Tuesday, April 21, 2009

INDIAN MUSICOLOGY REVISITED: Pramana Sruti:Amplification Notes: 22 Srutis

    The West envisioned their musical ‘Notes’ as mathematical ‘fractions’ occurring between ‘1’ and ‘1/2’ (i.e. the lower and the upper boundaries of an octave). Western musicologists could, therefore, modify their ‘Notes’ mathematically, in order to keep pace with changing times. But how did they discover at all that ‘mathematical fractions’ and music were deeply related? The core idea seems to have descended from the age-old Sumerian tradition (4000 B.C.) of worshipping gods in the form of ‘fractions’. It is incredible to realize that a ‘primitive’ civilization such as the Sumerians could ever conceptualize an advanced mathematical concept such as ‘fractions’ in their culture. As I followed this thread further, I was in for bigger surprises! Their pantheon of twelve major gods in effect, symbolized a “family of 22 simple fractions” which appears to be the basic building blocks for an advanced class of music that existed during a pre-historic era! Interesting? For more details, please read my ‘Blog’ and ‘Presentation Slides’ placed on the internet:
Gods of Sumeria symbolize our Ancient Music of 22 Srutis (Blog):   http://sumeriangods.blogspot.com/
Gods of Sumeria symbolize our Ancient Music of 22 Srutis (Presentation):
As we turn towards India, we are in for even greater surprises! Vedic Indians (3500 B.C.) conceptualized their musical octave in a ‘mystical and extraordinary’ manner. They calibrated the octave in an abstract ‘tonal domain’, i.e. in terms of degree of ‘shrillness’. The limits for this ‘shrillness’ were set between ‘0’ and ‘22’. Within this octave, the ‘rising index of shrillness’ was calibrated in 22 equal steps. Each step was known as a ‘sruti’ (‘Shruti’ as per Shastriya Sangeet traditions) or more specifically, the ‘Pramana Sruti’ (i.e. the most elemental sruti). In other words, the Indian octave comprised of 22 ‘Pramana srutis’. Such a fact, however, raises several eyebrows within the mathematical community. ‘Tonal calibration’ of the octave, as  a  concept,  presumes that the ancient Indian musicians knew how to determine  the 22nd root of Number ‘2’! (Incredible indeed! Our civilization had learnt to determine even the 12th root of number ‘2’, only a few centuries back; in this backdrop, granting our primitive ancestors a capability to determine the 22nd root of number ‘2’ would be an absurd presumption)!
         Bharata Muni (200 B.C; the earliest scribe who had documented the erstwhile oral traditions of Indian musicology) had described that a set of seven ‘Divine’ tones of ‘Sama Veda’ (Sama Veda is a musical mode of chanting the Holy Scripture that dates back to an antiquity of 3500 B.C.) formed the foundation for music, in the name of ‘Sadja grama’. These ‘seven tones’ (known as ‘swaras’ in Indian musicology) were designed in three different bunches of Pramana srutis (i.e. bunches of ‘2’ or ‘3’ or ‘4’): The swaras ‘Sadja’, ‘Madhyama’ and ‘Panchama’ measured ‘4’ Pramana srutis; ‘Rishabha’ and ‘Dhaivata’ measured ‘3’ Pramana srutis and ‘Gandhara’ and ‘Nishada’ measured ‘2’ Pramana srutis;  the aggregate of these seven swaras accounted for the 22 Pramana srutis within the octave. ‘Seats’ (known as ‘swara-sthaanas’) of these seven swaras were quantified and assigned in the octave: The Tonic ‘Sadja’ = at the ‘0’th Pramana sruti position, ‘Rishabha’ (the ‘Second’) at the 3rd Pramana sruti position, ‘Gandhara’ (the ‘Third’) at the 5th Pramana sruti position, ‘Madhyama’ (the ‘Fourth’) at the 9th Pramana sruti position, ‘Panchama’ (the ‘Fifth’) at the 13th Pramana sruti position, ‘Dhaivata’ (the ‘Sixth’) at the 16th Pramana sruti position, ‘Nishada’ (the ‘Seventh’) at the 18th Pramana sruti position and the ‘Octave Sadja’ at the 22nd Pramana sruti position (i.e. the ‘0’th Pramana sruti position of the Higher Octave).
