Question

To play or recite Dugun and Chaugun of Aadachautaal once in one aavartan of same taal, one have to start exactly after which matra to reach the sam.

• A. \(3\frac{1}{2}\)
• B. \(3\frac{1}{4}\)
• C. \(3\frac{3}{4}\)
• D. \(3\frac{2}{3}\)

Hint:

Formula: \(\text{Start Position} = \text{Total Matras} - \left( \frac{\text{Taal Matras}}{\text{Speed 1}} + \frac{\text{Taal Matras}}{\text{Speed 2}} \right)\). For this question: \(14 - \left(\frac{14}{2} + \frac{14}{4}\right) = 14 - (7 + 3.5) = 3.5 = 3\frac{1}{2}\).

Answer 1

The Correct Option is A

Concept: To find the exact starting beat (Jaga) for a dynamic phrase layout to complete perfectly on the first beat (Sam) of the subsequent cycle, we calculate the mathematical time-space occupied by the custom performance sequence.

Step 1: Determine total metrics of the cycle and the segments.

• Aadachautaal contains a total length of 14 matras.
• Dugun (double speed) means playing at 2 notes per beat. Performing 1 complete cycle of Aadachautaal (14 notes) at double speed consumes: \[ \text{Time consumed} = \frac{14}{2} = 7 \text{ matras} \]
• Chaugun (quadruple speed) means playing at 4 notes per beat. Performing 1 complete cycle of Aadachautaal (14 notes) at quadruple speed consumes: \[ \text{Time consumed} = \frac{14}{4} = 3.5 \text{ matras} \]

Step 2: Calculate total space and starting position.
Summing both performance durations yields the total time consumed: \[ \text{Total Duration} = 7 + 3.5 = 10.5 \text{ matras} \] Subtracting this total duration from the 14-matra cycle length gives the precise point after which the recitation must begin: \[ \text{Starting Point} = 14 - 10.5 = 3.5 = 3\frac{1}{2} \text{ matras} \]