A Raritätenkabinett is a collection of things, living or more often dead, which are considered valuable, or at any rate worth collecting and perhaps exhibiting, because they are rare - not such things, though, whose commodity or exchange value would grow with rareness, but ones whose very existence, contrary to experience or indeed reason, makes the beholder marvel at the design of the universe.
The rara, rarissima, and singularia collected here come from the realm of grammar, wondrous enough in its everyday manifestations.
A rarum is a trait (of any conceivable sort: a form, a relationship between forms, a matching of form and meaning, a category, a construction, a rule, a constraint, a relationship between rules or constraints, ...) which is so uncommon across languages as not even to occur in all members of a single (middle to lower level) family or diffusion area (for short: sprachbund), although it may occur in a few languages from a few different families or sprachbünde. Diachronically speaking, a rarum is a trait which has only been retained, or only been innovated, in a few members of a single family or sprachbund or of a few of them.
Thus, on this definition, a trait may well be infrequent (an infrequentale, so to speak; Latin purists might prefer infrequens) without being a rarum. Just think of such precious family or (former) sprachbund possessions as syntactically governed word-initial segmental alternations, generally infrequent but omnipresent at least in Celtic and Berber, and also heard in Nias (Malayo-Polynesian, Austronesian) and in Iwaidja and Marrgu (Iwaidjan, Australian); triliteral roots, found throughout Semitic and possibly Berber; or clicks, shared by the entire Khoisan family, though outside only by some (former) Bantu neighbours as well as, at some distance, by Dahalo (Cushitic, Afroasiatic). Presumably, however, allowances ought to be made for single-member families (i.e., isolates) also being able to host rara rather than only infrequentalia.
A rarissimum is even rarer than a rarum.
A singulare (or, less highfalutinly, a nonesuch) is unique to individual languages.
The items collected here are, as it were, individuals, or sometimes also systems with only a very few intrinsically coherent components. Not included are combinatory rara/rarissima/nonesuches, i.e., unique combinations of traits which individually couldn't be more ordinary. To give an example: it is not unusual to have (i) syllable-final devoicing, or (ii) four cases cumulated with two numbers, or (iii) non-concatenative tense marking on (a subset of) verbs, or (iv) a definite and an indefinite article, or (v) relative pronouns identical to either demonstrative or interrogative pronouns, or (vi) (but this is arguably rare even individually) strict verb-second in declarative main clauses; but having all of these properties in combination is very rare, probably even unique (to German). And, naturally, the more numerous the traits-in-combination you take into account the nonesucher.
It might seem to follow that being rare entails being transient; but it is really an open question whether rara (or also infrequentalia), rarissima, and singularia, once innovated, cannot be as pertinacious as what is crosslinguistically more common. Being picked up by generation after generation within one particular speech community, a trait may nonetheless remain rare - as long as it fails to get borrowed by other speech communities or to be spread with its entire language supplanting others.
In relation to the laws supposedly reining in crosslinguistic diversity, rara, rarissima, or even singularia may be harmless, not offending against any universals on record (that is, so far as I am aware of what is on record). Less harmlessly, there are many exhibits in the present collection (carrying a cross-reference to THE UNIVERSALS ARCHIVE) which do infringe on published universals - which naturally throws doubt on those universals, interpreted categorically.
If interested in universals as such, visit THE UNIVERSALS ARCHIVE at: https://typo.uni-konstanz.de/archive/ What is also archived there is the known counterevidence to universals. However, not all of the transgressions on record are rare enough to merit an entry in the RARITÄTENKABINETT.
As yet, the documentation of the RARITÄTENKABINETT leaves much to be desired: often references are only given to secondary literature where a trait has been noted as being rare, but not to original sources. This will be remedied in future.
Needless to add that, at this stage, claims of rarumhood, rarissimumhood, and nonesuchhood should be considered no less tentative than ones of universality. Too often they rest on half-knowledge (to exaggerate vastly) and credulity. What is now believed to be rare may prove to be less unusual upon wider and more diligent probing. What has been endorsed as an anomaly may vanish upon critical scrutiny as a figment of someone's imagination.
omnia rara praeclara