There are 484 arohs/avrohs (ascendings/descendings) possible in each Thaat, thus there are 484 opportunities to make unique Raags in each Thaat. Here are some of the points that govern this theory and the illustrations below:
1. There are 3 main Jaties. (Sampooran, Chhadav and Audav)
2. There is only one (1) Sampooran scale in each Thaat.
3. There are six (6) Chhadav scales in each Thaat,
4. There are fifteen (15) Audav scales in each Thaat.
5. Raags need an ascending and a descending defined.
6. When used in pairs to make arohs/avrohs (ascendings/descendings), the three categories make Nine (9) subcategories.
7. All the examples shown here are in Bilaval Thaat (natural scale from ‘C’). It can be applied to any of the 10 Thaats mentioned in this post. So theoretically there are 4840 Raags in Northern Indian music.
8. The following illustrations are in Flash format. If you do not see anything, please download free flash player here.

Let’s count the Raags in all nine subcategories.
1. Sampooran-Sampooran (7-7): This category uses all 7 notes in Aroh and Avroh. As no alteration is possible, so every Thaat can have only one unique Sampooran-Sampooran aroh/avroh.
2. Sampooran-Chhadav (7-6): There are six (6) Chhadav scales available in each Thaat. When we pair them with one (1) Sampooran scale, it gives us 1×6=6 unique Raags. Use the next and previous arrows in the flash movie to navigate through the scales.
3. Sampooran- Audav (7-5): There are fifteen (15) Audav scales in each Thaat. When we pair them with one (1) Sampooran scale, it gives us 1×15=15 unique Raags.
4. Chhadav- Sampooran (6-7): In this Jati, the Aroh is Chhadav (6 notes) and the Avroh is Sampooran (7 notes). This gives us 1×6=6 unique Raags. This Jati is the flip side of Sampooran-Chhadav (2nd Jati).
5. Chhadav-Chhadav (6-6): Chhadav Arohs paired with Chhadav Avrohs give us 6 scales on both sides. When we put them together, we get 6×6=36 unique Raags.
6. Chhadav- Audav (6-5): when we pair six (6) types of Chhadav Arohs with 15 types of Audav Avrohs, we get 6×15=90 Raags.
7. Audav- Sampooran (5-7): this is the flip side of Sampooran-Audav (3rd Jati). Pairing 15 Audav Avrohs with 1 Sampooran Avroh give us 15×1=15 Raags.
8. Audav-Chhadav (5-6): When we pair 15 types of Audav (5 notes) Arohs with 6 types of Chhadav (6 notes) Avrohs, we get 15×6=90 Raags.
9. Audav- Adudav (5-5): 15 types of Audav Arohs, paired with 15 types of Audav Avrohs give us 15×15=225 unique Raags.

When we add the Raags created in all nine Jaties, it equals to (1+6+15+6+36+90+15+90+225) 484. Now by making the notes flat and sharp in each Thaat, we can multiply these by 10 (there are 10 Thaats),to create 4840 Raags.

sangtar.com > Music Theory > Basic Theory