Talaprasthara (Combinatorics)

Tālam & Layam related topics
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msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Post by msakella »

Dear member, sbala, You are correct. It is a bit difficult to render or follow Talas with un-sequential Talangas. If at all you analyse things, generally, there will, definitely, be some background or other in arranging things by our ancestors. No doubt at all, they are very very clever. They have chosen only 7 Talas for a common man and they are very small in size when compared to bigger ones of 108 Talas. Even among them they have included only one Tala of odd number of Kriyas too which is Triputa. Even in choosing Jaatis they have given highest preference of 4 times to odd-numbers i.e., one even number of 4 and 4 odd-numbers of 3,5,7 & 9. It is very difficult to manage with an odd fellow. Isn’t it? That is why they have selected 4 odd-jaatis and only one even-jaati to strengthen us in Laya aspect. Even in Svara aspect they have created three very difficult notes, Saharana-gandhara, Shuddha-madhyama and Kashiki-nishada, having extra-ordinary range of swinging unlike in any other music of the world. Even centuries back, even when computers or even calculators are not available, they have formulated this Prastara in Tala with precisive rules and regulations to make our music more effective and at the same time scientific too. In fact, while none of the chapters of the great Sangita Ratnakara is relevant with our present day music, only this Prastara is still relevant either with our present day Tala or Svarakalpana. See the greatness of our ancestors and always try to keep our culture in tact and pass it on to the posterity. Wishing you all the best, amsharma.
Last edited by msakella on 13 Jan 2007, 15:30, edited 1 time in total.

msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Post by msakella »

3rd part:
NASHTA, UDDISHTA & KALITA

In order to avoid the Himalayan task of the process of permutation, for which a human life is too short, some interesting, important and easy methods are furnished in this Prastara to obtain
(a) The series of figures of a particular serial number of permutation,
(b) The serial number of a particular prastara containing a particular series of figures,
(c)The details of all the figures of different denominations obtained up to a
particular number of permutation with the help of few figures.
They are named as ‘Nashta, Uddishta and Kalita’ respectively and are elaborated hereunder along with the relevant rules and examples.

NASHTA

The easy method of obtaining the series of figures of a permutation, containing a particular serial number with the help of Sankhya is called ‘Nashta’.

Rules for answering Nashta:

1. Write the figures of Sankhya up to the required units of permutation.

2. Subtract the question-number from the Sankhya and later subtract the respective proxies consecutively from the remainder.

3. If the first proxy is not subtracted from the remainder, write it’s figure and repeat the process of subtraction of the relevant proxies of the ‘un-subtracted-proxy’ from the remainder. For the subtraction of the 1st proxy, consider the ‘non-subtraction’ of the 2nd proxy. For the consecutive subtraction of the 1st & 2nd proxies, consider the ‘non-subtraction’ of the 3rd proxy. For the consecutive subtraction of the 1st, 2nd & 3rd proxies, consider the ‘non-subtraction’ of the 4th proxy. For the consecutive subtraction of the 1st, 2nd, 3rd & 4th proxies, consider the ‘non-subtraction’ of the 5th proxy - thus always considering the ‘non-subtraction’ of the last proxy, write its corresponding figure and leave away its proxy. Repeat the process of subtraction by subtracting the relevant proxies of the ‘un-subtracted-proxy’. In the absence of the remainder no figure needs to be left off.

4. Figures should always be written by subtracting the existing respective
proxies observing relevant rules and restrictions.

5. To answer the Nashta of Akhanda-prastara, one or more figures of the
least denomination should be written to fill-in the deficit value of the
permutation, when neither the remainder nor the proxy or both do not exist.

Note: 1. The figures of a permutation should always be cited from right to left only.

Examples:

1. What is the series of figures pertaining to the 1st permutation of 6-UP?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

As per rule No.2 the remainder is ‘31’ (32-1).

From this above remainder, as the 1st, 2nd, 3rd, 4th and 5th proxies can consecutively be subtracted (31-16=15-8=7-4=3-2=1-1=0) consider that the 6th proxy cannot be subtracted and write its figure ‘6’ as per rule No.3.

Thus this permutation contains ‘6’ in its series of figures.

2. What is the series of figures pertaining to the 2nd permutation of 6-UP?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

As per rule No.2 the remainder is ‘30’ (32-2).

From the above remainder, as the 1st, 2nd, 3rd and 4th proxies can consecutively be subtracted (30-16=14-8=6-4=2-2=0) and considering that the 5th proxy cannot be subtracted, write its figure ‘5’ as per rule No.3.

Till now, out of the total value of ‘6-units’ of the permutation, 5-units are derived and to fill-in the deficit value of 1-unit of the permutation write one figure ‘1’ in the left extreme of the permutation as per rule No.5.

Thus this permutation contains ‘1 5’ in its series of figures.

3. What is the series of figures pertaining to the 3rd permutation of 6-UP?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

As per rule No.2 the remainder is ‘29’ (32-3).

From the above remainder, as the 1st, 2nd and 3rd proxies could consecutively be subtracted (29-16=13-8=5-4=1) and considering that the 4th proxy cannot be subtracted , write its figure ‘4’ leaving off its proxy ‘2’ as per rule No.3 to continue the process.

Now, as per rule 3, the process of Nashta starts afresh basing upon the above left-off proxy ‘2’ and from the last remainder ‘1’, as its 1st proxy ‘1’ can be subtracted (1-1=0)and considering that the 2nd proxy cannot be subtracted, write its figure ‘2’ as per rule No.3.

Thus this permutation contains ‘2 4’ in its series of figures.

4. What is the series of figures pertaining to the 6th permutation of 6-UP?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

As per rule No.2 the remainder is ‘26’ (32-6).

From the above remainder, as the 1st and 2nd proxies can consecutively be subtracted (26-16=10-8=2) and considering that the 3rd proxy cannot be subtracted , write its figure ‘3’ leaving off its proxy ‘4’ as per rule No. 3 to continue the process.

Now, as per rule No. 3, the process of Nashta starts again from the beginning basing upon the above left-off proxy ‘4’ and from the last remainder ‘2’, as its 1st proxy ‘2’ can be subtracted (2-2=0) and considering that the 2nd proxy cannot be subtracted , write its figure ‘2’ as per rule No. 3.

