Talaprasthara (Combinatorics)

Tālam & Layam related topics
msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#51

Post by msakella »

8th part:
Examples:
Panchanga-nashta:
1.What is the series of Angas pertaining to the 1st prastara of 6-Druta-permutation (6-DP) of Panchanga-prastara (2-6-19/1 - among them while ‘2’ represents Panchanga-prastara, ‘6’ represents the total number of units of the permutation 6-DP, ‘19’ represents the respective Sankhya and the last ‘1’represents the question-number)?
To write the Sankhya of Panchanga-prastara, the total of the existing figures of the preceding 1st, 2nd, 4th, 6th and 8th houses, which are the respective proxies of Panchanga-prastara, should be written and now, as per rule No.1 write the figures of Sankhya upto the required 6-DP (refer table).
Now, as per rule No.2, subtract the question number ‘1’ from the Sankhya figure ‘19’ of 6-DP and the remainder is (19-1=) 18.
From the above remainder ‘18’, as the 1st, 2nd and 4th proxies could consecutively be subtracted (18-10=8-6=2-2=0) consider the non-subtraction of the 6th proxy ‘1’ and write the Anga, Pluta of the same proxy as per rule No.3. Thus, this prastara consists of ‘Śâ€™.

2.What is the series of Angas pertaining to the 2nd prastara of 6-DP of Panchanga-prastara (2-6-19/2)?
As per rule No.1 write the figures of Sankhya upto the required 6-DP (refer table).
Now, as per rule No.2, subtract the question number ‘2’ from the Sankhya figure 19 of 6-DP and the remainder is (19-2=) 17.
Later, from the above remainder ‘17’, as the 1st and 2nd proxies could consecutively be subtracted (17-10=7-6=1) consider the non-subtraction of the 4th proxy ‘2’ and write its Anga, Guru as per rule No.3 leaving away its figure ‘2’ to continue the process.
Later, from the last remainder ‘1’, as the 1st proxy of the last left-off proxy ‘2’ could be subtracted (1-1=0) consider the non-subtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of ‘l S’.

3.What is the series of Angas pertaining to the 3rd prastara of 6-DP of Panchanga-prastara (2-6-19/3)?
As per rule No.1 write the figures of Sankhya upto the required 6-DP (refer table).
Now, as per rule No.2, subtract the question number ‘3’ from the Sankhya figure 19 of 6-DP and the remainder is (19-3=) 16.
Later, from the above remainder ‘16’, as the 1st and 2nd proxies could consecutively be subtracted (16-10=6-6=0) consider the non-subtraction of the 4th proxy and write its Anga, Guru as per rule No.3.
Later, to fill in the deficit value of the permutation write two Drutas consecutively as per rule No.5. Thus, this prastara consists of ‘0 0 S’.

4.What is the series of Angas pertaining to the 4th prastara of 6-DP of Panchanga-prastara (2-6-19/4)?
As per rule No.1 write the figures of Sankhya upto the required 6-DP (refer table).
Now, as per rule No.2, subtract the question number ‘4’ from the Sankhya figure 19 of 6-DP and the remainder is (19-4=) 15.
Later, from the above remainder ‘15’, as the 1st proxy only could be subtracted (15-10=5) consider the non-subtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3 leaving away its proxy ‘6’ to continue the process.
Later, from the last remainder ‘5’, the 1st and 2nd proxies of the last left-off proxy ‘6’ could consecutively be subtracted (5-3=2-2=0) consider the non-subtraction of the 4th proxy and write its Anga, Guru as per rule No.3. Thus, this prastara consists of ‘S l’.

5.What is the series of Angas pertaining to the 5th prastara of 6-DP of Panchanga-prastara (2-6-19/5)?
As per rule No.1 write the figures of Sankhya upto the required 6-DP (refer table).
Now, as per rule No.2, subtract the question number ‘5’ from the Sankhya figure 19 of 6-DP and the remainder is (19-5=) 14.
Later, from the above remainder ‘14’, as the 1st proxy could be subtracted (14-10=4) consider the non-subtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3 leaving away its proxy ‘6’ to continue the process.
Later, from the last remainder ‘4’, as the 1st proxy ‘3’ of the last left-off proxy ‘6’ could be subtracted (4-3=1) consider the non-subtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3 leaving away its proxy ‘2’ to continue the process.
Later, from the last remainder ‘1’, as the 1st proxy ‘1’ of the last proxy ‘2’ could be subtracted (1-1=0) consider the non-subtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of ‘l l l’.

6.What is the series of Angas pertaining to the 7th prastara of 6-DP of Panchanga-prastara (2-6-19/7)?
As per rule No.1 write the figures of Sankhya upto the required 6-DP (refer table).
Now, as per rule No.2, subtract the question number ‘5’ from the Sankhya figure 19 of 6-DP and the remainder is (19-7=) 12.
Later, from the above remainder ‘12’, as the 1st proxy could be subtracted (12-10=2) consider the non-subtraction of the 2nd proxy and write its Anga, Laghu leaving away its proxy ‘6’ to continue the process.
Later, from the last remainder ‘2’, as the 1st proxy ‘3’ of the last left-off proxy ‘6’ could not be subtracted write the Anga, Druta of the same proxy as per rule No.3 to continue the process.
Later, from the last remainder ‘2’, as the 1st proxy ‘2’ of the last un-deducted proxy ‘3’ could be subtracted (2-2=0) consider the non-subtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3.
Later, to fill-in the deficit value of the units, write only one Druta as per rule No.5. Thus, this prastara consists of ‘0 l 0 l’.

