The Sangeeta Ratnakara, a treatise accepted by both the Hindustani and the Carnatic traditions, was written by whom?

The correct answer is B, Sarangadeva. Sarangadeva wrote the Sangeeta Ratnakara in the thirteenth century while attached to the Yadava court at Devagiri in the Deccan. Because it has seven chapters it is also called the Saptadhyayi, and because it was written before the northern and southern traditions drew apart, both of them still treat it as authoritative.

Option A, Matanga, wrote the Brihaddeshi, the work remembered for using the word raga in something close to its modern meaning, but not the Sangeeta Ratnakara. Option C, Bharata Muni, is the author of the Natya Shastra, the treatise on drama that contains the earliest systematic description of swaras and shrutis. Option D, Venkatamakhin, belongs to the seventeenth century and to the south; his Chaturdandi Prakashika set out the scheme of seventy-two melakarta ragas that Carnatic music still uses. All four are treatise writers, which is exactly why they are offered together.