Till now, out of the total value of ‘6-units’ of the permutation, 5-units are derived and to fill-in the deficit value of 1-unit of the permutation write one figure ‘1’ in the extreme left of the permutation as per rule No.5.

Thus this permutation contains ‘1 2 3’ in its series of figures.

5. What is the series of figures pertaining to the 7th permutation of 6-UP?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

As per rule No.2 the remainder is ‘25’ (32-7).

From the above remainder, as the 1st and 2nd proxies can consecutively be subtracted (25-16=9-8=1) and considering that the 3rd proxy cannot be subtracted, write its figure ‘3’ leaving off its proxy ‘4’ as per rule No. 3 to continue the process.

Later, as per rule No. 3, the process of Nashta starts again basing upon the above left-off proxy ‘4’. Accordingly, from the last remainder ‘1’, as its 1st proxy ‘2’ cannot be subtracted, write the figure ‘1’ of the 1st proxy itself and continue the process.

Now, again as per rule No. 3, the process of Nashta starts again basing upon the last un-deducted proxy ‘2’ and from the last remainder ‘1’, as its 1st proxy ‘1’ cannot be subtracted (1-1=0) and considering that the 2nd proxy cannot be subtracted ,write its figure ‘2’ as per rule No. 3.

Thus this permutation contains ‘2 1 3’ in its series of figures.

6. What is the series of figures pertaining to the 14th permutation of 6-UP?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

As per rule No. 2 the remainder is ‘18’ (32-14).

From the above remainder, as the 1st proxy could only be subtracted (18-16=2) consider that the 2nd proxy could not be subtracted and write its figure ‘2’ leaving off its proxy ‘8’ as per rule No. 3 to continue the process.

Later, as per rule No. 3, the process of Nashta starts again basing upon the above left-off proxy ‘8’ and from the last remainder ‘2’, its 1st proxy ‘4’ cannot be subtracted, being higher than the remainder, write the figure ‘1’ of the same 1st proxy itself and continue the process as per rule No.3.

Now, again as per rule No. 3, the process of Nashta starts again basing upon the last un-deducted proxy ‘4’ and from the last remainder ‘2’, as its 1st proxy ‘2’ can be subtracted (2-2=0)and considering that the 2nd proxy cannot be subtracted, write its figure ‘2’ as per rule No. 3.

Till now, out of the total value of ‘6-units’ of the permutation, in total, 5-units are derived and to fill-in the deficit value of 1-unit of the permutation write one figure ‘1’ in the extreme left of the permutation as per rule No.5.

Thus this permutation contains ‘1 2 1 2’ in its series of figures.

7. What is the series of figures pertaining to the 19th permutation of 6-UP?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

As per rule No.2 the remainder is ‘13’ (32-19).

From the above remainder, as the 1st proxy ‘16’ cannot be subtracted write the figure ‘1’ of the same 1st proxy itself and continue the process as per rule No.3.

Later, as per rule No. 3, the process of Nashta starts again basing upon the last un-deducted proxy ‘16’ and from the above remainder ‘13’, as its 1st and 2nd proxies can be subtracted consecutively (13-8=5-4=1) and considering that the 3rd proxy cannot be subtracted, write its figure ‘3’ leaving off its proxy ‘2’ as per rule No. 3 to continue the process.

Now, again as per rule No. 3, the process of Nashta starts again basing upon the last left-off proxy ‘2’ and from the last remainder ‘1’, as its `1st proxy ‘1’ can be subtracted (1-1=0) and considering that the 2nd proxy cannot be subtracted, write its figure ‘2’ as per rule No. 3.

Thus this permutation contains ‘2 3 1’ in its series of figures.

8. What is the series of figures pertaining to the 23rd permutation of 6-UP?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

As per rule No.2 the remainder is ‘9’ (32-23).

From the above remainder, as the 1st proxy ‘16’ could not be subtracted write the figure ‘1’ of the same 1st proxy itself as per rule No.3 and continue the process.

Later, as per rule No. 3, the process of Nashta starts again basing upon the last un-deducted proxy ‘16’ and from the remainder ‘9’, as its 1st proxy ‘8’ can be subtracted (9-8=1) and considering that the 2nd proxy cannot be subtracted , write its figure ‘2’ leaving off its proxy ‘4’ as per rule No. 3 to continue the process.

Now, again as per rule No. 3, the process of Nashta starts again basing upon the last left-off proxy ‘4’ and from the last remainder ‘1’, as its 1st proxy ‘2’ cannot be subtracted, write the figure ‘1’ of the 1st proxy as per rule No.3 and continue the process.

Now, again as per rule No. 3, the process of Nashta starts again basing upon the last un-deducted proxy ‘2’ and from the last remainder ‘1’, as its 1st proxy ‘1’ can now be subtracted (1-1=0) and considering that the 2nd proxy cannot be subtracted write its figure ‘2’ as per rule No. 3.

Thus this permutation contains ‘2 1 2 1’ in its series of figures.

9. What is the series of figures pertaining to the 27th permutation of 6-UP?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

As per rule No.2 the remainder is ‘5’ (32-27).

From the above remainder, as the 1st and 2nd proxies, ‘16 & 8’ respectively, cannot be subtracted write figures ‘1 1’ representing the same 1st proxy itself as per rule No. 3 and continue the process.

Now, as per rule No. 3, the process of Nashta starts again basing upon the un-deducted last proxy ‘8’ and from the above remainder ‘5’, as its 1st proxy ‘4’ can be subtracted (5-4=1) and considering that the 2nd proxy cannot be subtracted, write its figure ‘2’ leaving off its proxy ‘2’ to continue the process.

Now, again as per rule No. 3, the process of Nashta starts again basing upon the last left-off proxy ‘2’ and from the last remainder ‘1’, as its 1st proxy ‘1’ can be subtracted (1-1=0) and considering that the 2nd proxy cannot be subtracted, write its figure ‘2.’

Thus this permutation contains ‘2 2 1 1’ in its series of figures.
Last edited by msakella on 15 Jan 2007, 14:17, edited 1 time in total.

msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Post by msakella »

Hello brothers and sisters of our forum!!!
I wish you all a very happy Sankranthi / Pongal. I hereby request all the aspirants who have started learning Talaprastara through our forum to kindly give me their e-mail addresses and telephone numbers (both landline and cell) to enable me to invite you to the workshops on ‘Talaprastara’ to be arranged at different places like
Chennai, Bangalore, Mumbai, Delhi etc., at the time of my visits to these places. You all can send these details to my e-mail address ‘msakella2002@yahoo.co.in’. Wishing you all the best, amsharma.

