preternatural

adj. supernatural, exceeding the usual powers of nature; unnatural, exceptional, abnormal

The preternatural or praeternatural is that which appears outside or beyond (Latin ) the natural. While this may include what is more commonly called the supernatural, it may also simply indicate extremity - an ordinary phenomenon taken 'beyond' the natural. One may have, for example, a preternatural desire, a preternatural curiosity, a preternaturally acute ear (sense of hearing), or even preternaturally big ears.
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Adjective
1. surpassing the ordinary or normal; "Beyond his preternatural affability there is some acid and some steel"- George Will
(similar) extraordinary
2. existing outside of or not in accordance with nature; "find transcendental motives for sublunary action"-Aldous Huxley
(synonym) nonnatural, otherworldly, transcendental
(similar) supernatural

adj. preternatural, unnatural

adj. preternatural, supernatural