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Conceptual Overview

Medieval Indian musicologists belonging to the era of 200 B.C.

Conceptual Overview

Medieval Indian musicologists belonging to the era of 200 B.C.

*(Bharata Muni and Dattila Muni)*contended that ‘Ancient Indian Music’ was founded on 22 tones per octave*(vis-a-vis the contemporary design of 12**tones**per octave, adopted by Western and Eastern musicians alike).*
Seven out of these
‘22’ tones were in the direct ‘perceptual domain’ (by way of audible ‘tones’ of
Holy Sama Veda, being chanted for several millennia

*vis-à-vis the Western manner of theorizing music in the conceptual domain through ‘mathematical fractions’).*Quite surprisingly, ancient Indian musicology could precisely ‘quantify’ these seven tones over an octave that was calibrated into “22 equal divisions”*(known as 22 ‘Srutis’).*Such a ‘grouping’ of seven tones was known as ‘Sadja-grama’, as narrated in Bharata Muni’s Natya Sastra.
Details of the

**remaining ‘15’ tones were not known**. However, it was stated that the ‘sthaana’*(i.e. assignment of all the 22 tones within the octave)*will be realized once ‘Madhyama-grama’ and ‘Murchanas’ were also derived. This vital hint notwithstanding, the remaining ‘15’ tones could not be unravelled by the medieval musicologists.
What went wrong? I
had attempted a few “constructs” in an effort to de-mystify the riddle.

**.**

__Step-1__
Consider
‘Sadja-grama’

*(the earliest format of music handed down to us by Bharata Muni)*to begin with. Bharata Muni had narrated that the octave was calibrated in terms of ‘22 srutis’; this implies that the octave was**‘geometrically divided’**into 22 equal segments.
Let us pause for a
while here, to comprehend such a “heavily loaded” narrative from Bharata. When
we divide the octave into 22 equal segments, the elemental segment (sruti)
would measure 2

^{-22}. For the Western Mathematicians, this is an “impossible” feat, as no historical evidence is ever available to establish that our ancients possessed the knowledge of logarithms; without this mathematical tool, determination of the value of 2^{-22}is well-nigh impossible! That’s how they reject Bharata Muni’s narrative, out rightly, as a ‘pique of imagination’. Viewed from a rational plane, this criticism does appear to stick. Unfortunately, no Indian musicologist has ever come out with a valid argument to counter such a criticism from the Western experts, till now! On my part, I would prefer to remain content by merely highlighting the track-record of our ancient designers of music, wherein such an ‘unimaginable feat’ has been actually accomplished; I would not attempt to address more challenging questions such as: How did they achieve such a feat without the help of modern mathematical tools? Did they possess some different tools that are yet unknown to us? It is an enigma for me too!
Let me steer away
from this small diversion and focus on the main observations/ interpretations.
As per Bharata, within such a “scientifically calibrated” octave, the seven
tones of Holy Sama Veda were assigned as: Sadja (tonic)

*(i.e. the Reference Note)*= at ‘0.00’ sruti; Rishabha = ‘3.00’ srutis; Gandhara = ‘5.00’ srutis; Madhyama = ‘9.00’ srutis; Panchama = ‘13.00’ srutis; Dhaivata = ‘16.00’ srutis; Nishada = ‘18.00’ srutis; and Sadja (octave) = ‘22.00’ srutis.
Let us now, focus
on the ‘Panchama’ swara that has a tall stature within the octave, only next to
Sadja. It is identified as the fraction ‘3/2’ by musicologists of the East as
well as the West. If we mathematically transform this fraction ‘3/2’ into its
equivalent tonal value in an octave of 22 srutis, that would work out as ‘12.87’
srutis. This happens to be very close to the Sadja-grama value of ‘13.00’
srutis. Similarly, Suddha Madhyama which is identified as fraction ‘4/3’ by the
musicologists of the East and West, would have a tonal value of ‘9.13’ srutis
in the 22-srutis octave format. This happens to be, again, very close to the
Sadja-grama value of ‘9.00’ srutis. It is interesting to note that if we
reverse-convert the whole number sruti values (such as, say, Panchama = ‘13.00’
srutis) back into their equivalent fractional values, they will reveal
themselves as ‘complex fractions’: for example, ’13.00’ sruti value will reveal
the very complex fraction of the type: ‘(1483324002567 ÷ 990000000000);
similarly if reverse-convert ‘9.00’ srutis into its equivalent fraction, that
would work out as another very complex fraction of the order: (1321491453381 ÷
990000000000).