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

Post by sbala »

Msakella Sir,
I have furnished the 4th, 5th and 8th perumutations of the 6 unit permutation and the 4th and 11th permutations of 7-UP. Please verify when you have time.

4th Permutation of 6-UP.
1. Deduct the serial number from the Sankhya. 32-4=28
2. Start deducting the proxies. 28-16-8-4=0. 4th proxy is not deducted. Therefore, write 4.
3. Deficit is 2. Has to be filled with the lowest denomination units possible ie 1 1
4. Therefore, the 4th permutation is 114.

5th permutation of 6-UP.
1. 32-5=27
2. 27-16-8=3. Undeducted proxy=3
3. Start the process from the 3rd proxy.
4. 3-2-1=0. Undeducted proxy=3.
5. 5th permutation is 33.

8th permutation of 6-UP
1. 32-8=24
2. 24-16-8=0. 3rd proxy undeducted.
3. deficit is 3. to be filled as 111.
4. 8th permutation is 1113

4th permutation of 7-UP
1. 64-4=60
2. 60-32-16-8-4=0. Undeducted proxy=5
3. Deficit=2.
4. 4th permutation is 115

11th permutation of 7-UP
1. 64-11=53
2. 53-32-16=5. Undeducted proxy=3.
3. 5-4=1. Undeducted proxy=2.
4. 1-1=0. Undeducted proxy=2.
5. 11th permutation of 7-UP is 223
1.
Last edited by sbala on 16 Jan 2007, 12:16, edited 1 time in total.

msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Post by msakella »

Member, sbala dear, Hearty congrats. Extremely well. You got it.
Get a small-square-ruled-book, please make the permutations up to 9-units, at the least, and do the Nashta to many of them. Regular practice is a must for music. Never forget it. You have very successfully got it. That is why I am posting the next two parts, Uddishta & Kalita. Go through them successfully and report back. I wish you should become the teacher of Talaprastara in Chennai as early as possible to propagate this rare topic of our Indian culture. Wishing you all the best, amsharma.
Last edited by msakella on 19 Jan 2007, 21:31, edited 1 time in total.

msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Post by msakella »

4th part:
UDDISHTA

Uddishta is the easy method to obtain the serial number of a permutation containing a particular series of figures, based upon the figures of Sankhya. However the rules are the same as in Nashta.

(a) As per the rules governing Nashta the un-deducted proxies always derive the least figure i.e. ‘1’ and the successfully deducted proxies always derive other higher figures. In a series of figures of a permutation, take out the relevant proxies of the figures which are successfully subtracted which in turn derive the ‘Adhikanga-janita-Sankhya’ (AS, i.e; the figure from which the higher Angas/figures are derived). Later, subtract the AS from the Sankhya and the remainder is the serial number.

E X A M P L E S:

1. What is the serial number of the 6-UP containing ‘6’ in its series of figures?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

By the figure ‘6’ of the permutation it should be presumed that this is derived by the consecutive subtraction of five proxies i.e., 1st proxy ‘16’, 2nd proxy ‘8’, 3rd proxy ‘4’, 4th proxy ‘2’ and 5th proxy ‘1’ and the non-subtraction of the 6th proxy ‘1’ as per rule No. 3.

Thus the AS is ‘31’ (16+8+4+2+1) and as per rule No. (a) the remainder ‘1’(32-31) is the serial number.

2. What is the serial number of the 6-UP containing ‘1 1 4’ in its series of figures?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

By the first figure ‘4’ of the permutation it should be presumed that this is derived by the consecutive subtraction of three proxies i.e., 1st proxy ‘16’, 2nd proxy ‘8’ and 3rd proxy ‘4’ and the non-subtraction of the 4th proxy ‘2’ as per rule No. 3.

By the next two least figures ‘1 1’ of the permutation it should always be presumed that they are written only to fill-in the deficit value of the permutation as per rule No. 5.

Thus the AS is ‘28’ (16+8+4) and as per rule No.(a) the remainder ‘4’ (32-28) is the serial number.

3. What is the serial number of the 6-UP containing ‘3 3’ in its series of figures?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

By the first figure ‘3’ of the permutation it should be presumed that this figure ‘3’ is derived by the consecutive subtraction of the 1st proxy ‘16’ and 2nd proxy ‘8’ and the non-subtraction of the 3rd proxy after which its proxy ‘4’ has to be left-off as per rule No. 3 to continue the process.

Later, by the next figure ‘3’ of the permutation it should be presumed that, basing upon the above left-off proxy ‘4’ the process is continued and this figure ‘3’ is also derived by the consecutive subtraction of the 1st proxy ‘2’ and 2nd proxy ‘1’ and the non-subtraction of the 3rd proxy ‘1’ as per rule No. 3.

Thus the AS is ‘27’ (16+8+2+1) and as per rule No.(a) the remainder ‘5’ (32-27) is the serial number.

4. What is the serial number of the 6-UP containing ‘2 2 2’ in its series of figures?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

By the first figure ‘2’ of the permutation it should be presumed that this figure is derived by the subtraction of the 1st proxy ‘16’ and the non-subtraction of the 2nd proxy after which its proxy ‘8’ has to be left-off as per rule No. 3 to continue the process.

Later, by the next figure ‘2’ of the permutation it should be presumed that, basing upon the above left-off proxy ‘8’ the process is continued and again this figure ‘2’ also is derived in the same way by the subtraction of the 1st proxy ‘4’ and the non-subtraction of the 2nd proxy after which its proxy ‘2’ has to be left-off as per rule No. 3 to continue the process.

Again, by the last figure ‘2’ of the permutation it should be presumed that, basing upon the above left-off proxy ‘2’ the process is continued and again this figure ‘2’ also is derived in the same way by the subtraction of the 1st proxy ‘1’ and the non-subtraction of the 2nd proxy as per rule No. 3.

Thus the AS is ‘21’ (16+4+1) and as per rule No. (a) the remainder is ‘11’ (32-21) is the serial number.

5. What is the serial number of the 6-UP containing ‘2 1 1 2’ in its series of figures?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

By the first figure ‘2’ of the permutation it should be presumed that it is derived by the subtraction of the 1st proxy ‘16’ and the non-subtraction of the 2nd proxy after which its proxy ‘8’ has to be left-off as per rule No. 3 to continue the process.

