Ravi Shankar, who has died aged 92 after undergoing heart surgery, was the Indian maestro who put the sitar on the musical map. George Harrison called him "the godfather of world music" and it was Shankar's vision that brought the sounds of the raga into western consciousness. He was thus the first performer and composer to substantially bridge the musical gap between India and the west.

He was still winning awards in the new century: in 2002 his album Full Circle: Live at Carnegie Hall (2000) achieved a Grammy for best world music album. Shankar's distinction as a sitar player lay in his brilliant virtuosity, creativity and musicianship. In the west his name is synonymous with the music of India.

Ravindra Shankar – in Bengali, Robindro Shaunkar – Chowdhury was born in the holy city of Benares, now Varanasi. The youngest of five sons, he belonged to a family of Bengali Brahmins from Jessore, now in Bangladesh, who were much influenced by the reformist ideas of writers such as Rabindranath Tagore, one of the major figures of the Indian Renaissance.

Ravi's father was a Sanskrit scholar who became chief minister of Jhalawar state, in the north-west of India. As a child in Benares, Ravi had his passion for music awakened by Vedic chants. But his first commitment was to dance.

His eldest brother, Uday, had worked as a dancer with Anna Pavlova before setting up an Indian music and dance company to perform in the west. Along with his mother and brothers, in 1930 Ravi joined him in Paris and became the youngest member of the company, specialising in cameo dance roles.

For two years, he led the life of a French schoolboy and became fluent in the language. While in Paris he heard western classical music for the first time. He loved the guitar artistry of Andrés Segovia and the singing of Feodor Chaliapin. Opera, too, enchanted him.

However, once back in India, he set his heart on becoming a sitarist after listening to the melodious playing of an older boy. He resolved to learn from the famous sitar teacher and performer Inayat Khan, the father of the sitarist Vilayat Khan and the surbahar player Imrat Khan, but on the day of the initiation ceremony Shankar fell ill with typhoid.

Later, at the age of 18, he was apprenticed to Allauddin Khan, a disciple of Wazir Khan, who was a direct descendent of the legendary Tansen, the chief musician of the Mughal emperor Akbar. For seven years Khan was Shankar's mentor and through this connection Shankar inherited a great tradition of classical music. In his autobiography, My Music, My Life (1969), Shankar says that Baba, as he called his teacher, made his pupils practise for hours on end and often resorted to corporal punishment. However, on only one occasion did Baba smack him on the hands. In 1941, Shankar married Khan's daughter Annapurna, herself an accomplished musician, and they had a son, Shubhendra, before separating later in the decade. Another musician, he went on to accompany his father, and died in 1992.

Shankar gave his first concert in 1939, and the following year began giving recitals with Khan's son Ali Akbar Khan, the sarodist, on All India Radio. He first made an impression in his own right with scores written in Mumbai for two notable Indian films of 1946, Dharti ke Lal (Children of the Earth) and Neecha Nagar (The City Below), and composed for the Indian People's Theatre Association. In 1946-47 he was involved with producing and composing music for a ballet entitled The Discovery of India, based on the book by Jawaharlal Nehru. He later founded and became the musical director of All India Radio's first National Orchestra and was sent on foreign cultural tours by the Indian government.

In addition to an arduous performing schedule, he composed the music for the films comprising Satyajit Ray's Apu Trilogy (1955-59). He also composed a concerto (1971), which he performed with the London Symphony Orchestra, conducted by André Previn. Shankar's initial exploration of the possibilities of combining jazz and Indian classical music led to the album Improvisations (1961). He went on to teach Indian music to the jazz musicians John Coltrane and Don Ellis, and for the drummer Buddy Rich and tabla player Alla Rakha he composed Rich à la Rakha (1968).

His first meeting with George Harrison and Paul McCartney of the Beatles came in 1966, at a friend's house in London. Harrison took up the sitar and later that year went to India for a period of intensive tuition. From this partnership came Shankar Family & Friends (1974).

Shankar also created a musical partnership with Yehudi Menuhin. They had met in 1951 when the violinist was visiting India, though Shankar vividly recalled having seen him at rehearsals when they were boys in Paris in the 30s. In 1967, they played for the UN general assembly at a human rights day event. They also recorded three albums together, the first of which, East Meets West, won a Grammy award in 1967.

Performances at the great pop festivals of the time – Monterey, California, in 1967; Woodstock in 1969; and Concert for Bangladesh, New York, in 1971 – brought Shankar even more firmly into the west's popular gaze and saw him established as a pioneer of crossover sounds.

His Kinnara School of Music functioned both in Mumbai and Los Angeles. In his 70th year celebration concert at the Royal Albert Hall, he performed with Menuhin, the flautist Jean-Pierre Rampal, the harpist Marielle Nordmann and Rakha, with whom he had a particularly long and fruitful relationship.

Though Shankar had many friends and admirers, in India especially there were classical musicians who were envious of his international success and criticised his association with the popular music of the west. His technique was faultless, but his flair for showmanship was resented by some.

His genius, of course, lay in a combination of gravitas and gaiety. Shankar not only transcended culture, race and geography, but also had no difficulty with the generation gap and differences of social class. The flower-power generation and their successors listened to what he had to offer with open minds. He was showered with citations and awards: in 1999 he was appointed a Bharat Ratna (Jewel of India), in 2000 a Commandeur de la Légion d'Honneur in France, and in 2001 an honorary KBE in Britain. In the US he was an honorary member of the American Academy of Arts and Letters. In later years he divided his time between Encinitas, California, and Chanakyapuri, New Delhi, where the Ravi Shankar Institute of Music and the Performing Arts was the culmination of his lifelong dream. Housed in an elegant pink granite building, it attracts students from all over the world.

He is survived by his second wife, Sukanya, and their daughter, Anoushka, also a well-known sitar player; both father and daughter have been nominated for the 2013 Grammy awards. With the New York concert producer Sue Jones he had another daughter, Norah Jones, herself the winner of several Grammies as a singer.

• Ravi (Ravindra) Shankar Chowdhury, musician and composer, born 7 April 1920; died 11 December 2012

• This article was amended on 14 December 2012. The original referred to Imrat Khan as a sarodist.

Contributor

Reginald Massey

The GuardianTramp

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