Carnatic music has a well-defined mathematical structure, primarily in its swara system, ragas, and talas: 1. Swara System (7 Notes & 12 Variants) The Sapta Swaras (Sa, Ri, Ga, Ma, Pa, Da, Ni) have 12 distinct pitch positions due to variations in Ri, Ga, Ma, Da, and Ni. Mathematically, these variations create 72 Melakarta ragas (fundamental scales), arranged in a structured matrix. 2. Melakarta Raga System (Combinatorial Structure) There are 72 parent ragas, systematically formed based on permutations of swaras in ascending (Arohana) and descending (Avarohana) orders. 3. Tala System (Rhythmic Cycles & Permutations) Talas are based on cycles of beats with subdivisions. The Suladi Sapta Tala system uses 7 basic talas, each having variations based on different laghu (beat groupings), leading to 35 combinations. Mathematical expansion allows infinite rhythmic patterns. 4. Gamaka (Microtonal Variations & Frequencies) Carnatic music heavily uses microtones (shruti) beyond the 12-tone scale, introducing further complexity in frequency modulation. This precise structuring makes Carnatic music both mathematically intricate and artistically expressive. read less