Karnatic is never for Dummies. But, it seems to be possible to build a 'Karnatic Keyboard' where ragams (not all) can be configured which helps the musician to concentrate more on the sequcencing of notes rather than on keying correct notes.
To demonstrate this, take a yoyo ball (it is heavier and rubberized) roll it over the black keys(half tones) of a $10 organ. Depends on how you view it, you are playing either 'hindOLam', 'maddhyamaavathi', 'mOhanam', 'udayaragam', 'suddha-saavEri', or Sreeraagam. All these ragams have the note frequency difference sequence 2 3 2 2 3 in clockwise loop. Rolling the of the ball will natuarally be karnatic style because adjacent notes with the 'gamagam' are used a lot in karnatic. You can also Westernize it a bit by taking the ball and dropping it on a little far off (5 to 6 keys) black keys frequently.
In order to play a different ragam other than 2 3 2 2 3 sequence pluck out the black keys and arrange them in a different fasion.
To recap - The Ragam notes are:
0 - S
1 - R1
2 - R2, G1
3 - R3, G2
4 - G3
5 - M1
6 - M2
7 - P
8 - D1
9 - D2, N1
10 - D3, N2
11 - N3
12 - S
So the Karnatic ragam construction rule can be simplied as follows:
First fix note-0 (Sa), note-7(Pa), note-12(high Sa). Then choose 2 notes from Notes1-4. Call the first one Ra and the second Ga. Then choose one note from Notes:5-6. Call it Ma. Last choose 2 from Notes:8-11. Call the first one Dha and second one Ni.
Then total possible number of ragams will be: 4C2 * 2C1 * 4C2 = 72.
References:
Malayalavedhi
Ragam list
Ragam list 2
2003-08-04
Karnatic Ragam: new Ragams
Here are the new Carnatic Ragams for you to try:
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.
Sequence of note-gaps with value 1 has maximum length 3 in following necklaces:
1122321
1123221
1121331
These necklaces produce following EMRs:
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.
--------------------------------------
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.
--------------------------------------
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:
--------------------------------------
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.
Karnatic Ragam: SruthibhEdam reduces number of Ragams to 36 from 72
