It seems counterintuitive that what I'm talking about should be the case, you'd think that having the strings tuned spot on would yield the best resonance. Perhaps it's something to do with the bowing pulling the string sharp? But it seems to be like that even with very soft, smooth bowing, at least on my instrument-
An interesting question.
Firstly, I'd say that this is not connected with the bowing. The bowing, even if applied hard, should set off the fundamental note of the playing string, and by transference the matching fundamental note of the appropriate sympathetic. And I don't think it matters whether you use a pick, or a nail, as I do, to pluck the string.
It's really down to the physics of a plucked string, and harmonics. I don't pretend to have a full grasp of this, but I'll try and explain how I understand it.
It's fairly easy to find by experiment that the whole tone of a plucked sympathetic changes depending on where you pluck it. Also this is clearly demonstarted on the main playing strings. Even though the fundamental frequency of the string does not change - the physics - which is essentially dependent on string length, mass and tension.
Plucked in the centre the string will sound very different from the same string plucked at the end. If plucked dead centre this is because half the harmonics, the even harmonics, are missing. If plucked very near the end the string the whole load of extra harmonics will make the string sound brighter, and enough for us to perceive the string as tuned to a higher pitch than it actually is (ie exactly the same as when we pluck in the middle, when it is a lot duller - but NOT flatter). Mainly because the funadmental is hidden by all those bright sounding higher harmonics. This effect is even more apparent on the sympathetics if you pluck close to the jawari, this introduces a whole host of extra confusing bright overtones.
This I think explains what you are finding. You're not actually
tuning to a higher pitch, but you've got used to your ear thinking you are.
I have always thought the best place to pluck a sympathetic is somewhere near the centre of the string, certainly between the centre and about a third of the way along. This should apply to any sympathetics, including eg sitar, and also, significantly, tanpura. I actually believe it is a mistake to pluck near the end of the string, whichever end.
But whichever point you pluck at, on the sarangi the acid test is whether the string resonates to the bowed note. The more it does, the better you have got the fundamental note of the sympathetic right.
I'd also say that although the coarse tuning of the playing strings can be done by plucking the fine tuning has definitely to be done by bowing.