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Behind the art of music lies an exact science, wherein a practical application of mathematics is found, in the form of series, progressions, arithmetic mean and so on. This wonderful relationship between music and mathematics is as ancient as it defies understanding. It nevertheless makes for an interesting study. Many great mathematicians have also been great lovers of music. Mathematics is found abundantly in music and in playing Musical Instruments. Using the concept of the 12 notes, the 72 Melakarta or scales have been evolved by means of permutation. Other scales and ragas have also been arrived at by the permutation or omission / addition of the 12 notes. The Pallavi, of an Ragam-Tanam-Pallavi is highly mathematical, (Pallavi meaning pada- laya -vinyasam) requiring the musician to sing the same line in different degrees of speed, gati etc. The Pallavi (of Ragam Tanam Pallavi) uses geometrical progression of speeds in anulomam by doubling and quadrupling the speed of the melody while keeping the speed of the Tala constant. In pratilomam the speed of the melody is kept constant and the reckoning of the Tala by the fingers shows the geometric progression. Musical / rhythmic patterns like the Yatis (e.g., Gopuccha, Damaru, Mrdanga, Srotovaha etc) have specific geometrical patterns. The Katapayadi formula, an interesting formula that combines language and mathematics, has been used to coin the nomenclature of the 72 Melakartas with their serial numbers.

107 The interesting relationship between Music and Mathematics: Both music and mathematics are abstract, subtle as well as concrete. They need not reflect situations and objects of the concrete world as in literature and painting. Both seek the beauty of balance and symmetry. Intricate mathematical calculations expressed in Jatis with raga bhava give this form a brisk sprightly tone. Rhythm gives vitality and order to melody, as already implied in the aphorism - srutir mata Layah pita. The Tala system is also based on mathematics. The Suladi Sapta Talas are 7 varieties of Talas systematized by Purandaradasa. Each of these 7 Talas is capable of 5 varieties through change of the laghu count, which gives us 35 different Talas. Each of these 35 Talas is capable of variations of gati (value per unit) viz., Catusra (4) gati, Tisra (3) gati, Misra (7) gati, Khanda (5) gati and Sankirna (9) gati. The total varieties are thus 35 times 5, which is 175 Talas. Accuracy is the essence of math. Similarly, in music one has to be accurate in Tala. The calculations have to be exact in both rhythm and proportion. Rhythm was considered an innate quality, whereas calculation in music was acquired. The terms Laya is for rhythm and Tala is for calculation. The basic rhythm is called Sarva laghu, which is an even progression in fours. Mathematics is a vital component of Indian Classical Music. Tala, which binds a composition and preserves it for posterity is mathematics in action. Mathematics is thus the very heartbeat of Indian music.