Leafing through Hock's "Principles of Historical Linguistics"
looking for Very Important Subjects I found (15.2, p. 441)
"For instance, in the early German/Danish dialect continuum, the High
German sound shift originated in the south and spread toward the
north. At the same time, however, a development which originated in
the north was arriving in the south, namely the voicing of fricatives
in syllable-initial prevocalic environment. This change is ultimately
responsible for the voiced outcome of PGmc. *þ in all the German
dialects; cf. *þu > du "you (sg.)"."
What German/Danish dialect continuum? When there was a dialect
continuum it was a German/Norse continuum; the division within North
Germanic are much younger; and there are no transitional dialects
along the Danish/German border. Elsewhere Hock consistently refers to
the Danes in the Danelaw ín quotes as "'Danes'" or "so-called Danes";
what's going on in the mind of this so-called German. In Danish (if
that is the language I speak, you can never be sure these days) /þ/
went > /t/ but /þ/ went > /d/ in exactly those mono-syllabic pronouns
and particles (which usually live in unstressed syllables) in whose
English cognates /þ/ went > /ð/ (tempting to speculate that /þ/ > /ð/
> /d/).
There is no "voicing of fricatives in syllable-initial prevocalic
environment" anywhere in any Danish dialect. No /z/'s anywhere.
Torsten