Why did German <d> and <t> flip over?

Question

I speak English and Norwegian and a little German and a little Dutch and I discovered a pattern while thinking about words which are obviously cognate. The pattern is wherever English, Norwegian and Dutch have <d>, German often has <t>.

There are also example of almost the opposite case too, where German has <d> and Norwegian has <t>, and English has voiceless <th>. Dutch in this case seems to have <d>, the same as German.

Some examples:

English    Norwegian    Dutch    German
day        dag          dag      Tag
door       dør          deur     Tür
dance      dans         dans     Tanz
middle     midten       middel   Mitte
think      tenke        denken   denken
thatch     tak          dak      Dach
through    trenge?      deur     durch

As for the Norwegian gloss "midten", it's pronounced as /t:/ but I believe it was historically voiced as evidenced by the spelling. And I'm not so sure that trenge is cognate with through. But that word can mean "squeeze through" or "force one's way into".

Some counter-examples which I cannot explain:

English    Norwegian    Dutch    German
though     dog          toch     doch
there      der          daar     da
salad      salat        salade   Salate

What I found especially puzzling is that the voicedness seems to have flipped over in German.

So have I spotted a correspondence of some sort here?

Answer 1

You have a few different correspondences here; I'll go through them individually.

day ~ dag ~ dag ~ Tag

This is part of the second German consonant shift (or the High German consonant shift). Among other things, voiced plosives at the start of words turned voiceless in German.

think ~ tenke ~ denken ~ denken

This is due to Germanic dental fricative loss. Some people consider it part of the second German consonant shift, but it affected languages other than German, so I consider it separate.

Basically, late Proto-Germanic had two dental fricatives *þ and *ð, created through Grimm's Law. They started as allophones but eventually split in many languages. In English and Icelandic, they persisted all the way to the present. But in most (all?) other Germanic languages, they merged into either /t/ or /d/. In German and Dutch the result is always /d/; in Norwegian it keeps the original voicing.

there ~ der ~ daar ~ da
though ~ dog ~ toch ~ doch

Same as above; Norwegian preserves the voiced-ness of the original *ð, while German and Dutch use /d/ exclusively. (Dutch used to have toch and doch alternating freely; doch is the expected form etymologically.)

salad ~ salat ~ salade ~ Salat

This is unrelated to the others, and doesn't come from Proto-Germanic: it stems from Italian (in)salata. Some languages got it through French, which voiced the /t/, while others didn't. (Also note that German Salate is plural, with an extra morpheme added; the root is Salat.)