Feat, the Allman Brothers Band and Jefferson Airplane.

From 1999 to 2003, a version of the band called the Phil Lesh Quintet became its most permanent incarnation, and they recorded a couple of live albums and the studio album There and Back Again (2002). In 2008 the group was augmented by Weir and Hart for a concert in support of Barack Obama’s presidential campaign.

The group also performed at Terrapin Crossroads, a restaurant and music venue opened by Lesh in San Rafael, California, in 2012, where Lesh’s sons, Grahame and Brian, both musicians, often played with the house band. In 2009 Lesh and Weir had reunited in Furthur, a sextet playing music by or in the spirit of the Grateful Dead.

Lesh rejoined Weir, Hart and Grateful Dead drummer Bill Kreutzmann in 2015 for three concerts at Soldier Field stadium, Chicago, billed as Fare Thee Well: Celebrating 50 Years of the Grateful Dead.

In 2006 Lesh had undergone surgery for prostate cancer, the disease that had killed his father. In 2015, he revealed he had had surgery for bladder cancer.

He is survived by his wife, Jill, with whom he formed the Unbroken Chain Foundation to support music, education and environment charities, Grahame and Brian, and a grandson.

• Phillip Chapman Lesh, musician, singer and composer, born 15 March 1940; died 25 October 2024