PRAMANA SRUTI
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:
Sadja-grama
(Blog): http://sadjagrama-nambirajan.blogspot.com
Sadja-grama--(Presentation): https://docs.google.com/open?id=0B6Qw6H3PDIHNM1kwRi1TWVlIUEk
Murchanas (Presentation): https://docs.google.com/open?id=0B6Qw6H3PDIHNdEp1Q1cwOHA3dzg
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).