I was studing how many equivalence classes of Ragams are there when the 'Sruthi-bhEdam' is considered. I could see that more melodious of the lot - hanumanthOTi, reethigauLa, Sreeraagam, harikaambOji, sankaraabharaNam, kalyaaNi - has infact the same note frequency sequences. Their note frequencies differ by: 1 2 2 2 1 2 2. This difference sequence should be read in a circular clockwise loop. Depends upon where you start reading the sequence, the Ragam will be one of the 6 melody Ragams I mentioned earlier. Here is the full list of all Mela-kartha ragams with their equivalences:
01. R1 G1 M1 D1 N1 ... 1 1 3 2 1 1 3 ... equivalence = 01 51
02. R1 G1 M1 D1 N2 ... 1 1 3 2 1 2 2 ... equivalence = 02 19 53
03. R1 G1 M1 D1 N3 ... 1 1 3 2 1 3 1 ... equivalence = 03 54 55
04. R1 G1 M1 D2 N2 ... 1 1 3 2 2 1 2 ... equivalence = 04 25
05. R1 G1 M1 D2 N3 ... 1 1 3 2 2 2 1 ... equivalence = 05 61
06. R1 G1 M1 D3 N3 ... 1 1 3 2 3 1 1 ... equivalence = 06
07. R1 G2 M1 D1 N1 ... 1 2 2 2 1 1 3 ... equivalence = 07 17 63
08. R1 G2 M1 D1 N2 ... 1 2 2 2 1 2 2 ... equivalence = 08 20 22 28 29 65
09. R1 G2 M1 D1 N3 ... 1 2 2 2 1 3 1 ... equivalence = 09 35 56 66
10. R1 G2 M1 D2 N2 ... 1 2 2 2 2 1 2 ... equivalence = 10 23 26 64
11. R1 G2 M1 D2 N3 ... 1 2 2 2 2 2 1 ... equivalence = 11 62
12. R1 G2 M1 D3 N3 ... 1 2 2 2 3 1 1 ... equivalence = 12
13. R1 G3 M1 D1 N1 ... 1 3 1 2 1 1 3 ... equivalence = 13 69
14. R1 G3 M1 D1 N2 ... 1 3 1 2 1 2 2 ... equivalence = 14 21 58 71
15. R1 G3 M1 D1 N3 ... 1 3 1 2 1 3 1 ... equivalence = 15 57 72
16. R1 G3 M1 D2 N2 ... 1 3 1 2 2 1 2 ... equivalence = 16 27 59
17. R1 G3 M1 D2 N3 ... 1 3 1 2 2 2 1 ... equivalence = 07 17 63
18. R1 G3 M1 D3 N3 ... 1 3 1 2 3 1 1 ... equivalence = 18 43
19. R2 G2 M1 D1 N1 ... 2 1 2 2 1 1 3 ... equivalence = 02 19 53
20. R2 G2 M1 D1 N2 ... 2 1 2 2 1 2 2 ... equivalence = 08 20 22 28 29 65
21. R2 G2 M1 D1 N3 ... 2 1 2 2 1 3 1 ... equivalence = 14 21 58 71
22. R2 G2 M1 D2 N2 ... 2 1 2 2 2 1 2 ... equivalence = 08 20 22 28 29 65
23. R2 G2 M1 D2 N3 ... 2 1 2 2 2 2 1 ... equivalence = 10 23 26 64
24. R2 G2 M1 D3 N3 ... 2 1 2 2 3 1 1 ... equivalence = 24 32
25. R2 G3 M1 D1 N1 ... 2 2 1 2 1 1 3 ... equivalence = 04 25
26. R2 G3 M1 D1 N2 ... 2 2 1 2 1 2 2 ... equivalence = 10 23 26 64
27. R2 G3 M1 D1 N3 ... 2 2 1 2 1 3 1 ... equivalence = 16 27 59
28. R2 G3 M1 D2 N2 ... 2 2 1 2 2 1 2 ... equivalence = 08 20 22 28 29 65
29. R2 G3 M1 D2 N3 ... 2 2 1 2 2 2 1 ... equivalence = 08 20 22 28 29 65
30. R2 G3 M1 D3 N3 ... 2 2 1 2 3 1 1 ... equivalence = 30 34 44