7.What is the series of Angas pertaining to the 12th prastara of 6-DP of Panchanga-prastara (2-6-19/12)?
As per rule No.1 write the figures of Sankhya upto the required 6-DP (refer table).
Now, as per rule No.2, subtract the question number ‘12’ from the Sankhya figure 19 of 6-DP and the remainder is (19-12=) 7.
Later, from the above remainder ‘7’, as the 1st proxy ‘10’ could not be subtracted write its Anga, Druta and continue the process.
Later, from the above remainder ‘7’, as the 1st proxy ‘6’ of the last un-deducted proxy ‘10’ could be subtracted (7-6=1) consider the non-subtraction of the 2nd proxy and write its Anga, Laghu leaving away its proxy ‘3’ as per rule No.3 to continue the process.
Later, from the last remainder ‘1’, as the 1st proxy ‘2’ of the last left-off proxy ‘3’ could not be subtracted write its Anga, Druta as per rule No.3 and continue the process.
Later, from the last remainder ‘1’, as the 1st proxy ‘1’ of the last un-deducted proxy ‘2’ could be subtracted (1-1=0) consider the non-subtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of ‘l 0 l 0’.

8.What is the series of Angas pertaining to the 16th prastara of 6-DP of Panchanga-prastara (2-6-19/16)?
As per rule No.1 write the figures of Sankhya upto the required 6-DP (refer table).
Now, as per rule No.2, subtract the question number ‘16’ from the Sankhya figure 19 of 6-DP and the remainder is (19-16=) 3.
Later, from the above remainder ‘3’, as the 1st proxy ‘10’ and again its 1st proxy ‘6’ could not be subtracted, write two Angas, Drutas of the the same 1st proxy and continue the process.
Later, from the above remainder ‘3’, as the 1st proxy ‘3’ of the last un-deducted proxy ‘6’ could be subtracted (3-3=0) consider the non-subtraction of the 2nd proxy and write its Anga, Laghu as per rule No.3
Later, to fill in the deficit value of the total units of the permutation write two Drutas as per rule No.5. Thus, this prastara consists of ‘0 0 l 0 0’.

Shadanga - trisra-jaati - nashta:
1.What is the series of Angas pertaining to the 15th prastara of 6-Anudruta-permutation (6-ADP) of Shadanga-trisra-jaati-prastara (3-6-25/15)?
As per rule No.1 write the figures of Sankhya upto the required 6-ADP (refer table).
Now, as per rule No.2, subtract the question number ‘15’ from the Sankhya figure ‘25’ of 6-ADP and the remainder is (25-15=) 10.
Later, from the above remainder ‘10’, as the 1st proxy ‘13’ could not be subtracted, write its Anga, Anudruta as per rule No.3 and continue the process.
Later, from the above remainder ‘10’, as the 1st proxy ‘7’ of the last un-deducted proxy ‘13’ could be subtracted (10-7=3) consider the non-subtraction of the 2nd proxy and write its Anga, Druta leaving away its proxy ‘4’ to continue the process.
Later, from the last remainder ‘3’, as the 1st and 2nd proxies of the last left-off proxy ‘4’ could consecutively be subtracted (3-2=1-1=0) consider the non-subtraction of the 3rd proxy and write its Anga, Laghu. Thus, this prastara consists of ‘l 0 U’.

Shadanga - chaturashra-jaati - nashta:
1.What is the series of Angas pertaining to the 16th prastara of 7-ADP of Shadanga-chaturashra-jaati-prastara (4-7-31/16)?
As per rule No.1 write the figures of Sankhya upto the required 7-ADP (refer table).
Now, as per rule No.2, subtract the question number ‘16’ from the Sankhya figure ‘31’ of 7-ADP and the remainder is (31-16=) 15.
Later, from the above remainder ‘15’, as the 1st proxy ‘18’ could not be subtracted, write its Anga, Anudruta as per rule No.3 and continue the process.
Later, from the above remainder ‘15’, as the 1st proxy ‘10’ of the last un-deducted proxy ‘18’ could be subtracted (15-10=5), consider the non-subtraction of the 2nd proxy and write its Anga, Druta leaving away its proxy ‘6’ as per rule No.3 to continue the process.
Later, from the last remainder ‘5’, as the 1st and 2nd proxies of the last left-off proxy ‘6’ could consecutively be subtracted (5-3=2-2=0) consider the non-subtraction of the 4th proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of ‘l 0 U’.

Shadanga - khanda - jaati - nashta :
1.What is the series of Angas pertaining to the 3rd prastara of 7-ADP of Shadanga-khanda-jaati-prastara (5-7-26/3)?
As per rule No.1 write the figures of Sankhya upto the required 7-ADP (refer table).
Now, as per rule No.2, subtract the question number ‘3’ from the Sankhya figure ‘26’ of 7-ADP and the remainder is (26-3=) 23.
Later, from the above remainder ‘23’, as the 1st proxy could be subtracted (23-15=8) consider the non-subtraction of the 2nd proxy and write its Anga, Druta leaving away its proxy ‘9’ as per rule No.3 to continue the process.
Later, from the last remainder ‘8’, as the 1st and 2nd proxies of the last left-off proxy ‘9’ could consecutively be subtracted (8-5=3-3=0) consider the non-subtraction of the 5th proxy and write its Anga, Laghu. Thus, this prastara consists of ‘l 0’.

