The correct statement about the musical culture in 18th and 19th century South India is option 3: "Three great composers, Tyagaraja, Diksitar, and Syama Sastri experimented with the kriti form to set the foundations for modern Carnatic music."

Option 1, which states that musical developments were spearheaded by the Arcot court, is incorrect. The music culture in South India during the 18th and 19th centuries was not solely driven by the Arcot court. There were various other influential musicians and composers during this time.

Option 2, which suggests that Tanjavur replaced Madras as the cultural capital of classical music in the second half of the 19th century, is also incorrect. While Tanjavur did play a significant role in the development and patronage of classical music, Madras (now Chennai) has always been a major cultural center for music in South India.

Therefore, the correct answer is option 3: 3 only.