31. R3 G3 M1 D1 N1 ... 3 1 1 2 1 1 3 ... equivalence = 31
32. R3 G3 M1 D1 N2 ... 3 1 1 2 1 2 2 ... equivalence = 24 32
33. R3 G3 M1 D1 N3 ... 3 1 1 2 1 3 1 ... equivalence = 33 60
34. R3 G3 M1 D2 N2 ... 3 1 1 2 2 1 2 ... equivalence = 30 34 44
35. R3 G3 M1 D2 N3 ... 3 1 1 2 2 2 1 ... equivalence = 09 35 56 66
36. R3 G3 M1 D3 N3 ... 3 1 1 2 3 1 1 ... equivalence = 36 45
37. R1 G1 M2 D1 N1 ... 1 1 4 1 1 1 3 ... equivalence = 37
38. R1 G1 M2 D1 N2 ... 1 1 4 1 1 2 2 ... equivalence = 38
39. R1 G1 M2 D1 N3 ... 1 1 4 1 1 3 1 ... equivalence = 39
40. R1 G1 M2 D2 N2 ... 1 1 4 1 2 1 2 ... equivalence = 40
41. R1 G1 M2 D2 N3 ... 1 1 4 1 2 2 1 ... equivalence = 41
42. R1 G1 M2 D3 N3 ... 1 1 4 1 3 1 1 ... equivalence = 42
43. R1 G2 M2 D1 N1 ... 1 2 3 1 1 1 3 ... equivalence = 18 43
44. R1 G2 M2 D1 N2 ... 1 2 3 1 1 2 2 ... equivalence = 30 34 44
45. R1 G2 M2 D1 N3 ... 1 2 3 1 1 3 1 ... equivalence = 36 45
46. R1 G2 M2 D2 N2 ... 1 2 3 1 2 1 2 ... equivalence = 46 70
47. R1 G2 M2 D2 N3 ... 1 2 3 1 2 2 1 ... equivalence = 47
48. R1 G2 M2 D3 N3 ... 1 2 3 1 3 1 1 ... equivalence = 48
49. R1 G3 M2 D1 N1 ... 1 3 2 1 1 1 3 ... equivalence = 49
50. R1 G3 M2 D1 N2 ... 1 3 2 1 1 2 2 ... equivalence = 50
51. R1 G3 M2 D1 N3 ... 1 3 2 1 1 3 1 ... equivalence = 01 51
52. R1 G3 M2 D2 N2 ... 1 3 2 1 2 1 2 ... equivalence = 52
53. R1 G3 M2 D2 N3 ... 1 3 2 1 2 2 1 ... equivalence = 02 19 53
54. R1 G3 M2 D3 N3 ... 1 3 2 1 3 1 1 ... equivalence = 03 54 55
55. R2 G2 M2 D1 N1 ... 2 1 3 1 1 1 3 ... equivalence = 03 54 55
56. R2 G2 M2 D1 N2 ... 2 1 3 1 1 2 2 ... equivalence = 09 35 56 66
57. R2 G2 M2 D1 N3 ... 2 1 3 1 1 3 1 ... equivalence = 15 57 72
58. R2 G2 M2 D2 N2 ... 2 1 3 1 2 1 2 ... equivalence = 14 21 58 71
59. R2 G2 M2 D2 N3 ... 2 1 3 1 2 2 1 ... equivalence = 16 27 59
60. R2 G2 M2 D3 N3 ... 2 1 3 1 3 1 1 ... equivalence = 33 60
61. R2 G3 M2 D1 N1 ... 2 2 2 1 1 1 3 ... equivalence = 05 61
62. R2 G3 M2 D1 N2 ... 2 2 2 1 1 2 2 ... equivalence = 11 62
63. R2 G3 M2 D1 N3 ... 2 2 2 1 1 3 1 ... equivalence = 07 17 63
64. R2 G3 M2 D2 N2 ... 2 2 2 1 2 1 2 ... equivalence = 10 23 26 64
65. R2 G3 M2 D2 N3 ... 2 2 2 1 2 2 1 ... equivalence = 08 20 22 28 29 65
66. R2 G3 M2 D3 N3 ... 2 2 2 1 3 1 1 ... equivalence = 09 35 56 66
67. R3 G3 M2 D1 N1 ... 3 1 2 1 1 1 3 ... equivalence = 67
68. R3 G3 M2 D1 N2 ... 3 1 2 1 1 2 2 ... equivalence = 68
69. R3 G3 M2 D1 N3 ... 3 1 2 1 1 3 1 ... equivalence = 13 69
