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Grandmother on its own (i.e without an article) is seanmháthair
The diminutive form just adds an -ín at the end, i.e. an tseanmháthairín (pronounced 'on tann-wah-hir-een'
I've just found sth. else:
Most English-speaking children call their grandmothers Granny, Grandma, or Nana/Nanna.
There are a few different words for Grandmother in Irish, including Seanmháthair (shan a WAW her), máthair mhór (maw her aWOR), and
máthair Chríona (MAW her KHREE un na). These literally mean "old mother", "great mother" and "mother of the heart." These words are not
used to actually address the grandmother, though. Children would call a grandmother Maimeó (MAM o), or perhaps Móraí (MO ree). http://www.namenerds.com/irish/granny.html
Someone else posted this question earlier today (grandma). I just copied and pasted what I entered there.