During this era, musicological knowledge was confined to these ‘seven tones’ only. The underlying mathematics for the design of this 22-sruti octave as well as the seven Sama Vedic tones was unknown to the musicologists. They were also not aware of any process that would resolve and distil out a single pramana sruti from the bunches of Pramana srutis, to enable further vertical development of music. These seven tones were described as ‘Suddha’ (i.e. ‘pure’) as they were derived directly from the Sama Veda. Even musicologists of high stature such as Bharata Muni and Dattila Muni would not dare to enlarge the swara base of seven ‘Suddha’ tones through experimentations, due to the apprehension that it might lead to ‘distortions’ (i.e. creation of vikrta swaras) and would amount to breaching Vedic Holiness.   
Bharata Muni also describes another ‘group of swaras’, known as ‘Madhyama grama’. This was required to be derived from ‘Sadja grama’. (These two ‘gramas’ acted as equal partners in the subsequent vertical development of music in India, by way of ‘murchanas’ and ‘Tanas’. Therefore, understanding the design of ‘Madhyama grama’ is quite important).  Bharata Muni scribes an age-old musicological Rule: “Madhyama grama will get evolved when the Panchama swara of Sadja grama is reduced by one Pramana sruti”. There can be two interpretations for implementing this age-old musicological Rule. However, all Indian musicologists since the medieval era, have trekked the ‘beaten track’ of only one of the methods, to arrive at the following configuration for ‘Madhyama grama’: The Tonic ‘Sadja’ = at the ‘0’th Pramana sruti position, ‘Rishabha’ at the 3rd Pramana sruti position, ‘Gandhara’ at the 5th Pramana sruti position, ‘Madhyama’ at the 9th Pramana sruti position, ‘Panchama’ at the 12th Pramana sruti position, ‘Dhaivata’ at the 16th Pramana sruti position, ‘Nishada’ at the 18th Pramana sruti position and the ‘Octave Sadja’ at the 22nd Pramana sruti position. Only one change in the configuration of the new entity is noticeable; i.e. the swara-sthaana of ‘Panchama’ has been lowered by one position (from the 13th to the 12th). By observing this ‘triviality’ of the difference between the two ‘gramas’, some modern critics state that our understanding of the concept of derivation of ‘Madhyama-grama’ had been quite inadequate.
I decided to study the hitherto ‘unexplored’ “alternative option” for the derivation of Madhyama grama. I was amazed myself to discover that a new phenomenon had remained ‘hidden’ from our view, all these days! This option brought about a major change in the profile of Madhyama grama, as given: On reducing one Pramana sruti from ‘Panchama’, the ‘Madhyama’ swara-sthaana moved from position ‘9.00’ to ‘10.00’ srutis with respect to the tonic. Similarly, ‘Gandhara swara sthaana’ moved from position ‘5.00’ to ‘6.00’; ‘Rishabha swara sthaana’ moved from ‘3.00’ to ‘4.00’; ‘Nishada swara sthaana’ moved from ‘18.00’ to ‘19.00’ and ‘Dhaivata swara sthaana’ moved from ‘16.00’ to ‘17.00’. However, the ‘Panchama swara sthaana’ continued to remain at 13.00 srutis. The viewers may please appreciate that this is an important deduction. ‘Panchama’ is a very important Note that stands tall in an octave and is next in importance to the Tonic Sadja. The ‘Panchama swara sthaana’ had been fixed at 13.00 srutis by the Sama Veda itself and hence its sanctified seat should not be altered in both ‘gramas’! It is also common knowledge that the position assigned to ‘Panchama’ at 13.00 srutis is a universal practice followed in all other traditions of music also.