*(We may recall Pythagoras’s wise declaration that “simples fractions are ‘music’; and complex fractions are ‘noise”).*Complex fractions happen to be most jarring for human ears, something like the roaring of a jet engine! Surely, our Sama Vedic ancestors would not have forced down such jarring tones for the ears of their own posterity, as ‘music’! Therefore, we have to infer that ‘12.87’ srutis (that represents the simple fraction ‘3/2’) is, in fact, rounded off to the nearest whole number ‘13’ so that it is easier to trickle down such a number through the oral traditions, to the posterity. Similarly ‘9.13’ srutis (that represents the simple fraction ‘4/3’) is rounded off to the nearest whole number ‘9’. From this analysis, what do we wish to deduce? The most logical thinking would be: the Vedic ancestors, most probably, desired that the posterity should interpret these numbers**‘intelligently’**in order to re-map the ‘design nuances’ of our ancient music. Once we accept this rationale to serve as our first ‘construct’, it would be easier to re-frame the Sadja-grama format, as follows: Sadja (tonic) = ‘0.00’ (i.e. ‘1/1’); Rishabha = 2.76 (i.e. the nearest simple fraction ‘12/11’); Gandhara = 4.89 (i.e. the nearest simple fraction ‘7/6’); Madhyama = 9.13 (i.e. the nearest simple fraction ‘4/3’); Panchama = 12.87 (i.e. the nearest simple fraction ‘3/2’); Dhaivata = 16.21 (i.e. the nearest simple fraction ‘5/3’); Nishada = ‘17.76 (i.e. the nearest simple fraction ’7/4’) and Sadja (octave) = 22.00 (i.e. the nearest simple fraction ‘2/1’).
Did our Vedic
ancestors actually divide the octave geometrically into 22 equal segments and
then went about to evaluate the famous ‘Sadja-grama sruti values’? or is it
only a pique of imagination on the part of Bharata? In order to investigate the
truth, I had done a paper-exercise by ‘geometrically dividing’ the octave in various
permutations and combinations; i.e. in terms of 12, 13, 14, .. upto 30 equal
segments and evaluated the sruti values corresponding to the eight fractions
1/1, 12/11, 7/6, 4/3, 3/2, 5/3, 7/4 and 2/1. I am enclosing an EXCEL file
wherein I had attempted these permutations and combinations. It may be observed
that the ‘Sadja-grama numbers’ (i.e. 0,3,5,9,13,16,18 and 22) would prove to be
irrelevant in all octaves other than the one that is geometrically divided into
22 equal segments. In my view, this is evidence enough to establish that the so
called ‘primitive’ Vedic ancestors of India, indeed, did possess the ‘mathematical
know-how’ to address the mathematical challenge of evaluating the 22

^{nd}root of ‘2’ and accordingly calibrate the octave in terms of 22 equal segments!**.**

__Step-2__
Let us now consider
Madhyama-grama. As per Bharata, it is

**derived by reducing one sruti from Panchama swara.**It is observed that our medieval musicologists went about interpreting this narrative, by reducing Panchama’s swara-sthaana, by way of reducing it from position ‘13.00’ to position ‘12.00’; and thereby erred on two counts: Firstly, the sanctified sruti value of Panchama was downgraded and this has not been palatable to the posterity even today! Secondly, the resulting format of Madhyama-grama was, after all, not so very different from Sadja-grama.
Now, I have re-interpreted
this narrative by stating that reduction of the

**sruti-content of Panchama swara**should be attempted at its ‘leading edge’ rather than at its ‘trailing edge’. (Bharata’s narrative, the traditional interpretation, my re-interpreted findings etc. may be better comprehended through an illustrated analysis; I have described my analysis in a PPT file that would be found at link: https://docs.google.com/open?id=0B6Qw6H3PDIHNbWhVQmU2Y210OU0 )
This approach results
in the evolution of an alternative Madhyama-grama format which contains the
‘majors’ for the five Notes: Ri, Ga, Ma, Dha and Ni. In other words, we have an
alternative option to view the ‘grama formats’ as: Sadja-grama is a grouping of
‘minor’ Notes and Madhyama-grama, a grouping of ‘major’ Notes.