Shadanga - mishra - jaati - nashta :
1.What is the series of Angas pertaining to the 1st prastara of 8-ADP of Shadanga-mishra-jaati-prastara (8-7-36/1)?
As per rule No.1 write the figures of Sankhya upto the required 8-ADP (refer table).
Now, as per rule No.2, subtract the question number ‘1’ from the Sankhya figure ‘36’ of 8-ADP and the remainder is (36-1=) 35.
Later, from the above remainder ‘35’, as the 1st and 2nd proxies could consecutively be subtracted (35-22=13-13=0) consider the non-subtraction of the 7th proxy and write its Anga, Laghu as per rule No.3.
Later, to fill in the deficit value of units of the permutation write one Anudruta as per rule No.5. Thus, this prastara consists of ‘U l’.

Shadanga - sankeerna - jaati - nashta :
1.What is the series of Angas pertaining to the 1st prastara of 9-ADP of Shadanga-sankeerna-jaati-prastara (9-9-56/1)?
As per rule No.1 write the figures of Sankhya upto the required 9-ADP (refer table).
Now, as per rule No.2, subtract the question number ‘1’ from the Sankhya figure ‘56’ of 9-ADP and the remainder is (56-1=) 55.
Later, from the above remainder ‘55’, as the 1st and 2nd proxies could consecutively be subtracted (55-34=21-21=0) consider the non-subtraction of the 9th proxy and write its Anga, Laghu as per rule No.3. Thus, this prastara consists of ‘l’.

In the same manner the respective Nashta of other permutations should also be answered basing upon the respective proxies.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#52

Post by sbala »

Dear Msakella Sir,

As you had asked, I attempted to do the Panchanga Prastara Kalita for 7-UP. Please verify and let me know if I have understood this right.

Here a unit stands for 1 Drutam.

1. No 8th proxy. So no kakapadam.

2. 6th proxy. S+M=1+1=2
1 figure of S' and 1 other figure as per M
S+M indicates that there should be only 2 figures of S' in all the 33 permutations

DA: 1/O,1/S'.

3. 4th proxy S+M=3+7=10

3 figures of S. 7 other figures.
S+M=10 indicates that there are only 10 figures of S in all the permutations


DA: 2/|,5/O,3/S

4. 2nd proxy. S+M=10+34=44
10|, 34 other figures.
There should be only 44 laghus in all the 33 permutations.

DA : 2/S,10/|,22/O,10/|

5. 1st proxy. S+M=19+72=91
19 O. 72 other figures.
There should be only 91 O's in all the permutations
DA: 1/S', 5/S, 22/|, 44/|, 19/O

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#53

Post by msakella »

Dear member, sbala, It should be cited as 7-DP in Panchanga-prastara, 7-AP in Shadanga-prastara and 7-UP in Samyuktanga-prastara. You can get the symbol, ‘Śâ€™ of Pluta in the ‘Arial’ of symbols in your PC and you can use that. For the symbol, Laghu you can use the alphabet small Ell ‘l’ or figure one, ‘1’.
There are 3 kinds of applications of each one of these proxies and you should write down all of them as follows.
(You should write them applying to the proxies from right to left only but not from left to right)
1. (a) As per the first-1st proxy there are 19 Dritantya-prastaras consisting of 72 other Angas, (b) among these 72 other Angas, apart from these 19 Drutas lying in the right extreme of each one of these 19 Drutantya-prastaras, as per the first-1st proxy there are (10 + 34 =) 44 Drutas, second-2nd proxy there are (6 + 16 =) 22 Laghus, third-4th proxy there are (2 + 3 = ) 5 Gurus, fourth-6th proxy there is only 1 Pluta arriving at a total of (44D + 22L + 5G + 1P =) 72 (c) in all these 33 permutations there are only (72 + 19 =) 91 Drutas.
In the same manner you should write to all the respective proxies. Proceed.
Also go through the 7th chapter of my book ‘Indian genius in Talaprastara’ and tally the matter furnished in my another book ‘Systematisation of Prastara details of Deshi Talas’. amsharma.
Last edited by msakella on 29 Jan 2007, 21:12, edited 1 time in total.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#54

Post by msakella »

9th part:
KHANDA-PRASTARA

The process of Khanda-prastara should also be made following the same rules of Akhanda-prastara but observing some restrictions like devoid or containing a particular Anga. This is of two kinds and they are namely 1.Heena-prastara (Devoid-permutation), this is Anga-heena-prastara in which the process of permutation should be made devoid of a particular Anga and 2.Yukta-prastara (Containing-permutation), this is like Ekanga-yukta-prastara, Dviyanga-yukta-prastara, Trianga-yukta-prastara and so on in which the process of permutation should be made containing a particular number of a particular Anga ( among them the word ‘Anga’ should be replaced with the name of an Anga among the six Talangas or ‘Amsha’ or unit like Anudruta-heena-prastara, Druta-heena-prastara of the respective Panchanga & Shadanga-prastaras, Ekamsha-heena-prastara, Dviamsha-heena-prastara of Samyuktanga-prastara of Heena-prastara, Ekanudruta-yukta-prastara, Dvianudruta-yukta-prastara, Tridruta-yukta-prastara, Chaturlaghu-yukta-prastara of the respective Panchanga & Shadanga-prastaras and Eka-ekamsha-yukta-prastara, Dvi-ekamsha-yukta-prastara, Tri-dviamsha-yukta-prastara, Chatur-chaturamsha-yukta-prastara of Samyuktanga-prastara and so on of Yukta-prastara.
Example: If you carefully observe the 33 Akanda-prastaras of 7-DP you will find that Druta-heena-prastaras are ‘0’, Eka-druta-yukta-prastaras are ‘12’, Tri-druta-yukta-prastaras are ‘14’, Pancha-druta-yukta-prastaras are ‘5’ and Sapta-druta-prastara is ‘1’ in Khanda-prastara arriving at the total (12 + 14 + 6 + 1 =) 33. The same should be applied to all.

