The Minor Phrase (MiP, aka accentual phrase) is the prosodic constituent that immediately dominates the prosodic word (PWd) in the prosodic structure hierarchy; it may consist of one or more PWd. In Japanese all MiPs are marked by an initial LH rise. This paper examines the scaling of the initial rise in single-word MiPs in Japanese as a function of the syllable/mora length of the word constituting the MiP, the position of the MiP with respect to edges of prosodic major phrase (MaP), and the composition of MiP in terms of lexical accent. These rises are found to be subject to two types of scaling: (i) local, edge-based scaling, specifically the upward "resetting" of f0 seen at the left edge of MaP (aka intermediate phrase) [1, 2 3], and (ii) global, lookahead-based scaling, in this case the upward scaling of the f0 of MiP-initial peaks as a function of the overall length of the MiP in terms of syllables/moras. Word length also turns out to have an indirect influence on local, edge-based scaling in Japanese, since it can be shown that word length has an effect on the number and distribution of major and minor prosodic phrases in the phonological representation as well.