Later, by the next two figures ‘1 1’ of the permutation it should be presumed that, basing upon the above left-off proxy ‘8’ the process is continued and these figures ‘1 1’ are derived by the consecutive non-subtraction of the 1st proxy ‘4’ of the above left-off proxy ‘8’ and again the 1st proxy ‘2’ of the last un-deducted proxy ‘4’ as per rule No. 3 to continue the process.

Now, by the last figure ‘2’ of the permutation it should be presumed that, basing upon the un-deducted last proxy ‘2’ the process is continued and this figure ‘2’ is derived by the subtraction of the 1st proxy ‘1’ and the non-subtraction of the 2nd proxy as per rule No. 3.

Thus the AS is ‘17’ (16+1) and as per rule No.(a) the remainder ‘15’ (32-17) is the serial number.

6. What is the serial number of the 6-UP containing ‘3 2 1’ in the series of figures?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

By the first figure ‘1’ of the permutation it should be presumed that this figure is derived by the non-subtraction of the 1st proxy ‘16’ as per rule No.3 and the process is continued.

Later, by the next figure ‘2’ of the permutation it should be presumed that, basing upon the last un-deducted proxy ‘16’ the process is continued and this figure ‘2’ is derived by the subtraction of the 1st proxy ‘8’ and the non-subtraction of the 2nd proxy after which its proxy ‘4’ has to be left-off as per rule No. 3 to continue the process.

Now, by the last figure ‘3’ of the permutation it should be presumed that, basing upon the above left-off proxy ‘4’ the process is continued and this figure ‘3’ is derived by the consecutive subtraction of the 1st proxy ‘2’, and the 2nd proxy ‘1’ and the non-subtraction of the 3rd proxy ‘1’ as per rule No. 3.

Thus the AS is ‘11’ ( 8+2+1) and as per rule No.(a) the remainder ‘21’ (32-11) is the serial number.

7. What is the serial number of the 6-UP containing ‘2 1 2 1’ in the series of figures?

As per rule No.1 write the figures of Sankhya up to the required units of permutation.

By the first figure’1’ of the permutation it should be presumed that this figure is derived by the non-subtraction of the 1st proxy ‘16’ as per rule No.3 and the process is continued.

Later, by the next figure ‘2’ of the permutation it should be presumed that, basing upon the last un-deducted proxy ‘16’ the process is continued and this figure ‘2’ is derived by the subtraction of the 1st proxy ‘8’ and the non-subtraction of the 2nd proxy after which its proxy ‘4’ has to be left-off as per rule No. 3 to continue the process.

Later, by the next figure ‘1’ of the permutation it should be presumed that, basing upon the above left-off proxy ‘4’ the process is continued and this figure ‘1’ is derived by the non-subtraction of the 1st proxy ‘2’ as per rule No. 3 and the process is continued.

Now, by the last figure ‘2’ of the permutation it should be presumed that, basing upon the last un-deducted proxy ‘2’ the process is continued and this figure ‘2’ is derived by the subtraction of the 1st proxy ‘1’ and the non-subtraction of the 2nd proxy as per rule No.3.

Thus the AS is ‘9’ (8+1) and as per rule No.(a) the remainder ‘23’ (32-9) is the serial number.


5th part:
KALITA

Kalita is the method for obtaining the full particulars of all the figures/ Angas used in the process of permutation up to the required prastara in question avoiding the laborious process of permutation.

E X A M P L E S:

1.Give the particulars of all the Figures of 6-UP (6-units-permutation).

In Samyuktanga-prastara the figures of all the preceding houses (including the figure ‘1’ written in the extreme left as per the general-key-rule) are the proxies of which the total of all forms the Sankhya.

According to the general table of permutations it should be analysed that as per the ---

1st proxy there is/are ‘16’ 1-UEPs with ‘48’ other figures
2nd ,, ‘8’ 2-UEPs ‘20’ ,,
3rd ,, ‘4’ 3-UEPs ‘8’ ,,
4th ,, ‘2’ 4-UEPs ‘3’ ,,
5th ,, ‘1’ 5-UEPs ‘1’ ,,
6th ,, ‘1’ 6-UEPs ‘1’ ,,

(Note:- UEP (unit-ending permutation) i.e., permutation ending with a particular figure)

----- thus arriving at the total of ‘32’ permutations along with ‘112’ figures.
These ‘32’ permutations starting from the figure ‘6’ in the 1st permutation should be analysed in the following manner.

(a) As per the Sankhya ‘1’ of the corresponding sixth proxy of 6-UEP (6-units-ending permutation), it should be understood that there is only one 6-UEP with a single figure 6 as its corresponding Mahapatala does not exist.

(b) According to the analysis, as per the Sankhya ‘1’ and its Mahapatala ‘1’ of the corresponding fifth proxy pertaining to the 5-UEP, it should be understood that, apart from the ‘5’ in the right extreme end of this 5-UEP, there is another figure ‘1’ also in this permutation as per the Sankhya ‘1’ of its corresponding first proxy of 1-UEP --- thus totaling to two (1+1) figures in this 5-UEP. Here it is also interesting to know that there are only two figures of ‘5’ in all these 32 permutations.

(c) According to the brief analysis, as per the Sankhya ‘2’ and its Mahapatala ‘3’ of the corresponding fourth proxy pertaining to the 4-UEP, it should be understood that, apart from the two figures of 4 which are in the right extreme end of these two 4-UEPs, there are ‘3’ other figures also --- thus totaling to five (2+3) figures in all these two 4-UEPs. Here it is also interesting to know that there are only five figures of 4 in all these 32 permutations. According to the detailed analysis it should also be understood that, in these two 4-UEPs, there are two figures of 4 (2/4) as per the Sankhya ‘2’, one figure of 2 (1/2) as per the Sankhya ‘1’ (no Mahapatala) of the corresponding second proxy of 2-UEP and two figures of 1 (2/1) as per the SM-figure (combined figure of Sankhya and Mahapatala (1+1) ‘2’ of the corresponding first proxy of 1-UEP of the same 4-UEP proxy --- thus totaling to five (2+3) figures (2/4, 1/2 & 2/1=5 figures).