2-7-1-0-12
0 Ś - 01
0 l S - 02
l 0 S - 03
0 S l - 04
0 l l l - 05
l 0 l l - 06
S 0 l - 07
l l 0 l - 08
Ś 0 - 09
l S 0 -10
S l 0 - 11
l l l 0 - 12

2-7-1-1-14
0 0 0 S - 01
0 0 0 l l - 02
0 0 l 0 l - 03
0 l 0 0 l - 04
l 0 0 0 l - 05
0 0 S 0 - 06
0 0 l l 0 - 07
0 l 0 l 0 - 08
l 0 0 l 0 - 09
0 S 0 0 - 10
0 l l 0 0 - 11
l 0 l 0 0 - 12
S 0 0 0 - 13
l l 0 0 0 - 14

2-7-1-5-6
0 0 0 0 0 l - 01
0 0 0 0 l 0 - 02
0 0 0 l 0 0 - 03
0 0 l 0 0 0 - 04
0 l 0 0 0 0 - 05
l 0 0 0 0 0 - 06

2-7-1-7-1
0 0 0 0 0 0 0 - 01

Like the ‘Table of general permutations’ bringing out the details of Sankhya and Mahapatala of all the units of permutations of Akhanda-prastara, in Khanda-prastara, to bring out the details of the respective Sankhya and Mahapatala of Heena-prastara and Yukta-prastara of all respective Angas independent tables of each and every Anga have to be prepared. Thus, in Panchanga-prastara, where five Angas are used in the process of permutation, an independent table to each of these five Angas have to be prepared, in Shadanga-prastara, where six Angas are used in the process of permutation, six tables have to be prepared and in Samyuktanga-prastara, depending upon the desired units of permutation, an independent table to each increased-unit should be prepared. For example please go through the item ‘2.3.2.Khanda-prastara and 2.4.Tables of angas and their application’ in page 10 and the different tables of Druta, Laghu, Guru, Pluta and Kakapada of Panchanga-prastara in Chapter-3 of my book ‘Indian genius in Talaprastara’. amsharma.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#55

Post by msakella »

Dear member, sbala, Most of the month, February, 2007, I shall be on tour covering all the 12 Govt. Colleges of Music & Dance of Andhra Pradesh being my last visit. Whenever time and things permit I shall try to attend to your posts and reply. In the meantime try to finish off Khanda-prastara also going through all the tables furnished in my book, ‘Indian Genius in Talaprastara’. Wishing you all the best, amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#56

Post by sbala »

Dear Msakella Sir,
I have given the details for the remaining permutations of 6-DP Panchanga Nashta
1. (2-6-19/6)
a. 19-6=13
b. 13-10=3. 2nd proxy 6 undeducted. 1
c. 3-3=0 2nd proxy undeducted. 1
d. Remainder - 2 O
e. 0011

2.(2-6-19/8)
a. 19-8=11
b.11-10=1. 2nd proxy 6 undeducted. 1
c. 1st proxy 3 undeducted. 0
d.1st proxy 2 undeducted. 0
e. 1-1=0 2nd proxy undeducted. 1
f. 1001

I will post the other permutations next. Please verify whenever you have time
Last edited by sbala on 04 Feb 2007, 11:33, edited 1 time in total.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#57

Post by sbala »

(2-6-19/9)
a. 19-9=10.
b. 10-10=0 2nd proxy not deducted. 1
c. remainder - 4 0
d. 00001

(2-6-19/10)
a.19-10=9
b.1st proxy 10 not deducted. 0
c.9-6-3=0. 4th proxy not deducted S
d. remainder - 1 O
e. 0S0

(2-6-19/11)
a.19-11=8
b. 1st proxy 10 not deducted. O.
c. 8-6=2. 2nd proxy 3 not deducted. 1
d. 2-2=0 2nd proxy 2 not deducted. 1
e. Remainder - 1 O
f. 0110

(2-6-19/13)
a. 19-13=6
b. 1st proxy 10 not deducted. O
c.6-6=0. 2nd proxy not deducted. 1
d. Remainder 3 O
e. 00010

(2-6-19/14)
a. 19-14=5
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d. 5-3-2=0. 4th proxy not deducted. S
e. S00

(2-6-19/15)
a. 19-15=4
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d.4-3=1 2nd proxy 2 not deducted. 1
e. 1-1=0 2nd proxy 1 not deducted 1
f. 1100

(2-6-19/17)
a. 19-17=2
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d. 1st proxy 3 not deducted. O
e. 2-2=0. 2nd proxy 1 not deducted. 1
f. remainder 1 0
g. 01000

(2-6-19/18)
a. 19-18=1
b. 1st proxy 10 not deducted. O
c. 1st proxy 6 not deducted. O
d. 1st proxy 3 not deducted. O
e. 1st proxy 2 not deducted O
f. 1-1=0 2nd proxy not deducted 1
g. 10000

(2-6-19/19)
a. 19-19=0
b. remainder 6 O
c. 000000
Last edited by sbala on 04 Feb 2007, 11:32, edited 1 time in total.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#58

Post by msakella »

Dear member, sbala, Gone through your 56th & 57th posts and found correct. Your progress is very nice. Please apply this Nashta to all other Jaatis of Shadanga-prastara also basing upon their respective proxies. After finishing this Akhanda-nashta you can proceed to Khanda-prastara furnished by me in 54th & 55th posts and the instructions of them. From tomorrow onwards my trip to outstations starts and I shall get into touch with your posts whenever and wherever it becomes possible to me. Thinking of my absence don’t neglect to do things. Wishing you all the best, amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#59

Post by sbala »

Dear Msakella Sir,
I have given the Nashta for the first 6 permutations below. I will provide the remaining in subsequent posts. Please verify whenever you have time.

