Saturday, April 25, 2009


What is ‘SADJA-GRAMA’ ?

     Please read this ‘Blog’ in conjunction with ‘Presentation Slides’ given at the following link, where finer details are suitably illustrated, for improving comprehension:
Indian musicology defines ‘Sadja-grama’ as a group of seven ‘Notes’  ‘identifiable’ within an octave that is calibrated in 22 equal divisions (alternatively known as  ‘22 srutis’). In Sadja-grama, each ‘Note’ represents a bunch of frequencies  and these ‘bunches’ happen to be dissimilar (i.e. bunches of ‘2’, ‘3’ and ‘4’ srutis). These seven Notes put together, (measuring 22 ‘srutis’), account for the total octave range. Each Note is assigned a name and a position within the octave, in the following manner: Sadja (Tonic) - 0.00 srutis, Rishabha- 3 srutis, Gandhara- 5 srutis, Madhyama- 9 srutis, Panchama- 13 srutis, Dhaivata- 16 srutis, Nishada- 18 srutis and Sadja (Octave) - 22 srutis. The highest frequency within each bunch of a Note is designated as the ‘Seat’ of the Note.
            Let us, now, look at the Western scenario. Ancient Sumerians worshipped ‘simple fractions’, as gods (example, An = 1/1; Sin = ½; Enki = 2/3; Enlil = 5/6). Subsequent civilizations regarded Numbers lying between ‘1’ and ‘12’ as ‘sacred’; they, however, disregarded numbers lying between ‘13’ and  ‘18’ as the  ‘ Devil’s Domain’ . This unique ‘status’ accorded to numbers between ‘1’ and ‘12’ attracted me. An elementary mathematical analysis revealed that a maximum of only ‘22 fractions’ could be formulated from these twelve ‘sacred’ numbers. Let us call this set as the ‘Family of 22 Fractions’.
For more details please refer to the Presentation slides at following link:
I classified this ‘Family of 22 fractions’ as per their increasing order of shrillness, within the octave (i.e. between ‘Sadja’ Tonic and ‘Sadja’ Upper). This ‘classification’ has been done by me by employing contemporary mathematical tools. The Reader will be able to observe that the value of ‘srutis’ traditionally assigned to the Indian ‘Sadja-grama’ are nothing but the “rounded off” values of seven members belonging to the ‘Family of 22 Fractions’.
            Any Reader would tend to conclude that this could, at best, be only a ‘chance coincidence’; because the ‘shrillness index’ for the ‘Family of 22 fractions’ as determined by me now is based on contemporary mathematical tools and the ‘vedic Indians’ (who belonged to an era of scientific primitivity) could not have evolved the ‘seven tones’ of Holy Sama Veda, with a similar scientific approach (due to lack of higher mathematical knowledge).
This notwithstanding, I decided to extend my observations to the other ancient musicological doctrines known as ‘Madhyama-grama’ and ‘Murchana’s (which were the fountain-head for the vertical development of Indian music since the days of Bharata and Dattila Munis). Repeated deliberations led me to the ‘finding’ that the ‘Family of 22 fractions’ lying between ‘1’ and ‘12’ had been “embedded” into these entities (by the ‘ancient’ designers) with high scientific precision!
            In order not to clutter up this blog more, I have written separate blogs related to my observations on Madhyama-grama and Murchanas; please see details at following links:  (Blog)
I would request the viewers to deliberate in depth and attempt to comprehend this ‘subtlety’ embedded in the ancient Indian musicology, as it is nothing short of a “grand miracle”!
We encounter a similar ‘miracle’, as we observe the ancient Sumerian theology too! ‘Encoding’ of this very same ‘Family of 22 simple fractions’ have been achieved by the ancient Sumerians, by way of ‘deification’, (in the form of the ancient Sumerian Pantheon of gods). The tradition of worshipping such deities continued unabated over the ensuing several millennia, although their names, forms and associated mythologies kept changing with the emergence of newer civilizations! For details, please see my blog and Presentation slides:  (Blog)  (Presentation) 
Plenty of mind-boggling queries! How did Vedic Indians gain access to advanced mathematics that enabled them to calibrate the octave in terms of ‘22 srutis’ (which pre-supposes the mathematical expertise for evaluating the 22nd Root of ‘2’ without the knowledge of ‘logarithms’)? How did they know that there were 22 simple fractions lying between the integers ‘1’ and ‘12’ which were most suited for designing music? What mathematics did they use to ‘transform’ all these 22 mathematical fractions into the tonal domain and embed them within the ‘gramas’ and ‘murchanas’? How did they identify that only seven tones out of these 22 tones were adequate to serve as ‘seed tones’ before embedding them into the Sama Veda? How did they compute the formulae that would enable the posterity to derive all the remaining tones through ‘Madhyama-grama’ and the 14 ‘Murchanas’? The most vital question is: ‘How did they wield so much influence on our Indian ancestors who continued to chant the Holy Veda in these seven tones, with precision, for the ensuing several millennia? Similarly, how did they influence our Western ancestors such that they continued with the worship of deities for the ensuing several millennia? I have more questions than answers! However, one thing is certain; the Note-positions of Sadja-grama {i.e. Sa (tonic) – 0, Ri – 3, Ga – 5, Ma – 9, Pa – 13, Dha – 16, Ni – 18 and Sa (octave) – 22} are not garble or some chance occurrences; these have been assigned during the pre-Vedic period with highest precision. In case we do not appreciate this rationale, these numerical figures would continue to haunt us forever, as ‘garble’.       
For more details, contact me on Teles: 91 20 26729256, 9890266845, and 98501 21834. E-mail: Please visit my Web-site:  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).