(d) According to the brief analysis as per the Sankhya ‘4’ and its Mahapatala ‘8’ of the corresponding third proxy pertaining to the 3-UEP proxy, it should be understood that, apart from the four figures of 3 which are in the right extreme end of these four 3-UEPs, there are ‘8’ other figures also thus totaling to (4+8) ‘12’ figures in all these four 3-UEPs. Here it is also interesting to know that there are only four figures of 3 in all these 32 permutations. According to the detailed analysis it should also be understood that, in these four 3-UEPs, there are four figures of 3 (4/3) as per the Sankhya ‘4’, one figure of ‘3’ (1/3) as per the Sankhya ‘1’ (no Mahapatala) of the corresponding third proxy of 3-UEP, two figures of 2 (2/2) as per the SM-figure (1+1) ‘2’ of the corresponding second proxy of 2-UEP and five figures of 1 (5/1) as per the SM-figure (2+3=) ‘5’ of the corresponding first proxy of 1-UEP of the same 3-UEP proxy --- thus totaling to twelve (4+8) figures (4/3, 1/3, 2/2 & 5/1=12 figures).


(e) According to the brief analysis as per the Sankhya ‘8’ and its Mahapatala ‘20’ of the corresponding second proxy pertaining to the 2-UEP, it should be understood that, apart from the eight figures of 2 which are in the right extreme end of these eight 2-UEPs, there are 20 other figures also thus totaling to (8+20) ‘28’ figures in all these eight 2-UEPs. Here it is also interesting to know that there are only eight figures of 2 in all these 32 permutations. According to the detailed analysis it should also be understood that, in these eight 2-UEPs, there are eight figures of 2 (8/2) as per the Sankhya ‘8’, one figure of 4 (1/4) as per the Sankhya ‘1’ (no Mahapatala) of the corresponding fourth proxy of 4-UEP, two figures of 3 (2/3) as per the SM-figure (1+1) ‘2’ of the corresponding third proxy of 3-UEP, five figures of 2 (5/2) as per the SM-figure (2+3=) ‘5’ of the corresponding second proxy of 2-UEP and twelve figures of 1 (12/1) as per the SM-figure (4+8=) ‘12’ of the corresponding first proxy of 1-UEP of the same 2-UEP proxy --- thus totaling to (8+20=) ‘28’ figures (8/2, 1/4, 2/3, 5/2 12/1=28 figures).

(f) According to the brief analysis as per the Sankhya ‘16’ and its Mahapatala ‘48’ of the corresponding first proxy pertaining to the 1-UEP, it should be understood that, apart from the sixteen figures of 1 which are in the right extreme end of these ‘16’ 1-UEPs, there are ‘48’ other figures also thus totaling to (16+48) ‘64’ figures in all these ‘16’ 1-UEPs. Here it is also interesting to know that there are only sixteen figures of 1 in all these 32 permutations. According to the detailed analysis it should also be understood that in these sixteen 1-UEPs, there are sixteen figures of 1 (16/1) as per the Sankhya ‘16’, one figure of 5 (1/5) as per the Sankhya ‘1’ (no Mahapatala) of the corresponding fifth proxy of 5-UEP, two figures of 4 (2/4) as per the SM-figure (1+1) ‘2’ of the corresponding fourth proxy of 4-UEP, five figures of 3 (5/3) as per the SM-figure (2+3) ‘5’ of the corresponding third proxy of 3-UEP, twelve figures of 2 (12/2) as per the SM-figure (4+8) ‘12’ of the corresponding second proxy of 2-UEP and twenty-eight figures of 1 (28/1) as per the SM-figure (8+20) ‘28’ of the corresponding first proxy of the 1-UEP proxy of the same 1-UEP proxy --- thus totaling to ‘64’ (16+48) figures (16/1, 1/5, 2/4, 5/3, 12/2 & 28/1=64 figures) and, at last, arriving at a grand total of (1+2+5+12+28+64=) ‘112’ figures in the grand total of 32 permutations.

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

Post by sbala »

Thanks Msakella Sir. I already got the squared ruled note book yesterday and had my first exposure to a Nagaswaram concert at Krishna Gana Sabha. I do like teaching but I'm a rank beginner in music to teach a topic that I presume even some of the musicians might not understand. I can definitely try this topic on some of the programmers in my team :-)

sbala
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Joined: 30 Jul 2006, 08:56

Post by sbala »

MsAkella Sir,
I have completed the Nashta upto 5 units. I will complete the remaining over the weekend and then proceed to Uddishta and Kalita.

mridhangam
Posts: 976
Joined: 04 Dec 2006, 13:56

Post by mridhangam »

Thanks Akella sir for the pains you are taking in publishing rare and interesting topics. they are long enough and take time to absorb and assimilate. Thinking about the time you might have spent in acquiring such vast knowledge i am wondering whether by being a mere performer we can reach such Alpine heights of knowledge and wisdom. Thanks once again sir

msakella
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Joined: 30 Sep 2006, 21:16

Post by msakella »

Dear member, sbala, My computer has gone to hospital and just returned today after incurring a bill for Rs.14,000/. S0, I was unable to contact you. Very happy to know that you are able to go through Nashta successfully. Please proceed. You learn it fully and then you can try to propagate. Keep me informed about your progress and I shall post the necessary material. With best wishes, amsharma.

msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Post by msakella »

Dear member, mridhangam, As an aged person knowing a few more details than our youngsters, I feel it as my duty to enlighten my brothers and sisters who are enthusiastic to learn it. It is not pains taking to me at all. More over it gives me great pleasure.
‘Mookam karothi vaachaalam’ the Almighty had decided to bring this rare chapter out through this body. HE can do any thing in this universe. Thus, HE had chosen a fool (me) who successfully failed twice in SSLC, to bring this chapter out. This is HIS greatness not mine at all. If HE proposes anybody can do wonders. In the same manner I did. That’s all. Thanking you for your kind appreciation, amsharma.

rshankar
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Joined: 02 Feb 2010, 22:26

Post by rshankar »

A review of our Sri Akella M Sarama's lec-dem in included in this article:
http://www.hindu.com/fr/2007/01/19/stor ... 960300.htm

msakella
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Joined: 30 Sep 2006, 21:16

Post by msakella »

Dear moderator, rshankar, Thank you very much for your kind reference of my Lec-dem. amsharma.

sbala
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Joined: 30 Jul 2006, 08:56

Post by sbala »

Msakella Sir,
I think I understood the Uddishta process. I have given the details of a a few permutations below.

