Amonkar, 84 , died here last night after a brief illness.
Those who attended the cremation at the Dadar crematorium included Maharashtra cultural affairs minister Vinod Tawde, santoor maestro Pandit Shivkumar Sharma, musician Abhijit Pohankar, actor Vikram Gokhale, acclaimed percussionist Taufiq Qureshi and noted playback singer Suresh Wadkar.
Singer Mahesh Kale and theatre and film director Vijaya Mehta also paid their tributes to Amonkar, whose body was draped in the national tricolour before the cremation.
Amonkar's body was kept at the Ravindra Natya Mandir in Prabhadevi area to enable people to pay their last respects and was then taken to Dadar crematorium for the last rites.
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Paying his tributes, Prime Minister Narendra Modi said the demise of Amonkar is an irreparable loss to Indian classical music.
"Deeply pained by her demise. May her soul rest in peace. The works of Kishori Amonkar will always remain popular among people for years to come," he tweeted.
Congress President Sonia Gandhi said the country has lost the most prominent exponent of Jaipur Gharana.
Congress Vice President Rahul Gandhi said that Hindustani classical music has lost a legend.
"A rare and extraordinary talent, her voice will remain with us always," he said on twitter.
West Bengal Chief Minister Mamata Banerjee also conveyed her condolences to the family members of the singer.
"Let me express deep regret over the death of legendary classical musician Kishori Amonkar...Her death has caused immense loss to the world of Hindustani classical music," Banerjee said in a message.
"...Wo ek asaadharan gayika thi. Unke jaane se shastriya sangeet jagat ki bahut haani hui hai.(She was an extraordinary singer. With her passing away, the world of classical music has suffered a great loss."
"The greatest KISHORI AMONKARJI is no more !! A very big loss for Indian Classical Music ! Her music will live on forever," tweeted music composter and singer Shankar Mahadevan.
Maharashtra chief minister Devendra Fadnavis and Governor C Vidyasagar Rao, in their condolence messages, described Amonkar as a doyen of classical music.
Born on April 10, 1932 in Mumbai, Amonkar was recognised as one of the foremost singers in the Hindustani tradition and as an innovative exponent of the Jaipur gharana.
While learning the finer points and techniques of the Jaipur gharana from her mother, Amonkar also developed her own personal style, which reflected the influence of other gharanas and was generally regarded as an individual variant of the Jaipur tradition.
Amonkar cultivated a deep understanding of her art, largely through extensive study of the ancient texts on music, and her repertoire was grand in its sweep.
She was known primarily for her skillful singing of classical khayal songs set in the traditional ragas of Hindustani music, but also performed the lighter classical thumri repertoire, bhajan, devotional songs and film music.
As she prioritised the expression of emotion in her music, she frequently departed from the gharana's conventions of rhythm, ornamentation and broader musical structure in order to intensify the impact of the music.
Besides being a renowned musician, Amonkar was a popular speaker. She travelled throughout India giving lectures, most notably on the theory of 'rasa' in music.
In recognition of her contribution to the arts, Amonkar, who is survived by two sons, received many awards, including the Padma Bhushan (1987) and the Padma Vibhushan (2002), two of India's top civilian honours.
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