Once again
applying the ‘simple fractions’ rationale discussed in Step-1, we get the new
Madhyama-grama format as follows: Sadja (tonic) = ‘0.00’ (i.e. ‘1/1’); Rishabha
= 3.74 (i.e. the nearest simple fraction ‘9/8’); Gandhara = 5.79 (i.e. the
nearest simple fraction ‘6/5’); Madhyama = 10.11 (i.e. the nearest simple
fraction ‘11/8’);

**Panchama (No Change in swara-sthaana)**= 12.87 (i.e. the nearest simple fraction ‘3/2’); Dhaivata = 17.11 (i.e. the nearest simple fraction ‘12/7’); Nishada = ‘18.66 (i.e. the nearest simple fraction ’9/5’) and Sadja (octave) = 22.00 (i.e. the nearest simple fraction ‘2/1’).**. Lastly, let us consider the ‘Murchanas’. Here we follow the procedure narrated in the traditional literature almost verbatim, with a minor modification; the only change will be that the tonal values assigned in the formats of Sadja-grama and Madhyama-grama will be their nearest ‘simple-fractions’, as explained by me in Step-1. Once we derive all the 14 murchanas as stipulated in our traditional literature, we find that the remaining members of the family of 22 tones, which were hidden from our view so far, are also ‘resident’ within these murchanas. Once again this aspect is better comprehensible only when the same is illustrated; please see my PPT file at link: (https://docs.google.com/open?id=0B6Qw6H3PDIHNdEp1Q1cwOHA3dzg)**

__Step-3__
I had ventured a
bit deeper into the ‘structures’ interior to this ‘family of 22 fractions’.
Following features are unique:

·
Each fraction is a

**‘sonant’**, i.e. each one is a**‘simple fraction’**with respect to the Tonic (0.00). These tones are, therefore, inherently**‘serene and tranquil’**(somewhat similar to the tones of the drone/ tanpura).
·
While composing melodic
phrases, we should always configure the

**‘Intervals’**between successive ‘Notes’ as**‘simple fractions’;**the resulting melodic phrases would sound far more appealing to our ears. I have described this method in my PPT file at link: https://docs.google.com/open?id=0B6Qw6H3PDIHNeE1vZGg5UlUxTEk
·
Certain ‘triads’ of adjacent
tones

*(similar to the term ‘anu-vadis’, as known to contemporary Indian musicologists)*beat with one another, to generate additional melodic depths in a composition.*This phenomenon may be interpreted as***‘assonance’.**
·
These three features can be synergised in order to restore the much
needed ‘melody’ in our classical music.

I have fabricated
a ‘lyre’ (vina) and a ‘harmonium’ for demonstrating these unique melodic
features.

In addition, I have
developed some computerised models of music with typical melodic phrases; these
have been uploaded on the net so that any keen musician could listen, grasp their
fundamental features and innovate further with greater artistic skill. I am confident
that some magnanimous musician would be kind enough to step in and render his
‘artistic touch’ and improvise further.

Please listen to
the following links and tune into my perceptions of 22 srutis music please;
‘R1’ to ‘R6’ denote the ‘Rishabha’ notes on which the melodic structures are
founded:

R1: https://drive.google.com/file/d/0B6Qw6H3PDIHNaDJqaUpKV2JwQk0/view?usp=sharing

R2: https://drive.google.com/file/d/0B6Qw6H3PDIHNSHlscHMzbDFsRW8/view?usp=sharing

R3: https://drive.google.com/file/d/0B6Qw6H3PDIHNLUl6anFaZm5BMHM/view?usp=sharing

R4: https://drive.google.com/file/d/0B6Qw6H3PDIHNb21WejdSVzFnZ28/view?usp=sharing

R5: https://drive.google.com/file/d/0B6Qw6H3PDIHNZ2ZYMW1JU2FGMUE/view?usp=sharing

R6: https://drive.google.com/file/d/0B6Qw6H3PDIHNblRFdnZiODkwV1U/view?usp=sharing

One may ask: “The contemporary classical music is quite good and
meets the aspirations of the audience; Why should we attempt to resurrect some
different family of tones at all?” In this context, please refer to my blog at
link: http://blogs.rediff.com/ancientmusic/

Please visit website: http://www.22sruti.com/
and peruse my articles on musicology pertaining to our ‘Ancient Music of 22
Srutis’ by clicking on the sub-head termed as “USEFUL LINKS”.