Contemporary music comprises of 12
tones. Medieval Indian musicologists had ‘sensed’ the existence of a far
superior ‘ancient music’ that was founded on a more structured resource-base
consisting of ‘22 tones’. However, this ancient music remained buried under the
hard encrustations of a pre-historic past and not much evidence could be
adduced by these visionaries in support of their ‘hunch’.
This age-old ‘belief’ motivated me to
undertake a humble fact-finding Study. I have narrated in my Book “The
Mystic Citadel of 22 Srutis Music”, as to how my work got ‘stone-walled’ by
the lack of musicological records, prior to first millennium B.C. I, however,
continued with the ‘study’ drawing from traces of past ‘cultural histories’.
The cultural history of the West has been fairly well documented, thanks to the
extensive research work undertaken by scholars!
Sumerians, the earliest civilization as
per our recorded history (approximately 4000 B.C.), worshipped their gods in the form of
‘fractions’. My initial response was one of utter disbelief as to how an
abjectly primitive society could ever entertain higher mathematical concepts
such as ‘fractions’! Obviously, there was something ‘mysterious’ about these Sumerians!
To quote Laurence Gardner, historian on Sumeria: “…To this
day, everyone concerned is baffled by the sudden, extraordinary emergence of
the Sumerians, seemingly from nowhere. But there is no doubt that, upon their
advent in southern Mesopotamia, they were already highly advanced, to a
level far beyond that recorded or sustained in any place from where
logically they could have emanated. Nowhere on Earth was there a culture like
that of the Sumerians, who appeared soon after 4000BC….”
There are plenty of speculations about
their mystic origin. To quote one: “.... civilizations
with large cities and complex societies do not just spring up from
nothing.... The Sumerians, who do not
seem to be related to the earlier inhabitants of the region, had to have
inherited their civilization from somewhere, either an antecedent culture
or, as Sitchin, Gardner and others have suggested, it was given to them by
beings from elsewhere who came to Earth around that time”.
To quote Ernest G. McClain, historian on Sumeria: “…For
reasons that have been vigorously argued but remain unclear, they developed a
base-60 number system. Waiting to be recognized within it--and in ways obvious
to any scribal adept, although invisible to the illiterate--were the main
patterns of harmonical theory that appear later in India, Babylon, and
Greece…”
To quote Zecharia Sitchin, another historian on
Sumeria: “We always knew that
there was music in the earlier Assyrio-Babylonian civilization, but until this
deciphering we did not know that it had the same heptatonic-diatonic scale that
is characteristic of contemporary Western music, and of Greek music of the
first millennium BC.... Until now it was thought that Western music originated
in Greece; now it has been established that our music – as so much else of
Western civilization – originated in Mesopotamia. This should not be
surprising, for the Greek scholar Philo had already stated that the
Mesopotamians were known to "seek world-wide harmony and unison
through the musical tones."
To quote more from Ernest G.McClain: “Sumerian numbers were
impressed on small clay tablets .... A ‘60’ was made as a large ‘1’ by pressing
the stylus more firmly into the clay.... Computation was made easy by tables of
"reciprocals, multiplications, squares and square roots, cubes and cube
roots, ...exponential functions, coefficients giving numbers for practical
computation,...and numerous metrological calculations giving areas of
rectangles, circles… "Regular numbers" up to 60 are shown with their
reciprocals, transcribed... so that the reciprocal of 40/60 = 2/3 reads 1,30,
meaning 90/60 = 3/2. Notice that only the most important fractions of 60 are
deified (1/6, 1/5, 1/4, 1/3, 1/2, 2/3, and 5/6)”.
In the ambience of such ‘extraordinary’
inputs, I turned on my spot lights over the cosmology of Sumerians. The numbers/gods worshipped by Sumerians
were: 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10 and 5 . All were indicated as
the fractions of “An” (60) who was their most supreme God. Sumerians wrote the
number ‘60’ as a large ‘1’ and used it as their ‘reference’ number for
everything! Therefore, ‘An’ Himself got depicted as 60/60 = 1/1. Enlil (50) got
depicted as 50/60 = 5/6. Ea/Enki (40)
was 40/60 = 2/3, Nanna/Sin (30) was 30/60 = 1/2, Utu/Samash (20) was 20/60 =
1/3 and Ishkur/Adad (10) was 10/60 = 1/6.
Sumerian pantheon had many more gods and goddesses;
but only six gods and six goddesses were “deified” formally in
the following manner:
60 An /Anu (God) 55 Antu (Goddess)
50 Enlil (God) 45 Ninlil (Goddess)
40 Ea/Enki (God) 35 Ninki (Goddess)
30 Nanna/Sin (God) 25 Ningal (Goddess)
20 Utu/Samash (God) 15 Inanna/Ishtar (Goddess)
10 Ishkur/Adad (God) 05 Ninhursag (Goddess)
After pondering over these observations a bit longer,
I realized that these “extraordinary Sumerians” have left some vital
musicological ‘clues’ in the garb of their twelve ‘deities’, for the posterity
to infer and extrapolate; their ‘theology’ is the ‘symbolization’ of an ancient
‘musicology’ and should, therefore, be viewed through the musicological prism.