Shadanga Prastara Trisra Jathi 6ADP


(3-6-25/1)
1. 25-1=24
2. 24-13-7-4=0 6th proxy undedudcted
3. S

(3-6-25/2)
1.25-2=23
2. 23-13-7=3. 3rd proxy 4 undeducted. 1
3. 3-2-1=0 3rd proxy 1 undeducted 1
4. 11

(3-6-25/3)
1. 25-3=22
2. 22-13-7=2 3rd proxy 4 undeducted. 1
3. 2-2=0 2nd proxy undeducted O
4. 1 U remainder
5. U01

(3-6-25/4)
1.25-4=21
2. 21-13-7=1 3rd proxy 4 undeducted 1
3. 1st proxy 2 undeducted. U
4.1-1=0. 2nd proxy 1 undeducted O
5. 0U1

(3-6-25/5)
1. 25-5=20
2. 20-13-7=0 3rd proxy 4 undeducted 1
3. remainder 3 U
4. UUU1

(3-6-25/6)
1.25-6=19
2. 19-13=6 2nd proxy 7 undeducted O
3. 6-4-2=0 3rd proxy 1 undeducted 1
4. Remainder 1 U
4. U10

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#60

Post by sbala »

Shandanga Prasthara Chaturasra Jathi 7ADP
(4-7-31/14)
1. 31-14=17
2. 1st proxy 18 Undeducted U
3. 17-10-6=1 4th proxy 2 undeducted 1
4. 1-1=0 2nd proxy undeducted O
5. O1U

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#61

Post by msakella »

Dear member, sbala, Last night I returned, saw your 59th & 60th posts and found correct. Very nice. Proceed further.
Again tomorrow I am leaving and return on 25th only again to leave on the same evening and to come back on 28th. From 1st March mostly I am free and regularly attend the posts of our forum. In the meantime try to finish the different kinds of Khanda-prastara also. Wishing you all the best, amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#62

Post by sbala »

Dear msakella Sir,
I'm now reading your book and based on that I have given the anuloma prastara for 5-DP. Please verify when you have time.

Pancanga Prastara (Akhanda)

Anuloma for 5DP
0S - 01
011 - 02
101 - 03
0001 - 04
S0 - 05
110 - 06
0010 - 07
0100 -08
1000 -09
00000 -10
Last edited by sbala on 25 Feb 2007, 16:56, edited 1 time in total.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#63

Post by msakella »

Dear member, sbala, Very nice. You got it. Proceed further. amsharma.

sandhyashree
Posts: 29
Joined: 01 Oct 2006, 15:27

#64

Post by sandhyashree »

Hello Sbala

You are AMAZING!!!!!!!!!!!!!!!!

Sandhya

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#65

Post by sbala »

Hello Sandhya,
The credit completely goes to Sharmaji. He has not only researched this rare topic but has documented it as well and he is willing to share his knowledge with anyone.

sandhyashree
Posts: 29
Joined: 01 Oct 2006, 15:27

#66

Post by sandhyashree »

Sbala,
I know,since i learn from him..........i am also learning Talaprastara.But i got stuck midway midway due to my mother's illness and since then i havent really gone back to it. But i am amazed at your speed and that too since you are learning on the net. You have inspired me!!!!!!!!!!!
Last edited by sandhyashree on 28 Feb 2007, 21:55, edited 1 time in total.

coolkarni

#67

Post by coolkarni »

and sbala says he is afraid of quiz..
:rolleyes:

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#68

Post by sbala »

Sandhya - Good to know I'm inspiring someone. But, I prefer to lie low till I understand this completely. Why don't you share your experiences learning with Sharmaji and other subjects you have learnt from him? I know he has done lot of work on teaching methods for kalpanaswaras and raga alaapanais

sbala
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Joined: 30 Jul 2006, 08:56

#69

Post by sbala »

kji,
I dont know if you have been poked in your waist my mamis asking you to name the raga during concerts. I have had to endure the interrogation, my waistline has reduced and I'm yet to open the scoreboard in the "mami's quiz".
Last edited by sbala on 16 Mar 2007, 13:06, edited 1 time in total.

sandhyashree
Posts: 29
Joined: 01 Oct 2006, 15:27

#70

Post by sandhyashree »

Sbala,
Yes, definitely........
You can shoot an email to [email protected] since it might mean a deviation from the topic here....
i'll be more than glad to share my learning experiences with you........

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#71

Post by sbala »

Dear Sharmaji,
Please check the details of Viloma Prastara. What is the significance of Viloma apart from it just being the opposite of anuloma? I have heard his terms being used in the context of pallavis.

Akhanda Viloma Prastara for 6-DP

000000 01
10000 02
01000 03
00100 04
1100 05
S00 06
00010 07
1010 08
0110 09
0S0 10
00001 11
1001 12
0101 13
0011 14
111 15
S1 16
00S 17
1S 18
Ś 19
Last edited by sbala on 10 Mar 2007, 13:05, edited 1 time in total.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#72

Post by sbala »

Dear Sharmaji,
Please verify the details of Khanda Prastara for 6-DP.

Hina Prastara

Drutha Devoid Permutations(DDP) for 6DP.

S' 01
1S 02
S1 03
111 04

Laghu devoid Permutations for 6DP

S' 01
00S 02
0S0 03
S00 04
000000 05

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#73

Post by sbala »

Dear Sharmaji,
I've attempted the Yukta Prastara. Please verify if this is correct.

