Vidyasankar Sundaresan <vidya> wrote:
The acala vINA, true to its name, is left untouched in the course of Bharata's
demonstration, once it has been tuned to shaDja grAma. It is the cala vINA that
gets retuned.
pps. Most lists of retro-fit ratio values to "Bharata's 22 Srutis" rely on a >perfect fifths cycle. But these lists also include values like 5/4 and 5/3 for
gAndhAra and dhaivata respectively. These numbers could not have come from a >pure fifths cycle, but this fact is rarely, if ever, appreciated by most modern
Indian writers.
It is evident from these works that the cycle of fifths was indeed used to tune
the yAzh (harp-like?). Consonance and dissonance relationships between notes are described in terms of naTpu (friendship) and pakai (enmity). kural (shaDja)
and iLi (pancama) are said to be in naTpu. The process of taking repeated fifths is known in tamizh as iLikramam. The description of tuning pAlaiyAzh (equivalent to harikAmbhoji - khamAj) leaves no room for doubt that the cycle of fifths is used to tune the strings of the instrument. What is even more interesting is that there is evidence that the tamizh musicians also modified this cycle in the case of the kaikkiLai (= gAndhAra) and viLari (= dhaivata). This is done because the iLikramam would give a third that is dissonant with the tonic. aTiyArkunallar clearly describes the reduction of the pitch of the kaikkiLai (gAndhAra) to bring it into consonance with the tonic (kural), so that the pakai is removed and naTpu is re-established. The viLari (dhaivata) is
also correspondingly reduced, in order to be in naTpu with the reduced kaikkiLai. If we were to attach a simple ratio of integers to this verbal description, it is clear that only a value of 5/4 could be meant for the new, reduced kaikkiLai. The presence of the fifth harmonic is very pronounced, especially in vibrations of thick strings, and it is obvious that the reduction
of the kaikkiLai (gAndhAra) is to bring it in resonance with this harmonic. The
corresponding value for the reduced viLari (dhaivata) would then be 5/3. What strikes me in this description is that the modification of the cycle of fifths
is done not to maintain the consonance of the uzhai (madhyama), but that of the
kaikkiLai (gAndhAra). The consonance of the uzhai is ensured because the iLikramam is started from tAram (nishAda), so that uzhai is determined as the fifth of tAram and kural as the fifth of uzhai. It has always puzzled me that the notes in Indian references have always been reckoned from the nishAda. There is even a story that originally there were only six notes, and that the shaDja was introduced because it was given by Siva. It may be that the reckoning from nishAda is just a way of maintaining the consonance of the fourth even while determining notes using a cycle of fifths. On the other hand,
I haven't seen such an explicit description of gAndhAra consonance with shaDja
in any samskr.ta source. Of course, this does not mean that it wasn't recognized in practice.
The reason I am doubtful
about it is because unlike in Bharata's case, the tamizh sources do not mention
anything equivalent to a madhyama grAma.
There always remains the question of influence from the Greeks, which I won't go into now.
S. Vidyasankar
--------
Interesting to read about shadja-gandhar conosonance in old Tamil shastras .
This site talks about Shadaj-Gandhar Bhav :
https://www.chandraveena.com/blog/grammar-of-music/
Dr Oke ( 22 shruti reasearch + harmonium ) also writes extensively about the Shadja Gandhar relationship :
http://www.22shruti.com/research_topic_31.asp http://www.22shruti.com/research_topic_12.asp --- importance of Ga
Dharambir Singh goes into the details :
http://www.dharambir.com/indian-classical-music-research/svara-and-tunings/
" Starting with the tonic Shadaj the fourth tone was tuned as a perfect fourth interval called Madyam. This Madyam was used to establish its perfect fourth the last note in the series called Nishãd. This Nishad helped to establish the third tone called
Gandhãr a perfect fifth down. From Madyam as reference a perfect third was tuned and called Dhaivat. From this Dhiavat the second tone Rishab was tuned as a perfect fifth below. The perfect fifth was tuned from Shadaj as reference to complete the basic
seven tone basic Grãma (tuning reference).
In a perfectly tuned Tānpūrā, the perfect third overtone heard in the Mandra Shadaj string of the 5/4 ratio is Bharata’s Antra Gandhār. Though Bharata did not include this interval as Samvād but in the establishment of the Grāma he has
highlighted the importance of Antra Gandhār. This importance will be evident in the proceeding couplets. It is important to remember that Matanga has mentioned the seven shrūti interval in Madhyama Grāma as samvād and that is same as the S –G
interval. In Brhaddeshi (page 16) this interval has been given more prominence than the shadaja pancham and shadaja madhyama. One reason for this is that in the overtones this note is the most prominent and second that in the establishment of the Grāma
s the use of this is worth looking at. In the next couplets both samvād are mentioned.
The only method to tune Dhaivat on the sixth string is through the Seven Shruti Shadaj Gandhār samvād. From this Dhaivat tune the Rishab on the second string through avroh Shadaj pancham samvād. "
It seems that somehow or other the Shadja Gandhar samvaad was there in ancient North Indian texts also . ( ma Dha tuning in Shadja Grama )
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