This paper shows how with syntax defined as progressive projection of semantic representations along the left-right dimension provided by the sequence of words (Cann et al 2005), natural explanations can be provided for local and (multiple) nonlocal scrambling of NPs in Japanese and Korean which follow from general principles of tree growth, explaining differences between the languages while nevertheless retaining an integrated account of scrambling itself (following Kiaer 2007, Kempson and Kiaer forthcoming). This formalism has many similarities with the parsing mechanism of Miyamoto 2002, but goes further in using such mechanisms as the base grammar formalism. In place of concepts of movement, concepts of structural underspecification representing partial semantic representations are invoked, with growth of such structure within a derivation following the time-linear dynamics of parsing. The account extends the Cann et al analysis of Japanese scrambling to encompass multiple long-distance dependency, capturing both the attendant relative locality restriction on the constituents moved, and the interaction of this restriction with scopeconstrual effects. Scope construal variability is straightforwardly expressible as interaction between individual lexical specifications for the two languages and general constraints on scope construal; and the relative locality constraint on the construal of the expressions involved in multiple long-distance dependency is shown to follow as an immediate consequence of the general dynamics of the framework. The result is an account within the Hawkins program of defining grammars relative to performance considerations.