Yukta Prastara (7-DP 1-DCP)

0S' -01
01S -02
10S -03
0S1 -04
0111 -05
1011 -06
S01 -07
1101 -08
S'0 -09
1S0 -10
S10 -11
1110 -12
Last edited by sbala on 14 Mar 2007, 15:38, edited 1 time in total.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#74

Post by msakella »

Dear member, sbala, Your Akhanda-viloma-prastara is OK.
While writing the figures in obverse order is natural and necessary writing them in reverse order also is just another variety to make all of us more acquainted with them. In our younger days our parents are used to make all of us recite the mathematical tables both in obverse and reverse orders just to give more acquaintance with them. In the same manner this Viloma-prastara also helps to give us more acquaintance with the process of permutation. In fact, this was first mentioned in ‘Nartananirnaya’ of Pandarika Vithala of 16th century in the name of Vipareeta-prastara. But, to make the names of both obverse and reverse patterns of prastara, I have myself coined these names of Anuloma-prastara and Viloma-prastara. In our Indian Culture the obverse and reverse orders are called Anuloma and Viloma respectively and these names are appended to the things which have used these orders and in the same manner in our music also this has been utilized.
Your progress is excellent. Keep it up. But, a small correction. In 2-7-1-1-12 the permutation ‘S’0’ becomes the 9th but not 11th. Please note. Mostly you have got good acquaintance with the process of permutation and you need to maintain this level of acquaintance by attending to it regularly tallying their Sankhya with the relevant tables. Now, try to concentrate much upon Khanda-nashta, uddishta and kalita basing upon the respective rules and regulations furnished in the book. Proceed and write postings for clarification. I hope you will definitely be able to get through with them also. Wishing you all the best, amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#75

Post by sbala »

Dear Sharmaji,
Thank you for the response. Maybe, I'm deviating, but I heard the terms anuloma and viloma first in the context of pallavis. Could you explain what it means in a pallavi?

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#76

Post by msakella »

Dear member, sbala, No deviation at all. Later you may forget to ask this. This is only to share our ideas with all our Indian brothers and sisters. Sometimes we may be wrong, I can’t say. Better to clear off our doubts at the earliest.
In the context of Pallavis - in Anuloma the lyric of the Pallavi should be sung in obverse order, in Viloma the lyric of the Pallavi should be sung in reverse order and in Pratiloma the lyric of the Pallavi should be sung in a single speed but the Tala should be rendered in three speeds. Even though, presently, I am unable to recollect, some more technical terms are there in this context about which I shall define them later if I can recollect them. amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#77

Post by sbala »

Dear Sharmaji,
Could you give some examples to illustrate these concepts? I don't understand how a lyric can be sung in reverse order and yet make sense.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#78

Post by msakella »

Dear member, sbala, I recollect that, many years back, I read some where about such Viloma Sahitya composed by our Maha Vaidyanatha Iyer, the great but, I do not remember the exact lyric as my main concentration has always been on Talaprastara for more than four decades. Also there are two kinds in singing Viloma like that, one kind is of singing lyric like ‘Vi-Ka-Ta-Ka-Vi’ and second one is of singing notation ‘RGMDNDMGR’ in Kalyani-raga. Among them Viloma Sahitya is still more difficult. While all the people remain under the control of language we come across a very few people under whom the language itself remains under their control. Such people only can do such incredible things. amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#79

Post by sbala »

Dear Sharmaji,
In another thread, you pointed out that thalams containing Samyuktangas should not be peformed as it contradicts the other requirements that the first kriya of any anga should be sounded. What is the purpose of Samyuktanga if it cannot be rendered?
Last edited by sbala on 14 Mar 2007, 15:18, edited 1 time in total.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#80

Post by sbala »

msakella wrote:In 2-7-1-1-12 the permutation ‘S’0’ becomes the 9th but not 11th. Please note.
Sharmaji, I have made the change.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#81

Post by msakella »

Dear member, sbala, For example, in 6-units’ permutation of Samyuktanga-prastara consisting of Sankhya of ‘32’, in Trisra-jati the 2nd, 3rd, 4th , 9th, 17th, 18th & 25th permutations,
in Chaturashra-jati the 1st, 2nd, 5th, 6th, 7th, 8th, 10th , 13th, 17th, 19th, 20th, 21st, 26th & 29th permutations, in Khanda-jati the
1st, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 13th, 18th, 19th, 20th, 21st, 25th, 26th & 29th permutations, in Mishra & Sankeerna-jatis the 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 13th, 17th, 18th, 19th, 20th, 21st, 25th, 26th & 29th permutations carry Samyuktangas and these rhythmical forms should not be used as Talas but as mathematical forms in Svarakalpana. The rhythmical forms incorporating Samyuktangas can only be used in Svarakalpana for mathematical purpose but not as Talas. After having gone through the different processes of permutation, I hope, now, you can understand this. amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#82

Post by sbala »

Dear Sharmaji,
The reason why it cannot be used in thala is because the first kriya of every anga has to be sounded and in case of samyuktangas that rule will be violated. Is that right? I'm interested to know the application of talaprastara to kalpanaswaras. Is it too early or can we discuss the same?

