different between singularly vs unnaturally

English

From singular +? -ly.

singularly (comparative more singularly, superlative most singularly)

Strangely; oddly.
He behaved most singularly when we met him last night.
Extremely; remarkably.
- 1895, H. G. Wells, The Time Machine Chapter X
  I fancied at first the stuff was paraffin wax, and smashed the jar accordingly. But the odor of camphor was unmistakable. It struck me as singularly odd, that among the universal decay, this volatile substance had chanced to survive, perhaps through many thousand years.
In the singular number; in terms of a single thing.

From Middle English unnaturelly, equivalent to unnatural +? -ly and/or un- +? naturally.

unnaturally (comparative more unnaturally, superlative most unnaturally)

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