6 UP, Figure 3 1 1 1
Undeducted figures = 16,8,4
deducted figures =2,1
Sum of deducted figures=3
Serial Number = 32-3=29.

7UP, Figure 3 4
Deducted Figures - 32,16,8 and 2,1
Sum of deducted figures=59
Serial Number=64=59=5.

7UP, Figure 2 3 2
Deducted figures - 32,8,4,1
Serial Number = 64-45=19

Please verify and if this is fine, I will try to proceed to Kalita

msakella
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Post by msakella »

Dear member, sbala, Congratulations. All your answers are correct. Very nice. Proceed on. amsharma.

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

Post by sbala »

Dear Msakella Sir,
I have a clarification in the kalita section. Shouldn't section d say 12 figures of 3 in all the 32 permutations? Similarly in sections e and f, should we not have 28 figures of 2 in 32 permutations and 64 figures of 1 in the 32 permutations?

msakella
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Joined: 30 Sep 2006, 21:16

Post by msakella »

Dear member, sbala, What you say is correct. You got this also. Very nice. Congrats. The same has already been furnished in the brief analysis I have given. But, along with it, another detailed analysis is also furnished. If you go through it again carefully and patiently you can very easily understand the detailed analysis also. Eagerly awaiting your positive response, amsharma.

msakella
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Joined: 30 Sep 2006, 21:16

Post by msakella »

6th part:

Rules for the process of permutation of Talangas:
1.The value of any prastara should be cited in number of the least (inferior) Angas only occurring in a particular mode of permutation and for the value of such prastara, minimum possible number of Angas only should be written in the 1st prastara, carefully observing the relevant rules and restrictions, if any,. If two or more Angas are to be written in the 1st prastara they should be written anti-clockwise only in descending order of value from right to left of the 1st prastara.
2.If there is more than one Anga in the prastara, the permutable Anga at the extreme left should at first be permuted.
3.If the Angas in the left extreme are so minute that they cannot further be permuted, the immediate next permutable Anga to their right only should be permuted.
4.To permute an Anga write down the immediate lower Anga in value than of the upper Anga in the same column.
5.After writing down the lower Anga than of the upper Anga, for the remainder, a suitable independent Anga should be written to the left of the Anga already written. For this remainder, if two or more Angas are to be written they should be written anti-clockwise only in descending order of value to the left of the Anga already written.
6.If there are Angas to the left of the upper Anga the remainder value of the permuted Anga should be added to the total value of all the left side Angas and a suitable Anga should be written to the left of the Anga already written and if two or more Angas are to be written for this total value they should be written anti-clockwise to the left of the Anga already written in descending order of value.
7.The Angas, if any, which are at the right of the Anga be permuted, should be brought down and written as they are in the same columns.
8.Carefully observing the relevant rules and restrictions, if any, the process of permutation should be continued until all the Angas become so minute that none of them could further be permuted.
9.Among all the prastaras the total value of all the Angas of each prastara should always be one and the same.

List of the first Talangas to be written in the processes of permutation

Unit- Panchanga Shadanga
Value 2 3 – 4 – 5 – 7 – 9

01 0 U U U U U
02 l 0 0 0 0 0
03 0l l U0 U0 U0 U0
04 S Ul l 00 00 00
05 0S 0l Ul l U00 U00
06 Ś S 0l Ul 000 000
07 0Ś US U0l 0l l U000
08 + 0S S U0l Ul 0000
09 0+ Ś US 00l 0l l
10 l+ UŚ 0S S U0l Ul

(Important note: The Talangas written above in the respective Jaatis of Shadanga-prastara should be written one above the other while replacing the respective figures of Samyuktanga-prastara with the respective Talangas of the different Jaatis)

Examples:

Pamchanga-prastara: (restricted to Chaturashra-jati having the least Anga, Druta)

1-unit: 0 01

2-units: l 01
0 0 02

3-units: 0 l 01
l 0 02
0 0 0 03

4-unirts: S 01
1 l 02
0 0 1 03
0 1 0 04
1 0 0 05
0 0 0 0 06

5-units: 0 S 01
0 1 1 02
1 0 1 03
0 0 0 1 04
S 0 05
1 1 0 06
0 0 1 0 07
0 1 0 0 08
1 0 0 0 09
0 0 0 0 0 10

6-units: Ś 01
1 S 02
0 0 S 03
S 1 04
1 1 1 05
0 0 1 1 06
0 1 0 1 07
1 0 0 1 08
0 0 0 0 1 09
0 S 0 10
0 1 1 0 11
1 0 1 0 12
0 0 0 1 0 13
S 0 0 14
1 1 0 0 15
0 0 1 0 0 16
0 1 0 0 0 17
1 0 0 0 0 18
0 0 0 0 0 0 19


Shadanga-prastara: (Trisra-jaati):

1-unit: U 01

2-units: 0 01
U U 02

3-units: l 01
U 0 02
0 U 03
U U U 04

4-units: U l 01
0 0 02
U U 0 03
U 0 U 04
0 U U 05
U U U U 06

5-units: 0 l 01
U U l 02
l 0 03
U 0 0 04
0 U 0 05
U U U 0 06
U l U 07
0 0 U 08
U U 0 U 09
l U U 10
U 0 U U 11
0 U U U 12
U U U U U 13

Shadanga-prastara: (Chaturashra-jaati):

1-unit: U 01

2-units: 0 01
U U 02

3-units: U 0 01
0 U 02
U U U 03

4-units: l 01
0 0 02
U U 0 03
U 0 U 04
0 U U 05
U U U U 06

Shadanga-prastara: (Khanda-jaati):

1-unit: U 01

2-units: 0 01
U U 02

3-units: U 0 01
0 U 02
U U U 03


4-units: 0 0 01
U U 0 02
U 0 U 03
0 U U 04
U U U U 05

5-units: l 01
U 0 0 02
0 U 0 03
U U U 0 04
0 0 U 05
U U 0 U 06
U 0 U U 07
0 U U U 08
U U U U U 09

In the same manner, the process of permutation of the Talangas, Laghu, Guru, Pluta and Kakapada should carefully be made always keeping the respective value of Jaati in mind.