Having studied the basic features of the ancient musical culture of Sumeria and India, I decided to draw some comparison between them. However, direct comparison was difficult as the Sumerian tradition was founded on ‘fractions’ and the Indian tradition was based on ‘tones’. I therefore, mathematically transformed the family of 22 simple fractions (i.e. the Sumerian gods) into the tonal domain of a 22-srutis octave and tabulated the results. I was amazed to realize that the Indian Sama Vedic tones (i.e. the swaras of Sadja grama) were nothing but the replicas of seven Sumerian gods! As I compared the swaras of the newly evolved ‘Madhyama grama’, again I found that they were the replicas of some more members of the Sumerian god family. I extended this observation by experimenting on the age-old Indian concept of ‘murchanas’ {‘murchans’ were the fountain-head for the vertical development of music in medieval India. Seven ‘murchanas’ each were derived from each ‘grama’. These are somewhat similar to the seven ‘modes’ of ancient Greek music.} and found that the remaining gods of the Sumerian Pantheon were embedded there in the form of tones! In other words, the god-fractionss worshipped by the Sumerians and the tones advocated in ancient Indian musicology were the same! For details, please read my ‘Blogs’ and ‘Presentation Slides’ on the Internet:
Madhyama grama, (Blog):   http://madhyamagrama.blogspot.com/ 
Murchanas re-interpreted (Blog):   http://murchanas.blogspot.com/  
Having achieved some spectacular breakthrough with my earlier experiments, I decided to extend the same towards validating the contention of Bharata Muni with regard to the “Pramana Sruti”. Bharata Muni narrates in ‘Natyasastra’ verses 27 and 28 that the phenomenon of Pramana Sruti is ‘realizable’ at the ‘Panchama’ boundary when Sadja grama is transformed into Madhyama grama. I, therefore, compared the positions of ‘Panchama’ swara in both the ‘grama groupings’. I found that the upper boundary of ‘Panchama’ (i.e. the swara-sthaana of ‘Panchama’) remained unaltered in both the gramas. However, the lower boundary of ‘Panchama’ was found ‘shifted’ from its erstwhile position of ‘9.13’ srutis (in Sadja grama) to ‘10.11’ srutis (in Madhyama grama), i.e. a difference of ‘one Pramana-sruti’ (‘0.98’ srutis to be mathematically exact!). For better comprehension, please see my ‘Presentation Slides’ placed on the internet: https://docs.google.com/open?id=0B6Qw6H3PDIHNbnh1aWdXNHVBN0E
Let us now take a re-look at this ‘phenomenon’ from the angle of ‘Sumerian- Fractions’! When ‘Panchama’ is compressed at its lower boundary, the ‘Madhyama swara sthaana’ moves from position ‘3/4’ to position ‘8/11’. For quantifying the ‘shift’ that had occurred, we have to divide ‘3/4’ by ‘8/11’; and we get the result as ‘33/32’. This may be mathematically re-written as 1.03125. This value very favourably compares with the modern accuracy of 1.032000828, which has been obtained by finding the 22nd root of number ‘2’.
There is another method for determining the value of Pramana sruti too! The octave extends between ‘1’ and ‘1/2’, i.e. a length of ‘1/2’. If we apportion this segment between 22 sruti entities, each sruti segment will measure ‘1/44’ length; i.e. Pramana Sruti should measure a segmental length of ‘1/44’. With this background, let us examine the gramas once again. We have seen in the earlier paragraph that the ‘Madhyama swara sthaana’ had moved from position ‘3/4’ to position ‘8/11’. For quantifying this ‘shift’, let us subtract ‘8/11’ from ‘3/4’; we get ‘1/44’!
These accuracies are quite amazing indeed! This method of validation of Indian Sastric statements with the help of Sumerian Divine Fractions, establishes that there was “Total Covergence” between the ancient Indians and the Sumerians in the field of musicology and religion. The sophistication of mathematical knowledge displayed in these two traditions indicates that the ‘pre-historic music’ inherited by them in ‘coded forms’ must be a priceless cultural gift passed on to our civilization by our pre-historic ancestors!
            For more details, contact me on Teles: 91 20 26729256, 9890266845, 98501 21834. E-mail: snnambirajan@rediffmail.com. Please also visit my web-site which provides links to access my other ‘Blogs’ and ‘Presentation Slides’ pertaining to ‘Our Ancient Music of 22 srutis’: http://www.22sruti.com . I would also recommend the viewers to peruse my Book: “The Mystic Citadel of 22 Srutis Music” (available at my postal address: Srinivasan Nambirajan, A-7/ 103, Florida Estate, Keshav Nagar, Mundhwa, Pune-411036).