Step 1: Comprehend the Inquiry:
The query seeks to identify a singular, all-encompassing ancient Indian document that addresses the principal performing arts: dramatics, choreography, and melody.
Step 2: Elaborate on the Findings:
- The Natyashastra, credited to the sage Bharata Muni, stands as India's most ancient and complete exposition on the performing arts. Referred to as the "fifth Veda," it forms the bedrock for classical Indian drama, dance (Natya), and music (Gandharva).
- Abhinayadarpanam and Abhinaya Chandrika are significant but concentrate more narrowly on dance methodologies (Abhinaya).
- Sangeet Ratnakara, authored by Sarangadeva, is a substantial 13th-century work, though it predominantly details music and dance and originates much later than the Natyashastra.
Step 3: Conclude the Resolution:
The Natyashastra is the initial and most thorough treatise covering theatre, dance, and music.