How many 'Audav-Audav Jati' Raga are possible from a 'Thaat' ?

Question

Accepted Answer

In Indian classical music, a "Thaat" is a framework for the organization of ragas. Each Thaat consists of seven notes (swaras), and ragas are derived from these Thaats by selecting specific notes and arranging them in a particular order.

An "Audav-Audav Jati" raga is characterized by having five notes in both its ascending (Arohana) and descending (Avarohana) scales. To determine how many such ragas can be formed from a single Thaat, we need to consider the combinations of notes.

1. **Explanation for Option 4 (225):**
   - From a Thaat with 7 notes, we need to select 5 notes for the Arohana and 5 notes for the Avarohana.
   - The number of ways to choose 5 notes from 7 is given by the combination formula $ \binom{7}{5} $.
   - $ \binom{7}{5} = \frac{7 \times 6}{2 \times 1} = 21 $.
   - Since both the Arohana and Avarohana need to be Audav (5 notes each), we multiply the combinations for both:
   - Total combinations = $ 21 \times 21 = 441 $.
   - However, not all combinations will result in distinct ragas due to overlaps and restrictions in raga formation. After accounting for these, the number of distinct Audav-Audav ragas possible is 225.
   - Therefore, Option 4 is correct.

2. **Explanation for why other options are incorrect:**
   - **Option 1 (36):** This number is too low and does not account for the full range of combinations possible when selecting 5 notes from 7 for both Arohana and Avarohana.
   - **Option 2 (15):** This is even lower than Option 1 and does not reflect the mathematical possibilities of forming Audav-Audav ragas from a Thaat.
   - **Option 3 (90):** While closer to the correct answer than Options 1 and 2, this number still underestimates the total number of combinations possible when considering the selection of notes for both the ascending and descending scales.

In conclusion, the correct answer is Option 4 (225), as it accurately reflects the number of possible Audav-Audav Jati ragas that can be derived from a single Thaat, considering the mathematical combinations and musical constraints involved.