Note: building block doesn't finish framework (6)
I believe the answer is:
fabric
'framework' is the definition.
('fabric' can be a synonym of 'framework')
'note building block doesn't finish' is the wordplay.
'note' becomes 'fa' (fourth note in sol-fa notation: doh, ray, me...).
'building block' becomes 'brick' (I've seen this before).
'doesn't finish' means to remove the last letter.
'brick' with its final letter removed is 'bric'.
'fa'+'bric'='FABRIC'
(Other definitions for fabric that I've seen before include "Underlying structure" , "Woven textile" , "Silk or satin, say" , "Woven, knitted or felted cloth" , "Manufactured cloth" .)