I have just encountered the word "Zweisamkeit". Till this moment I knew only "Einsamkeit" und "Gemeinsamkeit". Do you know any other words like this?
I made a quick search in some word lists and found 133 words with ~samkeit.
There are many repetition because of compound words.
Double suffixation "-sam" and "-keit"
This admittedly peculiar construct results from a double suffixation. In the first place a noun was turned to an adjective by adding the suffix -sam, then it is turned back to a noun with another suffix "-keit".
This is a rather old suffix which is already present in Old High German, but also in Old English. It was and still is used to convert a noun to an adjective with the meaning of something being of the kind or nature of the noun it was added to. Later this suffix was also used to convert verbs to adjectives.
The likewise old suffixes "-keit", and "-heit" are both used in the same meaning. Originally it was used for a shape, person, nature, standing but when added to an adjective this was thereby nominalized with the noun being something of the shape or nature of the adjective it was added to.
When suffixing adjectives from above that were build by suffixing a noun with -sam we end with the resulting double suffixed noun from your examples (which then will have a different meaning from the rooting noun):
It is not unusual to have constructs being build from several suffixes leading to such hard to decompose words like
Unter dem Begriff „Zweisamkeit“ versteht man meist ein harmonisches, oft romantisches Zusammensein von zwei Personen, ohne störende andere Personen oder negative Einflüsse.
That means, “Zweisamkeit” is used to describe a harmonic, romantic partnership/situation of 2 people without negative influence of other people or any negative aspect.
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