In the 19th century, the Britain became the dominant colonial power in India, and in 1858 India became officially apart of the British empire.

Currently today. 80.5% of all of India is associated with Hinduism, while 13.4% associate with Muslim, but after plenty of years since the British Colonization, 2.3% of India is Christian.

Hindu, being the largest religion in today's India, played a big role in their music. Ancient Hindu scriptures called Vedas, were believed to have been the early beginnings to classical Indian music.

Bhajan - devotional songs and hymns of the Hindu religion

Even though there are many differences between Islam, Sikhs, and the Hindu religion, Sufism (a form of Islam) shared many beliefs with Hinduism about how music creates a connection between humans and deities.

Qawwali - a style of music that stemmed from Sufism that involves singing, clapping, and rhythmic drumming

Nusrat Fateh Ali Khan - Qawwali singer (16:33-17:10)
https://www.youtube.com/watch?v=kLBFmA87tyg

During the raga performance, if an instrumentalist is not playing, or stops playing for a few beats, they keep the beat silently with their hands. 
This is called Keeping Tal, and it is a more organized way of keeping the beat as another instrumentalist is playing.
The beat is kept by finger touching, silent clapping, or waving the hand.

Anoushka Shankar - Hindustani raga performance (2:10-4:30)
https://youtu.be/-wra4p4zARw?t=2m10s

Ravi Shankar - a famous and talented Hindustani musician who studied in Paris and London, making connections between European instruments and bringing the traditions of Indian Hindustani to an international level.

Ravi was a master at playing the sitar and taught The Beatle's George Harrison how to play, connecting Western music with traditional Indian music and raga instruments. The Beatles released their album Rubber Soul in 1965 which featured the song "Norwegian Wood" and became famous for George Harrison's sitar solo. After the sitar grew to be a favorite exotic instrument in the United States, Harrison decided to formally begin studying under Ravi Shankar.
https://www.youtube.com/watch?v=t79aI-I6ucA

Another musician that took an interest in classical music was John McLaughlin who was a famous guitarist and composer. He led a jazz-rock fusion band called Mahavishnu Orchestra which was influenced greatly by classical Indian music. McLaughlin also studied under Ravi Shankar and eventually converted to Hinduism. He later created another band of Indian-jazz fusion music called Shakti and it featured other talented musicians such as Ravi's nephew L. Shankar, and Zakir Hussain. McLaughlin developed his own acoustic guitar that was modified to resemble some features of the sitar.