Postby msakella » 31 Aug 2008, 21:26
Dear (as I am unable to take you either as a brother or sister from you name) b/s-member, frpatte, I am very glad for your intricate findings of Nashta. In my previous post I also forgot to mention about my another book, Talaprastara of Nisshanka Sharngadevaâ€™s Sangita Ratnakara â€“ a critical interpretation in which I have furnished the inconsistencies of the topic.
In fact, I know very little of the language, Sanskrit. But, having some how been blessed by the Almighty I am able to get through the latent secrets of Nashta and Uddishta of this Talaprastara. Even after writing these books my research has not been concluded and in due course I could further delve into this topic to find still easier short-cut methods in regard to Nashta and Uddishta than the ones already furnished in my book. But, being physically unable to re-write this entire book again at this old age of 70 years, I have made some additions of notes in this regard in this book in page 35.
However, I shall hereunder give the updated details of Nashta
by which the Sanskrit version has to be modified suitably.
Updated rules for answering Nashta:
01.Write the â€˜Sankhyaâ€™ line of figures up to the required units of permutation.
02.Subtract the question-number from the Sankhya and later from the remainder subtract the respective proxies consecutively.
03.In the process of subtraction of the relevant proxies if the 1st proxy is not subtracted from the remainder write the Anga of it and start again fresh the process of subtraction by subtracting the relevant proxies of the â€˜un-subtracted-proxyâ€™ from the beginning from the remainder. For the successful subtraction of the 1st proxy consider the â€˜non-subtractionâ€™ of the 2nd proxy only, for the successful consecutive subtraction of 1st & 2nd proxies consider the â€˜non-subtractionâ€™ of the 4th proxy only, for the successful consecutive subtraction of the 1st, 2nd & 4th proxies consider the â€˜non-subtractionâ€™ of the 6th proxy onloy and for the successful consecutive subtraction of the 1st, 2nd, 4th & 6th proxies consider the â€˜non-subtractionâ€™ of the 8th proxy only thus always considering only the â€˜non-subtractionâ€™ of the last proxy and leaving if off to write the Anga of it and start again fresh the process of subtraction by subtraction the relevant of the â€˜un-subtracted-proxyâ€™. In the absence of the remainder no figure is needed to be left off.
04.To fill in the deficit value of the permutation one or more least Angas should only be written in the left extreme irrespective of their number.
Accordingly, in the 1st example of 22nd permutation pertaining to 7-drutas, as per rule No.2, if the question-number is subtracted from the respective Sankhya (33-22) â€˜11â€™ is the remainder.
From this remainder â€˜11â€™, as per rule No.3, as the 1st proxy â€˜19â€™ could not be subtracted write the Anga of the 1st proxy which is Druta.
Later, as per rule No.3, starting the subtraction afresh, from this remainder â€˜11â€™, as the 1st proxy â€˜10â€™ could be subtracted
(11-10=1), considering only the â€˜non-subtraction of the 2nd proxy â€˜6â€™ from the remainder, write the Anga, Laghu of the 2nd proxy and leave off the 2nd proxy â€˜6â€™.
Later, as per rule No.3, starting the subtraction afresh, from the last remainder â€˜1â€™, as the 1st proxy â€˜3â€™ of the last un-deducted proxy â€˜6â€™ and, again, as the 1st proxy â€˜2â€™ of the last un-deducted proxy â€˜3â€™ could not consecutively be subtracted twice, write two Drutas representing the 1st proxy.
Later, as per rule No.3, starting the subtraction afresh, from the last remainder â€˜1â€™, as the 1st proxy â€˜1â€™ of the last un-deducted proxy â€˜2â€™ could successfully be subtracted, considering only the â€˜non-subtractionâ€™ of the 2nd proxy â€˜1â€™ of the last un-deducted proxy â€˜2â€™, write the Anga, Laghu of the 2nd proxy (Hope you know that, as per rules, figure â€˜1â€™ should always be written even before the 1st house in the Sankhya-line of figures).
Thus, you get (Angas or figures of any permutation should always be cited from right to left only in respect of Talaprastara) â€˜l 0 0 l 0â€™.
Accordingly, in the 2nd example, as per rule No.2, if the question-number is subtracted from the respective Sankhya
(60-40=) â€˜20â€™ is the remainder.
From this remainder â€˜20â€™, as per rule No.3, as the 1st proxy â€˜33â€™ could not be subtracted, write the Anga, Druta of the 1st proxy.
Later, as per rule No.3, starting the subtraction afresh, as the 1st proxy of the last un-deducted proxy â€˜20â€™ could successfully be subtracted (20-19=1) considering only the â€˜non-subtractionâ€™ of the 2nd proxy, write the Anga, Laghu of the 2nd proxy and leave of the figure â€˜10â€™ of the 2nd proxy as you have to continue the process of subtraction again with the remainder â€˜1â€™.
Later, as per rule No.3, starting the subtraction afresh, the 1st proxy â€˜6â€™ of the last un-deducted proxy â€˜10â€™, again the 1st proxy â€˜3â€™ of the last un-deducted proxy â€˜6â€™ and again the 1st proxy â€˜2â€™ of the last un-deducted proxy â€˜3â€™ could not consecutively be subtracted thrice from the remainder â€˜1â€™, write three Angas, Drutas consecutively.
Later, as per rule No.3, starting the subtraction afresh, from the remainder â€˜1â€™, the 1st proxy â€˜1â€™ of the last un-deducted proxy â€˜2â€™ could successfully be subtracted (1-1=0) considering only the â€˜non-subtractionâ€™ of the 2nd proxy, write the Anga, Laghu of the 2nd proxy.
Thus, you will get â€˜l 0 0 0 l 0â€™.
Most unfortunately, in the annals of our music literature itself, neither of the author or commentators or editors of any treatise have nowhere explained this â€˜Nashtaâ€™ clearly without any ambiguity to the reader.
As I am not well educated like you people there may be some lacuna in my explanations. Please feel free to ask any number of questions. amsharma.