70. R3 G3 M2 D2 N2 ... 3 1 2 1 2 1 2 ... equivalence = 46 70
71. R3 G3 M2 D2 N3 ... 3 1 2 1 2 2 1 ... equivalence = 14 21 58 71
72. R3 G3 M2 D3 N3 ... 3 1 2 1 3 1 1 ... equivalence = 15 57 72
01. R1 G1 M1 D1 N1 ... 1 1 3 2 1 1 3 ... equivalence = 01 51
02. R1 G1 M1 D1 N2 ... 1 1 3 2 1 2 2 ... equivalence = 02 19 53
03. R1 G1 M1 D1 N3 ... 1 1 3 2 1 3 1 ... equivalence = 03 54 55
04. R1 G1 M1 D2 N2 ... 1 1 3 2 2 1 2 ... equivalence = 04 25
05. R1 G1 M1 D2 N3 ... 1 1 3 2 2 2 1 ... equivalence = 05 61
06. R1 G1 M1 D3 N3 ... 1 1 3 2 3 1 1 ... equivalence = 06
07. R1 G2 M1 D1 N1 ... 1 2 2 2 1 1 3 ... equivalence = 07 17 63
08. R1 G2 M1 D1 N2 ... 1 2 2 2 1 2 2 ... equivalence = 08 20 22 28 29 65
09. R1 G2 M1 D1 N3 ... 1 2 2 2 1 3 1 ... equivalence = 09 35 56 66
10. R1 G2 M1 D2 N2 ... 1 2 2 2 2 1 2 ... equivalence = 10 23 26 64
11. R1 G2 M1 D2 N3 ... 1 2 2 2 2 2 1 ... equivalence = 11 62
12. R1 G2 M1 D3 N3 ... 1 2 2 2 3 1 1 ... equivalence = 12
13. R1 G3 M1 D1 N1 ... 1 3 1 2 1 1 3 ... equivalence = 13 69
14. R1 G3 M1 D1 N2 ... 1 3 1 2 1 2 2 ... equivalence = 14 21 58 71
15. R1 G3 M1 D1 N3 ... 1 3 1 2 1 3 1 ... equivalence = 15 57 72
16. R1 G3 M1 D2 N2 ... 1 3 1 2 2 1 2 ... equivalence = 16 27 59
17. R1 G3 M1 D2 N3 ... 1 3 1 2 2 2 1 ... equivalence = 07 17 63
18. R1 G3 M1 D3 N3 ... 1 3 1 2 3 1 1 ... equivalence = 18 43
19. R2 G2 M1 D1 N1 ... 2 1 2 2 1 1 3 ... equivalence = 02 19 53
20. R2 G2 M1 D1 N2 ... 2 1 2 2 1 2 2 ... equivalence = 08 20 22 28 29 65
21. R2 G2 M1 D1 N3 ... 2 1 2 2 1 3 1 ... equivalence = 14 21 58 71
22. R2 G2 M1 D2 N2 ... 2 1 2 2 2 1 2 ... equivalence = 08 20 22 28 29 65
23. R2 G2 M1 D2 N3 ... 2 1 2 2 2 2 1 ... equivalence = 10 23 26 64
24. R2 G2 M1 D3 N3 ... 2 1 2 2 3 1 1 ... equivalence = 24 32
25. R2 G3 M1 D1 N1 ... 2 2 1 2 1 1 3 ... equivalence = 04 25
26. R2 G3 M1 D1 N2 ... 2 2 1 2 1 2 2 ... equivalence = 10 23 26 64
27. R2 G3 M1 D1 N3 ... 2 2 1 2 1 3 1 ... equivalence = 16 27 59
28. R2 G3 M1 D2 N2 ... 2 2 1 2 2 1 2 ... equivalence = 08 20 22 28 29 65
29. R2 G3 M1 D2 N3 ... 2 2 1 2 2 2 1 ... equivalence = 08 20 22 28 29 65
30. R2 G3 M1 D3 N3 ... 2 2 1 2 3 1 1 ... equivalence = 30 34 44
31. R3 G3 M1 D1 N1 ... 3 1 1 2 1 1 3 ... equivalence = 31
32. R3 G3 M1 D1 N2 ... 3 1 1 2 1 2 2 ... equivalence = 24 32
33. R3 G3 M1 D1 N3 ... 3 1 1 2 1 3 1 ... equivalence = 33 60
34. R3 G3 M1 D2 N2 ... 3 1 1 2 2 1 2 ... equivalence = 30 34 44
