Monday, April 27, 2009



                               What is ‘MADHYAMA GRAMA’ ?
       (Please read this ‘Blog’ in conjunction with  ‘Presentation Slides’ given at the following link, where the animated diagrams would enable better comprehension):

A brief preamble pertaining to the ancient doctrines of Indian musicology is necessary to enable the viewers to appreciate the concept of ‘Madhyama-grama’.
 Among the oldest sacred Scriptures of the Hindus, Holy Sama Veda occupies a unique place because its verses are chanted by using seven different tones of an octave. These seven sacred tones of Holy Sama Veda were archetypal for the Indian Music, under the terminology ‘Sadja-grama’.
‘Madhyama-grama’ was another grouping of seven Notes derived from Sadja-grama. From these two ‘gramas’, vertical development of music took place in the form of 14 (fourteen) ‘Murchanas’ which were somewhat similar to the modal music of ancient Greece. These gramas and murchanas were the fountainhead for the evolution of contemporary Indian classical music.
In my earlier blog on ‘Sadja-grama’, the viewers have been acquainted with the Sadja-grama format that was traditionally defined as: Sadja (Tonic) - 0.00 srutis, Rishabha (the ‘second’) - 3.00 srutis (approximately 163 cents), Gandhara (the ‘third’) - 5.00 srutis (approximately 273 cents), Madhyama (the ‘fourth’) - 9.00 srutis (approximately 491 cents),, Panchama (the ‘Perfect Fifth’) - 13.00 srutis (approximately 709 cents), Dhaivata (the ‘sixth’) - 16.00 srutis (approximately 873 cents),, Nishada (the ‘seventh’) - 18.00 srutis (approximately 982 cents),  and Sadja Upper (the ‘octave’) - 22.00 srutis (1200 cents). (Note: ‘sruti’ was an ancient Indian yardstick for measuring the spectral contents within an octave, similar to the term ‘cent’ as used in contemporary context.  One ancient Indian ‘sruti’ corresponds to approximately 54.5 cents). Please see my ‘Blog’ and ‘Presentation Slides’ on Sadja grama: (Blog).  (Presentation).
As per Bharat Muni (the earliest known Indian scribe who lived in 200 B.C.), when the ‘Panchama’ Note (i.e. the ‘Perfect Fifth’) that ocupied a bunch of four sruti-units within the Sadja grama format, was reduced by ‘one-sruti’ unit, ‘Madhyama-grama’ would get evolved.
Long-held Indian ‘traditions’ interpreted Bharata Muni’s statement to attribute the following definition for Madhyama grama: Sadja (Tonic) - 0.00 srutis, Rishabha- 3.00 srutis, Gandhara- 5.00 srutis, Madhyama- 9.00 srutis, Panchama- 12.00 srutis (approximately 655 cents), Dhaivata- 16.00 srutis, Nishada- 18.00 srutis and Sadja (Upper) - 22.00 srutis.
Observing the two gramas in the ambience of this traditional interpretation, the viewer tends to think that the difference between the two gramas is rather ‘trivial’ as the ‘difference’ is confined only to a single variable, namely, the ‘Perfect Fifth’; i.e. ‘Panchama’ in the Madhyama-grama is seated at a position 12.00 srutis (approximately 655 cents) above the Tonic as opposed to the fact that ‘Panchama’ in the Sadja-grama is seated at 13.00 srutis (approximately 709 cents) above the Tonic. There appears to be no other major distinguishing features that separate the two gramas!
Dr. Mukund Lath who wrote a commentary on ‘Dattilam’ is a highly regarded musicologist of contemporary Indian music. He is the only person who seems to have suspected that ‘all is not well’ with this understanding of Sadja-grama and Madhyama-grama schemes, as interpreted by our traditional musicologists. His remarks are very significant: “…. The two gramas in ancient texts have been carefully separated and the importance of the distinction in ancient practice can in no way be belittled. Tanas, murchanas, even the jatis and the jati-born ragas were all classified on the basis of gramas. Indeed the entire range of musical conception, it seems, was classified into two distinct compartments on the basis of the two gramas. This obviously leads us to the conclusion that there was some core of difference between the gramas which was probably basic and central to ancient music. This core, however, eludes us”.
These comments emanating from a celebrity of Dr. Mukund Lath’s eminence and stature did have a profound effect in my thought-process. I had re-examined the whole process of evolution of Madhyama-grama from Sadja-grama. There were two glaring aberrations: firstly, the distinction between the gramas rested only on a single variable and therefore, reduced to a state of ‘triviality’, as pointed out earlier. Secondly, ‘Panchama’ swara (i.e. the ‘Perfect Fifth’) which stands tall only next to ‘Sadja’ within the octave, got de-sanctified due to its demotion from its authorised position of ’13.00 srutis (approximately 709 cents) above tonic’ to a lower position of only ‘12.00 srutis (approximately 655 cents) above the tonic’. This appears to be somewhat unnatural as all cultures of music (even our contemporary systems of music) have always accorded a sanctified status for ‘Panchama’ (the ‘Perfect Fifth’), i.e. at the position of 702 cents above the tonic in the 1200 cents per contemporary norm (i.e. 12.87 srutis above the Tonic, as per the 223 srutis octave norm of ancient Indian music)!
