In the Madhyama Grama Pancama should be made deficient in one Sruti. The difference which occurs in Pancama when it is raised or lowered, by a Sruti and when consequential slackness3 or tenseness [of strings] occurs, will indicate a typical (pramana) Sruti. We shall explain the system of these [Srutis]. The two Vinas with beams (danda) and strings of similar measure, and with similar adjustment of the latter in the Sadja Grama should be made [ready]. [Then] one of these should be tuned in the Madhyama Grama by lowering Pancama [by one of Sruti]. The same (Vina) by adding one Sruti ( lit. due to adding of one Sruti ) to Pancama will be tuned in the Sadja Grama. This is the meaning of decreasing a Sruti (lit. thus a Sruti is decreased). Again due to the decrease of a Sruti in another [Vina] Gandhara and Nisada will merge with Dhaivata and Rsbha respectively, when there is an interval of two Srutis between them. Again due to the decrease of a Sruti in another (Vina) Rsbha and Dhaivata will merge with Sadja and Pancama respectively when there is an interval of [three] Srutis. Similarly the same [one] Sruti being again decreased Pancama, Madhyama and Sadja will merge with Madhyama, Gandhara and Nisada respectively when there is an in interval of four Srutis between them. Thus according this system of Srutis, [each of] the two Gramas should be taken as consisting of twentytwo Srutis.

It is theoretically possible if there's a veena with 22 precisely spaced frets per octave (for which the exact positions of the 22 intervals on a string need to be known). You need two of them, and tune one to the next lowest note played on the other.

Let's call these intervals as S,r1,r2,R1,R2,g1,g2,G1,G2,M1,M2,m1,m2,P, d1,d2,D1,D2,n1,n2,N1,N2 (the 22) and finally top S. Each of the 12 notes we know got 2 values from the algorithm that derived the shrutis, and the ratio between the higher and the lower is 81/80. S and P got frozen, the experiment will not work otherwise, so there's our 22.

Now here's the mistake in the ubertext - implying that the veena is being tuned down by 1 pramana shruti (80/81) every time. No, It isn't. The shrutis follow a certain sequence of ratios up and down the scale and they can only be decreased or increased according to that order.

I am not going to show the math in this post (a simple matter of ratio adjustment). I will if anyone's interested in a subsequent post.

1) First you tune the second veeNa's P to m2.

2) Then when you tune the P down one more shruti to m1, then g2 merges with R2, g1 merges with R1, n2 and n1 merge with D1 and D2 respectively. So far so good.

3) Then when you go another step further, down to M2, then R1 merges with S, and D1 will merge with P. Check. Note, d1 and r1 cannot merge with P and S.

4) Then when the P is decreased down to M1, then P and M1 have merged. Meanwhile, M2 merges with g2 (not G2), M1 merged with g1. S merges with n1 (NOT N1 as so many have wrongly understood!!). Check. Therefore by virtue of detuning by 4 shrutis, there is a 4 shruti gap between n1 and S.

Some people have wrongly interpreted this as a 4 shruti gap between N2 and S (and they also implied that S has 4 values), but the math clearly shows that it's between n1 and S.

**The whole confusion here is that no one has bothered to clarify specifically which interval merged with what!** They didn't say WHICH gandhara merged with which rishabha, when each of them has 4 possibilities. We don't even know if bharata muni himself used this kind of labelling scheme - if he didn't, then what he wrote up there won't make any sense and it's up to the math to tell us what's really going on.

And this is what has baffled musicologists till date and caused all the confusion. Otherwise the debate on 22 shrutis would have been closed from the math long ago.

So what we need here are 2 identically tuned veenas with 22 frets, such that the intervals fall at these locations :

http://www.22shruti.com/research_topic_33.asp
Then one veena plays m2, m1, M2 and M1 and the other veena tunes the P string successively downward to these intervals. And then the other strings of the second veena are tuned to match the reduced P. This is definitely doable.

The whole idea of arbitrarily tuning down a veena by several pramaNa shrutis was absurd enough, whoever said that definitely hasn't tuned strings in their life. If you check the revised ratios with that assumption, it guarantees that no interval will ever sync with the first veena again.

And the idea of tuning down the second veena arbitrarily by ear is ridiculous. I mean, that is an interval of 21.5 cents, so you need to be precise to 0.5 cents, which is 1/200th of the gap between two semitones. The only way to determine the Pythogorean comma properly is to actually hear it on a piano tuned to 5ths, or play R2 on both the S and lower P strings of a modern veena and hear it for oneself.

But the above solution is doable and the only mathematically possible one, provided they can figure out how to get the frets to work. If they managed to get a harmonium to do it, I think it is possible to create a custom veena as well.