--------------------------------------
S R1 R2 R3 M1 M2 P D1 D2 D3 S
Name G1 G2 G3 N1 N2 N3
--------------------------------------
0 1 2 3 4 5 6 7 8 9 10 11 12
--------------------------------------
N * * * * * * * *
I * * * * * * * *
K * * * * * * * *
If you are curious about the details, please read on...
Before we start here are some technical terms to familiarize... Note-gap is the number of notes different between two adjacent notes of a raga. For example, note-gap between S and G1 is 2. The note-gaps of a raga written in circular fashion is called note-gap necklace. A cluster of ragas could be corresponding to a single note-gap necklace. For example, both 'hanumanthodi #8' and 'kharaharapriya #22' have the note-gap necklace 2 1 2 2 1 2 2 (visualize this sequence in a circle). This essentially mean, both 'hanumanthodi' and 'kharaharapriya' are Sruthibhedams of each other.
Due to the Melakarttha restrictions, the set of ragas generated from certain note-gap necklaces are missing from 72 Melakarttha ragas. I will call the new ragas generated from the missing necklaces as EMRs - Extra-Melakartha Ragas. Of course, there are so many missing note-gap necklaces; but only few necklaces will potentially produce musically pleasing ragas. To get only those, I have put some heuristical restrictions on these necklaces:
1. there is no note-gap greater than 3
2. no more than 3 note-gaps with value 1 are adjacent
These restrictions will reject necklaces which are overly skewed to one side. Thus we get following groups of note-gap necklaces:
Sequence of note-gaps with value 1 has maximum length 2 in following necklaces:
1212321
1232121
1213221
These necklaces produce following EMRs. Among these ragas, I would bet my money on N2, I2 and K3.
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S R1 R2 R3 M1 M2 P D1 D2 D3 S
Note Diff G1 G2 G3 N1 N2 N3
--------------------------------------
0 1 2 3 4 5 6 7 8 9 10 11 12
--------------------------------------
N1 1 1 2 1 2 3 2 * * * * * * * *
N2 1 2 1 2 3 2 1 * * * * * * * *
N3 1 2 3 2 1 1 2 * * * * * * * *
N4 2 1 1 2 1 2 3 * * * * * * * *
N5 2 1 2 3 2 1 1 * * * * * * * *
N6 2 3 2 1 1 2 1 * * * * * * * *
N7 3 2 1 1 2 1 2 * * * * * * * *
I1 1 1 2 3 2 1 2 * * * * * * * *
I2 1 2 1 1 2 3 2 * * * * * * * *
I3 1 2 3 2 1 2 1 * * * * * * * *
I4 2 1 1 2 3 2 1 * * * * * * * *
I5 2 1 2 1 1 2 3 * * * * * * * *
I6 2 3 2 1 2 1 1 * * * * * * * *
I7 3 2 1 2 1 1 2 * * * * * * * *
K1 1 1 2 1 3 2 2 * * * * * * * *
K2 1 2 1 3 2 2 1 * * * * * * * *
K3 1 3 2 2 1 1 2 * * * * * * * *
K4 2 1 1 2 1 3 2 * * * * * * * *
K5 2 1 3 2 2 1 1 * * * * * * * *
K6 2 2 1 1 2 1 3 * * * * * * * *
K7 3 2 2 1 1 2 1 * * * * * * * *
Sequence of note-gaps with value 1 has maximum length 3 in following necklaces:
1122321
1123221
1121331
These necklaces produce following EMRs:
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S R1 R2 R3 M1 M2 P D1 D2 D3 S
Note Diff G1 G2 G3 N1 N2 N3
--------------------------------------
0 1 2 3 4 5 6 7 8 9 10 11 12
--------------------------------------
A1 1 1 1 2 1 3 3 * * * * * * * *
A2 1 1 2 1 3 3 1 * * * * * * * *
A3 1 2 1 3 3 1 1 * * * * * * * *
A4 1 3 3 1 1 1 2 * * * * * * * *
A5 2 1 3 3 1 1 1 * * * * * * * *
A6 3 1 1 1 2 1 3 * * * * * * * *
A7 3 3 1 1 1 2 1 * * * * * * * *
B1 1 1 1 2 2 3 2 * * * * * * * *
B2 1 1 2 2 3 2 1 * * * * * * * *
B3 1 2 2 3 2 1 1 * * * * * * * *
B4 2 1 1 1 2 2 3 * * * * * * * *
B5 2 2 3 2 1 1 1 * * * * * * * *
B6 2 3 2 1 1 1 2 * * * * * * * *
B7 3 2 1 1 1 2 2 * * * * * * * *
C1 1 1 1 2 3 2 2 * * * * * * * *
C2 1 1 2 3 2 2 1 * * * * * * * *
C3 1 2 3 2 2 1 1 * * * * * * * *
C4 2 1 1 1 2 3 2 * * * * * * * *
C5 2 2 1 1 1 2 3 * * * * * * * *
C6 2 3 2 2 1 1 1 * * * * * * * *
C7 3 2 2 1 1 1 2 * * * * * * * *
Sequence of note-gaps with value 1 has maximum length 4 in following necklaces:
1123311
1133211
I am not bothering to list this last catagory of EMRs because most probably, they would be useless.
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