7th part:

TABLE OF GENERAL-PERMUTATIONS

Amsha-
Shreni: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9

1 - 1 - 1 2 4 8 16 32 64 128 256
1 3 6 20 48 112 256 576 1280

2 - 1 - 1 2 3 6 10 19 33 61 108
1 3 7 16 34 72 147 299 596

3 - 1 - 1 2 4 7 13 25 46 86 162
1 3 8 19 43 95 204 431 900

4 - 1 - 1 2 3 6 10 18 31 56 98
1 3 7 16 34 71 143 286 562

5 - 1 - 1 2 3 5 9 15 26 44 75
1 3 7 15 31 62 122 235 447

7 - 1 - 1 2 3 5 8 13 22 36 60
1 3 7 15 30 58 110 205 378

9 - 1 - 1 2 3 5 8 13 21 34 56
1 3 7 15 30 58 109 201 366

In this above ‘Table of General Permutations’ the figures in the Amsha-shreni at the top are the units of permutations, the figures in the left side from top to bottom are the figures representing the modes of permutations, 1 pertaining to Samyuktanga-sarva-jati, 2 of Panchanga,
3 of Shadanga-trisra-jati, 4 of Shadanga-chaturashra-jati, 5 of Shadanga-khanda-jati, 7 of Shadanga-mishra-jati and 9 of Shadanga-sankeerna-jati and the respective figures in the upper line consists of ‘Sankhya’ and the lower line ‘Mahapatala’ of these above modes of permutations.

Explanation: Finding out the proxies:
(Important-note: For the purpose of Prastara the Talangas should always be cited from right to left only)
As was furnished in the beginning, in the modern period from when Kakapada has also been included in the process of permutation, mainly, there are three processes of permutation and they are 1.Panchanga-prastara 2.Shadanga-prastara and 3. Samyuktanga-prastara. In writing the figures of the respective tables and in getting the answers for Nashta, Uddishta and Kalita the Proxies (the figures of the respective preceding houses only) play a very important role. There is an easy method to find out the respective proxies of these three processes of permutation. In Panchanga-prastara in which the five Talangas, Druta, Laghu, Guru, Pluta and Kakapada are used in the process of permutation, the Druta is the lowest denomination of the five Talangas and the unit-value of the permutation should always be cited only in terms of Drutas i.e., Eka-druta-prastara, Dvi-druta-prastara, Tri-druta-prastara, Chatur-druta-prastara, Pancha-druta-prastara, Shad-druta-prastara and so on wherein the first Talanga is 0, l, 0l, S, Ś and so on respectively but not Druta-prastara, Laghu-prastara, Laghu-druta-prastara, Guru-prastara, Guru-druta-prastara, Pluta-prastara and so on. In the same manner, also in Shadanga-prastara in which the six Talangas, Anudruta, Druta, Laghu, Guru, Pluta and Kakapada are used in the process of permutation, the Anudruta is the lowest denomination of the six Talangas and the unit-value of the permutation should always be cited only in terms of Anudrutas i.e., Eka-anudruta-prastara, Dvi-anudruta-prastara, Tri-anudruta-prastara, Chatur-anudruta-prastara, Pancha-anudruta-prastara, Shad-anudruta-prastara and so on wherein the first Talanga is U, 0, l for Trisra-jati or U0 for other Jatis, Ul for Trisra-jati or l Chaturashra-jati or 00 for other Jatis, 0l for Trisra-jati or Ul for Chaturashra-jati or U00 for other Jatis, S for Trisra-jati or 0l for Chaturashra-jati or 000 for other Jatis and so on respectively but not Anudruta-prastara, Druta-prastara, Laghu-prastara for Trisra-jati or Druta-anudruta-prastara for other Jatis and so on. In the same manner, also in Samyuktanga-prastara (in which, at the first instance, numerals are used in the process of permutation) Eka-amsha or 1-unit is the lowest denomination and the unit-value of the permutation should always be cited in terms of Amshas i.e., Eka-amsha-prastara, Dvi-amsha-prastara, Tri-amsha-prastara, Chatur-amsha-prastara, Pancha-amsha-prastara, Shad-amsha-prastara and so on wherein the first Talanga is Anudruta, Druta, Laghu for Trisra-jati or Druta-virama (Samyuktanga of Virama written above the Druta together) for other Jatis, Samyuktanga of Laghu-virama for Trisra-jati Laghu for Chaturashra-jati or Samyuktanga of Dvi-druta for other Jatis, Samyuktanga of Laghu-druta for Trisra-jati or Samyuktanga of Laghu-virama for Chaturashra-jati or Samyuktanga of Dvi-druta-virama for other Jatis, Guru for Trisra-jati or Samyuktanga of Laghu-druta for Chaturashra-jati or Samyuktanga of Tri-druta for other Jatis and so on respectively but not Anudruta-prastara, Druta-prastara, Laghu-prastara for Trisra-jati or Druta-virama-prastara for other Jatis and so on. Thus, the respective proxies are: 1, 2, 3, 4, 5, 6, 7, 8, 9 etc., serially representing the required units of permutation in Samyuktanga-prastara, 1, 2, 4, 6 & 8 for Panchanga-prastara representing the respective unit-value of the five Talangas, Druta, Laghu, Guru, Pluta and Kakapada in terms of respective Drutas. and in Shadanga-prastara 1, 2, 3, 6, 9 & 12 for Trisra-jati, 1, 2, 4, 8, 12 & 16 for Chaturashra-jati, 1, 2, 5, 10 15 & 20 for Khanda-jati, 1, 2, 7, 14, 21 & 28 for Mishra-jati and 1, 2, 9, 18, 27 & 36 for Sankeerna-jati representing the respective unit-value of the six Talangas, Anudruta, Druta, Laghu, Guru, Pluta and Kakapada in terms of respective Anudrutas. By careful analysis one can easily understand that, while 1st & 2nd proxies are common to all, later all the numbers serially are the proxies for Samyuktanga-prastara, in Panchanga-prastara three consecutive multiples of 2 from the figure 4 i.e., 4, 6 & 8 are the respective proxies and in Shadanga-prastara the four consecutive multiples of the respective Jati-units i.e., 3, 6, 9 & 12 for Trisra-jati, 4, 8, 12 & 16 for Chaturashra-jati, 5, 10, 15 & 20 for Khanda-jati, 7, 14, 21 & 28 for Mishra-jati and 9, 18, 27 & 36 for Sankeerna-jati are the respective proxies. By all the above it is also very important to note that, always, while ‘1’ represents Samyuktanga-prastara, ‘2’ represents Panchanga-prastara, ‘3’ represents Trisra-jati-shadanga-prastara, ‘4’ represents Chaturashra-jati-shadanga-prastara, ‘5’ represents Khanda-jati-shadanga-prastara, ‘7’ represents Mishra-jati-shadanga-prastara and ‘9’ represents Sankeena-jati-shadanga-prastara.
Actually, in the tables of the respective figures, the respective proxies should always be observed from right to left only.
(A-Anudruta, D-Druta, L-Laghu, G-Guru, P-Pluta, K-Kakapada)