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#83

Post by msakella »

Dear member, sbala, You caught the point, while rendering any Samyuktanga the established rule has to be violated. That is why Samyuktangas should never be rendered at all.
Any thing must have relevancy with the present day life. Now, if is the time to discuss about this relevancy of this topic, Talaprastara, in our present day life. Even though many are not at all aware of it, Talaprastara has great relevancy with our Svarakalpana. Please go through the contents of the pages from x to xv of the Prologue of my book, Talaprastara Ratnakara and sing all the 25 varieties of 16-units furnished there along with the rhythmical form, its authentic serial number, Jati and notation of the rhythmical form to be used in our Svarakalpana. amsharma.

ram
Posts: 705
Joined: 02 Feb 2010, 22:48

#84

Post by ram »

Dear Sri msakella,

This thread is so educative and that too on a topic that is very hard to find even in many of the books. I don't know how I did not go through this for all the time this thread has been in existence now. I had bought two of your books from Karnatic Music Book Center as soon as I landed in Chennai a few months back but then have not had a chance to go through them till now. I think the time has come to take them out and also read this thread in detail. I hope it is ok to trouble you with any questions I might have.

Thank you so much for your efforts to educate us.

Regards,
Ram

msakella
Posts: 1939
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#85

Post by msakella »

Dear member, ram, Glad to know that you are interested in learning Talaprastara. Welcome. As I have taken the propagation of the easy methods in singing Svarakalpana and Ragalapana and Talaprastara as a mission of life, I am always ready to help you in every manner in learning this topic, Talaprastara with pleasure. No trouble at all. I have written 3 books on Talaprastara and they all are available in Karnatic Music Book Centre, Chennai. You take the 3rd book also. Mr. sbala, the Chennai-based brother-member of our forum had started learning this topic and covered much of it. You can take his g-mail address from this forum profiles and contact him to learn from him in person what he had already learnt.
amsharma.

ram
Posts: 705
Joined: 02 Feb 2010, 22:48

#86

Post by ram »

Thank you Sri msakella.

In fact I still recall the day I came to Chennai a few months back. I had gone to Karnatic Music Book Center and asked him if he has books on tala and tala numbers. I had tried going through a version of "Sangeetha Ratnakara" I had bought earlier but it was not very explanatory and was confusing too. He showed me a few that talked about the basic 35 talas. When I asked him if there is some treatise on talas, he showed me two books and said this is very good research material of very advanced nature. I bought them immediately but never got a chance to sit down and go through the material in detail. Little did I know back then that I would get a chance to interact with the author of the books himself in a helpful and educative forum like this !!

(When I read from cover of one of the books that you were a violin vidwan, the first thought that came to my mind was that many percussion artists do not even seem to care about knowing details of talas and tala numbers and how strange it was that a violin vidwan was researching this topic and publishing on the same)

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#87

Post by sbala »

Ram,
Welcome to the thread! I'm sure with your knowledge of music, you can ask deeper questions and contribute more .

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#88

Post by msakella »

Dear member, ram, Felt glad to go through your last post and to note the contents. As per a saying in Sanskrit - ‘Kshanashah Kanashachaiva Vidya Dhanamaarjayet’- one should always remain in the process of acquiring knowledge and money at the rate of one atom each second. Thus, knowledge should always be acquired and be distributed at all times by all. Then only our community flourishes. The Almighty had driven me into this rarest topic, Talaprastara of our Indian music and also blessed me with all the required devotion, patience and perseveration along with all the latent secrets of it which have never been brought out by any author of any century. But, it took four decades of my life and I don’t want to let any other brother/sister Indian struggle for his life to get it like me. That is why I have taken the propagation of this topic as a mission of my life. You people all must learn this rarest topic fully to pass on our cultural heritage to the posterity. Wishing you all the best, amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#89

Post by sbala »

Dear Sharmaji,
I have attempted to give a logical explanation of why the method of computation of Sankhya works as some people might be wondering about proxies and why we need to add them. Let me know if this explanation is right or if I need to modify anything.

Logical Justification of Sankhya computation.

Number of permutations of N units= Sum of the (Number of permutations ending with a particular anga) ,for all the angas that are part of the prastara.

Number of permutations of N units ending with a particular anga=Number of permutations of (N - the value of the anga) using all the angas which will correspond to the Sankhya of (N- value of anga) units.

This is the reason why we sum the relevant proxies for Sankhya to get the total number of permutations.
Last edited by sbala on 17 Mar 2007, 17:03, edited 1 time in total.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#90

Post by msakella »

Dear member, sbala, I am now 70 years of age and nowadays I do not want to think much about things and to retain them in my mind. But, as I always want to give away the knowledge blessed by the Almighty to my brothers and sisters until my last breath, I am trying my level best to do the same. At the same time, as I am not much educated like you all, at this juncture I cannot and do not want to try to understand more than what I need. Please don’t mistake me. In respect of these applications, as a highly educated person, you can try all kinds of logics to make it easier, understandable and digestible to the aspirants as you yourself should propagate this topic. amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#91

Post by sbala »

No problem Sharmaji. I'm just trying to present the same information in a different format so that others who come from a similar background like me may read this thread later and understand. Though, I have to admit, you have presented the information in the simplest fashion possible. Infact, the way you have presented the information in this forum is much easier to understand than even the book. In that sense, we are all lucky!

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#92

Post by msakella »

Chi. sbala dear, I feel extremely glad to know that you have started trying to distribute what you have already acquired in respect of Talaprastara in your own way just like a true soldier
of Talaprastara. While I am the senior most soldier, you are the junior soldier and our another brother-member, ram is the junior-most soldier. Irrespective of the capacity we all are the soldiers of Talaprastara Army. Just like in which way our entire Indian community is safe under the most vigilant brother-Indian-soldiers of our country we, the soldiers of Talaprastara Army also should always remain vigilant in enlightening our Indian brothers and sisters in this aspect and also to strive hard to keep it intact and pass on this great Indian culture to posterity. We all have to work hard in letter and spirit. Then only our great Indian culture remains alive perennially and survives. OK. Wishing you all the best, amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#93

Post by sbala »

Logical Proof for the method of computing Sankhya.

