Separated, note, catch up with one single daughter (11)

'separated' is the definition.
(partitioning is a kind of separating)

'note catch up with one single daughter' is the wordplay.
I cannot really see how this works, but
'note' could be 'ti' (musical note, as in do re mi so fa la ti do) and 'ti' is located in the answer.
'one' could be 'i' (Roman numeral) and 'i' is present in the answer.
'single' could be 'one' (a single thing - only one) and 'one' is located in the answer.
'daughter' could be 'd' (genealogical abbreviation) and 'd' is found in the answer.
The remaining letters 'part' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?