However, this direction to reduce the sruti of ‘Panchama’ by one measure had come from no less a person than Bharata Muni, who is held in the highest esteem by one and all. But then, have we erred somewhere in understanding him? Is there an alternative option for complying with the directions of Bharata Muni, without upsetting the sanctity accorded for the ‘Panchama’ swara-sthaana by the Holy Sama Veda?
I deliberated over this issue for quite some time; I attempted to innovate an alternative method, after some detailed experimentation. In Sadja-grama, the spread of ‘Panchama’ swara is confined between 9.00 srutis and 13.00 srutis. This spread is reduced (by one sruti unit) to lie between 9.00 and 12.00 srutis, as per the ‘traditional’ interpretation of Madhyama grama. Please note that this traditional method reduces the spread of ‘Panchama’ from the upper spectral end.
In my revised method, I proposed to effect this reduction from the LOWER spectral end of ‘Panchama’. Consequently, the ‘spread’ was limited between 10.00 and 13.00 srutis. As I attempted to comply with the mandate of Bharata Muni with this alternative interpretation, I discovered the unfolding of a new phenomenon that had remained ‘dormant’ from our view, all these days! This reduction had caused a complete ‘change’ in respect of the ‘seats’ of other swaras. I observed that the seat of Madhyama Note moved from position ‘9.00’ (approximately 491 cents) to ‘10.00’ srutis (approximately 546 cents) with respect to the tonic. Similarly, Gandhara moved from position ‘5.00’ (approximately 273 cents) to ‘6.00’ (approximately 327 cents); Rishabha moved from ‘3.00’ (approximately 164 cents)  to ‘4.00’ (approximately 218 cents); Nishada moved from ‘18.00’ (approximately 982 cents)  to ‘19.00’ (approximately 1036 cents)  and Dhaivata moved from ‘16.00’ (approximately 873 cents)  to ‘17.00’(approximately 927 cents)  . However, ‘Panchama’ continued to remain at 13.00 srutis (approximately 709 cents)! I have narrated this whole phenomenon in my Book (The Mystic Citadel of 22 Srutis Music) as the ‘Cascade effect’.
If we now examine this new formulation of Madhyama-grama, it may be noted that the two aberrations narrated earlier, are no longer there. ‘Panchama’ swara remains undisturbed in its position of sanctity (as bestowed by Holy Sama Veda) at 13.00 srutis. All the other swaras have assumed “sharper” profiles; i.e. ‘one-sruti’ (approximately 54.5 cents) higher than the Sadja-grama profile!
This led to a ‘paradigm-shift’ in my own thought process! I observed that these were the “rounded-off” values of five more members of the family of 22 simple fractions (formulated mathematically from the Numbers lying between ‘1’ and ‘12’). These are: Panchama- 13.00 srutis (rounded off value of 12.87 pertaining to fraction 3/2); Madhyama- 10.00 srutis (rounded off value of 10.11 pertaining to fraction 11/8); Gandhara- 6.00 srutis (rounded off value of 5.79 pertaining to fraction 6/5); Rishabha- 4.00 srutis (rounded off value of 3.74 pertaining to fraction 9/8); Nishada- (-) 19.00 srutis (rounded off value of 18.66 pertaining to fraction 9/5); Dhaivata- 17.00 srutis (rounded off value of 17.11 pertaining to fraction 12/7).
A critical re-orientation in our thought process would help to view this re-interpreted profile of Madhyama-grama as the format of a ‘major’ scale whereas the profile of Sadja-grama may be re-discovered as the format for a minor scale! It may please be observed that whereas Sadja-grama revealed six of the 22 simple fractions, Madhyama-grama reveals five more members of the family of 22 simple fractions.
In my view this is the true form of Madhyama-grama which couldn’t be unravelled by our medieval musicologists due to the non-availability of a sound mathematical infra structure.
I apprehended that there must be some ‘master hand’ at work while designing the mathematical models for music during the pre-historic days. I, therefore, decided to extend my research work to the domain of ‘Murchanas’. Please see my ‘Blog’ and ‘Presentation Slides’ pertaining to the ‘murchanas’:   (Presentation)
For more details, contact me on Teles: 91 20 26729256, 9890266845, 98501 21834. E-mail: Please visit my Web-site:  I would also recommend that the viewers, for the sake of better comprehension, should 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).