35. R3 G3 M1 D2 N3 ... 3 1 1 2 2 2 1 ... equivalence = 09 35 56 66
36. R3 G3 M1 D3 N3 ... 3 1 1 2 3 1 1 ... equivalence = 36 45
37. R1 G1 M2 D1 N1 ... 1 1 4 1 1 1 3 ... equivalence = 37
38. R1 G1 M2 D1 N2 ... 1 1 4 1 1 2 2 ... equivalence = 38
39. R1 G1 M2 D1 N3 ... 1 1 4 1 1 3 1 ... equivalence = 39
40. R1 G1 M2 D2 N2 ... 1 1 4 1 2 1 2 ... equivalence = 40
41. R1 G1 M2 D2 N3 ... 1 1 4 1 2 2 1 ... equivalence = 41
42. R1 G1 M2 D3 N3 ... 1 1 4 1 3 1 1 ... equivalence = 42
43. R1 G2 M2 D1 N1 ... 1 2 3 1 1 1 3 ... equivalence = 18 43
44. R1 G2 M2 D1 N2 ... 1 2 3 1 1 2 2 ... equivalence = 30 34 44
45. R1 G2 M2 D1 N3 ... 1 2 3 1 1 3 1 ... equivalence = 36 45
46. R1 G2 M2 D2 N2 ... 1 2 3 1 2 1 2 ... equivalence = 46 70
47. R1 G2 M2 D2 N3 ... 1 2 3 1 2 2 1 ... equivalence = 47
48. R1 G2 M2 D3 N3 ... 1 2 3 1 3 1 1 ... equivalence = 48
49. R1 G3 M2 D1 N1 ... 1 3 2 1 1 1 3 ... equivalence = 49
50. R1 G3 M2 D1 N2 ... 1 3 2 1 1 2 2 ... equivalence = 50
51. R1 G3 M2 D1 N3 ... 1 3 2 1 1 3 1 ... equivalence = 01 51
52. R1 G3 M2 D2 N2 ... 1 3 2 1 2 1 2 ... equivalence = 52
53. R1 G3 M2 D2 N3 ... 1 3 2 1 2 2 1 ... equivalence = 02 19 53
54. R1 G3 M2 D3 N3 ... 1 3 2 1 3 1 1 ... equivalence = 03 54 55
55. R2 G2 M2 D1 N1 ... 2 1 3 1 1 1 3 ... equivalence = 03 54 55
56. R2 G2 M2 D1 N2 ... 2 1 3 1 1 2 2 ... equivalence = 09 35 56 66
57. R2 G2 M2 D1 N3 ... 2 1 3 1 1 3 1 ... equivalence = 15 57 72
58. R2 G2 M2 D2 N2 ... 2 1 3 1 2 1 2 ... equivalence = 14 21 58 71
59. R2 G2 M2 D2 N3 ... 2 1 3 1 2 2 1 ... equivalence = 16 27 59
60. R2 G2 M2 D3 N3 ... 2 1 3 1 3 1 1 ... equivalence = 33 60
61. R2 G3 M2 D1 N1 ... 2 2 2 1 1 1 3 ... equivalence = 05 61
62. R2 G3 M2 D1 N2 ... 2 2 2 1 1 2 2 ... equivalence = 11 62
63. R2 G3 M2 D1 N3 ... 2 2 2 1 1 3 1 ... equivalence = 07 17 63
64. R2 G3 M2 D2 N2 ... 2 2 2 1 2 1 2 ... equivalence = 10 23 26 64
65. R2 G3 M2 D2 N3 ... 2 2 2 1 2 2 1 ... equivalence = 08 20 22 28 29 65
66. R2 G3 M2 D3 N3 ... 2 2 2 1 3 1 1 ... equivalence = 09 35 56 66
67. R3 G3 M2 D1 N1 ... 3 1 2 1 1 1 3 ... equivalence = 67
68. R3 G3 M2 D1 N2 ... 3 1 2 1 1 2 2 ... equivalence = 68
69. R3 G3 M2 D1 N3 ... 3 1 2 1 1 3 1 ... equivalence = 13 69
70. R3 G3 M2 D2 N2 ... 3 1 2 1 2 1 2 ... equivalence = 46 70
71. R3 G3 M2 D2 N3 ... 3 1 2 1 2 2 1 ... equivalence = 14 21 58 71
72. R3 G3 M2 D3 N3 ... 3 1 2 1 3 1 1 ... equivalence = 15 57 72
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