The ‘fusion’ of male gods with ‘Anu’ (as described above) led to the revelation
of certain ‘core’ musical fractions, such as: 1, 1/2, 2/3 and 5/6. On this
analogy, I attempted an extrapolation and discovered soon that many more such
combinations were feasible. I realized that the scope of such ‘fusions’ would
get fully unfolded only if we ‘unhinge’ the emphasis that was grossly
slanted towards this ‘Anu’ model. After listing all possible combinations, I
classified them into three broad categories: male/male; female/female and
male/female. In this analysis, I have deleted the result of those ‘fusions’
that yielded fractions like 1/3, 1/5 etc.; they belong to the higher octave of
music and, therefore, lie well outside the bounds (i.e. between ‘1’ and ‘1/2’)
of the “primary octave”: -
god/ god
|
goddess/ goddess
|
god/ goddess
|
60/60 = 1/1
|
45/55 = 9/11
|
55/60 = 11/12
|
50/60 = 5/6
|
35/55 = 7/11
|
45/60 = 3/4
|
40/60 = 2/3
|
35/45 = 7/9
|
35/60 = 7/12
|
30/60 = ½
|
25/45 = 5/9
|
50/55 = 10/11
|
40/50 = 4/5
|
25/35 = 5/7
|
40/55 = 8/11
|
30/50 = 3/5
|
15/25 = 3/5
|
30/55 = 6/11
|
30/40 = ¾
|
45/50 = 9/10
|
|
20/40 = ½
|
35/50 = 7/10
|
|
20/30 = 2/3
|
25/50 = 1/2
|
|
10/20 = ½
|
40/45 = 8/9
|
|
30/45 = 2/3
|
||
35/40 = 7/8
|
||
25/40 = 5/8
|
||
30/35 = 6/7
|
||
20/35 = 4/7
|
||
25/30 = 5/6
|
||
15/30 = 1/2
|
||
20/25 = 4/5
|
||
15/20 = 3/4
|
||
10/15 = 2/3
|
||
5/10 = 1/2
|
(This
Table couldn’t be rendered expressive enough in this blog-format. I would
therefore, request the viewers to read this blog in conjunction with my
Presentation Slides at: https://docs.google.com/open?id=0B6Qw6H3PDIHNRFVkekRlZG5lcVk )
After deleting the redundancies (marked
in red colour), we may observe that there are only 24 residual entities. Out of
these, the reference entity (i.e. the Tonic) is 1/1 which happens to be a
‘whole number’ and not a ‘fraction’; this should, therefore, be eliminated from
the outcome of the ‘fusion’ process. We should also exclude the entity ‘1/2’,
as it happens to be the reference note (i.e. the Tonic) that marks the
commencement of the succeeding higher octave. Thus, we are left with only 22 entities, all
being “simple fractions”. It is mathematically impossible to generate a family of
fractions which carry simpler integers than these! In my blogs, I have described this family
of 22 simple fractions as ‘god-fractions’ of Sumeria.
I found that ‘tonal transforms’ corresponding to these
22 ‘god-fractions’ have been ‘embedded’ into the ‘gramas’ and ‘murchanas’,
described in ancient Indian musicological literature. (However, the medieval and
contemporary Indian musicologists failed to uncover these 22 tones within the
octave, as the relevant details have been embedded in a ‘coded’ manner!). This feature is an amazing evidence to
establish that there was “Total Convergence” between
the thought-processes of ancient Sumerians and Vedic Indians with regard to the
identification of the building blocks (i.e. 22 vital ‘Tones’) that constituted
the pre-historic music.
I also observed that there are certain latent ‘melodic
patterns’ interior to the family of 22-Fractions that would guide us while ‘composing’
music in this new environment. For more details,
please refer to the following ‘Presentation Slides’: https://docs.google.com/open?id=0B6Qw6H3PDIHNeE1vZGg5UlUxTEk
For more details,
contact me on Teles: 91 20 26729256, 9890266845, 98501 21834. E-mail: snnambirajan@rediffmail.com. Please
visit my web-site wherein I have provided ‘links’ to access various ‘Blogs’ and
‘Presentations’ related to the pre-Historic Music of 22 Tones. I would also request
the viewers to peruse my Book: “The Mystic Citadel of 22 Srutis Music”, for
details (available at my postal address: Srinivasan Nambirajan, A-7/
103, Florida Estate, Keshav Nagar, Mundhwa, Pune-411036).