As can be seen from the process, the Sankhya for a given numberof units can be expressed as a sum of the Sankhya of lower number of units. The lower units to be chosen would vary from one pratara to another and depends on whether it is Akhanda or Khanda. For instance, if we want the details of the Druta-Meru prastaras for 0, 1 and 2 drutas.

To find the number of permutations of n units containing 0 drutas, it is clear that we need worry about only laghu, guru and kakapada ending permutations with no drutas which are the 2nd, 4th, 6th and 8th proxies. We should not count the first proxy as it denotes the number of druta ending permutations that contains 0 drutas which does not make sense. This is the reason why we sum the 2nd, 4th, 6th and 8th proxies for Duruta meru with 0 drutas in Pancanga Khanda Prastara.

Druta Meru for 1 Druta
Here, we have to find the number of permutations of n units using one Druta. All the permutations have to end with one of the possible angas. If we look at the number of druta ending permutations, that is the same as number of permutations of (n-value of druta) using 0 drutas. This is the reason we look at the first proxy in the lower line for this permutation and not on the same line.

Similarly, for the laghu ending permutations, we have to look at the number of permutations of 2nd proxy (n-value of laghu) units using 1 druta. This is on the same line and is nothing but the 2nd proxy.

Similarly, the same logic can be extended to 2-DCP as well.
Last edited by sbala on 18 Mar 2007, 15:51, edited 1 time in total.

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#94

Post by msakella »

Dear member, sbala, I am damn tired of my life after having spent four decades of my life on this very heavy strenuous research on this topic, Talaprastara. You do not know that, at last, I have reached a saturating point of research of this topic which was ending every time I try to think with my head with terrible heat and loosing the vision of my eyes for some minutes. There I was compelled to stop. That is why I always think that the Almighty blessed me with every thing of it but permitted me to solve 99.9% of this topic and this saturating point lies beyond that. I shall explain this to you when we meet in person, if you remind me. So, you please proceed with all this logical applications of it. I am already exhausted myself to the saturating point and cannot further concentrate upon any such thing. Try to proceed with the Nashta, Uddishta and Kalita of Khanda-prastara also with the help of my book. Wishing you all the best, amsharma.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#95

Post by sbala »

Dear Sharmaji,
I will try to cover the book as soon as possible. As I said earlier, I'm posting the logical explanations only for other members who might read this in the future, to understand the topic from a mathematical perspective and not for any other reason.

ram
Posts: 705
Joined: 02 Feb 2010, 22:48

#96

Post by ram »

sbala,

Though Sri msakella has explained everything in a easy-to-understand manner, please continue with your logical explanations too, if possible. When I was going through the process of permutations the other day, I was trying to derive a formula for sankhya and mahapatala calculation and just when I had done that and went a few posts ahead, I found you had already posted the same. I could have readily used your formula.

sbala
Posts: 629
Joined: 30 Jul 2006, 08:56

#97

Post by sbala »

Ram,
I gave the formula only for Samyuktanga. You could derive them for the other prastaras. My only fear is Math drives people away and that's why I stick to wordy explanations.

listener
Posts: 16
Joined: 06 Jul 2006, 21:09

#98

Post by listener »

All,

I just finished going through this topic...

For those (engineers/mathematicians)well acquainted with the binary system and the language of computation, I found that the Nashta, Uddhishta and Kalita computation for the Samyuktanga prastara can be easily summerized:

Samyuktanga Nashta/Uddhishta computation:

To obtain the constituent figures of the 'm'th permutation of 'n' units:

Write m-1 in binary form. Append the requisite number of zeros to make it a (n-1)-bit number. Consider the resulting representation as a string. Reverse it (eg., 00110101 -> 10101100). From the resulting string, form another string, by replacing every '0' in the original string with a '1' and every '1' in the original string with a '+1'. Append a '1' to the left of this string. This string will contain the angas separated by a '+' sign.

Eg.,

41st permutation of units:

41-1 = 40 = 101000 in binary ---> write in 8-1 = 7 bits ---> 0101000 ---> reverse ---> 0001010 ---> 111+11+11---> append '1' ---> 1111+11+11 ---> 4+2+2

the Uddhishta process is exactly the reverse of this.

Kalita:

Number of occurrences of figure 'k' in a prastara containing permutations of 'n' units can be summarized with a formula as follows:

N(n,k) = 2^(n-k) + (n-k-1)*2^(n-k-2), if k < n
= 1 if k=n
Last edited by listener on 26 Mar 2007, 05:26, edited 1 time in total.

listener
Posts: 16
Joined: 06 Jul 2006, 21:09

#99

Post by listener »

sbala wrote:Ram,
I gave the formula only for Samyuktanga. You could derive them for the other prastaras.
Unfortunately, I think exact formulas (even Sankhya and Mahapatala) cannot be obtained for the other prastaras (Panchanga and Shadanga) this would require us to factorize polynomials of degree 6. Will explain why if someone here is interested in knowing...

I think Sharmaji's 'Recursive' approach is the only way...

msakella
Posts: 1939
Joined: 30 Sep 2006, 21:16
x 2

#100

Post by msakella »

Dear brother-members, sbala, ram, listener, Today I feel extremely happy and am able to forget the hardship I have experienced for four decades (from 1963 to 2003) of my life to get this Talaprastara out. When I happen to come to Chennai in near future we shall all meet and I shall explain the very important details of Talaprastara which can only be explained easily in person. Wishing you all the best, amsharma.

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