Samyuktanga: 1 - 2 - 3 - 4 - 5 - 6 ---------

D L G P K
Panchanga: 1 - 2 - 4 - 6 - 8

Shadanga: A D L G P K
- Trisra-jati: 1 - 2 - 3 - 6 - 9 - 12
- Chaturashra-jati: 1 - 2 - 4 - 8 - 12 - 16
- Khanda-jati: 1 - 2 - 5 - 10 - 15 - 20
- Mishra-jati: 1 - 2 - 7 - 14 - 21 - 28
- Sankeerna-jati: 1 - 2 - 9 - 18 - 27 - 36
Last edited by msakella on 25 Jan 2007, 00:44, edited 1 time in total.

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

Post by sbala »

Dear Msakella Sir,
I have given the Kalita for the 5-UP below. Please let me know if this is right. I can then proceed to the next post.

As per Sankhya of 5, there should be a total of 16 permutations.

1. 5th proxy. S=1, M=0 S+M=1
1 figure of 5-UEP
Since M=0 there are no other figures
Detailed Analysis- 1/5

2. 4th proxy. S=1, M=1, S+M=2
1 figure of 4-UEP.
1 more figure as per M
Detailed Analysis - 1/1,1/4

3. 3rd proxy. S+M=2+3=5
2 figures of 3 UEP
3 more figures as per M
Detailed Analysis - 1/2,2/1,2/3

4. 2nd proxy. S+M=4+8=12
4 2UEPs
8 other figures
Detailed Analysis - 1/3,2/2,5/1,4/2

5. 1st proxy S+M=8+20=28
8 1-UEP
20 other figures
Detailed Analysis: 1/4,2/3,5/2,12/1,8/1

msakella
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Joined: 30 Sep 2006, 21:16

Post by msakella »

Dear member, sbala, Congrats. You got it. Very well. You can proceed further. Here after you are entering into the permutation of Talangas, but not with figures. OK. Wishing you all the best, amsharma.

msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Post by msakella »

Dear members, If you are learning this topic, Talaprastara you can also tally some of these permutations furnished in the 15th post under constructing Kalpana Svaras of the thread, Technical discussions. You can find them along with the rhythmical form in numbers of units, its serial number, jati and Svaras to sing in Svara-kalpana. You can apply the same to other compositions of the same Talas and other Talas also. I shall be glad if some of you post here some more varieties of the rhythmical forms of the same Talas or of even other talas in the same manner which obviously reveals that your are really working upon this enthusiastically. Wishing you all the best, amsharma.

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

Post by sbala »

Dear MsAkella Sir,
I have given the details of the panchanga prastara below for 7-units. These symbols make me nervous..Numbers seem much more comfortable :-)

0Ś 01
01S 02
10S 03
000S 04
0S1 05
0111 06
1011 07
00011 08
S01 09
1101 10
00101 11
01001 12
10001 13
000001 14
S0 15
1SO 16
00S0 17
S10 18
1110 19
00110 20
01010 21
10010 22
000010 23
0S00 24
01100 25
10100 26
000100 27
S000 28
11000 29
001000 30
010000 31
100000 32
0000000 33

msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Post by msakella »

Dear member, sbala, Congrats. You got it. Your progress is very well. Proceed further. OK. Surprisingly enough, even though some of our members started posting about some Talas, no other person, except yourself, seems to have started learning this topic. Very funny! Wishing you all the best, amsharma.

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

Post by sbala »

Dear Msakella Sir,
I have given below the details of Shadanga Prastara Chaturashra jathi 5 units.

U1 01
U00 02
OUO 03
UUUO 04
1U 05
OOU 06
UUOU 07
UOUU 08
OUUU 09
UUUUU 10

I did the Shadanga Prastara for trisram as well for 6 units (25 permutations). I will post the details separately.
Last edited by sbala on 26 Jan 2007, 20:22, edited 1 time in total.

msakella
Posts: 2127
Joined: 30 Sep 2006, 21:16

Post by msakella »

Dear member, sbala, Your permutations of Chaturashra-jaati are also OK.In the process of the permutation all the prastaras should consist of the right alignment. Even though we are doing the same this alignment is not maintained while pasting these prastaras in these posts (I would like to ask srkrisji about this whether there is any technique to maintain this alignment while pasting the matter in these posts)
If you take the respective figures of the ‘Table of General Permutations’, in Panchanga-prastara, you will find that the total of the first-1st proxy ‘19’ of Drutantya-prastaras, the second-2nd proxy ‘10’ of Laghvanta-prastaras, the third-4th proxy ‘3’ of Gurvanta-prastaras and the fourth-6th proxy ‘1’ of Plutanta-prastaras becomes the respective ‘Sankhya’ of (19 + 10 + 3 + 1=) 33 of 7-DP. In the same manner you can understand for all other permutations and apply the Kalita also. Do it and inform. amsharma.
Last edited by msakella on 27 Jan 2007, 04:38, edited 1 time in total.

msakella
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Joined: 30 Sep 2006, 21:16

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

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: 2127
Joined: 30 Sep 2006, 21:16

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: 2127
Joined: 30 Sep 2006, 21:16

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: 2127
Joined: 30 Sep 2006, 21:16

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

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

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: 2127
Joined: 30 Sep 2006, 21:16

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

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

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: 2127
Joined: 30 Sep 2006, 21:16

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

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: 2127
Joined: 30 Sep 2006, 21:16

Post by msakella »

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

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

Post by sandhyashree »

Hello Sbala

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

Sandhya

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

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

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

Post by coolkarni »

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

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

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

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

Post by sandhyashree »

Sbala,
Yes, definitely........
You can shoot an email to sandhyadharani@yahoo.co.in 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

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

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

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: 2127
Joined: 30 Sep 2006, 21:16

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

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?

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