"One of your grandfathers" is one of two specific males (yes, I know it could actually refer to only one, but let's avoid that bit of scandal).
"One of your great aunts" is one of the sisters of one of your four
"Your great aunt" could, informally, still mean one of the (possibly
numerous) great aunts you may have, but it could also tell someone that
three of your parent's parents have no sisters and that the remaining one
has only one. I believe that you'd not typically infer that, though. Not
in the culture I'm in, anyway.
"One of your grandfathers' sisters" (note the position of the apostrophe)
is the same as one of the sisters of one of those two males. Each
grandfather may have exactly one sister and we'd still be able to say
"One of your grandfather's sisters" (note the position of the apostrophe)
is still one of your great aunts but we may now plausibly infer that one
of your grandfathers had more than one sister, and that - if the other
grandfather had only one sister - the great aunt in question is one of
those rather than the single sister of that other grandfather. But you're
pushing things a bit there.
But in these last two we've already missed a possibility. It's caused by
the "One of" bit. It might actually not select a sister at all, as we have
assumed here, but a grandfather. It completely alters the meaning. It's
the difference between "one of (his (either grandfather)'s or (this
grandfather)'s) sisters" - which refers to one female - and "his (i.e. one
of my grandfathers) sisters" - which refers to a whole slew of them.
Without further clarification, it's not possible to tell which is meant.
I'm reasonably sure that the default, natural, interpretation is the
single female one. But even there it's probably more to do with usage than
syntax. In typical discourse of that nature you're simply more likely to
be referring to a specific individual.
Were you to continue the sentence and say "One of my grandfathers sisters
have formed a choir" (I've omitted the grandfatherly apostrophe - it
doesn't elucidate and you can't hear it anyway) it sounds wrong. You might
eventually work it out and realise it does both make sense and is accurate
- precisely and concisely informative even - but I suspect you might be a
tad annoyed at the speaker for having made you do all that work. In
practice you'd be expected to say just "My grandfather's sisters have
formed a choir" and leave open the question (or even relevance) of which
grandfather you mean. Or indeed of which sisters - since you still can't
hear the apostrophe, that choir may include all sisters of both
grandfathers, but that would be an unlikely intended meaning - again
mostly by dint of context rather than syntax.
The question is, is there a language where these ambiguities are removed
by syntax alone? Note that I'm not talking about vocabulary and syntax
helping out. For instance - and in (very) particular - in Latin we may
distinguish a maternal great aunt (matertera magna) from a paternal one
(amita magna) but any disambiguation therewith provided is simply an
accident of vocabulary. What I mean is, is there a language anywhere
(anywhen, even) which forces you - by syntax alone - to be specific so
that there's no doubt that the speaker means "the sister of one of your
grandfathers" and not "the sisters of one of your grandfathers" or "one of
the sisters of your grandfather" or "one of the sisters of your
grandfathers" by synthetic possessive/genitive syntactic marking rather
than by lengthy analytic expression?
And would it extend to the disambiguation of the rather large number of
possibilities intended by something such as "one of your grandfather's
sisters' cat's pyjamas", where the 'one-of' may select (one of)
grandfather, sister, cat, or pyjama?