Shruti: JND of a kind?

Since all the Tuning group members are well aware of JND, let me
summarize JND with only keywords/phrases:
Keywords/phrases: sensation; perception; discernibility; threshold
of hearing -- the upper and the lower limits, the dependence of JND
on the individual and on the frequency, sound level, and the duration
of the tone; critical bandwidth; JND = 5 cents is a good
approximation, etc.

The four-fold string movement, called chatuH- saaraNaa, is described
in Sharngadeva's sangita-ratnakara. It is an exposition which
unequivocally demonstrates the shruti-s on a pair of vina-s.
See 'sangita-ratnakara', Chapter I, section 3, verses 10-22. The
keywords there are:
two identical vina-s, one of them invariable, the other variable;
four movements; tuning the next string a little bit [the Sanskrit
word used is "manaak", (an indeclinable)] higher, in ascending
pitches; disallowing any intervening audible sound while maintaining
continuity between any two shruti-s -- this is JND, to be sure,
though, a different kind. We do not need to go into the details of
the four movements here.

Comparison between JND and shruti "JND":

JND Shruti "JND"

1. The participants: any listeners -- experts.
2. Detection: greater between 2 & 4 KHz Lowest vina sound (?)
3. An average approximation: 5 cents Less than 2 cents(?)
4. Sufficient to detect 50% of the time Every time
5. Sound source: loud Soft (gentle vina)
6. The second tone: Higher or lower Higher
etc. etc. ....
Note: As a mere guess, the lowest vina sound could be, say, 50 Hz.

The queries: (1) Sharngadeva wants only experts to perform this
experiment -- who better than the members of this tuning group?
(2) I am sure we can use an electronic device (computer?) to
substitute the two vina-s. Suggestions, please?

Has this ever been tried on a computer, using proper hardware and
software?

Thanks.
Haresh.

Haresh BAKSHI schrieb:
>
> Comparison between JND and shruti "JND":
>
> JND Shruti "JND"
>
> 1. The participants: any listeners -- experts.
> 2. Detection: greater between 2 & 4 KHz Lowest vina sound (?)
> 3. An average approximation: 5 cents Less than 2 cents(?)
> 4. Sufficient to detect 50% of the time Every time
> 5. Sound source: loud Soft (gentle vina)
> 6. The second tone: Higher or lower Higher
> etc. etc. ....
> Note: As a mere guess, the lowest vina sound could be, say, 50 Hz.
>
> The queries: (1) Sharngadeva wants only experts to perform this
> experiment -- who better than the members of this tuning group?
> (2) I am sure we can use an electronic device (computer?) to
> substitute the two vina-s. Suggestions, please?
>
> Has this ever been tried on a computer, using proper hardware and
> software?
>

Dear Haresh,

no, I haven't tried this, but I think for the experiment to work out
properly you would indeed need experts who know what the srutis are
beforehand. If all the srutis are really equal, the experiment
demonstrates equal temperament (or steps of "roughly" 129/125) with
109 cent for any two sruti, 163 for three, and 218 for four.
(Actually, my source - English translation by Dr. R. K. Shringy
under the supervision of Dr. Prem Lata Sharma, 1991 - presupposes
vinas of 22 strings, where a single one would be sufficient for such
a demonstration; also, they think it will only work in shadja
grama.)

I try to ignore this experiment. Reason:
My understanding of the sruti is that they were originally a fine
division of the vina fingerboard (?) to define and/or assist in
placing the frets for specific types of music (the gramas). From the
nut, it would start out with a ninefold harmonic division of the
fourth. In this case the first movement would be by 28/27 or 63
cents, the second by 29/27 or 124 cents, the third by 10/9 or 182
cents, the fourth by 31/27 or 239 cents: only the three sruti
movement would yield the desired result. For even more ludicrous
results, you can take your sruti size from the retuned vina and
repeat the 63 cent steps.
Or you could take your steps from the fourfold division of the 9/8
between the fourth and the fifth. The moves would be 33/32 (53
cents), 17/16 (105 cents), 35/32 (155 cents), and 9/8 (204 cents).
If you don't care about the difference between 16/15 and 17/16 (just
about 5 cents and therefore not necessarily "sruti", i.e. audible?),
you get sensible results for the two and four sruti movements.

On the other hand, you could take the expected results and determine
the sruti:
The lower part of shadja grama is 1, 9/8, 5/4, 4/3, and 3/2.
Your first transpositions could be anything, but the second would
have to add up with it to 16/15 (112 cents).
Now Ni will have the same pitch as the original Ma: 16/15, 6/5, 4/3,
64/45, 8/5.
The next move is by 25/24 (71 cents); the pitch of Ga reappears as
Ri: 5/4, 25/18, 40/27, 5/3.
And finally, there is just a komma (81/80; 22 cents) missing to make
Ma equal to the original Pa: 81/64, 45/32, 3/2, 27/16.
Paul Lanski stayed within 5-limit and took the first two
transpositions to be 256/243 and 81/80 (adding up to 16/15).

Of course, this last experiment could easily be done with two only
slightly sophisticated synthesizers.

klaus