In a complete cycle of 'Chautal', the 'Aad' laya of which taal pair's one cycle can be set ?

Question

Accepted Answer

The correct option is 1:
The core of this problem lies in understanding the mathematical relationship between the 'Aad' laya (rhythm) and the total time frame provided by a 'Chautal' cycle. Chautal is a well-known ancient Hindustani Taal comprising 12 matras (beats). The 'Aad' laya refers to a speed ratio of 3:2, meaning three notes (or matras) are played in the time normally allotted to two notes (or matras) of the base tempo. To find the total number of matras (M) that can be accommodated in *Aad* laya within the duration of a 12-matra cycle of Chautal (at the base laya), we multiply the base cycle length by the 'Aad' ratio (3/2). The required total matras M = 12 \* (3/2) = 18 matras. Option 1, Keherwa (8 matras) and Jhaptal (10 matras), is the only pair whose matra counts add up precisely to 18 (8 + 10 = 18), making this combination the correct theoretical solution.

The incorrect option is 2:
Dhamar and Ektal together contain 26 matras (Dhamar is 14 matras and Ektal is 12 matras). If a 26-matra composition were played in 'Aad' laya, it would occupy the time equivalent to 26 \* (2/3) or approximately 17.33 matras of the base tempo. This duration is significantly longer than the 12-matra cycle of Chautal, meaning the complete cycle of this pair cannot be set exactly within one Chautal cycle. The sum of matras must be exactly 18 for a perfect fit.

The incorrect option is 3:
Dadra and Deepchandi form a pair with a total of 20 matras (Dadra is 6 matras and Deepchandi is 14 matras). An 'Aad' laya setting for this 20-matra composition would have a duration of 20 \* (2/3) which equals approximately 13.33 matras of the base tempo. This duration exceeds the 12-matra limit of the Chautal cycle. Thus, neither the total number of matras (20) nor the final duration in 'Aad' laya aligns with the 18 matras required for the exercise.

The incorrect option is 4:
Tilwada and Rupak's matra count is 23 (Tilwada is 16 matras and Rupak is 7 matras). Converting this total into the time occupied in 'Aad' laya would result in a duration of 23 \* (2/3), which is approximately 15.33 matras of the base tempo. This is too large to fit exactly into a 12-matra Chautal cycle. Furthermore, the matra total of 23 is far from the calculated requirement of 18 matras necessary for a rhythmic alignment in the 3:2 'Aad' ratio.